[{"article_processing_charge":"No","external_id":{"arxiv":["1702.05172"],"isi":["000444141200005"]},"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"first_name":"Anton","full_name":"Petrunin, Anton","last_name":"Petrunin"}],"publist_id":"7948","title":"Long geodesics on convex surfaces","citation":{"apa":"Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5","short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.","mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:10.1007/s00283-018-9795-5.","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31.","chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"quality_controlled":"1","publisher":"Springer","page":"26 - 31","date_created":"2018-12-11T11:44:40Z","doi":"10.1007/s00283-018-9795-5","date_published":"2018-09-01T00:00:00Z","year":"2018","isi":1,"publication":"Mathematical Intelligencer","day":"01","type":"journal_article","status":"public","_id":"106","department":[{"_id":"HeEd"}],"date_updated":"2023-09-13T08:49:16Z","main_file_link":[{"url":"https://arxiv.org/abs/1702.05172","open_access":"1"}],"scopus_import":"1","intvolume":" 40","month":"09","abstract":[{"text":"The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below.","lang":"eng"}],"oa_version":"Preprint","issue":"3","volume":40,"publication_status":"published","language":[{"iso":"eng"}]},{"ec_funded":1,"volume":68,"publication_status":"published","language":[{"iso":"eng"}],"file":[{"checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_id":"5953","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2018_Edelsbrunner.pdf","date_created":"2019-02-12T06:47:52Z","file_size":708357,"date_updated":"2020-07-14T12:46:38Z","creator":"dernst"}],"scopus_import":"1","intvolume":" 68","month":"03","abstract":[{"lang":"eng","text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software."}],"oa_version":"Preprint","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:38Z","date_updated":"2023-09-13T08:59:00Z","ddc":["000"],"type":"journal_article","status":"public","_id":"530","page":"119 - 133","date_created":"2018-12-11T11:46:59Z","doi":"10.1016/j.comgeo.2017.06.014","date_published":"2018-03-01T00:00:00Z","year":"2018","isi":1,"has_accepted_license":"1","publication":"Computational Geometry: Theory and Applications","day":"01","oa":1,"quality_controlled":"1","publisher":"Elsevier","article_processing_charge":"No","external_id":{"isi":["000415778300010"]},"publist_id":"7289","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel"}],"title":"Multiple covers with balls I: Inclusion–exclusion","citation":{"ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"date_updated":"2023-09-13T09:13:12Z","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"_id":"193","conference":{"location":"Incheon, Republic of Korea","end_date":"2018-06-08","start_date":"2018-06-04","name":"ASIACCS: Asia Conference on Computer and Communications Security "},"type":"conference","status":"public","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"abstract":[{"text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/783"}],"scopus_import":"1","month":"06","citation":{"chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534.","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534","apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","ieee":"J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000516620100005"]},"publist_id":"7723","author":[{"id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","first_name":"Joel F","full_name":"Alwen, Joel F","last_name":"Alwen"},{"last_name":"Gazi","full_name":"Gazi, Peter","first_name":"Peter"},{"id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","first_name":"Chethan","last_name":"Kamath Hosdurg","full_name":"Kamath Hosdurg, Chethan"},{"first_name":"Karen","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","last_name":"Klein","full_name":"Klein, Karen"},{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"},{"first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","full_name":"Pietrzak, Krzysztof Z","orcid":"0000-0002-9139-1654","last_name":"Pietrzak"},{"last_name":"Reyzin","full_name":"Reyzin, Lenoid","first_name":"Lenoid"},{"last_name":"Rolinek","full_name":"Rolinek, Michal","first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"},{"id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rybar","full_name":"Rybar, Michal"}],"title":"On the memory hardness of data independent password hashing functions","project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"},{"name":"Teaching Old Crypto New Tricks","grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"year":"2018","isi":1,"publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","day":"01","page":"51 - 65","date_created":"2018-12-11T11:45:07Z","doi":"10.1145/3196494.3196534","date_published":"2018-06-01T00:00:00Z","acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","oa":1,"quality_controlled":"1","publisher":"ACM"},{"department":[{"_id":"HeEd"}],"date_updated":"2023-09-13T09:34:38Z","status":"public","article_type":"original","type":"journal_article","_id":"312","volume":32,"issue":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["08954801"]},"publication_status":"published","month":"03","intvolume":" 32","scopus_import":"1","main_file_link":[{"url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf","open_access":"1"}],"oa_version":"Submitted Version","abstract":[{"text":"Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice.","lang":"eng"}],"title":"On the optimality of the FCC lattice for soft sphere packing","publist_id":"7553","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel"}],"article_processing_charge":"No","external_id":{"isi":["000428958900038"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.","short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M1097201","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201."},"project":[{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"doi":"10.1137/16M1097201","date_published":"2018-03-29T00:00:00Z","date_created":"2018-12-11T11:45:46Z","page":"750 - 782","day":"29","publication":"SIAM J Discrete Math","isi":1,"year":"2018","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1,"acknowledgement":"This work was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35 of the Austrian Science Fund (FWF)."},{"title":"On the number of non-hexagons in a planar tiling","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"}],"publist_id":"7420","external_id":{"arxiv":["1805.01652"],"isi":["000430402700009"]},"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414.","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005.","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005","ama":"Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005","mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005."},"quality_controlled":"1","publisher":"Elsevier","oa":1,"date_published":"2018-04-01T00:00:00Z","doi":"10.1016/j.crma.2018.03.005","date_created":"2018-12-11T11:46:19Z","page":"412-414","day":"01","publication":"Comptes Rendus Mathematique","isi":1,"year":"2018","status":"public","article_type":"original","type":"journal_article","_id":"409","department":[{"_id":"HeEd"}],"date_updated":"2023-09-13T09:34:12Z","month":"04","intvolume":" 356","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1805.01652","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons."}],"issue":"4","volume":356,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1631073X"]},"publication_status":"published"},{"publication_status":"published","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"issue":"5","volume":28,"abstract":[{"text":"Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1705.02870","open_access":"1"}],"month":"10","intvolume":" 28","date_updated":"2023-09-15T12:10:35Z","department":[{"_id":"HeEd"}],"_id":"87","type":"journal_article","article_type":"original","status":"public","isi":1,"year":"2018","day":"01","publication":"Annals of Applied Probability","page":"3215 - 3238","date_published":"2018-10-01T00:00:00Z","doi":"10.1214/18-AAP1389","date_created":"2018-12-11T11:44:33Z","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"citation":{"short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","apa":"Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389","ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238. doi:10.1214/18-AAP1389","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.","ista":"Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5), 3215–3238.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"7967","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Nikitenko","full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000442893500018"],"arxiv":["1705.02870"]},"article_processing_charge":"No","title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}]},{"project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"e7","author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"article_processing_charge":"No","title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","citation":{"ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"date_published":"2018-05-31T00:00:00Z","doi":"10.1017/fms.2018.7","date_created":"2019-04-30T06:09:57Z","isi":1,"has_accepted_license":"1","year":"2018","day":"31","publication":"Forum of Mathematics, Sigma","type":"journal_article","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)"},"status":"public","_id":"6355","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:47:28Z","date_updated":"2023-09-19T14:50:12Z","ddc":["510"],"month":"05","intvolume":" 6","abstract":[{"text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle.","lang":"eng"}],"oa_version":"Published Version","related_material":{"record":[{"id":"8156","status":"public","relation":"dissertation_contains"}]},"volume":6,"ec_funded":1,"publication_identifier":{"issn":["2050-5094"]},"publication_status":"published","file":[{"file_name":"2018_ForumMahtematics_Akopyan.pdf","date_created":"2019-04-30T06:14:58Z","file_size":249246,"date_updated":"2020-07-14T12:47:28Z","creator":"dernst","file_id":"6356","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}]},{"intvolume":" 59","month":"06","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets."}],"ec_funded":1,"issue":"4","volume":59,"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"5844","file_size":482518,"date_updated":"2019-01-18T09:27:36Z","creator":"dernst","file_name":"2018_DiscreteComp_Akopyan.pdf","date_created":"2019-01-18T09:27:36Z"}],"publication_status":"published","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"status":"public","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)"},"type":"journal_article","article_type":"original","_id":"1064","file_date_updated":"2019-01-18T09:27:36Z","department":[{"_id":"HeEd"}],"ddc":["516","000"],"date_updated":"2023-09-20T12:08:51Z","oa":1,"quality_controlled":"1","publisher":"Springer","date_created":"2018-12-11T11:49:57Z","date_published":"2018-06-01T00:00:00Z","doi":"10.1007/s00454-017-9883-x","page":"1001-1009","publication":"Discrete & Computational Geometry","day":"01","year":"2018","isi":1,"has_accepted_license":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000432205500011"]},"publist_id":"6324","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"},{"first_name":"Mikhail","full_name":"Grigorev, Mikhail","last_name":"Grigorev"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.","ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.","apa":"Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009.","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018."}},{"month":"09","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"publisher":"arXiv","oa_version":"Preprint","abstract":[{"text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization.","lang":"eng"}],"date_created":"2018-12-11T11:44:30Z","ec_funded":1,"related_material":{"record":[{"id":"8156","status":"public","relation":"dissertation_contains"}]},"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","language":[{"iso":"eng"}],"day":"13","year":"2018","publication_status":"published","status":"public","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"type":"preprint","article_number":"1804.03057","_id":"75","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"title":"Convex fair partitions into arbitrary number of pieces","article_processing_charge":"No","external_id":{"arxiv":["1804.03057"]},"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Avvakumov","full_name":"Avvakumov, Sergey","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-12-18T10:51:02Z","citation":{"mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057."}},{"page":"211 - 229","date_created":"2018-12-11T11:46:43Z","doi":"10.1142/S0218195916600050","date_published":"2017-04-13T00:00:00Z","year":"2017","has_accepted_license":"1","publication":"International Journal of Computational Geometry and Applications","day":"13","oa":1,"publisher":"World Scientific Publishing","quality_controlled":"1","acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","publist_id":"7338","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"title":"Planar matchings for weighted straight skeletons","citation":{"mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.","ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"10892","status":"public","relation":"earlier_version"}]},"volume":26,"issue":"3-4","publication_status":"published","language":[{"iso":"eng"}],"file":[{"creator":"system","date_updated":"2020-07-14T12:46:35Z","file_size":769296,"date_created":"2018-12-12T10:09:34Z","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"4758","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e"}],"scopus_import":1,"intvolume":" 26","month":"04","abstract":[{"text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings.","lang":"eng"}],"oa_version":"Published Version","file_date_updated":"2020-07-14T12:46:35Z","department":[{"_id":"HeEd"}],"date_updated":"2023-02-21T16:06:22Z","ddc":["004","514","516"],"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)"},"type":"journal_article","pubrep_id":"949","status":"public","_id":"481"},{"volume":215,"date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.topol.2016.10.005","date_created":"2018-12-11T11:46:56Z","page":"45 - 57","day":"01","language":[{"iso":"eng"}],"publication":"Topology and its Applications","publication_identifier":{"issn":["01668641"]},"year":"2017","publication_status":"published","month":"01","intvolume":" 215","quality_controlled":"1","publisher":"Elsevier","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension."}],"title":"Higson compactification and dimension raising","department":[{"_id":"HeEd"}],"publist_id":"7299","author":[{"first_name":"Kyle","full_name":"Austin, Kyle","last_name":"Austin"},{"first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","full_name":"Virk, Ziga","last_name":"Virk"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:01:21Z","citation":{"ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","chicago":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005.","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","mla":"Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005."},"status":"public","type":"journal_article","_id":"521"},{"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T08:03:12Z","status":"public","type":"journal_article","_id":"568","ec_funded":1,"issue":"2","volume":19,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["15320073"]},"intvolume":" 19","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"scopus_import":1,"oa_version":"Submitted Version","abstract":[{"text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).","lang":"eng"}],"title":"Persistence of zero sets","author":[{"full_name":"Franek, Peter","last_name":"Franek","first_name":"Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7246","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16."},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","grant_number":"701309","_id":"2590DB08-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"date_created":"2018-12-11T11:47:14Z","doi":"10.4310/HHA.2017.v19.n2.a16","date_published":"2017-01-01T00:00:00Z","page":"313 - 342","publication":"Homology, Homotopy and Applications","day":"01","year":"2017","oa":1,"publisher":"International Press","quality_controlled":"1"},{"conference":{"name":"IWCIA: International Workshop on Combinatorial Image Analysis","start_date":"2017-06-19","end_date":"2017-06-21","location":"Plovdiv, Bulgaria"},"type":"book_chapter","status":"public","_id":"5803","department":[{"_id":"HeEd"}],"date_updated":"2022-01-28T07:48:24Z","extern":"1","alternative_title":["LNCS"],"intvolume":" 10256","place":"Cham","month":"05","abstract":[{"lang":"eng","text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept."}],"oa_version":"None","volume":10256,"publication_status":"published","publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"language":[{"iso":"eng"}],"article_processing_charge":"No","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"first_name":"Partha","last_name":"Bhowmick","full_name":"Bhowmick, Partha"}],"title":"Construction of persistent Voronoi diagram on 3D digital plane","citation":{"mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8.","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","apa":"Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8","ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","quality_controlled":"1","publisher":"Springer Nature","page":"93-104","date_created":"2019-01-08T20:42:56Z","date_published":"2017-05-17T00:00:00Z","doi":"10.1007/978-3-319-59108-7_8","year":"2017","publication":"Combinatorial image analysis","day":"17"},{"date_updated":"2021-01-12T08:09:26Z","ddc":["514","516"],"file_date_updated":"2020-07-14T12:47:42Z","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"_id":"688","type":"conference","conference":{"start_date":"2017-07-04","end_date":"2017-07-07","location":"Brisbane, Australia","name":"Symposium on Computational Geometry, SoCG"},"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)"},"status":"public","pubrep_id":"895","publication_identifier":{"issn":["18688969"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4856","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","file_size":990546,"date_updated":"2020-07-14T12:47:42Z","creator":"system","file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","date_created":"2018-12-12T10:11:03Z"}],"language":[{"iso":"eng"}],"volume":77,"abstract":[{"text":"We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"alternative_title":["LIPIcs"],"month":"06","intvolume":" 77","citation":{"ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","chicago":"Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","ieee":"H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. 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Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017.","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062","apa":"Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell, 2017. https://doi.org/10.1112/blms.12062.","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . 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Gromov on the waist of the unit ball."}],"oa_version":"Preprint","issue":"4","volume":49,"ec_funded":1,"publication_identifier":{"issn":["00246093"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"707","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T08:11:41Z"},{"oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","page":"745 - 767","date_created":"2018-12-11T11:48:07Z","date_published":"2017-09-01T00:00:00Z","doi":"10.1017/apr.2017.20","year":"2017","publication":"Advances in Applied Probability","day":"01","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"external_id":{"arxiv":["1607.05915"]},"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Nikitenko","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"},{"last_name":"Reitzner","full_name":"Reitzner, Matthias","first_name":"Matthias"}],"publist_id":"6962","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","citation":{"ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20.","ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20","apa":"Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.","mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1607.05915"}],"scopus_import":1,"intvolume":" 49","month":"09","abstract":[{"text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"issue":"3","volume":49,"publication_status":"published","publication_identifier":{"issn":["00018678"]},"language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"718","department":[{"_id":"HeEd"}],"date_updated":"2023-09-07T12:07:12Z"},{"_id":"6287","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)"},"type":"dissertation","pubrep_id":"873","status":"public","date_updated":"2023-09-15T12:10:34Z","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"ddc":["514","516","519"],"file_date_updated":"2020-07-14T12:47:26Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's."