[{"scopus_import":1,"day":"01","page":"484 - 490","citation":{"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","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.","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.","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","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.","short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","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."},"publication":"Proceedings of the Annual Symposium on Computational Geometry","date_published":"2014-06-01T00:00:00Z","type":"conference","abstract":[{"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).","lang":"eng"}],"title":"The morse theory of Čech and Delaunay filtrations","status":"public","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2155","oa_version":"Submitted Version","month":"06","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1312.1231","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1145/2582112.2582167","conference":{"start_date":"2014-06-08","location":"Kyoto, Japan","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry"},"ec_funded":1,"publist_id":"4851","department":[{"_id":"HeEd"}],"publisher":"ACM","publication_status":"published","year":"2014","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","date_updated":"2021-01-12T06:55:38Z","date_created":"2018-12-11T11:56:01Z","author":[{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}]},{"type":"conference","abstract":[{"lang":"eng","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."}],"publist_id":"4805","title":"On the computational complexity of betti numbers reductions from matrix rank","publication_status":"published","status":"public","publisher":"SIAM","department":[{"_id":"HeEd"}],"year":"2014","_id":"2177","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:55:48Z","date_created":"2018-12-11T11:56:09Z","oa_version":"None","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Parsa","first_name":"Salman","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","full_name":"Parsa, Salman"}],"scopus_import":1,"day":"01","month":"01","quality_controlled":"1","page":"152 - 160","publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","citation":{"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","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.","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.","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","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.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 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."},"language":[{"iso":"eng"}],"conference":{"name":"SODA: Symposium on Discrete Algorithms","start_date":"2014-01-05","location":"Portland, USA","end_date":"2014-01-07"},"doi":"10.1137/1.9781611973402.11","date_published":"2014-01-01T00:00:00Z"},{"type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"3","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2184","status":"public","title":"Computing all maps into a sphere","intvolume":" 61","oa_version":"Preprint","scopus_import":1,"day":"01","publication":"Journal of the ACM","citation":{"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","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.","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.","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","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.","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014).","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."},"date_published":"2014-05-01T00:00:00Z","article_number":"17 ","publist_id":"4797","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).","year":"2014","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","author":[{"last_name":"Čadek","first_name":"Martin","full_name":"Čadek, Martin"},{"first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"first_name":"Francis","last_name":"Sergeraert","full_name":"Sergeraert, Francis"},{"full_name":"Vokřínek, Lukáš","first_name":"Lukáš","last_name":"Vokřínek"},{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568"}],"date_updated":"2021-01-12T06:55:50Z","date_created":"2018-12-11T11:56:12Z","volume":61,"month":"05","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1105.6257"}],"quality_controlled":"1","doi":"10.1145/2597629","language":[{"iso":"eng"}]},{"month":"01","conference":{"end_date":"2012-07-07","location":"Kraków, Poland","start_date":"2012-07-02","name":"ECM: European Congress of Mathematics"},"doi":"10.4171/120-1/3","language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:45:52Z","publist_id":"3842","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Morozovy, Dmitriy","last_name":"Morozovy","first_name":"Dmitriy"}],"date_updated":"2021-01-12T07:00:36Z","date_created":"2018-12-11T12:00:16Z","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.","year":"2014","publication_status":"published","publisher":"European Mathematical Society Publishing House","department":[{"_id":"HeEd"}],"day":"01","has_accepted_license":"1","article_processing_charge":"No","date_published":"2014-01-01T00:00:00Z","citation":{"ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","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","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.","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","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.","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.","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 31–50."