[{"publication_identifier":{"issn":["1612-3786"],"eisbn":["9783319040998"],"eissn":["2197-666X"],"isbn":["9783319040981"]},"month":"03","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_4","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"quality_controlled":"1","ec_funded":1,"place":"Cham","volume":1,"date_created":"2022-03-21T07:11:23Z","date_updated":"2022-06-21T12:01:47Z","author":[{"full_name":"Kasten, Jens","last_name":"Kasten","first_name":"Jens"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Reich","first_name":"Wieland","full_name":"Reich, Wieland"},{"full_name":"Scheuermann, Gerik","first_name":"Gerik","last_name":"Scheuermann"}],"editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"},{"last_name":"Pascucci","first_name":"Valerio","full_name":"Pascucci, Valerio"},{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","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.","year":"2014","article_processing_charge":"No","day":"19","series_title":"Mathematics and Visualization","scopus_import":"1","date_published":"2014-03-19T00:00:00Z","page":"55-69","citation":{"mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.","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.","chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_4.","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4","ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.","apa":"Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4","ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69."},"publication":"Topological Methods in Data Analysis and Visualization III ","abstract":[{"text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data.","lang":"eng"}],"type":"book_chapter","oa_version":"None","intvolume":" 1","title":"Toward the extraction of saddle periodic orbits","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"10893"},{"scopus_import":1,"has_accepted_license":"1","day":"16","citation":{"ama":"Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 2014;24(1):61-86. doi:10.1142/S0218195914500034","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.","apa":"Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034","ieee":"S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” International Journal of Computational Geometry and Applications, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.","mla":"Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 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."},"publication":"International Journal of Computational Geometry and Applications","page":"61 - 86","date_published":"2014-03-16T00:00:00Z","type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1816","intvolume":" 24","title":"Topology-preserving watermarking of vector graphics","status":"public","ddc":["000"],"pubrep_id":"443","file":[{"checksum":"be45c133ab4d43351260e21beaa8f4b1","date_created":"2018-12-12T10:08:43Z","date_updated":"2020-07-14T12:45:17Z","file_id":"4704","relation":"main_file","creator":"system","file_size":991734,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf"}],"oa_version":"Published Version","month":"03","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","doi":"10.1142/S0218195914500034","language":[{"iso":"eng"}],"publist_id":"5290","file_date_updated":"2020-07-14T12:45:17Z","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","year":"2014","department":[{"_id":"HeEd"}],"publisher":"World Scientific Publishing","publication_status":"published","author":[{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"last_name":"Meerwald","first_name":"Peter","full_name":"Meerwald, Peter"},{"full_name":"Kwitt, Roland","last_name":"Kwitt","first_name":"Roland"}],"volume":24,"date_created":"2018-12-11T11:54:10Z","date_updated":"2021-01-12T06:53:23Z"},{"scopus_import":1,"day":"14","month":"11","publication":"Discrete & Computational Geometry","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7004"}],"citation":{"ama":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79. doi:10.1007/s00454-014-9646-x","apa":"Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x","ieee":"J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” Discrete & Computational Geometry, vol. 53, no. 1. Springer, pp. 64–79, 2014.","ista":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.","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.","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."},"oa":1,"page":"64 - 79","date_published":"2014-11-14T00:00:00Z","doi":"10.1007/s00454-014-9646-x","language":[{"iso":"eng"}],"type":"journal_article","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"}],"issue":"1","publist_id":"5260","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"1842","year":"2014","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","publication_status":"published","status":"public","title":"On the geometric ramsey number of outerplanar graphs","intvolume":" 53","publisher":"Springer","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"author":[{"last_name":"Cibulka","first_name":"Josef","full_name":"Cibulka, Josef"},{"last_name":"Gao","first_name":"Pu","full_name":"Gao, Pu"},{"last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"},{"last_name":"Valla","first_name":"Tomáš","full_name":"Valla, Tomáš"},{"last_name":"Valtr","first_name":"Pavel","full_name":"Valtr, Pavel"}],"date_updated":"2021-01-12T06:53:33Z","date_created":"2018-12-11T11:54:18Z","oa_version":"Submitted Version","volume":53},{"doi":"10.17323/1609-4514-2014-14-3-491-504","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1211.7053"}],"oa":1,"external_id":{"arxiv":["1211.7053"]},"quality_controlled":"1","publication_identifier":{"issn":["16093321"]},"month":"07","author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Glazyrin, Alexey","first_name":"Alexey","last_name":"Glazyrin"},{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"}],"volume":14,"date_updated":"2022-03-03T11:47:09Z","date_created":"2018-12-11T11:54:29Z","year":"2014","department":[{"_id":"HeEd"}],"publisher":"Independent University of Moscow","publication_status":"published","publist_id":"5220","date_published":"2014-07-01T00:00:00Z","citation":{"ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 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","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.","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","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.","mla":"Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504."},"publication":"Moscow Mathematical Journal","page":"491 - 504","article_type":"original","article_processing_charge":"No","day":"01","scopus_import":"1","oa_version":"Submitted Version","_id":"1876","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 14","status":"public","title":"Functionals on triangulations of delaunay sets","issue":"3","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"}],"type":"journal_article"},{"article_processing_charge":"No","day":"16","scopus_import":"1","date_published":"2014-11-16T00:00:00Z","citation":{"apa":"Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. Springer. https://doi.org/10.1007/s10958-014-2165-8","ieee":"V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” Journal of Mathematical Sciences, vol. 203, no. 6. Springer, pp. 754–760, 2014.","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.","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","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.","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.","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."},"publication":"Journal of Mathematical Sciences","page":"754 - 760","article_type":"original","issue":"6","abstract":[{"lang":"eng","text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales."}],"type":"journal_article","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1929","intvolume":" 203","title":"An algorithm for cartographic generalization that preserves global topology","status":"public","publication_identifier":{"eissn":["1573-8795"],"issn":["1072-3374"]},"month":"11","doi":"10.1007/s10958-014-2165-8","language":[{"iso":"eng"}],"quality_controlled":"1","publist_id":"5165","author":[{"full_name":"Alexeev, V V","last_name":"Alexeev","first_name":"V V"},{"full_name":"Bogaevskaya, V G","last_name":"Bogaevskaya","first_name":"V G"},{"full_name":"Preobrazhenskaya, M M","first_name":"M M","last_name":"Preobrazhenskaya"},{"last_name":"Ukhalov","first_name":"A Y","full_name":"Ukhalov, A Y"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Yakimova, Olga","last_name":"Yakimova","first_name":"Olga"}],"volume":203,"date_created":"2018-12-11T11:54:46Z","date_updated":"2022-05-24T10:39:06Z","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.","year":"2014","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published"}]