}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"month":"10","publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2019-04-09T14:54:51Z","file_name":"2017_Thesis_Nikitenko.pdf","date_updated":"2020-07-14T12:47:26Z","file_size":2324870,"creator":"dernst","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","file_id":"6289","content_type":"application/pdf","access_level":"open_access","relation":"main_file"},{"access_level":"closed","relation":"source_file","content_type":"application/zip","checksum":"99b7ad76e317efd447af60f91e29b49b","file_id":"6290","creator":"dernst","date_updated":"2020-07-14T12:47:26Z","file_size":2863219,"date_created":"2019-04-09T14:54:51Z","file_name":"2017_Thesis_Nikitenko_source.zip"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"718"},{"relation":"part_of_dissertation","id":"5678","status":"public"},{"status":"public","id":"87","relation":"part_of_dissertation"}]},"citation":{"mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873.","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873","ama":"Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873","short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017.","chicago":"Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873.","ista":"Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","author":[{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko"}],"title":"Discrete Morse theory for random complexes ","oa":1,"publisher":"Institute of Science and Technology Austria","year":"2017","has_accepted_license":"1","day":"27","page":"86","date_created":"2019-04-09T15:04:32Z","doi":"10.15479/AT:ISTA:th_873","date_published":"2017-10-27T00:00:00Z"},{"project":[{"grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008."},"title":"Phat - Persistent homology algorithms toolbox","author":[{"first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","first_name":"Jan"},{"last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5765","article_processing_charge":"No","external_id":{"isi":["000384396000005"]},"publisher":"Academic Press","quality_controlled":"1","oa":1,"day":"01","publication":"Journal of Symbolic Computation","isi":1,"year":"2017","date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.jsc.2016.03.008","date_created":"2018-12-11T11:51:59Z","page":"76 - 90","_id":"1433","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-09-20T09:42:40Z","department":[{"_id":"HeEd"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology."}],"month":"01","intvolume":" 78","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":[" 07477171"]},"publication_status":"published","related_material":{"record":[{"relation":"earlier_version","id":"10894","status":"public"}]},"volume":78,"ec_funded":1},{"ec_funded":1,"volume":308,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00018708"]},"intvolume":" 308","month":"02","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"scopus_import":"1","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T11:21:27Z","status":"public","type":"journal_article","_id":"1180","date_created":"2018-12-11T11:50:34Z","date_published":"2017-02-21T00:00:00Z","doi":"10.1016/j.aim.2016.12.026","page":"627 - 644","publication":"Advances in Mathematics","day":"21","year":"2017","isi":1,"oa":1,"quality_controlled":"1","publisher":"Academic Press","title":"Algebraic vertices of non-convex polyhedra","article_processing_charge":"No","external_id":{"isi":["000409292900015"]},"publist_id":"6173","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"first_name":"Imre","full_name":"Bárány, Imre","last_name":"Bárány"},{"full_name":"Robins, Sinai","last_name":"Robins","first_name":"Sinai"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026","ama":"Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026","ieee":"A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017.","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","mla":"Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026.","ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","chicago":"Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026."},"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"oa":1,"quality_controlled":"1","publisher":"Springer","acknowledgement":"This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876.","page":"887 - 910","date_created":"2018-12-11T11:50:32Z","doi":"10.1007/s00493-016-3308-y","date_published":"2017-10-01T00:00:00Z","year":"2017","isi":1,"publication":"Combinatorica","day":"01","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"article_processing_charge":"No","external_id":{"isi":["000418056000005"]},"author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Glazyrin","full_name":"Glazyrin, Alexey","first_name":"Alexey"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"},{"orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"}],"publist_id":"6182","title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","citation":{"ista":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5), 887–910.","chicago":"Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.","short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","ieee":"H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane,” Combinatorica, vol. 37, no. 5. Springer, pp. 887–910, 2017.","ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y","mla":"Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:10.1007/s00493-016-3308-y."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"url":"https://arxiv.org/abs/1411.6337","open_access":"1"}],"scopus_import":"1","intvolume":" 37","month":"10","abstract":[{"lang":"eng","text":"We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions."}],"oa_version":"Submitted Version","ec_funded":1,"volume":37,"issue":"5","publication_status":"published","publication_identifier":{"issn":["02099683"]},"language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1173","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T11:23:53Z"},{"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"article_processing_charge":"No","external_id":{"isi":["000398030400024"],"arxiv":["1312.1231"]},"publist_id":"6311","author":[{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"title":"The Morse theory of Čech and delaunay complexes","citation":{"ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society. American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.","ama":"Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991","apa":"Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6991","short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","ieee":"U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,” Transactions of the American Mathematical Society, vol. 369, no. 5. American Mathematical Society, pp. 3741–3762, 2017.","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","acknowledgement":"This research has been supported by the EU project Toposys(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 DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”.","page":"3741 - 3762","date_created":"2018-12-11T11:49:59Z","doi":"10.1090/tran/6991","date_published":"2017-05-01T00:00:00Z","year":"2017","isi":1,"publication":"Transactions of the American Mathematical Society","day":"01","article_type":"original","type":"journal_article","status":"public","_id":"1072","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T12:05:56Z","main_file_link":[{"url":"https://arxiv.org/abs/1312.1231","open_access":"1"}],"scopus_import":"1","intvolume":" 369","month":"05","abstract":[{"text":"Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":369,"issue":"5","publication_status":"published","language":[{"iso":"eng"}]},{"citation":{"apa":"Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003","ama":"Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003","ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.","short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003.","ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29.","chicago":"Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000399506600005"]},"article_processing_charge":"No","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","last_name":"Osang"}],"publist_id":"6323","title":"Pushdown reachability with constant treewidth","project":[{"call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory"},{"name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"year":"2017","has_accepted_license":"1","isi":1,"publication":"Information Processing Letters","day":"01","page":"25 - 29","date_created":"2018-12-11T11:49:57Z","doi":"10.1016/j.ipl.2017.02.003","date_published":"2017-06-01T00:00:00Z","oa":1,"quality_controlled":"1","publisher":"Elsevier","date_updated":"2023-09-20T12:08:18Z","ddc":["000"],"file_date_updated":"2019-10-15T07:44:51Z","department":[{"_id":"KrCh"},{"_id":"HeEd"}],"_id":"1065","type":"journal_article","pubrep_id":"991","status":"public","publication_status":"published","publication_identifier":{"issn":["00200190"]},"language":[{"iso":"eng"}],"file":[{"file_size":247657,"date_updated":"2019-10-15T07:44:51Z","creator":"system","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","date_created":"2018-12-12T10:13:17Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4998"}],"ec_funded":1,"volume":122,"abstract":[{"text":"We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs.","lang":"eng"}],"oa_version":"Submitted Version","scopus_import":"1","intvolume":" 122","month":"06"},{"publist_id":"6373","author":[{"last_name":"Pranav","full_name":"Pranav, Pratyush","first_name":"Pratyush"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Rien","last_name":"Van De Weygaert","full_name":"Van De Weygaert, Rien"},{"full_name":"Vegter, Gert","last_name":"Vegter","first_name":"Gert"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"full_name":"Jones, Bernard","last_name":"Jones","first_name":"Bernard"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000395170200039"]},"title":"The topology of the cosmic web in terms of persistent Betti numbers","citation":{"mla":"Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.","apa":"Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M., Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. Oxford University Press. https://doi.org/10.1093/mnras/stw2862","ama":"Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862","short":"P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B. Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017) 4281–4310.","ieee":"P. Pranav et al., “The topology of the cosmic web in terms of persistent Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4. Oxford University Press, pp. 4281–4310, 2017.","chicago":"Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter, Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.","ista":"Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B, Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"4281 - 4310","date_published":"2017-01-01T00:00:00Z","doi":"10.1093/mnras/stw2862","date_created":"2018-12-11T11:49:44Z","isi":1,"year":"2017","day":"01","publication":"Monthly Notices of the Royal Astronomical Society","publisher":"Oxford University Press","quality_controlled":"1","oa":1,"acknowledgement":"Part of this work has been supported by the 7th Framework Programme for Research of the European Commission, under FETOpen grant number 255827 (CGL Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random Systems via Algebraic Topology) number 320422.","department":[{"_id":"HeEd"}],"date_updated":"2023-09-22T09:40:55Z","type":"journal_article","status":"public","_id":"1022","issue":"4","volume":465,"publication_identifier":{"issn":["00358711"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1608.04519","open_access":"1"}],"month":"01","intvolume":" 465","abstract":[{"text":"We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys.","lang":"eng"}],"oa_version":"Submitted Version"},{"_id":"737","type":"journal_article","status":"public","date_updated":"2023-09-27T12:53:01Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action."}],"oa_version":"None","scopus_import":"1","intvolume":" 231","month":"11","publication_status":"published","publication_identifier":{"issn":["01668641"]},"language":[{"iso":"eng"}],"volume":231,"citation":{"apa":"Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015","ama":"Virk Z, Zastrow A. A new topology on the universal path space. Topology and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015","ieee":"Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","mla":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.","chicago":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","external_id":{"isi":["000413889100012"]},"author":[{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"full_name":"Zastrow, Andreas","last_name":"Zastrow","first_name":"Andreas"}],"publist_id":"6930","title":"A new topology on the universal path space","quality_controlled":"1","publisher":"Elsevier","year":"2017","isi":1,"publication":"Topology and its Applications","day":"01","page":"186 - 196","date_created":"2018-12-11T11:48:14Z","date_published":"2017-11-01T00:00:00Z","doi":"10.1016/j.topol.2017.09.015"},{"year":"2017","isi":1,"publication":"Special Sessions in Applications of Computer Algebra","day":"27","page":"119 - 136","date_created":"2018-12-11T11:48:46Z","date_published":"2017-07-27T00:00:00Z","doi":"10.1007/978-3-319-56932-1_8","quality_controlled":"1","publisher":"Springer","citation":{"chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8.","ista":"Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with the Kronecker canonical form. Special Sessions in Applications of Computer Algebra. ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.","mla":"Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” Special Sessions in Applications of Computer Algebra, vol. 198, Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.","apa":"Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In Special Sessions in Applications of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8","ama":"Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: Special Sessions in Applications of Computer Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8","ieee":"M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps with the Kronecker canonical form,” in Special Sessions in Applications of Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000434088200008"]},"article_processing_charge":"No","publist_id":"6812","author":[{"first_name":"Marc","full_name":"Ethier, Marc","last_name":"Ethier"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","last_name":"Jablonski","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"first_name":"Marian","last_name":"Mrozek","full_name":"Mrozek, Marian"}],"title":"Finding eigenvalues of self-maps with the Kronecker canonical form","project":[{"grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publication_status":"published","publication_identifier":{"isbn":["978-331956930-7"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":198,"abstract":[{"text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.","lang":"eng"}],"oa_version":"None","alternative_title":["PROMS"],"scopus_import":"1","intvolume":" 198","month":"07","date_updated":"2023-09-26T15:50:52Z","department":[{"_id":"HeEd"}],"_id":"836","conference":{"location":"Kalamata, Greece","end_date":"2015-07-23","start_date":"2015-07-20","name":"ACA: Applications of Computer Algebra"},"type":"conference","status":"public"},{"author":[{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa","last_name":"Heiss"},{"full_name":"Wagner, Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert"}],"publist_id":"6815","article_processing_charge":"No","external_id":{"isi":["000432085900032"]},"title":"Streaming algorithm for Euler characteristic curves of multidimensional images","editor":[{"first_name":"Michael","full_name":"Felsberg, Michael","last_name":"Felsberg"},{"full_name":"Heyden, Anders","last_name":"Heyden","first_name":"Anders"},{"first_name":"Norbert","last_name":"Krüger","full_name":"Krüger, Norbert"}],"citation":{"short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.","apa":"Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:10.1007/978-3-319-64689-3_32","mla":"Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","publisher":"Springer","oa":1,"page":"397 - 409","doi":"10.1007/978-3-319-64689-3_32","date_published":"2017-07-28T00:00:00Z","date_created":"2018-12-11T11:48:45Z","isi":1,"year":"2017","day":"28","type":"conference","conference":{"location":"Ystad, Sweden","end_date":"2017-08-24","start_date":"2017-08-22","name":"CAIP: Computer Analysis of Images and Patterns"},"status":"public","_id":"833","department":[{"_id":"HeEd"}],"date_updated":"2023-09-26T16:10:03Z","scopus_import":"1","alternative_title":["LNCS"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.02045"}],"month":"07","intvolume":" 10424","abstract":[{"lang":"eng","text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams."}],"oa_version":"Submitted Version","volume":10424,"publication_identifier":{"issn":["03029743"]},"publication_status":"published","language":[{"iso":"eng"}]},{"status":"public","type":"book_chapter","series_title":"Handbook of Discrete and Computational Geometry","_id":"84","editor":[{"full_name":"Toth, Csaba","last_name":"Toth","first_name":"Csaba"},{"first_name":"Joseph","full_name":"O'Rourke, Joseph","last_name":"O'Rourke"},{"first_name":"Jacob","last_name":"Goodman","full_name":"Goodman, Jacob"}],"title":"Computational topology for structural molecular biology","department":[{"_id":"HeEd"}],"article_processing_charge":"No","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"last_name":"Koehl","full_name":"Koehl, Patrice","first_name":"Patrice"}],"publist_id":"7970","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-10-16T11:15:22Z","citation":{"chicago":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601.","ista":"Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735.","mla":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35, doi:10.1201/9781315119601.","ieee":"H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in Handbook of Discrete and Computational Geometry, Third Edition, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.","short":"H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis, 2017, pp. 1709–1735.","apa":"Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor & Francis. https://doi.org/10.1201/9781315119601","ama":"Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational Geometry, Third Edition. Handbook of Discrete and Computational Geometry. Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601"},"month":"11","quality_controlled":"1","publisher":"Taylor & Francis","scopus_import":"1","oa_version":"None","abstract":[{"lang":"eng","text":"The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind."}],"date_created":"2018-12-11T11:44:32Z","doi":"10.1201/9781315119601","date_published":"2017-11-09T00:00:00Z","page":"1709 - 1735","language":[{"iso":"eng"}],"publication":"Handbook of Discrete and Computational Geometry, Third Edition","day":"09","year":"2017","publication_status":"published","publication_identifier":{"eisbn":["9781498711425"]}},{"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"On the lengths of curves passing through boundary points of a planar convex shape","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Vysotsky","full_name":"Vysotsky, Vladislav","first_name":"Vladislav"}],"publist_id":"6534","external_id":{"arxiv":["1605.07997"],"isi":["000413947300002"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588.","ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:10.4169/amer.math.monthly.124.7.588.","apa":"Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596. doi:10.4169/amer.math.monthly.124.7.588","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” The American Mathematical Monthly, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596."},"quality_controlled":"1","publisher":"Mathematical Association of America","oa":1,"doi":"10.4169/amer.math.monthly.124.7.588","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:49:09Z","page":"588 - 596","day":"01","publication":"The American Mathematical Monthly","isi":1,"year":"2017","status":"public","article_type":"original","type":"journal_article","_id":"909","department":[{"_id":"HeEd"}],"date_updated":"2023-10-17T11:24:57Z","month":"01","intvolume":" 124","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.07997"}],"oa_version":"Submitted Version","abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"volume":124,"issue":"7","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00029890"]},"publication_status":"published"},{"date_updated":"2021-01-12T06:48:38Z","citation":{"apa":"Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005","ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47.","ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” Applied Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.","mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier, 2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.","ista":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47.","chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Miyaji, Tomoyuki","last_name":"Miyaji","first_name":"Tomoyuki"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Gameiro","full_name":"Gameiro, Marcio","first_name":"Marcio"},{"last_name":"Kokubu","full_name":"Kokubu, Hiroshi","first_name":"Hiroshi"},{"first_name":"Konstantin","full_name":"Mischaikow, Konstantin","last_name":"Mischaikow"}],"publist_id":"6209","title":"A study of rigorous ODE integrators for multi scale set oriented computations","department":[{"_id":"HeEd"}],"_id":"1149","type":"journal_article","project":[{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps"}],"status":"public","year":"2016","publication_status":"published","language":[{"iso":"eng"}],"publication":"Applied Numerical Mathematics","day":"01","page":"34 - 47","ec_funded":1,"date_created":"2018-12-11T11:50:25Z","date_published":"2016-09-01T00:00:00Z","volume":107,"doi":"10.1016/j.apnum.2016.04.005","abstract":[{"text":"We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.","lang":"eng"}],"acknowledgement":"MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper.","oa_version":"None","scopus_import":1,"publisher":"Elsevier","quality_controlled":"1","intvolume":" 107","month":"09"},{"year":"2016","publication_status":"published","publication":"Archives of Mechanics","language":[{"iso":"eng"}],"day":"01","page":"55 - 80","date_created":"2018-12-11T11:50:46Z","issue":"1","volume":68,"date_published":"2016-01-01T00:00:00Z","abstract":[{"lang":"eng","text":"A framework fo r extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of acceleration zeros) are extracted and discriminated into vortices and saddle points, based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These feature points are tracked in time with a robust algorithm for tracking features. Thus, a space-time hierarchy of the minima is built and vortex merging events are detected. We apply the acceleration feature extraction strategy to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure field and minima of λ2."