},"page":"31 - 50","abstract":[{"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.","lang":"eng"}],"type":"conference","pubrep_id":"544","oa_version":"Submitted Version","file":[{"checksum":"1d4a046f1af945c407c5c4d411d4c5e4","date_updated":"2020-07-14T12:45:52Z","date_created":"2018-12-12T10:16:43Z","relation":"main_file","file_id":"5232","content_type":"application/pdf","file_size":435320,"creator":"system","access_level":"open_access","file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf"}],"_id":"2905","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Persistent homology: Theory and practice","status":"public","ddc":["000"]},{"month":"11","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783319130743"],"eisbn":["9783319130750"],"issn":["0302-9743"]},"quality_controlled":"1","language":[{"iso":"eng"}],"conference":{"name":"ISAAC: International Symposium on Algorithms and Computation","end_date":"2014-12-17","start_date":"2014-12-15","location":"Jeonju, Korea"},"doi":"10.1007/978-3-319-13075-0_10","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","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.","year":"2014","date_updated":"2023-02-23T12:20:55Z","date_created":"2022-03-21T07:09:03Z","volume":8889,"author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"full_name":"Huber, Stefan","last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"481"}]},"scopus_import":"1","day":"08","article_processing_charge":"No","page":"117-127","publication":"25th International Symposium, ISAAC 2014","citation":{"short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127.","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.","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.","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","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","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.","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."},"date_published":"2014-11-08T00:00:00Z","alternative_title":["LNCS"],"type":"conference","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."}],"title":"Planar matchings for weighted straight skeletons","status":"public","intvolume":" 8889","_id":"10892","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None"},{"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","status":"public","title":"A Short Course in Computational Geometry and Topology","_id":"6853","year":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","date_created":"2019-09-06T09:22:33Z","date_updated":"2022-03-04T07:47:54Z","edition":"1","related_material":{"link":[{"relation":"other","description":"available as eBook via catalog IST BookList","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106"},{"url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842","description":"available via catalog IST BookList","relation":"other"}]},"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"place":"Cham","type":"book","abstract":[{"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.","lang":"eng"}],"page":"IX, 110","quality_controlled":"1","citation":{"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.","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","ieee":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.","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","ista":"Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p."},"language":[{"iso":"eng"}],"date_published":"2014-01-01T00:00:00Z","doi":"10.1007/978-3-319-05957-0","series_title":"SpringerBriefs in Applied Sciences and Technology","scopus_import":"1","publication_identifier":{"issn":["2191-530X"],"eisbn":["9-783-3190-5957-0"],"isbn":["9-783-3190-5956-3"],"eissn":["2191-5318"]},"article_processing_charge":"No","month":"01","day":"01"},{"page":"249-262","quality_controlled":"1","citation":{"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.","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","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.","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."},"publication":"Topological Methods in Data Analysis and Visualization III ","language":[{"iso":"eng"}],"date_published":"2014-03-19T00:00:00Z","doi":"10.1007/978-3-319-04099-8_16","scopus_import":"1","article_processing_charge":"No","publication_identifier":{"issn":["1612-3786"],"eisbn":["9783319040998"],"isbn":["9783319040981"],"eissn":["2197-666X"]},"month":"03","day":"19","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","status":"public","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10886","year":"2014","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","oa_version":"None","date_updated":"2023-09-05T14:13:16Z","date_created":"2022-03-18T13:05:39Z","author":[{"full_name":"Zobel, Valentin","last_name":"Zobel","first_name":"Valentin"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"}],"alternative_title":["Mathematics and Visualization"],"type":"conference","abstract":[{"lang":"eng","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."}]},{"year":"2014","acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","department":[{"_id":"HeEd"}],"editor":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo","last_name":"Bremer"},{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"},{"last_name":"Pascucci","first_name":"Valerio","full_name":"Pascucci, Valerio"},{"full_name":"Peikert, Ronald","last_name":"Peikert","first_name":"Ronald"}],"publisher":"Springer Nature","publication_status":"published","author":[{"full_name":"Günther, David","last_name":"Günther","first_name":"David"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"},{"last_name":"Seidel","first_name":"Hans-Peter","full_name":"Seidel, Hans-Peter"},{"first_name":"Tino","last_name":"Weinkauf","full_name":"Weinkauf, Tino"}],"date_updated":"2023-09-05T15:33:45Z","date_created":"2022-03-04T08:33:57Z","place":"Cham","ec_funded":1,"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","doi":"10.1007/978-3-319-04099-8_9","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1612-3786"],"eisbn":["9783319040998"],"isbn":["9783319040981"],"eissn":["2197-666X"]},"month":"03","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10817","status":"public","title":"Notes on the simplification of the Morse-Smale complex","oa_version":"None","type":"book_chapter","abstract":[{"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.","lang":"eng"}],"citation":{"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.","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.","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.","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","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.","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."