}],"acknowledgement":"The authors acknowledge funding of the German Re-\r\nsearch Foundation (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence 'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM) of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics Foundation for additional support. A part of this\r\nwork was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912","oa_version":"Published Version","oa":1,"main_file_link":[{"open_access":"1","url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf"}],"publisher":"Polish Academy of Sciences Publishing House","quality_controlled":"1","scopus_import":1,"intvolume":" 68","month":"01","date_updated":"2021-01-12T06:49:09Z","citation":{"ista":"Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M. 2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 68(1), 55–80.","chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House, 2016.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80.","ieee":"J. Kasten et al., “Acceleration feature points of unsteady shear flows,” Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016.","ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 2016;68(1):55-80.","apa":"Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., & Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives of Mechanics. Polish Academy of Sciences Publishing House.","mla":"Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Kasten, Jens","last_name":"Kasten","first_name":"Jens"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hotz, Ingrid","last_name":"Hotz","first_name":"Ingrid"},{"first_name":"Hans","full_name":"Hege, Hans","last_name":"Hege"},{"last_name":"Noack","full_name":"Noack, Bernd","first_name":"Bernd"},{"first_name":"Guillaume","full_name":"Daviller, Guillaume","last_name":"Daviller"},{"first_name":"Marek","full_name":"Morzyński, Marek","last_name":"Morzyński"}],"publist_id":"6118","department":[{"_id":"HeEd"}],"title":"Acceleration feature points of unsteady shear flows","_id":"1216","type":"journal_article","status":"public"},{"date_updated":"2021-01-12T06:49:11Z","department":[{"_id":"HeEd"}],"_id":"1222","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":55,"abstract":[{"text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1212.0649"}],"scopus_import":1,"intvolume":" 55","month":"01","citation":{"ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer, pp. 1–20, 2016.","short":"O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6","apa":"Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-015-9742-6","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20.","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-015-9742-6."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"6111","author":[{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"title":"Optimal packings of congruent circles on a square flat torus","year":"2016","publication":"Discrete & Computational Geometry","day":"01","page":"1 - 20","date_created":"2018-12-11T11:50:48Z","doi":"10.1007/s00454-015-9742-6","date_published":"2016-01-01T00:00:00Z","acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","oa":1,"publisher":"Springer","quality_controlled":"1"},{"acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","publisher":"Springer","quality_controlled":"1","year":"2016","day":"02","page":"140 - 151","date_created":"2018-12-11T11:50:52Z","date_published":"2016-06-02T00:00:00Z","doi":"10.1007/978-3-319-39441-1_13","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"citation":{"chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13.","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","mla":"Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.","short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","apa":"Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13","ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6096","title":"Computation of cubical Steenrod squares","abstract":[{"text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem.","lang":"eng"}],"oa_version":"None","scopus_import":1,"alternative_title":["LNCS"],"intvolume":" 9667","month":"06","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"volume":9667,"_id":"1237","conference":{"name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15","end_date":"2016-06-17","location":"Marseille, France"},"type":"conference","status":"public","date_updated":"2021-01-12T06:49:18Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}]},{"acknowledgement":"The authors gratefully acknowledge the support of the Lorenz Center which\r\nprovided an opportunity for us to discuss in depth the work of this paper. Research leading to these results has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033 (supporting PP). The work of the first and third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019, 1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029), Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan.","oa":1,"quality_controlled":"1","publisher":"American Mathematical Society","publication":"Proceedings of the American Mathematical Society","day":"01","year":"2016","date_created":"2018-12-11T11:50:57Z","date_published":"2016-04-01T00:00:00Z","doi":"10.1090/proc/12812","page":"1787 - 1801","project":[{"grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 144(4), 1787–1801.","chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” Proceedings of the American Mathematical Society, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801.","apa":"Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/12812","ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801. doi:10.1090/proc/12812","mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:10.1090/proc/12812."},"title":"Inducing a map on homology from a correspondence","article_processing_charge":"No","external_id":{"arxiv":["1411.7563"]},"author":[{"full_name":"Harker, Shaun","last_name":"Harker","first_name":"Shaun"},{"first_name":"Hiroshi","full_name":"Kokubu, Hiroshi","last_name":"Kokubu"},{"first_name":"Konstantin","full_name":"Mischaikow, Konstantin","last_name":"Mischaikow"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6075","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points."}],"intvolume":" 144","month":"04","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.7563"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1088-6826"]},"ec_funded":1,"issue":"4","volume":144,"_id":"1252","status":"public","article_type":"original","type":"journal_article","date_updated":"2022-05-24T09:35:58Z","department":[{"_id":"HeEd"}]},{"acknowledgement":"AG and PP were partially supported by Abdus Salam International Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS, and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics of Kyoto University for providing access\r\nto their server for conducting computations for this\r\nproject.","publisher":"Taylor and Francis","quality_controlled":"1","oa":1,"day":"02","publication":"Experimental Mathematics","year":"2016","date_published":"2016-04-02T00:00:00Z","doi":"10.1080/10586458.2015.1048011","date_created":"2018-12-11T11:50:58Z","page":"116 - 124","project":[{"call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics. Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011.","ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124.","mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.","ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124. doi:10.1080/10586458.2015.1048011","apa":"Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124.","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” Experimental Mathematics, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016."},"title":"Uniform expansivity outside a critical neighborhood in the quadratic family","author":[{"full_name":"Golmakani, Ali","last_name":"Golmakani","first_name":"Ali"},{"full_name":"Luzzatto, Stefano","last_name":"Luzzatto","first_name":"Stefano"},{"last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6071","oa_version":"Preprint","abstract":[{"text":"We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critical neighborhood outside which the map is uniformly expanding. This radius is taken as small as possible, yet large enough for our numerical procedure to succeed in proving that the expansivity exponent outside this neighborhood is positive. Then, for each of the intervals, we compute a lower bound for this expansivity exponent, valid for all the parameters in that interval. We illustrate and study the distribution of the radii and the expansivity exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.","lang":"eng"}],"month":"04","intvolume":" 25","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1504.00116","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":25,"issue":"2","ec_funded":1,"_id":"1254","status":"public","type":"journal_article","date_updated":"2021-01-12T06:49:25Z","department":[{"_id":"HeEd"}]},{"file_date_updated":"2020-07-14T12:44:42Z","department":[{"_id":"HeEd"}],"ddc":["004","516"],"date_updated":"2021-01-12T06:49:32Z","status":"public","pubrep_id":"694","type":"journal_article","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"_id":"1272","volume":13,"issue":"5","file":[{"creator":"system","file_size":1678369,"date_updated":"2020-07-14T12:44:42Z","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","date_created":"2018-12-12T10:16:20Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"5206","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e"}],"language":[{"iso":"eng"}],"publication_status":"published","month":"09","intvolume":" 13","scopus_import":1,"oa_version":"Published Version","abstract":[{"text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams.","lang":"eng"}],"title":"Generalized offsetting of planar structures using skeletons","publist_id":"6048","author":[{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.","chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications. Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718.","short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” Computer-Aided Design and Applications, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721. doi:10.1080/16864360.2016.1150718","apa":"Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:10.1080/16864360.2016.1150718."},"doi":"10.1080/16864360.2016.1150718","date_published":"2016-09-02T00:00:00Z","date_created":"2018-12-11T11:51:04Z","page":"712 - 721","day":"02","publication":"Computer-Aided Design and Applications","has_accepted_license":"1","year":"2016","quality_controlled":"1","publisher":"Taylor and Francis","oa":1,"acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15."},{"type":"journal_article","status":"public","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"_id":"1295","publist_id":"5976","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"HeEd"}],"title":"Multiple covers with balls II: Weighted averages","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol. 54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2016.09.030","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier, pp. 169–174, 2016.","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.endm.2016.09.030.","ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174."},"date_updated":"2021-01-12T06:49:41Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","scopus_import":1,"publisher":"Elsevier","intvolume":" 54","month":"10","abstract":[{"lang":"eng","text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls."}],"acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","oa_version":"None","page":"169 - 174","date_created":"2018-12-11T11:51:12Z","ec_funded":1,"date_published":"2016-10-01T00:00:00Z","volume":54,"doi":"10.1016/j.endm.2016.09.030","publication_status":"published","year":"2016","publication":"Electronic Notes in Discrete Mathematics","language":[{"iso":"eng"}],"day":"01"},{"_id":"1292","type":"journal_article","status":"public","date_updated":"2021-01-12T06:49:40Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds."}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1605.00794","open_access":"1"}],"scopus_import":1,"intvolume":" 150","month":"12","publication_status":"published","language":[{"iso":"eng"}],"volume":150,"issue":"2","citation":{"chicago":"Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4.","ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","mla":"Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp. 441–55, doi:10.1007/s10474-016-0648-4.","short":"S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.","ieee":"S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer, pp. 441–455, 2016.","apa":"Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4","ama":"Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"6023","author":[{"last_name":"Durst","full_name":"Durst, Sebastian","first_name":"Sebastian"},{"first_name":"Marc","full_name":"Kegel, Marc","last_name":"Kegel"},{"full_name":"Klukas, Mirko D","last_name":"Klukas","id":"34927512-F248-11E8-B48F-1D18A9856A87","first_name":"Mirko D"}],"title":"Computing the Thurston–Bennequin invariant in open books","acknowledgement":"The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful discussions and advice and Christian Evers for helpful remarks on a draft version.","oa":1,"quality_controlled":"1","publisher":"Springer","year":"2016","publication":"Acta Mathematica Hungarica","day":"01","page":"441 - 455","date_created":"2018-12-11T11:51:11Z","doi":"10.1007/s10474-016-0648-4","date_published":"2016-12-01T00:00:00Z"},{"publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"volume":216,"issue":"2","abstract":[{"text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}],"scopus_import":1,"intvolume":" 216","month":"10","date_updated":"2021-01-12T06:49:56Z","department":[{"_id":"HeEd"}],"_id":"1330","type":"journal_article","status":"public","year":"2016","publication":"Israel Journal of Mathematics","day":"15","page":"833 - 845","date_created":"2018-12-11T11:51:24Z","doi":"10.1007/s11856-016-1429-z","date_published":"2016-10-15T00:00:00Z","acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","oa":1,"quality_controlled":"1","publisher":"Springer","citation":{"ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845, 2016.","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.","apa":"Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z","ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:10.1007/s11856-016-1429-z.","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics. 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We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. ","lang":"eng"}],"volume":144,"issue":"10","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","publist_id":"5885","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"},{"first_name":"Roman","full_name":"Karasev, Roman","last_name":"Karasev"},{"first_name":"Anastasia","full_name":"Sharipova, Anastasia","last_name":"Sharipova"}],"article_processing_charge":"No","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062.","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016.","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","apa":"Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062."},"quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"acknowledgement":"The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved).","date_published":"2016-10-01T00:00:00Z","doi":"10.1090/proc/13062","date_created":"2018-12-11T11:51:34Z","page":"4501 - 4513","day":"01","publication":"Proceedings of the American Mathematical Society","year":"2016"},{"publisher":"Springer","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","date_published":"2016-07-01T00:00:00Z","doi":"10.1007/s00454-016-9794-2","date_created":"2018-12-11T11:51:51Z","page":"126 - 164","day":"01","publication":"Discrete & Computational Geometry","has_accepted_license":"1","year":"2016","project":[{"name":"Robust invariants of Nonlinear Systems","grant_number":"M01980","call_identifier":"FWF","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"title":"On computability and triviality of well groups","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"last_name":"Krcál","full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5799","article_processing_charge":"Yes (via OA deal)","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2.","ama":"Franek P, Krcál M. On computability and triviality of well groups. Discrete & Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2","apa":"Franek, P., & Krcál, M. (2016). On computability and triviality of well groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164, 2016.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164."},"month":"07","intvolume":" 56","scopus_import":1,"oa_version":"Published Version","abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.","lang":"eng"}],"issue":"1","related_material":{"record":[{"status":"public","id":"1510","relation":"earlier_version"}]},"volume":56,"ec_funded":1,"file":[{"file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","date_created":"2018-12-12T10:10:55Z","file_size":905303,"date_updated":"2020-07-14T12:44:53Z","creator":"system","file_id":"4846","checksum":"e0da023abf6b72abd8c6a8c76740d53c","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_status":"published","status":"public","pubrep_id":"614","type":"journal_article","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)"},"_id":"1408","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:44:53Z","ddc":["510"],"date_updated":"2023-02-23T10:02:11Z"},{"citation":{"mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Pattern Recognition Letters, vol. 83, no. 1, Elsevier, 2016, pp. 13–22, doi:10.1016/j.patrec.2015.12.012.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.","ieee":"O. Dunaeva et al., “The classification of endoscopy images with persistent homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22, 2016.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 2016;83(1):13-22. doi:10.1016/j.patrec.2015.12.012","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev, R., & Kashin, S. (2016). The classification of endoscopy images with persistent homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2015.12.012","chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images with Persistent Homology.” Pattern Recognition Letters. Elsevier, 2016. https://doi.org/10.1016/j.patrec.2015.12.012.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin S. 2016. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 83(1), 13–22."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"6027","author":[{"full_name":"Dunaeva, Olga","last_name":"Dunaeva","first_name":"Olga"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anton","last_name":"Lukyanov","full_name":"Lukyanov, Anton"},{"first_name":"Michael","full_name":"Machin, Michael","last_name":"Machin"},{"first_name":"Daria","last_name":"Malkova","full_name":"Malkova, Daria"},{"first_name":"Roman","last_name":"Kuvaev","full_name":"Kuvaev, Roman"},{"full_name":"Kashin, Sergey","last_name":"Kashin","first_name":"Sergey"}],"article_processing_charge":"No","title":"The classification of endoscopy images with persistent homology","has_accepted_license":"1","year":"2016","day":"01","publication":"Pattern Recognition Letters","page":"13 - 22","date_published":"2016-11-01T00:00:00Z","doi":"10.1016/j.patrec.2015.12.012","date_created":"2018-12-11T11:51:10Z","publisher":"Elsevier","quality_controlled":"1","oa":1,"date_updated":"2023-02-23T10:04:40Z","ddc":["004","514"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:44:42Z","_id":"1289","type":"journal_article","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"status":"public","pubrep_id":"975","publication_status":"published","file":[{"file_id":"6334","checksum":"33458bbb8c32a339e1adeca6d5a1112d","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2019-04-17T07:55:51Z","file_name":"2016-Edelsbrunner_The_classification.pdf","date_updated":"2020-07-14T12:44:42Z","file_size":1921113,"creator":"dernst"}],"language":[{"iso":"eng"}],"volume":83,"issue":"1","related_material":{"record":[{"status":"public","id":"1568","relation":"earlier_version"}]},"abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI) magnifying endoscopic (ME) images of the stomach, we combine methods from image processing, topology, geometry, and machine learning to classify patterns into three classes: oval, tubular and irregular. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"oa_version":"Submitted Version","scopus_import":1,"month":"11","intvolume":" 83"},{"_id":"1617","status":"public","type":"journal_article","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:52:02Z","citation":{"ama":"Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003","apa":"Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003","ieee":"F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.","short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216, doi:10.1016/j.jco.2015.11.003.","ista":"Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216.","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003."},"title":"On the discrepancy of jittered sampling","department":[{"_id":"HeEd"}],"author":[{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian"},{"first_name":"Stefan","last_name":"Steinerberger","full_name":"Steinerberger, Stefan"}],"publist_id":"5549","acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition.","oa_version":"Submitted Version","abstract":[{"text":"We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points.","lang":"eng"}],"intvolume":" 33","month":"04","main_file_link":[{"url":"http://arxiv.org/abs/1510.00251","open_access":"1"}],"oa":1,"quality_controlled":"1","scopus_import":1,"publisher":"Academic Press","publication":"Journal of Complexity","language":[{"iso":"eng"}],"day":"01","publication_status":"published","year":"2016","date_created":"2018-12-11T11:53:03Z","doi":"10.1016/j.jco.2015.11.003","volume":33,"date_published":"2016-04-01T00:00:00Z","page":"199 - 216"},{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"isbn":["978-3-319-32359-6"],"issn":["0302-9743","1611-3349"],"eisbn":["978-3-319-32360-2"]},"volume":9647,"oa_version":"None","abstract":[{"lang":"eng","text":"Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane."}],"intvolume":" 9647","month":"04","place":"Cham","alternative_title":["LNCS"],"extern":"1","date_updated":"2022-01-28T08:10:11Z","department":[{"_id":"HeEd"}],"_id":"5806","status":"public","conference":{"name":"DGCI: International Conference on Discrete Geometry for Computer Imagery","location":"Nantes, France","end_date":"2016-04-20","start_date":"2016-04-18"},"type":"conference","publication":"Discrete Geometry for Computer Imagery","day":"09","year":"2016","date_created":"2019-01-08T20:44:37Z","doi":"10.1007/978-3-319-32360-2_20","date_published":"2016-04-09T00:00:00Z","page":"256-267","publisher":"Springer Nature","quality_controlled":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"mla":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.","short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267.","ieee":"R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive sphere with application to circle drawing,” in Discrete Geometry for Computer Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.","apa":"Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants of naive sphere with application to circle drawing. In Discrete Geometry for Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20","ama":"Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere with application to circle drawing. In: Discrete Geometry for Computer Imagery. Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20","chicago":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.","ista":"Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive sphere with application to circle drawing. Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 9647, 256–267."},"title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","article_processing_charge":"No","author":[{"last_name":"Biswas","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}]},{"publisher":"Springer Nature","quality_controlled":"1","year":"2016","day":"02","publication":"Computational Topology in Image Context","page":"253-264","doi":"10.1007/978-3-319-39441-1_23","date_published":"2016-06-02T00:00:00Z","date_created":"2019-01-08T20:44:24Z","citation":{"ista":"Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.","chicago":"Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In Computational Topology in Image Context, 9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.","apa":"Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In Computational Topology in Image Context (Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23","ama":"Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23","ieee":"N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties of naive discrete sphere,” in Computational Topology in Image Context, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264.","mla":"Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"last_name":"Sen","full_name":"Sen, Nabhasmita","first_name":"Nabhasmita"},{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"}],"article_processing_charge":"No","title":"On some local topological properties of naive discrete sphere","abstract":[{"lang":"eng","text":"Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy."}],"oa_version":"None","alternative_title":["LNCS"],"month":"06","place":"Cham","intvolume":" 9667","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["978-3-319-39440-4"],"eisbn":["978-3-319-39441-1"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":9667,"_id":"5805","type":"book_chapter","conference":{"name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15","location":"Marseille, France","end_date":"2016-06-17"},"status":"public","date_updated":"2022-01-28T08:01:22Z","extern":"1","department":[{"_id":"HeEd"}]},{"article_processing_charge":"No","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","orcid":"0000-0002-5372-7890","full_name":"Biswas, Ranita","last_name":"Biswas"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"},{"first_name":"Valentin E.","last_name":"Brimkov","full_name":"Brimkov, Valentin E."}],"title":"On the connectivity and smoothness of discrete spherical circles","department":[{"_id":"HeEd"}],"citation":{"mla":"Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:10.1007/978-3-319-26145-4_7.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100.","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.","apa":"Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In Combinatorial image analysis (Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7","ama":"Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7","chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis, 9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.","ista":"Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100."},"date_updated":"2022-01-28T08:13:03Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","extern":"1","conference":{"start_date":"2015-11-24","end_date":"2015-11-27","location":"Kolkata, India","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"type":"book_chapter","status":"public","_id":"5809","page":"86-100","date_created":"2019-01-08T20:45:19Z","volume":9448,"doi":"10.1007/978-3-319-26145-4_7","date_published":"2016-01-06T00:00:00Z","publication_status":"published","year":"2016","publication_identifier":{"eisbn":["978-3-319-26145-4"],"eissn":["1611-3349"],"isbn":["978-3-319-26144-7"],"issn":["0302-9743"]},"publication":"Combinatorial image analysis","language":[{"iso":"eng"}],"day":"06","publisher":"Springer Nature","quality_controlled":"1","intvolume":" 9448","month":"01","place":"Cham","abstract":[{"text":"A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.","lang":"eng"}],"oa_version":"None"},{"publication_status":"published","language":[{"iso":"eng"}],"file":[{"file_id":"4928","checksum":"f8869ec110c35c852ef6a37425374af7","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","date_created":"2018-12-12T10:12:10Z","file_size":248985,"date_updated":"2020-07-14T12:45:10Z","creator":"system"}],"ec_funded":1,"volume":287,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"1399"}]},"abstract":[{"text":"We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball.","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"intvolume":" 287","month":"01","date_updated":"2023-09-07T11:41:25Z","ddc":["004"],"file_date_updated":"2020-07-14T12:45:10Z","department":[{"_id":"HeEd"}],"_id":"1662","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","pubrep_id":"774","status":"public","year":"2016","has_accepted_license":"1","publication":"Advances in Mathematics","day":"10","page":"674 - 703","date_created":"2018-12-11T11:53:20Z","date_published":"2016-01-10T00:00:00Z","doi":"10.1016/j.aim.2015.10.004","acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.","oa":1,"publisher":"Academic Press","quality_controlled":"1","citation":{"chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004.","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.","ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004","apa":"Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004","ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","last_name":"Pausinger"}],"publist_id":"5488","title":"Approximation and convergence of the intrinsic volume","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493"}]},{"volume":28,"date_published":"2015-12-01T00:00:00Z","date_created":"2018-12-11T11:51:56Z","page":"3070 - 3078","day":"01","language":[{"iso":"eng"}],"publication_status":"published","year":"2015","month":"12","intvolume":" 28","quality_controlled":"1","publisher":"Neural Information Processing Systems","alternative_title":["Advances in Neural Information Processing Systems"],"main_file_link":[{"url":"https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective","open_access":"1"}],"oa":1,"oa_version":"Submitted Version","acknowledgement":"This work was partially supported by the Austrian Science FUnd, project no. KLI 00012.","abstract":[{"lang":"eng","text":"We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data."}],"title":"Statistical topological data analysis-A kernel perspective","department":[{"_id":"HeEd"}],"author":[{"full_name":"Kwitt, Roland","last_name":"Kwitt","first_name":"Roland"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"full_name":"Niethammer, Marc","last_name":"Niethammer","first_name":"Marc"},{"full_name":"Lin, Weili","last_name":"Lin","first_name":"Weili"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer"}],"publist_id":"5782","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems, 2015.","ista":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078.","mla":"Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective. Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78.","short":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems, 2015, pp. 3070–3078.","ieee":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.","ama":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems; 2015:3070-3078.","apa":"Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems."},"date_updated":"2021-01-12T06:50:38Z","status":"public","type":"conference","conference":{"end_date":"2015-12-12","location":"Montreal, Canada","start_date":"2015-12-07","name":"NIPS: Neural Information Processing Systems"},"_id":"1424"},{"title":"A stable multi-scale kernel for topological machine learning","department":[{"_id":"HeEd"}],"author":[{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus"},{"last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","last_name":"Bauer"},{"first_name":"Roland","last_name":"Kwitt","full_name":"Kwitt, Roland"}],"publist_id":"5709","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:51:03Z","citation":{"ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106","apa":"Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","mla":"Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.","ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106."},"status":"public","conference":{"end_date":"2015-06-12","location":"Boston, MA, USA","start_date":"2015-06-07","name":"CVPR: Computer Vision and Pattern Recognition"},"type":"conference","_id":"1483","date_created":"2018-12-11T11:52:17Z","date_published":"2015-10-14T00:00:00Z","doi":"10.1109/CVPR.2015.7299106","page":"4741 - 4748","language":[{"iso":"eng"}],"day":"14","year":"2015","publication_status":"published","publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"month":"10","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1412.6821","open_access":"1"}],"publisher":"IEEE","scopus_import":1,"oa_version":"Preprint","abstract":[{"text":"Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.","lang":"eng"}]},{"month":"08","publisher":"Queen's University","scopus_import":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1505.03402","open_access":"1"}],"oa":1,"oa_version":"Submitted Version","abstract":[{"text":"Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. ","lang":"eng"}],"volume":"2015-August","date_published":"2015-08-01T00:00:00Z","ec_funded":1,"date_created":"2018-12-11T11:52:21Z","page":"128-135","day":"01","language":[{"iso":"eng"}],"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","year":"2015","publication_status":"published","status":"public","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"type":"conference","conference":{"name":"CCCG: Canadian Conference on Computational Geometry","start_date":"2015-08-10","end_date":"2015-08-12","location":"Ontario, Canada"},"_id":"1495","department":[{"_id":"HeEd"}],"title":"Relaxed disk packing","publist_id":"5684","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Vitaliy","last_name":"Kurlin","full_name":"Kurlin, Vitaliy"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:51:09Z","citation":{"ista":"Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational Geometry, 2015–August:128–35. Queen’s University, 2015.","short":"H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.","ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in Proceedings of the 27th Canadian Conference on Computational Geometry, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings of the 27th Canadian Conference on Computational Geometry. Vol 2015-August. Queen’s University; 2015:128-135.","apa":"Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk packing. In Proceedings of the 27th Canadian Conference on Computational Geometry (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.","mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the 27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s University, 2015, pp. 128–35."}},{"ec_funded":1,"related_material":{"record":[{"id":"1408","status":"public","relation":"later_version"}]},"volume":34,"publication_status":"published","language":[{"iso":"eng"}],"file":[{"checksum":"49eb5021caafaabe5356c65b9c5f8c9c","file_id":"5001","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:13:19Z","file_name":"IST-2016-503-v1+1_32.pdf","date_updated":"2020-07-14T12:44:59Z","file_size":623563,"creator":"system"}],"scopus_import":1,"alternative_title":["LIPIcs"],"intvolume":" 34","month":"06","abstract":[{"lang":"eng","text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r > 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. 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On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.","ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842","apa":"Franek, P., & Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SOCG.2015.842","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856.","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856.","mla":"Franek, Peter, and Marek Krcál. On Computability and Triviality of Well Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}]},{"year":"2015","publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","day":"01","page":"257 - 267","date_created":"2018-12-11T11:52:33Z","doi":"10.1007/978-3-319-15090-1_13","date_published":"2015-01-01T00:00:00Z","edition":"1","publisher":"Springer","quality_controlled":"1","citation":{"ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40. 1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","publist_id":"5640","author":[{"first_name":"Valentin","last_name":"Zobel","full_name":"Zobel, Valentin"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"}],"editor":[{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"first_name":"Thomas","full_name":"Schultz, Thomas","last_name":"Schultz"}],"title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","publication_status":"published","publication_identifier":{"isbn":["978-3-319-15089-5"]},"language":[{"iso":"eng"}],"volume":40,"abstract":[{"text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece.","lang":"eng"}],"oa_version":"None","alternative_title":["Mathematics and Visualization"],"scopus_import":"1","intvolume":" 40","month":"01","date_updated":"2022-06-10T09:50:14Z","department":[{"_id":"HeEd"}],"_id":"1531","type":"book_chapter","status":"public"},{"date_updated":"2021-01-12T06:51:34Z","ddc":["510"],"department":[{"_id":"HeEd"}],"_id":"1555","article_type":"original","type":"journal_article","status":"public","publication_identifier":{"eissn":["1536-0040"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":14,"issue":"2","ec_funded":1,"abstract":[{"text":"We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations.","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"main_file_link":[{"url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf","open_access":"1"}],"month":"01","intvolume":" 14","citation":{"ista":"Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.","chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.","apa":"Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934","ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017. doi:10.1137/140993934","mla":"Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Diána","full_name":"Knipl, Diána","last_name":"Knipl"},{"first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk"},{"full_name":"Röst, Gergely","last_name":"Röst","first_name":"Gergely"}],"publist_id":"5616","article_processing_charge":"No","title":"Rich bifurcation structure in a two patch vaccination model","project":[{"call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","name":"Persistent Homology - Images, Data and Maps","grant_number":"622033"}],"year":"2015","day":"01","publication":"SIAM Journal on Applied Dynamical Systems","page":"980 - 1017","doi":"10.1137/140993934","date_published":"2015-01-01T00:00:00Z","date_created":"2018-12-11T11:52:42Z","acknowledgement":"Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project.","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1},{"page":"7034731","doi":"10.1109/SYNASC.2014.81","related_material":{"record":[{"id":"1289","status":"public","relation":"later_version"}]},"date_published":"2015-02-05T00:00:00Z","date_created":"2018-12-11T11:52:46Z","publication_status":"published","year":"2015","day":"05","publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","language":[{"iso":"eng"}],"publisher":"IEEE","quality_controlled":"1","scopus_import":1,"month":"02","abstract":[{"text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions.","lang":"eng"}],"oa_version":"None","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","author":[{"last_name":"Dunaeva","full_name":"Dunaeva, Olga","first_name":"Olga"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Anton","full_name":"Lukyanov, Anton","last_name":"Lukyanov"},{"first_name":"Michael","last_name":"Machin","full_name":"Machin, Michael"},{"full_name":"Malkova, Daria","last_name":"Malkova","first_name":"Daria"}],"publist_id":"5603","title":"The classification of endoscopy images with persistent homology","department":[{"_id":"HeEd"}],"citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2015, p. 7034731.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D. (2015). The classification of endoscopy images with persistent homology. In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE; 2015:7034731. doi:10.1109/SYNASC.2014.81"},"date_updated":"2023-02-21T16:57:29Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","type":"conference","conference":{"start_date":"2014-09-22","location":"Timisoara, Romania","end_date":"2014-09-25","name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing"},"status":"public","_id":"1568"},{"title":"Shape, homology, persistence, and stability","department":[{"_id":"HeEd"}],"article_processing_charge":"No","publist_id":"5604","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_updated":"2022-01-28T08:25:00Z","citation":{"chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015.","ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd International Symposium, vol. 9411, Springer Nature, 2015.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.","apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411."},"status":"public","conference":{"name":"GD: Graph Drawing and Network Visualization","location":"Los Angeles, CA, United States","end_date":"2015-09-26","start_date":"2015-09-24"},"type":"conference","_id":"1567","date_created":"2018-12-11T11:52:46Z","date_published":"2015-01-01T00:00:00Z","volume":9411,"language":[{"iso":"eng"}],"publication":"23rd International Symposium","day":"01","year":"2015","publication_status":"published","intvolume":" 9411","month":"01","scopus_import":"1","publisher":"Springer Nature","quality_controlled":"1","alternative_title":["LNCS"],"oa_version":"None","abstract":[{"text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations.","lang":"eng"}]},{"issue":"1","doi":"10.12775/TMNA.2015.014","volume":45,"date_published":"2015-03-01T00:00:00Z","date_created":"2018-12-11T11:52:44Z","page":"273 - 286","day":"01","language":[{"iso":"eng"}],"publication":"Topological Methods in Nonlinear Analysis","year":"2015","publication_status":"published","month":"03","intvolume":" 45","scopus_import":1,"quality_controlled":"1","publisher":"Juliusz Schauder Center for Nonlinear Studies","oa_version":"None","abstract":[{"lang":"eng","text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}."}],"department":[{"_id":"HeEd"}],"title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","publist_id":"5608","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286.","chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.","apa":"Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014."},"date_updated":"2021-01-12T06:51:37Z","status":"public","type":"journal_article","_id":"1563"},{"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."}],"oa_version":"None","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","publisher":"Elsevier","quality_controlled":"1","scopus_import":1,"month":"08","intvolume":" 48","year":"2015","publication_status":"published","day":"01","language":[{"iso":"eng"}],"publication":"Computational Geometry","page":"507 - 519","issue":"7","doi":"10.1016/j.comgeo.2015.04.001","date_published":"2015-08-01T00:00:00Z","volume":48,"date_created":"2018-12-11T11:52:49Z","_id":"1578","type":"journal_article","status":"public","date_updated":"2021-01-12T06:51:43Z","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","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","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.","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.","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Cao","full_name":"Cao, Thanhtung","first_name":"Thanhtung"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Tiowseng","last_name":"Tan","full_name":"Tan, Tiowseng"}],"publist_id":"5593","department":[{"_id":"HeEd"}],"title":"Triangulations from topologically correct digital Voronoi diagrams"},{"year":"2015","has_accepted_license":"1","publication":"Computational Geometry: Theory and Applications","day":"01","page":"429 - 442","date_created":"2018-12-11T11:52:51Z","date_published":"2015-07-01T00:00:00Z","doi":"10.1016/j.comgeo.2015.01.004","oa":1,"quality_controlled":"1","publisher":"Elsevier","citation":{"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.","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","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","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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814"},{"first_name":"Dominik","last_name":"Kaaser","full_name":"Kaaser, Dominik"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"publist_id":"5587","title":"Reprint of: Weighted straight skeletons in the plane","publication_status":"published","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"5292","checksum":"5b33719a86f7f4c8e5dc62c1b6893f49","creator":"system","date_updated":"2020-07-14T12:45:03Z","file_size":508379,"date_created":"2018-12-12T10:17:36Z","file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf"}],"related_material":{"record":[{"status":"public","id":"1582","relation":"other"}]},"issue":"5","volume":48,"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."}],"oa_version":"Published Version","scopus_import":1,"intvolume":" 48","month":"07","date_updated":"2023-02-23T10:05:22Z","ddc":["000"],"file_date_updated":"2020-07-14T12:45:03Z","department":[{"_id":"HeEd"}],"_id":"1584","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)"},"type":"journal_article","pubrep_id":"475","status":"public"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","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","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","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.","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."},"title":"Weighted straight skeletons in the plane","publist_id":"5589","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber"},{"last_name":"Kaaser","full_name":"Kaaser, Dominik","first_name":"Dominik"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"publication":"Computational Geometry: Theory and Applications","day":"01","year":"2015","has_accepted_license":"1","date_created":"2018-12-11T11:52:51Z","doi":"10.1016/j.comgeo.2014.08.006","date_published":"2015-02-01T00:00:00Z","page":"120 - 133","oa":1,"publisher":"Elsevier","quality_controlled":"1","ddc":["000"],"date_updated":"2023-02-23T10:05:27Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:02Z","_id":"1582","pubrep_id":"474","status":"public","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)"},"type":"journal_article","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"c1ef67f6ec925e12f73a96b8fe285ab4","file_id":"5215","date_updated":"2020-07-14T12:45:02Z","file_size":505987,"creator":"system","date_created":"2018-12-12T10:16:28Z","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf"}],"publication_status":"published","volume":48,"issue":"2","related_material":{"record":[{"id":"1584","status":"public","relation":"other"}]},"oa_version":"Published Version","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."}],"intvolume":" 48","month":"02","scopus_import":1},{"_id":"1583","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)"},"type":"journal_article","pubrep_id":"473","status":"public","date_updated":"2021-01-12T06:51:45Z","ddc":["000"],"file_date_updated":"2020-07-14T12:45:03Z","department":[{"_id":"HeEd"}],"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."}],"oa_version":"Published Version","scopus_import":1,"intvolume":" 115","month":"02","publication_status":"published","language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:45:03Z","file_size":270137,"creator":"system","date_created":"2018-12-12T10:18:45Z","file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"2779a648610c9b5c86d0b51a62816d23","file_id":"5367"}],"volume":115,"issue":"2","citation":{"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.","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.","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.","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"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814"},{"last_name":"Kaaser","full_name":"Kaaser, Dominik","first_name":"Dominik"},{"last_name":"Palfrader","full_name":"Palfrader, Peter","first_name":"Peter"}],"publist_id":"5588","title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","oa":1,"quality_controlled":"1","publisher":"Elsevier","year":"2015","has_accepted_license":"1","publication":"Information Processing Letters","day":"01","page":"243 - 247","date_created":"2018-12-11T11:52:51Z","date_published":"2015-02-01T00:00:00Z","doi":"10.1016/j.ipl.2014.09.021"},{"citation":{"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.","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.","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","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.","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.","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."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publist_id":"5581","author":[{"full_name":"Aichholzer, Oswin","last_name":"Aichholzer","first_name":"Oswin"},{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"first_name":"Thomas","full_name":"Hackl, Thomas","last_name":"Hackl"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"article_processing_charge":"No","title":"Representing directed trees as straight skeletons","quality_controlled":"1","publisher":"Springer Nature","oa":1,"year":"2015","day":"27","publication":"Graph Drawing and Network Visualization","page":"335 - 347","doi":"10.1007/978-3-319-27261-0_28","date_published":"2015-11-27T00:00:00Z","date_created":"2018-12-11T11:52:54Z","_id":"1590","type":"book_chapter","conference":{"name":"GD: International Symposium on Graph Drawing","location":"Los Angeles, CA, United States","end_date":"2015-09-26","start_date":"2015-09-24"},"status":"public","date_updated":"2022-01-28T09:10:37Z","department":[{"_id":"HeEd"}],"abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","alternative_title":["LNCS"],"scopus_import":"1","main_file_link":[{"url":"http://arxiv.org/abs/1508.01076","open_access":"1"}],"month":"11","intvolume":" 9411","publication_identifier":{"isbn":["978-3-319-27260-3"],"eisbn":["978-3-319-27261-0"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":9411},{"day":"01","language":[{"iso":"eng"}],"publication":"Journal of the ACM","publication_status":"published","year":"2015","doi":"10.1145/2751524","volume":62,"issue":"4","date_published":"2015-08-01T00:00:00Z","date_created":"2018-12-11T11:53:27Z","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"month":"08","intvolume":" 62","quality_controlled":"1","scopus_import":1,"publisher":"ACM","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:52:30Z","citation":{"apa":"Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations. Journal of the ACM. ACM. https://doi.org/10.1145/2751524","ama":"Franek P, Krcál M. Robust satisfiability of systems of equations. Journal of the ACM. 2015;62(4). doi: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.","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.","ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26.","chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524."},"title":"Robust satisfiability of systems of equations","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"author":[{"last_name":"Franek","full_name":"Franek, Peter","first_name":"Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","full_name":"Krcál, Marek","last_name":"Krcál"}],"publist_id":"5466","article_number":"26","_id":"1682","status":"public","type":"journal_article"},{"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"publist_id":"5423","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"first_name":"Alexander","full_name":"Plakhov, Alexander","last_name":"Plakhov"}],"title":"Minimal resistance of curves under the single impact assumption","citation":{"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.","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","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","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","publisher":"SIAM","oa":1,"page":"2754 - 2769","date_published":"2015-07-14T00:00:00Z","doi":"10.1137/140993843","date_created":"2018-12-11T11:53:36Z","year":"2015","day":"14","publication":"Society for Industrial and Applied Mathematics","type":"journal_article","status":"public","_id":"1710","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:52:41Z","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1410.3736","open_access":"1"}],"month":"07","intvolume":" 47","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"}],"oa_version":"Preprint","issue":"4","volume":47,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}]},{"volume":160,"issue":"1","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"07","intvolume":" 160","scopus_import":1,"main_file_link":[{"open_access":"1","url":"arxiv.org/abs/1406.5313"}],"oa_version":"Preprint","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"}],"department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T06:53:28Z","status":"public","type":"journal_article","_id":"1828","date_published":"2015-07-01T00:00:00Z","doi":"10.1007/s10955-015-1238-5","date_created":"2018-12-11T11:54:14Z","page":"163 - 167","day":"01","publication":"Journal of Statistical Physics","year":"2015","publisher":"Springer","quality_controlled":"1","oa":1,"title":"Invariant measures of genetic recombination process","publist_id":"5276","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"full_name":"Pirogov, Sergey","last_name":"Pirogov","first_name":"Sergey"},{"first_name":"Aleksandr","full_name":"Rybko, Aleksandr","last_name":"Rybko"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","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."},"project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"page":"535 - 541","date_published":"2015-03-06T00:00:00Z","issue":"6","volume":379,"doi":"10.1016/j.physleta.2014.12.010","date_created":"2018-12-11T11:54:49Z","publication_status":"published","year":"2015","day":"06","publication":"Physics Letters, Section A","language":[{"iso":"eng"}],"scopus_import":1,"quality_controlled":"1","publisher":"Elsevier","month":"03","intvolume":" 379","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"}],"oa_version":"None","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":[{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Stefan","last_name":"Steinerberger","full_name":"Steinerberger, Stefan"}],"publist_id":"5152","title":"On the distribution of local extrema in quantum chaos","department":[{"_id":"HeEd"}],"citation":{"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.","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.","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.","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"},"date_updated":"2021-01-12T06:54:12Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","status":"public","_id":"1938"},{"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.","publisher":"Springer","quality_controlled":"1","oa":1,"day":"01","publication":"Foundations of Computational Mathematics","has_accepted_license":"1","year":"2015","doi":"10.1007/s10208-014-9223-y","date_published":"2015-10-01T00:00:00Z","date_created":"2018-12-11T11:55:20Z","page":"1213 - 1244","project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","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","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","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."},"title":"The persistent homology of a self-map","publist_id":"5022","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz"},{"first_name":"Marian","full_name":"Mrozek, Marian","last_name":"Mrozek"}],"oa_version":"Published Version","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"}],"month":"10","intvolume":" 15","scopus_import":1,"file":[{"file_id":"4670","checksum":"3566f3a8b0c1bc550e62914a88c584ff","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","date_created":"2018-12-12T10:08:10Z","creator":"system","file_size":1317546,"date_updated":"2020-07-14T12:45:26Z"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"5","volume":15,"ec_funded":1,"_id":"2035","status":"public","pubrep_id":"486","type":"journal_article","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)"},"ddc":["000"],"date_updated":"2021-01-12T06:54:53Z","file_date_updated":"2020-07-14T12:45:26Z","department":[{"_id":"HeEd"}]},{"project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493"}],"author":[{"first_name":"Dominique","last_name":"Attali","full_name":"Attali, Dominique"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724"},{"first_name":"Olivier","full_name":"Devillers, Olivier","last_name":"Devillers"},{"first_name":"Marc","last_name":"Glisse","full_name":"Glisse, Marc"},{"full_name":"Lieutier, André","last_name":"Lieutier","first_name":"André"}],"publist_id":"5305","title":"Homological reconstruction and simplification in R3","citation":{"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.","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.","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","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","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","quality_controlled":"1","page":"606 - 621","date_published":"2015-06-03T00:00:00Z","doi":"10.1016/j.comgeo.2014.08.010","date_created":"2018-12-11T11:54:06Z","year":"2015","day":"03","publication":"Computational Geometry: Theory and Applications","type":"journal_article","status":"public","_id":"1805","department":[{"_id":"HeEd"}],"date_updated":"2023-02-23T10:59:19Z","scopus_import":1,"month":"06","intvolume":" 48","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."}],"oa_version":"None","volume":48,"issue":"8","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2812"}]},"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}]},{"has_accepted_license":"1","year":"2015","day":"01","publication":"PLoS One","date_published":"2015-06-01T00:00:00Z","doi":"10.1371/journal.pone.0127657","date_created":"2018-12-11T11:54:02Z","publisher":"Public Library of Science","quality_controlled":"1","oa":1,"citation":{"short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","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.","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","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Symonova, Olga","last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Topp","full_name":"Topp, Christopher","first_name":"Christopher"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"publist_id":"5318","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","article_number":"e0127657","publication_status":"published","file":[{"creator":"system","date_updated":"2020-07-14T12:45:16Z","file_size":1850825,"date_created":"2018-12-12T10:15:30Z","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"d20f26461ca575276ad3ed9ce4bfc787","file_id":"5150"}],"language":[{"iso":"eng"}],"volume":10,"related_material":{"record":[{"id":"9737","status":"public","relation":"research_data"}]},"issue":"6","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"}],"oa_version":"Published Version","scopus_import":1,"month":"06","intvolume":" 10","date_updated":"2023-02-23T14:06:33Z","ddc":["000"],"department":[{"_id":"MaJö"},{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:16Z","_id":"1793","type":"journal_article","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)"},"status":"public","pubrep_id":"454"},{"title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"article_processing_charge":"No","author":[{"last_name":"Symonova","full_name":"Symonova, Olga","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Christopher","last_name":"Topp","full_name":"Topp, Christopher"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","date_updated":"2023-02-23T10:14:42Z","citation":{"short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","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.","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","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.","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.","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."},"status":"public","type":"research_data_reference","_id":"9737","date_created":"2021-07-28T06:20:13Z","date_published":"2015-06-01T00:00:00Z","doi":"10.1371/journal.pone.0127657.s001","related_material":{"record":[{"relation":"used_in_publication","id":"1793","status":"public"}]},"day":"01","year":"2015","month":"06","publisher":"Public Library of Science","oa_version":"Published Version"},{"day":"01","publication":"Journal of Complexity","language":[{"iso":"eng"}],"year":"2015","publication_status":"published","volume":31,"related_material":{"record":[{"id":"1399","status":"public","relation":"dissertation_contains"}]},"issue":"6","doi":"10.1016/j.jco.2015.06.002","date_published":"2015-12-01T00:00:00Z","date_created":"2018-12-11T11:54:02Z","page":"773 - 797","oa_version":"None","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.","abstract":[{"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.","lang":"eng"}],"month":"12","intvolume":" 31","quality_controlled":"1","scopus_import":1,"publisher":"Academic Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","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.","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 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","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","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."},"date_updated":"2023-09-07T11:41:25Z","title":"A Koksma-Hlawka inequality for general discrepancy systems","department":[{"_id":"HeEd"}],"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"},{"first_name":"Anne","full_name":"Svane, Anne","last_name":"Svane"}],"_id":"1792","status":"public","type":"journal_article"},{"page":"144","date_created":"2018-12-11T11:51:48Z","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1662"},{"relation":"part_of_dissertation","status":"public","id":"1792"},{"relation":"part_of_dissertation","status":"public","id":"2255"}]},"date_published":"2015-06-01T00:00:00Z","year":"2015","publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"day":"01","publisher":"Institute of Science and Technology Austria","alternative_title":["ISTA Thesis"],"month":"06","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."}],"oa_version":"None","article_processing_charge":"No","author":[{"first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian"}],"publist_id":"5808","title":"On the approximation of intrinsic volumes","department":[{"_id":"HeEd"}],"citation":{"ieee":"F. Pausinger, “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.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015.","mla":"Pausinger, Florian. 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.","chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015."},"date_updated":"2023-09-07T11:41:25Z","supervisor":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","type":"dissertation","status":"public","_id":"1399"},{"date_updated":"2022-06-21T12:01:47Z","department":[{"_id":"HeEd"}],"series_title":"Mathematics and Visualization","_id":"10893","status":"public","type":"book_chapter","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"issn":["1612-3786"],"eisbn":["9783319040998"]},"publication_status":"published","volume":1,"ec_funded":1,"oa_version":"None","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."}],"place":"Cham","month":"03","intvolume":" 1","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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.","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.","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."},"title":"Toward the extraction of saddle periodic orbits","editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"first_name":"Valerio","full_name":"Pascucci, Valerio","last_name":"Pascucci"},{"last_name":"Peikert","full_name":"Peikert, Ronald","first_name":"Ronald"}],"author":[{"first_name":"Jens","last_name":"Kasten","full_name":"Kasten, Jens"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Reich","full_name":"Reich, Wieland","first_name":"Wieland"},{"first_name":"Gerik","full_name":"Scheuermann, Gerik","last_name":"Scheuermann"}],"article_processing_charge":"No","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"day":"19","publication":"Topological Methods in Data Analysis and Visualization III ","year":"2014","doi":"10.1007/978-3-319-04099-8_4","date_published":"2014-03-19T00:00:00Z","date_created":"2022-03-21T07:11:23Z","page":"55-69","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.","publisher":"Springer","quality_controlled":"1"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","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.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 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."},"title":"Topology-preserving watermarking of vector graphics","publist_id":"5290","author":[{"orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"full_name":"Meerwald, Peter","last_name":"Meerwald","first_name":"Peter"},{"full_name":"Kwitt, Roland","last_name":"Kwitt","first_name":"Roland"}],"acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","quality_controlled":"1","publisher":"World Scientific Publishing","oa":1,"day":"16","publication":"International Journal of Computational Geometry and Applications","has_accepted_license":"1","year":"2014","doi":"10.1142/S0218195914500034","date_published":"2014-03-16T00:00:00Z","date_created":"2018-12-11T11:54:10Z","page":"61 - 86","_id":"1816","status":"public","pubrep_id":"443","type":"journal_article","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)"},"ddc":["000"],"date_updated":"2021-01-12T06:53:23Z","file_date_updated":"2020-07-14T12:45:17Z","department":[{"_id":"HeEd"}],"oa_version":"Published Version","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."}],"month":"03","intvolume":" 24","scopus_import":1,"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"be45c133ab4d43351260e21beaa8f4b1","file_id":"4704","creator":"system","file_size":991734,"date_updated":"2020-07-14T12:45:17Z","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","date_created":"2018-12-12T10:08:43Z"}],"language":[{"iso":"eng"}],"publication_status":"published","volume":24,"issue":"1"},{"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"title":"On the geometric ramsey number of outerplanar graphs","author":[{"last_name":"Cibulka","full_name":"Cibulka, Josef","first_name":"Josef"},{"first_name":"Pu","full_name":"Gao, Pu","last_name":"Gao"},{"first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","last_name":"Krcál"},{"last_name":"Valla","full_name":"Valla, Tomáš","first_name":"Tomáš"},{"first_name":"Pavel","full_name":"Valtr, Pavel","last_name":"Valtr"}],"publist_id":"5260","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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","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","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.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 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."},"date_updated":"2021-01-12T06:53:33Z","status":"public","type":"journal_article","_id":"1842","volume":53,"doi":"10.1007/s00454-014-9646-x","issue":"1","date_published":"2014-11-14T00:00:00Z","date_created":"2018-12-11T11:54:18Z","page":"64 - 79","day":"14","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","publication_status":"published","year":"2014","month":"11","intvolume":" 53","publisher":"Springer","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7004"}],"oa":1,"oa_version":"Submitted Version","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","abstract":[{"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.","lang":"eng"}]},{"publication_status":"published","publication_identifier":{"issn":["16093321"]},"language":[{"iso":"eng"}],"issue":"3","volume":14,"abstract":[{"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.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1211.7053"}],"scopus_import":"1","intvolume":" 14","month":"07","date_updated":"2022-03-03T11:47:09Z","department":[{"_id":"HeEd"}],"_id":"1876","article_type":"original","type":"journal_article","status":"public","year":"2014","publication":"Moscow Mathematical Journal","day":"01","page":"491 - 504","date_created":"2018-12-11T11:54:29Z","doi":"10.17323/1609-4514-2014-14-3-491-504","date_published":"2014-07-01T00:00:00Z","oa":1,"publisher":"Independent University of Moscow","quality_controlled":"1","citation":{"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.","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","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","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.","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["1211.7053"]},"publist_id":"5220","author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"}],"title":"Functionals on triangulations of delaunay sets"},{"volume":203,"issue":"6","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-8795"],"issn":["1072-3374"]},"publication_status":"published","month":"11","intvolume":" 203","scopus_import":"1","oa_version":"None","abstract":[{"lang":"eng","text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales."}],"department":[{"_id":"HeEd"}],"date_updated":"2022-05-24T10:39:06Z","status":"public","type":"journal_article","article_type":"original","_id":"1929","date_published":"2014-11-16T00:00:00Z","doi":"10.1007/s10958-014-2165-8","date_created":"2018-12-11T11:54:46Z","page":"754 - 760","day":"16","publication":"Journal of Mathematical Sciences","year":"2014","publisher":"Springer","quality_controlled":"1","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.","title":"An algorithm for cartographic generalization that preserves global topology","author":[{"last_name":"Alexeev","full_name":"Alexeev, V V","first_name":"V V"},{"last_name":"Bogaevskaya","full_name":"Bogaevskaya, V G","first_name":"V G"},{"last_name":"Preobrazhenskaya","full_name":"Preobrazhenskaya, M M","first_name":"M M"},{"first_name":"A Y","last_name":"Ukhalov","full_name":"Ukhalov, A Y"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Olga","full_name":"Yakimova, Olga","last_name":"Yakimova"}],"publist_id":"5165","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","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.","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.","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.","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."}},{"day":"31","publication":"IEEE Transactions on Visualization and Computer Graphics","language":[{"iso":"eng"}],"year":"2014","publication_status":"published","doi":"10.1109/TVCG.2014.2346432","issue":"12","volume":20,"date_published":"2014-12-31T00:00:00Z","date_created":"2018-12-11T11:54:46Z","page":"2585 - 2594","oa_version":"None","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","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"}],"month":"12","intvolume":" 20","publisher":"IEEE","quality_controlled":"1","scopus_import":1,"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:54:09Z","citation":{"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.","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","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","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.","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."},"title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","department":[{"_id":"HeEd"}],"publist_id":"5164","author":[{"first_name":"David","last_name":"Günther","full_name":"Günther, David"},{"last_name":"Jacobson","full_name":"Jacobson, Alec","first_name":"Alec"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus"},{"full_name":"Seidel, Hans","last_name":"Seidel","first_name":"Hans"},{"first_name":"Olga","last_name":"Sorkine Hornung","full_name":"Sorkine Hornung, Olga"},{"first_name":"Tino","last_name":"Weinkauf","full_name":"Weinkauf, Tino"}],"_id":"1930","status":"public","type":"journal_article"},{"_id":"2043","type":"conference","conference":{"start_date":"2014-01-05","location":"Portland, USA","end_date":"2014-01-05","name":"ALENEX: Algorithm Engineering and Experiments"},"status":"public","date_updated":"2021-01-12T06:54:56Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems [1], we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 6GB of memory per node."}],"oa_version":"Submitted Version","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1310.0710","open_access":"1"}],"month":"01","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"citation":{"apa":"Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland, USA: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4","ama":"Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology. In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2014:31-38. doi:10.1137/1.9781611973198.4","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2014, pp. 31–38.","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments, Portland, USA, 2014, pp. 31–38.","mla":"Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, Society of Industrial and Applied Mathematics, 2014, pp. 31–38, doi:10.1137/1.9781611973198.4.","ista":"Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent homology. Proceedings of the Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, 31–38.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society of Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer"},{"first_name":"Michael","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael","last_name":"Kerber"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan"}],"publist_id":"5008","title":"Distributed computation of persistent homology","editor":[{"first_name":"Catherine","full_name":" McGeoch, Catherine","last_name":" McGeoch"},{"first_name":"Ulrich","full_name":"Meyer, Ulrich","last_name":"Meyer"}],"quality_controlled":"1","publisher":"Society of Industrial and Applied Mathematics","oa":1,"year":"2014","day":"01","publication":"Proceedings of the Workshop on Algorithm Engineering and Experiments","page":"31 - 38","date_published":"2014-01-01T00:00:00Z","doi":"10.1137/1.9781611973198.4","date_created":"2018-12-11T11:55:23Z"},{"year":"2014","day":"19","publication":"Topological Methods in Data Analysis and Visualization III","page":"103 - 117","doi":"10.1007/978-3-319-04099-8_7","date_published":"2014-03-19T00:00:00Z","date_created":"2018-12-11T11:55:23Z","publisher":"Springer","quality_controlled":"1","oa":1,"citation":{"ama":"Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7","apa":"Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117.","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in Topological Methods in Data Analysis and Visualization III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.","mla":"Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.","ista":"Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5007","title":"Clear and Compress: Computing Persistent Homology in Chunks","editor":[{"full_name":"Bremer, Peer-Timo","last_name":"Bremer","first_name":"Peer-Timo"},{"full_name":"Hotz, Ingrid","last_name":"Hotz","first_name":"Ingrid"},{"full_name":"Pascucci, Valerio","last_name":"Pascucci","first_name":"Valerio"},{"first_name":"Ronald","full_name":"Peikert, Ronald","last_name":"Peikert"}],"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"abstract":[{"text":"We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation.","lang":"eng"}],"oa_version":"Submitted Version","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1303.0477","open_access":"1"}],"month":"03","date_updated":"2021-01-12T06:54:56Z","department":[{"_id":"HeEd"}],"series_title":"Mathematics and Visualization","_id":"2044","type":"book_chapter","status":"public"},{"main_file_link":[{"url":"http://arxiv.org/abs/1311.3681","open_access":"1"}],"oa":1,"publisher":"ACM","scopus_import":1,"quality_controlled":"1","month":"06","abstract":[{"lang":"eng","text":"We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s)."}],"oa_version":"Submitted Version","page":"355 - 364","ec_funded":1,"date_created":"2018-12-11T11:56:01Z","date_published":"2014-06-01T00:00:00Z","doi":"10.1145/2582112.2582168","year":"2014","publication_status":"published","language":[{"iso":"eng"}],"publication":"Proceedings of the Annual Symposium on Computational Geometry","day":"01","conference":{"location":"Kyoto, Japan","end_date":"2014-06-11","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"status":"public","_id":"2153","author":[{"last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"}],"publist_id":"4853","department":[{"_id":"HeEd"}],"title":"Induced matchings of barcodes and the algebraic stability of persistence","date_updated":"2021-01-12T06:55:38Z","citation":{"ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 355–364.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","apa":"Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In Proceedings of the Annual Symposium on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168","ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:355-364. doi:10.1145/2582112.2582168","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.","ista":"Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364.","chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},{"_id":"2156","type":"conference","conference":{"location":"Kyoto, Japan","end_date":"2014-06-11","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"status":"public","date_updated":"2021-01-12T06:55:39Z","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s)."}],"oa_version":"Submitted Version","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1307.2839"}],"month":"06","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"citation":{"ista":"Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.","chicago":"Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In Proceedings of the Annual Symposium on Computational Geometry, 464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.","ama":"Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169","apa":"Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb graphs. In Proceedings of the Annual Symposium on Computational Geometry (pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169","ieee":"U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 464–473.","short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.","mla":"Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73, doi:10.1145/2582112.2582169."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Bauer","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"last_name":"Ge","full_name":"Ge, Xiaoyin","first_name":"Xiaoyin"},{"first_name":"Yusu","last_name":"Wang","full_name":"Wang, Yusu"}],"publist_id":"4850","title":"Measuring distance between Reeb graphs","acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","publisher":"ACM","quality_controlled":"1","oa":1,"year":"2014","day":"01","publication":"Proceedings of the Annual Symposium on Computational Geometry","page":"464 - 473","date_published":"2014-06-01T00:00:00Z","doi":"10.1145/2582112.2582169","date_created":"2018-12-11T11:56:02Z"},{"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 484–490.","short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","apa":"Bauer, U., & Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In Proceedings of the Annual Symposium on Computational Geometry (pp. 484–490). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582167","ama":"Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:484-490. doi:10.1145/2582112.2582167","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–90, doi:10.1145/2582112.2582167.","ista":"Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 484–490.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In Proceedings of the Annual Symposium on Computational Geometry, 484–90. ACM, 2014. https://doi.org/10.1145/2582112.2582167."},"title":"The morse theory of Čech and Delaunay filtrations","author":[{"first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"publist_id":"4851","project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"publication":"Proceedings of the Annual Symposium on Computational Geometry","day":"01","year":"2014","date_created":"2018-12-11T11:56:01Z","doi":"10.1145/2582112.2582167","date_published":"2014-06-01T00:00:00Z","page":"484 - 490","acknowledgement":"This research is partially supported by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053","oa":1,"quality_controlled":"1","publisher":"ACM","date_updated":"2021-01-12T06:55:38Z","department":[{"_id":"HeEd"}],"_id":"2155","status":"public","conference":{"start_date":"2014-06-08","end_date":"2014-06-11","location":"Kyoto, Japan","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s)."}],"month":"06","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1312.1231"}],"scopus_import":1},{"oa_version":"None","abstract":[{"text":"We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity.","lang":"eng"}],"month":"01","publisher":"SIAM","quality_controlled":"1","scopus_import":1,"day":"01","language":[{"iso":"eng"}],"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","publication_status":"published","year":"2014","doi":"10.1137/1.9781611973402.11","date_published":"2014-01-01T00:00:00Z","date_created":"2018-12-11T11:56:09Z","page":"152 - 160","_id":"2177","status":"public","type":"conference","conference":{"name":"SODA: Symposium on Discrete Algorithms","start_date":"2014-01-05","end_date":"2014-01-07","location":"Portland, USA"},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:55:48Z","citation":{"ista":"Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.","chicago":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 152–60. SIAM, 2014. https://doi.org/10.1137/1.9781611973402.11.","ama":"Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11","apa":"Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM. https://doi.org/10.1137/1.9781611973402.11","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160.","ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.","mla":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–60, doi:10.1137/1.9781611973402.11."},"department":[{"_id":"HeEd"}],"title":"On the computational complexity of betti numbers reductions from matrix rank","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","first_name":"Salman","last_name":"Parsa","full_name":"Parsa, Salman"}],"publist_id":"4805"},{"article_number":"17 ","title":"Computing all maps into a sphere","publist_id":"4797","author":[{"last_name":"Čadek","full_name":"Čadek, Martin","first_name":"Martin"},{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Matoušek","full_name":"Matoušek, Jiří","first_name":"Jiří"},{"first_name":"Francis","last_name":"Sergeraert","full_name":"Sergeraert, Francis"},{"full_name":"Vokřínek, Lukáš","last_name":"Vokřínek","first_name":"Lukáš"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","last_name":"Wagner"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629.","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014).","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3. ACM, 2014.","ama":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629","apa":"Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner, U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM. ACM, 2014. https://doi.org/10.1145/2597629.","ista":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing all maps into a sphere. Journal of the ACM. 61(3), 17."},"quality_controlled":"1","publisher":"ACM","oa":1,"acknowledgement":"The research by M. K. was supported by project GAUK 49209. The research by M. K. was also supported by project 1M0545 by the Ministry of Education of the Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague (project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).","doi":"10.1145/2597629","date_published":"2014-05-01T00:00:00Z","date_created":"2018-12-11T11:56:12Z","day":"01","publication":"Journal of the ACM","year":"2014","status":"public","type":"journal_article","_id":"2184","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T06:55:50Z","month":"05","intvolume":" 61","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.6257"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable."}],"volume":61,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published"},{"file":[{"file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf","date_created":"2018-12-12T10:16:43Z","creator":"system","file_size":435320,"date_updated":"2020-07-14T12:45:52Z","file_id":"5232","checksum":"1d4a046f1af945c407c5c4d411d4c5e4","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_status":"published","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Persistent homology is a recent grandchild of homology that has found use in\r\nscience and engineering as well as in mathematics. This paper surveys the method as well\r\nas the applications, neglecting completeness in favor of highlighting ideas and directions."}],"month":"01","ddc":["000"],"date_updated":"2021-01-12T07:00:36Z","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:52Z","_id":"2905","status":"public","pubrep_id":"544","type":"conference","conference":{"name":"ECM: European Congress of Mathematics","end_date":"2012-07-07","location":"Kraków, Poland","start_date":"2012-07-02"},"day":"01","has_accepted_license":"1","year":"2014","date_published":"2014-01-01T00:00:00Z","doi":"10.4171/120-1/3","date_created":"2018-12-11T12:00:16Z","page":"31 - 50","acknowledgement":"This research is partially supported by NSF under grant DBI-0820624, by ESF under the Research Networking Programme, and by the Russian Government Project 11.G34.31.0053.","quality_controlled":"1","publisher":"European Mathematical Society Publishing House","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Edelsbrunner, H., & Morozovy, D. (2014). Persistent homology: Theory and practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics, Kraków, Poland: European Mathematical Society Publishing House. https://doi.org/10.4171/120-1/3","ama":"Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In: European Mathematical Society Publishing House; 2014:31-50. doi:10.4171/120-1/3","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 31–50.","ieee":"H. Edelsbrunner and D. Morozovy, “Persistent homology: Theory and practice,” presented at the ECM: European Congress of Mathematics, Kraków, Poland, 2014, pp. 31–50.","mla":"Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory and Practice. European Mathematical Society Publishing House, 2014, pp. 31–50, doi:10.4171/120-1/3.","ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","chicago":"Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory and Practice,” 31–50. European Mathematical Society Publishing House, 2014. https://doi.org/10.4171/120-1/3."},"title":"Persistent homology: Theory and practice","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Morozovy, Dmitriy","last_name":"Morozovy","first_name":"Dmitriy"}],"publist_id":"3842","article_processing_charge":"No"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in 25th International Symposium, ISAAC 2014, Jeonju, Korea, 2014, vol. 8889, pp. 117–127.","short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127.","apa":"Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature; 2014:117-127. doi:10.1007/978-3-319-13075-0_10","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” 25th International Symposium, ISAAC 2014, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:10.1007/978-3-319-13075-0_10.","ista":"Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 8889, 117–127.","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In 25th International Symposium, ISAAC 2014, 8889:117–27. Springer Nature, 2014. https://doi.org/10.1007/978-3-319-13075-0_10."},"title":"Planar matchings for weighted straight skeletons","article_processing_charge":"No","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"last_name":"Huber","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"acknowledgement":"T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.","publisher":"Springer Nature","quality_controlled":"1","publication":"25th International Symposium, ISAAC 2014","day":"08","year":"2014","date_created":"2022-03-21T07:09:03Z","date_published":"2014-11-08T00:00:00Z","doi":"10.1007/978-3-319-13075-0_10","page":"117-127","_id":"10892","status":"public","conference":{"name":"ISAAC: International Symposium on Algorithms and Computation","start_date":"2014-12-15","end_date":"2014-12-17","location":"Jeonju, Korea"},"type":"conference","date_updated":"2023-02-23T12:20:55Z","department":[{"_id":"HeEd"}],"oa_version":"None","abstract":[{"lang":"eng","text":"In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist.\r\nUsing our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"intvolume":" 8889","month":"11","scopus_import":"1","alternative_title":["LNCS"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eisbn":["9783319130750"],"isbn":["9783319130743"],"eissn":["1611-3349"],"issn":["0302-9743"]},"volume":8889,"related_material":{"record":[{"relation":"later_version","id":"481","status":"public"}]}},{"alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"publisher":"Springer Nature","scopus_import":"1","quality_controlled":"1","edition":"1","month":"01","place":"Cham","abstract":[{"lang":"eng","text":"This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields."}],"oa_version":"None","page":"IX, 110","doi":"10.1007/978-3-319-05957-0","date_published":"2014-01-01T00:00:00Z","related_material":{"link":[{"description":"available as eBook via catalog IST BookList","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106","relation":"other"},{"url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842","relation":"other","description":"available via catalog IST BookList"}]},"date_created":"2019-09-06T09:22:33Z","publication_identifier":{"issn":["2191-530X"],"eissn":["2191-5318"],"isbn":["9-783-3190-5956-3"],"eisbn":["9-783-3190-5957-0"]},"year":"2014","publication_status":"published","day":"01","language":[{"iso":"eng"}],"type":"book","status":"public","series_title":"SpringerBriefs in Applied Sciences and Technology","_id":"6853","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"}],"article_processing_charge":"No","title":"A Short Course in Computational Geometry and Topology","department":[{"_id":"HeEd"}],"date_updated":"2022-03-04T07:47:54Z","citation":{"ista":"Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.","chicago":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.","ama":"Edelsbrunner H. A Short Course in Computational Geometry and Topology. 1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0","apa":"Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology (1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0","ieee":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.","short":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014.","mla":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_published":"2014-03-19T00:00:00Z","doi":"10.1007/978-3-319-04099-8_16","date_created":"2022-03-18T13:05:39Z","page":"249-262","day":"19","publication":"Topological Methods in Data Analysis and Visualization III ","language":[{"iso":"eng"}],"publication_identifier":{"eisbn":["9783319040998"],"eissn":["2197-666X"],"isbn":["9783319040981"],"issn":["1612-3786"]},"publication_status":"published","year":"2014","month":"03","quality_controlled":"1","alternative_title":["Mathematics and Visualization"],"scopus_import":"1","publisher":"Springer","oa_version":"None","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","abstract":[{"text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set.","lang":"eng"}],"department":[{"_id":"HeEd"}],"title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","author":[{"first_name":"Valentin","full_name":"Zobel, Valentin","last_name":"Zobel"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"full_name":"Hotz, Ingrid","last_name":"Hotz","first_name":"Ingrid"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In Topological Methods in Data Analysis and Visualization III , 249–62. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_16.","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in Topological Methods in Data Analysis and Visualization III , 2014, pp. 249–262.","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In Topological Methods in Data Analysis and Visualization III (pp. 249–262). Springer. https://doi.org/10.1007/978-3-319-04099-8_16","ama":"Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: Topological Methods in Data Analysis and Visualization III . Springer; 2014:249-262. doi:10.1007/978-3-319-04099-8_16"},"date_updated":"2023-09-05T14:13:16Z","status":"public","type":"conference","_id":"10886"},{"acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","publisher":"Springer Nature","quality_controlled":"1","publication":"Topological Methods in Data Analysis and Visualization III.","day":"19","year":"2014","date_created":"2022-03-04T08:33:57Z","date_published":"2014-03-19T00:00:00Z","doi":"10.1007/978-3-319-04099-8_9","page":"135-150","project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:10.1007/978-3-319-04099-8_9.","ama":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:10.1007/978-3-319-04099-8_9","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III. (pp. 135–150). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-04099-8_9","short":"D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.","ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in Topological Methods in Data Analysis and Visualization III., P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In Topological Methods in Data Analysis and Visualization III., edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-04099-8_9.","ista":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150."},"title":"Notes on the simplification of the Morse-Smale complex","editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"last_name":"Pascucci","full_name":"Pascucci, Valerio","first_name":"Valerio"},{"full_name":"Peikert, Ronald","last_name":"Peikert","first_name":"Ronald"}],"article_processing_charge":"No","author":[{"first_name":"David","full_name":"Günther, David","last_name":"Günther"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Hans-Peter","full_name":"Seidel, Hans-Peter","last_name":"Seidel"},{"full_name":"Weinkauf, Tino","last_name":"Weinkauf","first_name":"Tino"}],"oa_version":"None","abstract":[{"lang":"eng","text":"The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption."}],"place":"Cham","month":"03","scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eisbn":["9783319040998"],"issn":["1612-3786"],"eissn":["2197-666X"],"isbn":["9783319040981"]},"ec_funded":1,"_id":"10817","series_title":"Mathematics and Visualization","status":"public","type":"book_chapter","date_updated":"2023-09-05T15:33:45Z","department":[{"_id":"HeEd"}]},{"status":"public","pubrep_id":"549","type":"journal_article","_id":"2255","file_date_updated":"2020-07-14T12:45:35Z","department":[{"_id":"HeEd"}],"ddc":["000"],"date_updated":"2023-09-07T11:41:25Z","month":"09","intvolume":" 50","scopus_import":1,"oa_version":"Submitted Version","abstract":[{"text":"Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm.","lang":"eng"}],"volume":50,"issue":"1","related_material":{"record":[{"id":"2843","status":"public","relation":"earlier_version"},{"relation":"dissertation_contains","status":"public","id":"1399"}]},"ec_funded":1,"file":[{"creator":"system","date_updated":"2020-07-14T12:45:35Z","file_size":3941391,"date_created":"2018-12-12T10:16:18Z","file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"2f93f3e63a38a85cd4404d7953913b14","file_id":"5204"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["09249907"]},"publication_status":"published","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"title":"Stable length estimates of tube-like shapes","publist_id":"4691","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer, 2014. https://doi.org/10.1007/s10851-013-0468-x.","ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x","apa":"Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x","short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x."},"quality_controlled":"1","publisher":"Springer","oa":1,"doi":"10.1007/s10851-013-0468-x","date_published":"2014-09-01T00:00:00Z","date_created":"2018-12-11T11:56:36Z","page":"164 - 177","day":"01","publication":"Journal of Mathematical Imaging and Vision","has_accepted_license":"1","year":"2014"},{"article_processing_charge":"No","author":[{"last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"title":"PHAT – Persistent Homology Algorithms Toolbox","citation":{"ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: ICMS 2014: International Congress on Mathematical Software. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:10.1007/978-3-662-44199-2_24","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_24","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143.","mla":"Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” ICMS 2014: International Congress on Mathematical Software, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:10.1007/978-3-662-44199-2_24.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software. ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In ICMS 2014: International Congress on Mathematical Software, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. https://doi.org/10.1007/978-3-662-44199-2_24."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","publisher":"Springer Berlin Heidelberg","page":"137-143","date_created":"2022-03-21T07:12:16Z","doi":"10.1007/978-3-662-44199-2_24","date_published":"2014-09-01T00:00:00Z","year":"2014","publication":"ICMS 2014: International Congress on Mathematical Software","day":"01","conference":{"name":"ICMS: International Congress on Mathematical Software","location":"Seoul, South Korea","end_date":"2014-08-09","start_date":"2014-08-05"},"type":"conference","status":"public","_id":"10894","series_title":"LNCS","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T09:42:40Z","scopus_import":"1","intvolume":" 8592","place":"Berlin, Heidelberg","month":"09","abstract":[{"lang":"eng","text":"PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations."}],"oa_version":"None","volume":8592,"related_material":{"record":[{"id":"1433","status":"public","relation":"later_version"}]},"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783662441985"],"eisbn":["9783662441992"]},"language":[{"iso":"eng"}]},{"citation":{"ista":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.","chicago":"Iglesias Ham, Mabel, Michael Kerber, and Caroline Uhler. “Sphere Packing with Limited Overlap.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1401.0468.","short":"M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.).","ieee":"M. Iglesias Ham, M. Kerber, and C. 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Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468."},"date_updated":"2023-10-18T08:06:45Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1401.0468"]},"article_processing_charge":"No","publist_id":"5064","author":[{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299"},{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","first_name":"Caroline","last_name":"Uhler","full_name":"Uhler, Caroline","orcid":"0000-0002-7008-0216"}],"title":"Sphere packing with limited overlap","department":[{"_id":"HeEd"},{"_id":"CaUh"}],"_id":"2012","article_number":"1401.0468","type":"preprint","status":"public","publication_status":"submitted","year":"2014","publication":"arXiv","language":[{"iso":"eng"}],"day":"01","date_created":"2018-12-11T11:55:12Z","date_published":"2014-01-01T00:00:00Z","doi":"10.48550/arXiv.1401.0468","abstract":[{"text":"The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of overlap with other balls. We study two natural choices of overlap measures and obtain the optimal lattice packings in a parameterized family of lattices which contains the FCC, BCC, and integer lattice.","lang":"eng"}],"acknowledgement":"We thank Herbert Edelsbrunner for his valuable discussions and ideas on the topic of this paper. The second author has been supported by the Max Planck Center for Visual Computing and Communication","oa_version":"Submitted Version","main_file_link":[{"url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf","open_access":"1"}],"oa":1,"month":"01"},{"abstract":[{"lang":"eng","text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon or planar straight-line graph. In this paper, we ask the reverse question: Given the straight skeleton (in form of a planar straight-line graph, with some rays to infinity), can we reconstruct a planar straight-line graph for which this was the straight skeleton? We show how to reduce this problem to the problem of finding a line that intersects a set of convex polygons. We can find these convex polygons and all such lines in $O(nlog n)$ time in the Real RAM computer model, where $n$ denotes the number of edges of the input graph. We also explain how our approach can be used for recognizing Voronoi diagrams of points, thereby completing a partial solution provided by Ash and Bolker in 1985.\r\n"}],"oa_version":"None","quality_controlled":"1","publisher":"IEEE","alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"scopus_import":1,"month":"12","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"year":"2013","publication_status":"published","day":"01","language":[{"iso":"eng"}],"page":"37 - 46","date_published":"2013-12-01T00:00:00Z","doi":"10.1109/ISVD.2013.11","date_created":"2018-12-11T11:56:20Z","_id":"2209","type":"conference","conference":{"start_date":"2013-07-08","end_date":"2013-07-10","location":"St. Petersburg, Russia","name":"ISVD: Voronoi Diagrams in Science and Engineering"},"status":"public","date_updated":"2021-01-12T06:56:00Z","citation":{"chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input,” 37–46. IEEE, 2013. https://doi.org/10.1109/ISVD.2013.11.","ista":"Biedl T, Held M, Huber S. 2013. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. ISVD: Voronoi Diagrams in Science and Engineering, 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) , , 37–46.","mla":"Biedl, Therese, et al. Recognizing Straight Skeletons and Voronoi Diagrams and Reconstructing Their Input. IEEE, 2013, pp. 37–46, doi:10.1109/ISVD.2013.11.","short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 37–46.","ieee":"T. Biedl, M. Held, and S. Huber, “Recognizing straight skeletons and Voronoi diagrams and reconstructing their input,” presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia, 2013, pp. 37–46.","apa":"Biedl, T., Held, M., & Huber, S. (2013). Recognizing straight skeletons and Voronoi diagrams and reconstructing their input (pp. 37–46). Presented at the ISVD: Voronoi Diagrams in Science and Engineering, St. Petersburg, Russia: IEEE. https://doi.org/10.1109/ISVD.2013.11","ama":"Biedl T, Held M, Huber S. Recognizing straight skeletons and Voronoi diagrams and reconstructing their input. In: IEEE; 2013:37-46. doi:10.1109/ISVD.2013.11"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber"}],"publist_id":"4763","department":[{"_id":"HeEd"}],"title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input"},{"oa_version":"Submitted Version","abstract":[{"text":"A straight skeleton is a well-known geometric structure, and several algorithms exist to construct the straight skeleton for a given polygon. In this paper, we ask the reverse question: Given the straight skeleton (in form of a tree with a drawing in the plane, but with the exact position of the leaves unspecified), can we reconstruct the polygon? We show that in most cases there exists at most one polygon; in the remaining case there is an infinite number of polygons determined by one angle that can range in an interval. We can find this (set of) polygon(s) in linear time in the Real RAM computer model.","lang":"eng"}],"month":"03","main_file_link":[{"open_access":"1","url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf"}],"oa":1,"publisher":"TU Braunschweig","language":[{"iso":"eng"}],"publication":"29th European Workshop on Computational Geometry","day":"01","year":"2013","publication_status":"published","date_created":"2018-12-11T11:56:21Z","date_published":"2013-03-01T00:00:00Z","page":"95 - 98","_id":"2210","status":"public","conference":{"start_date":"2013-03-17","end_date":"2013-03-20","location":"Braunschweig, Germany","name":"EuroCG: European Workshop on Computational Geometry"},"type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:56:00Z","citation":{"ista":"Biedl T, Held M, Huber S. 2013. Reconstructing polygons from embedded straight skeletons. 29th European Workshop on Computational Geometry. EuroCG: European Workshop on Computational Geometry, 95–98.","chicago":"Biedl, Therese, Martin Held, and Stefan Huber. “Reconstructing Polygons from Embedded Straight Skeletons.” In 29th European Workshop on Computational Geometry, 95–98. TU Braunschweig, 2013.","ama":"Biedl T, Held M, Huber S. Reconstructing polygons from embedded straight skeletons. In: 29th European Workshop on Computational Geometry. TU Braunschweig; 2013:95-98.","apa":"Biedl, T., Held, M., & Huber, S. (2013). Reconstructing polygons from embedded straight skeletons. In 29th European Workshop on Computational Geometry (pp. 95–98). Braunschweig, Germany: TU Braunschweig.","ieee":"T. Biedl, M. Held, and S. Huber, “Reconstructing polygons from embedded straight skeletons,” in 29th European Workshop on Computational Geometry, Braunschweig, Germany, 2013, pp. 95–98.","short":"T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98.","mla":"Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98."},"title":"Reconstructing polygons from embedded straight skeletons","department":[{"_id":"HeEd"}],"publist_id":"4762","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan"}]},{"page":"43 - 50","doi":"10.1016/j.endm.2013.07.008","date_published":"2013-09-05T00:00:00Z","volume":43,"date_created":"2018-12-11T11:56:53Z","year":"2013","publication_status":"published","day":"05","publication":"Electronic Notes in Discrete Mathematics","language":[{"iso":"eng"}],"scopus_import":1,"quality_controlled":"1","publisher":"Elsevier","month":"09","intvolume":" 43","abstract":[{"lang":"eng","text":"This extended abstract is concerned with the irregularities of distribution of one-dimensional permuted van der Corput sequences that are generated from linear permutations. We show how to obtain upper bounds for the discrepancy and diaphony of these sequences, by relating them to Kronecker sequences and applying earlier results of Faure and Niederreiter."}],"oa_version":"None","acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","last_name":"Pausinger"}],"publist_id":"4623","department":[{"_id":"HeEd"}],"title":"Van der Corput sequences and linear permutations","citation":{"short":"F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.","ieee":"F. Pausinger, “Van der Corput sequences and linear permutations,” Electronic Notes in Discrete Mathematics, vol. 43. Elsevier, pp. 43–50, 2013.","apa":"Pausinger, F. (2013). Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2013.07.008","ama":"Pausinger F. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 2013;43:43-50. doi:10.1016/j.endm.2013.07.008","mla":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008.","ista":"Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50.","chicago":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics. Elsevier, 2013. https://doi.org/10.1016/j.endm.2013.07.008."},"date_updated":"2021-01-12T06:56:39Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","status":"public","_id":"2304"},{"language":[{"iso":"eng"}],"file":[{"file_id":"5081","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:14:29Z","file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","creator":"system","date_updated":"2020-07-14T12:45:48Z","file_size":447945}],"publication_status":"published","month":"06","scopus_import":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces X; Y , a subspace A ⊆ X, and a (continuous) map f : A → Y , whether f can be extended to a map X → Y . For computational purposes, we assume that X and Y are represented as finite simplicial complexes, A is a subcomplex of X, and f is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov's result from the 1950s on uncomputability of the fundamental group π1(Y ). We thus study the problem under the assumption that, for some k ≥ 2, Y is (k - 1)-connected; informally, this means that Y has \\no holes up to dimension k-1" (a basic example of such a Y is the sphere Sk). We prove that, on the one hand, this problem is still undecidable for dimX = 2k. On the other hand, for every fixed k ≥ 2, we obtain an algorithm that solves the extension problem in polynomial time assuming Y (k - 1)-connected and dimX ≤ 2k - 1. For dimX ≤ 2k - 2, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups πk(Y ), k ≥ 2, for a 1-connected Y . Their computability was established by Brown in 1957; we show that πk(Y ) can be computed in polynomial time for every fixed k ≥ 2. On the other hand, Anick proved in 1989 that computing πk(Y ) is #P-hard if k is a part of input, where Y is a cell complex with certain rather compact encoding. We strengthen his result to #P-hardness for Y given as a simplicial complex. "}],"file_date_updated":"2020-07-14T12:45:48Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"ddc":["510"],"date_updated":"2021-01-12T06:59:51Z","pubrep_id":"533","status":"public","conference":{"name":"STOC: Symposium on the Theory of Computing","location":"Palo Alto, CA, United States","end_date":"2013-06-04","start_date":"2013-06-01"},"type":"conference","_id":"2807","date_created":"2018-12-11T11:59:42Z","doi":"10.1145/2488608.2488683","date_published":"2013-06-01T00:00:00Z","page":"595 - 604","publication":"45th Annual ACM Symposium on theory of computing","day":"01","year":"2013","has_accepted_license":"1","oa":1,"publisher":"ACM","quality_controlled":"1","title":"Extending continuous maps: Polynomiality and undecidability","author":[{"first_name":"Martin","full_name":"Čadek, Martin","last_name":"Čadek"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál","full_name":"Krcál, Marek"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"first_name":"Lukáš","last_name":"Vokřínek","full_name":"Vokřínek, Lukáš"},{"last_name":"Wagner","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"4078","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Lukáš Vokřínek, and Uli Wagner. “Extending Continuous Maps: Polynomiality and Undecidability.” In 45th Annual ACM Symposium on Theory of Computing, 595–604. ACM, 2013. https://doi.org/10.1145/2488608.2488683.","ista":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. 2013. Extending continuous maps: Polynomiality and undecidability. 45th Annual ACM Symposium on theory of computing. STOC: Symposium on the Theory of Computing, 595–604.","mla":"Čadek, Martin, et al. “Extending Continuous Maps: Polynomiality and Undecidability.” 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604, doi:10.1145/2488608.2488683.","ieee":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, and U. Wagner, “Extending continuous maps: Polynomiality and undecidability,” in 45th Annual ACM Symposium on theory of computing, Palo Alto, CA, United States, 2013, pp. 595–604.","short":"M. Čadek, M. Krcál, J. Matoušek, L. Vokřínek, U. Wagner, in:, 45th Annual ACM Symposium on Theory of Computing, ACM, 2013, pp. 595–604.","ama":"Čadek M, Krcál M, Matoušek J, Vokřínek L, Wagner U. Extending continuous maps: Polynomiality and undecidability. In: 45th Annual ACM Symposium on Theory of Computing. ACM; 2013:595-604. doi:10.1145/2488608.2488683","apa":"Čadek, M., Krcál, M., Matoušek, J., Vokřínek, L., & Wagner, U. (2013). Extending continuous maps: Polynomiality and undecidability. In 45th Annual ACM Symposium on theory of computing (pp. 595–604). Palo Alto, CA, United States: ACM. https://doi.org/10.1145/2488608.2488683"}},{"date_created":"2018-12-11T11:59:44Z","doi":"10.1145/2462356.2462373","date_published":"2013-06-01T00:00:00Z","related_material":{"record":[{"relation":"later_version","id":"1805","status":"public"}]},"page":"117 - 125","publication":"Proceedings of the 29th annual symposium on Computational Geometry","language":[{"iso":"eng"}],"day":"01","publication_status":"published","year":"2013","month":"06","main_file_link":[{"open_access":"1","url":"http://hal.archives-ouvertes.fr/hal-00833791/"}],"oa":1,"scopus_import":1,"quality_controlled":"1","publisher":"ACM","acknowledgement":"Some of the authors were partially supported by the GIGA ANR grant (contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).","oa_version":"Submitted Version","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 ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on 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."}],"title":"Homological reconstruction and simplification in R3","department":[{"_id":"HeEd"}],"publist_id":"4072","author":[{"first_name":"Dominique","last_name":"Attali","full_name":"Attali, Dominique"},{"orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","last_name":"Bauer","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Olivier","last_name":"Devillers","full_name":"Devillers, Olivier"},{"last_name":"Glisse","full_name":"Glisse, Marc","first_name":"Marc"},{"last_name":"Lieutier","full_name":"Lieutier, André","first_name":"André"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–25, doi:10.1145/2462356.2462373.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125.","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” in Proceedings of the 29th annual symposium on Computational Geometry, Rio de Janeiro, Brazil, 2013, pp. 117–125.","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. In: Proceedings of the 29th Annual Symposium on Computational Geometry. ACM; 2013:117-125. doi:10.1145/2462356.2462373","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2013). Homological reconstruction and simplification in R3. In Proceedings of the 29th annual symposium on Computational Geometry (pp. 117–125). Rio de Janeiro, Brazil: ACM. https://doi.org/10.1145/2462356.2462373","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” In Proceedings of the 29th Annual Symposium on Computational Geometry, 117–25. ACM, 2013. https://doi.org/10.1145/2462356.2462373.","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction and simplification in R3. Proceedings of the 29th annual symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 117–125."},"date_updated":"2023-02-23T10:15:15Z","status":"public","conference":{"start_date":"2013-06-17","location":"Rio de Janeiro, Brazil","end_date":"2013-06-20","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","_id":"2812"},{"page":"E1695 - E1704","date_created":"2018-12-11T11:59:47Z","date_published":"2013-04-30T00:00:00Z","doi":"10.1073/pnas.1304354110","year":"2013","publication":"PNAS","day":"30","oa":1,"quality_controlled":"1","publisher":"National Academy of Sciences","external_id":{"pmid":["25673779"]},"author":[{"first_name":"Christopher","full_name":"Topp, Christopher","last_name":"Topp"},{"full_name":"Iyer Pascuzzi, Anjali","last_name":"Iyer Pascuzzi","first_name":"Anjali"},{"full_name":"Anderson, Jill","last_name":"Anderson","first_name":"Jill"},{"first_name":"Cheng","last_name":"Lee","full_name":"Lee, Cheng"},{"first_name":"Paul","last_name":"Zurek","full_name":"Zurek, Paul"},{"full_name":"Symonova, Olga","last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Zheng","full_name":"Zheng, Ying","first_name":"Ying"},{"first_name":"Alexander","last_name":"Bucksch","full_name":"Bucksch, Alexander"},{"first_name":"Yuriy","full_name":"Mileyko, Yuriy","last_name":"Mileyko"},{"first_name":"Taras","last_name":"Galkovskyi","full_name":"Galkovskyi, Taras"},{"first_name":"Brad","full_name":"Moore, Brad","last_name":"Moore"},{"full_name":"Harer, John","last_name":"Harer","first_name":"John"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Thomas","last_name":"Mitchell Olds","full_name":"Mitchell Olds, Thomas"},{"last_name":"Weitz","full_name":"Weitz, Joshua","first_name":"Joshua"},{"first_name":"Philip","full_name":"Benfey, Philip","last_name":"Benfey"}],"publist_id":"3979","title":"3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture","citation":{"short":"C. Topp, A. Iyer Pascuzzi, J. Anderson, C. Lee, P. Zurek, O. Symonova, Y. Zheng, A. Bucksch, Y. Mileyko, T. Galkovskyi, B. Moore, J. Harer, H. Edelsbrunner, T. Mitchell Olds, J. Weitz, P. Benfey, PNAS 110 (2013) E1695–E1704.","ieee":"C. Topp et al., “3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture,” PNAS, vol. 110, no. 18. National Academy of Sciences, pp. E1695–E1704, 2013.","apa":"Topp, C., Iyer Pascuzzi, A., Anderson, J., Lee, C., Zurek, P., Symonova, O., … Benfey, P. (2013). 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1304354110","ama":"Topp C, Iyer Pascuzzi A, Anderson J, et al. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 2013;110(18):E1695-E1704. doi:10.1073/pnas.1304354110","mla":"Topp, Christopher, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS, vol. 110, no. 18, National Academy of Sciences, 2013, pp. E1695–704, doi:10.1073/pnas.1304354110.","ista":"Topp C, Iyer Pascuzzi A, Anderson J, Lee C, Zurek P, Symonova O, Zheng Y, Bucksch A, Mileyko Y, Galkovskyi T, Moore B, Harer J, Edelsbrunner H, Mitchell Olds T, Weitz J, Benfey P. 2013. 3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture. PNAS. 110(18), E1695–E1704.","chicago":"Topp, Christopher, Anjali Iyer Pascuzzi, Jill Anderson, Cheng Lee, Paul Zurek, Olga Symonova, Ying Zheng, et al. “3D Phenotyping and Quantitative Trait Locus Mapping Identify Core Regions of the Rice Genome Controlling Root Architecture.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1304354110."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"18","volume":110,"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/"}],"scopus_import":1,"intvolume":" 110","month":"04","abstract":[{"text":"Identification of genes that control root system architecture in crop plants requires innovations that enable high-throughput and accurate measurements of root system architecture through time. We demonstrate the ability of a semiautomated 3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative genetic basis of root system growth in a rice biparental mapping population, Bala x Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for a suite of 25 traits that quantified the distribution, shape, extent of exploration, and the intrinsic size of root networks at days 12, 14, and 16 of growth in a gellan gum medium. From these data we identified 89 quantitative trait loci, some of which correspond to those found previously in soil-grown plants, and provide evidence for genetic tradeoffs in root growth allocations, such as between the extent and thoroughness of exploration. We also developed a multivariate method for generating and mapping central root architecture phenotypes and used it to identify five major quantitative trait loci (r2 = 24-37%), two of which were not identified by our univariate analysis. Our imaging and analytical platform provides a means to identify genes with high potential for improving root traits and agronomic qualities of crops.","lang":"eng"}],"pmid":1,"oa_version":"Submitted Version","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"date_updated":"2021-01-12T06:59:58Z","type":"journal_article","status":"public","_id":"2822"},{"month":"02","intvolume":" 7749","alternative_title":["LNCS"],"quality_controlled":"1","scopus_import":1,"publisher":"Springer","oa_version":"None","abstract":[{"text":"Mathematical objects can be measured unambiguously, but not so objects from our physical world. Even the total length of tubelike shapes has its difficulties. We introduce a combination of geometric, probabilistic, and topological methods to design a stable length estimate for tube-like shapes; that is: one that is insensitive to small shape changes.","lang":"eng"}],"volume":7749,"doi":"10.1007/978-3-642-37067-0","date_published":"2013-02-21T00:00:00Z","related_material":{"record":[{"id":"2255","status":"public","relation":"later_version"}]},"date_created":"2018-12-11T11:59:53Z","page":"XV - XIX","day":"21","language":[{"iso":"eng"}],"publication":"17th IAPR International Conference on Discrete Geometry for Computer Imagery","publication_status":"published","year":"2013","status":"public","type":"conference","conference":{"name":"DGCI: Discrete Geometry for Computer Imagery","location":"Seville, Spain","end_date":"2013-03-22","start_date":"2013-03-20"},"_id":"2843","title":"Stable length estimates of tube-like shapes","department":[{"_id":"HeEd"}],"author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","first_name":"Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"3952","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” In 17th IAPR International Conference on Discrete Geometry for Computer Imagery, 7749:XV–XIX. Springer, 2013. https://doi.org/10.1007/978-3-642-37067-0.","ista":"Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes. 17th IAPR International Conference on Discrete Geometry for Computer Imagery. DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” 17th IAPR International Conference on Discrete Geometry for Computer Imagery, vol. 7749, Springer, 2013, pp. XV–XIX, doi:10.1007/978-3-642-37067-0.","apa":"Edelsbrunner, H., & Pausinger, F. (2013). Stable length estimates of tube-like shapes. In 17th IAPR International Conference on Discrete Geometry for Computer Imagery (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. https://doi.org/10.1007/978-3-642-37067-0","ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. In: 17th IAPR International Conference on Discrete Geometry for Computer Imagery. Vol 7749. Springer; 2013:XV-XIX. doi:10.1007/978-3-642-37067-0","short":"H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” in 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Seville, Spain, 2013, vol. 7749, pp. XV–XIX."},"date_updated":"2023-02-23T10:35:00Z"},{"volume":15,"issue":"1","language":[{"iso":"eng"}],"publication_status":"published","month":"05","intvolume":" 15","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1102.3389v1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Given a continuous function f:X-R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X=R3 has ramifications in the fields of medical imaging and scientific visualization."}],"department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T07:00:18Z","status":"public","type":"journal_article","_id":"2859","doi":"10.4310/HHA.2013.v15.n1.a3","date_published":"2013-05-01T00:00:00Z","date_created":"2018-12-11T11:59:58Z","page":"51 - 72","day":"01","publication":"Homology, Homotopy and Applications","year":"2013","publisher":"International Press","quality_controlled":"1","oa":1,"title":"Homology and robustness of level and interlevel sets","author":[{"last_name":"Bendich","full_name":"Bendich, Paul","first_name":"Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"full_name":"Morozov, Dmitriy","last_name":"Morozov","first_name":"Dmitriy"},{"first_name":"Amit","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","last_name":"Patel","full_name":"Patel, Amit"}],"publist_id":"3930","external_id":{"arxiv":["1102.3389"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Bendich, P., Edelsbrunner, H., Morozov, D., & Patel, A. (2013). Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2013.v15.n1.a3","ama":"Bendich P, Edelsbrunner H, Morozov D, Patel A. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 2013;15(1):51-72. doi:10.4310/HHA.2013.v15.n1.a3","ieee":"P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “Homology and robustness of level and interlevel sets,” Homology, Homotopy and Applications, vol. 15, no. 1. International Press, pp. 51–72, 2013.","short":"P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and Applications 15 (2013) 51–72.","mla":"Bendich, Paul, et al. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications, vol. 15, no. 1, International Press, 2013, pp. 51–72, doi:10.4310/HHA.2013.v15.n1.a3.","ista":"Bendich P, Edelsbrunner H, Morozov D, Patel A. 2013. Homology and robustness of level and interlevel sets. Homology, Homotopy and Applications. 15(1), 51–72.","chicago":"Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “Homology and Robustness of Level and Interlevel Sets.” Homology, Homotopy and Applications. International Press, 2013. https://doi.org/10.4310/HHA.2013.v15.n1.a3."}},{"pmid":1,"oa_version":"Published Version","abstract":[{"text":"Root system growth and development is highly plastic and is influenced by the surrounding environment. Roots frequently grow in heterogeneous environments that include interactions from neighboring plants and physical impediments in the rhizosphere. To investigate how planting density and physical objects affect root system growth, we grew rice in a transparent gel system in close proximity with another plant or a physical object. Root systems were imaged and reconstructed in three dimensions. Root-root interaction strength was calculated using quantitative metrics that characterize the extent towhich the reconstructed root systems overlap each other. Surprisingly, we found the overlap of root systems of the same genotype was significantly higher than that of root systems of different genotypes. Root systems of the same genotype tended to grow toward each other but those of different genotypes appeared to avoid each other. Shoot separation experiments excluded the possibility of aerial interactions, suggesting root communication. Staggered plantings indicated that interactions likely occur at root tips in close proximity. Recognition of obstacles also occurred through root tips, but through physical contact in a size-dependent manner. These results indicate that root systems use two different forms of communication to recognize objects and alter root architecture: root-root recognition, possibly mediated through root exudates, and root-object recognition mediated by physical contact at the root tips. This finding suggests that root tips act as local sensors that integrate rhizosphere information into global root architectural changes.","lang":"eng"}],"month":"02","intvolume":" 110","scopus_import":1,"main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"7","volume":110,"_id":"2887","status":"public","type":"journal_article","article_type":"original","date_updated":"2021-01-12T07:00:29Z","department":[{"_id":"HeEd"}],"quality_controlled":"1","publisher":"National Academy of Sciences","oa":1,"day":"12","publication":"PNAS","year":"2013","date_published":"2013-02-12T00:00:00Z","doi":"10.1073/pnas.1222821110","date_created":"2018-12-11T12:00:09Z","page":"2670 - 2675","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"S. Fang, R. Clark, Y. Zheng, A. Iyer Pascuzzi, J. Weitz, L. Kochian, H. Edelsbrunner, H. Liao, P. Benfey, PNAS 110 (2013) 2670–2675.","ieee":"S. Fang et al., “Genotypic recognition and spatial responses by rice roots,” PNAS, vol. 110, no. 7. National Academy of Sciences, pp. 2670–2675, 2013.","apa":"Fang, S., Clark, R., Zheng, Y., Iyer Pascuzzi, A., Weitz, J., Kochian, L., … Benfey, P. (2013). Genotypic recognition and spatial responses by rice roots. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1222821110","ama":"Fang S, Clark R, Zheng Y, et al. Genotypic recognition and spatial responses by rice roots. PNAS. 2013;110(7):2670-2675. doi:10.1073/pnas.1222821110","mla":"Fang, Suqin, et al. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS, vol. 110, no. 7, National Academy of Sciences, 2013, pp. 2670–75, doi:10.1073/pnas.1222821110.","ista":"Fang S, Clark R, Zheng Y, Iyer Pascuzzi A, Weitz J, Kochian L, Edelsbrunner H, Liao H, Benfey P. 2013. Genotypic recognition and spatial responses by rice roots. PNAS. 110(7), 2670–2675.","chicago":"Fang, Suqin, Randy Clark, Ying Zheng, Anjali Iyer Pascuzzi, Joshua Weitz, Leon Kochian, Herbert Edelsbrunner, Hong Liao, and Philip Benfey. “Genotypic Recognition and Spatial Responses by Rice Roots.” PNAS. National Academy of Sciences, 2013. https://doi.org/10.1073/pnas.1222821110."},"title":"Genotypic recognition and spatial responses by rice roots","author":[{"full_name":"Fang, Suqin","last_name":"Fang","first_name":"Suqin"},{"first_name":"Randy","last_name":"Clark","full_name":"Clark, Randy"},{"last_name":"Zheng","full_name":"Zheng, Ying","first_name":"Ying"},{"first_name":"Anjali","full_name":"Iyer Pascuzzi, Anjali","last_name":"Iyer Pascuzzi"},{"first_name":"Joshua","full_name":"Weitz, Joshua","last_name":"Weitz"},{"last_name":"Kochian","full_name":"Kochian, Leon","first_name":"Leon"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"first_name":"Hong","full_name":"Liao, Hong","last_name":"Liao"},{"last_name":"Benfey","full_name":"Benfey, Philip","first_name":"Philip"}],"publist_id":"3872","external_id":{"pmid":["23362379"]},"article_processing_charge":"No"}]