},"publication":"Topological Methods in Data Analysis and Visualization III.","page":"135-150","date_published":"2014-03-19T00:00:00Z","scopus_import":"1","series_title":"Mathematics and Visualization","article_processing_charge":"No","day":"19"},{"citation":{"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.","short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:10.1007/s10851-013-0468-x.","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","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014.","ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","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"},"publication":"Journal of Mathematical Imaging and Vision","page":"164 - 177","date_published":"2014-09-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01","_id":"2255","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 50","title":"Stable length estimates of tube-like shapes","status":"public","ddc":["000"],"pubrep_id":"549","file":[{"date_created":"2018-12-12T10:16:18Z","date_updated":"2020-07-14T12:45:35Z","checksum":"2f93f3e63a38a85cd4404d7953913b14","file_id":"5204","relation":"main_file","creator":"system","content_type":"application/pdf","file_size":3941391,"file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","access_level":"open_access"}],"oa_version":"Submitted Version","type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm."}],"oa":1,"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"quality_controlled":"1","doi":"10.1007/s10851-013-0468-x","language":[{"iso":"eng"}],"publication_identifier":{"issn":["09249907"]},"month":"09","year":"2014","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","related_material":{"record":[{"id":"2843","relation":"earlier_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"1399"}]},"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Pausinger, Florian","last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"volume":50,"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:56:36Z","ec_funded":1,"publist_id":"4691","file_date_updated":"2020-07-14T12:45:35Z"},{"_id":"10894","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"PHAT – Persistent Homology Algorithms Toolbox","intvolume":" 8592","oa_version":"None","type":"conference","abstract":[{"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.","lang":"eng"}],"publication":"ICMS 2014: International Congress on Mathematical Software","citation":{"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.","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.","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.","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","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.","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."},"page":"137-143","date_published":"2014-09-01T00:00:00Z","scopus_import":"1","series_title":"LNCS","day":"01","article_processing_charge":"No","year":"2014","publication_status":"published","publisher":"Springer Berlin Heidelberg","department":[{"_id":"HeEd"}],"author":[{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"},{"first_name":"Hubert","last_name":"Wagner","full_name":"Wagner, Hubert"}],"related_material":{"record":[{"id":"1433","status":"public","relation":"later_version"}]},"date_updated":"2023-09-20T09:42:40Z","date_created":"2022-03-21T07:12:16Z","volume":8592,"place":"Berlin, Heidelberg","quality_controlled":"1","conference":{"name":"ICMS: International Congress on Mathematical Software","end_date":"2014-08-09","location":"Seoul, South Korea","start_date":"2014-08-05"},"doi":"10.1007/978-3-662-44199-2_24","language":[{"iso":"eng"}],"month":"09","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783662441985"],"issn":["0302-9743"],"eisbn":["9783662441992"]}},{"publist_id":"5064","abstract":[{"lang":"eng","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."}],"type":"preprint","article_number":"1401.0468","oa_version":"Submitted Version","date_created":"2018-12-11T11:55:12Z","date_updated":"2023-10-18T08:06:45Z","author":[{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"},{"first_name":"Michael","last_name":"Kerber","orcid":"0000-0002-8030-9299","full_name":"Kerber, Michael"},{"full_name":"Uhler, Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216","first_name":"Caroline","last_name":"Uhler"}],"department":[{"_id":"HeEd"},{"_id":"CaUh"}],"publication_status":"submitted","title":"Sphere packing with limited overlap","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2012","year":"2014","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","article_processing_charge":"No","day":"01","month":"01","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.1401.0468","date_published":"2014-01-01T00:00:00Z","main_file_link":[{"url":"http://cccg.ca/proceedings/2014/papers/paper23.pdf","open_access":"1"}],"citation":{"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.).","mla":"Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468.","apa":"Iglesias Ham, M., Kerber, M., & Uhler, C. (n.d.). Sphere packing with limited overlap. arXiv. https://doi.org/10.48550/arXiv.1401.0468","ieee":"M. Iglesias Ham, M. Kerber, and C. Uhler, “Sphere packing with limited overlap,” arXiv. .","ista":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv, 1401.0468.","ama":"Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. doi:10.48550/arXiv.1401.0468"},"oa":1,"external_id":{"arxiv":["1401.0468"]},"publication":"arXiv"},{"quality_controlled":"1","page":"37 - 46","citation":{"short":"T. Biedl, M. Held, S. Huber, in:, IEEE, 2013, pp. 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.","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.","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","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","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."},"language":[{"iso":"eng"}],"conference":{"location":"St. Petersburg, Russia","start_date":"2013-07-08","end_date":"2013-07-10","name":"ISVD: Voronoi Diagrams in Science and Engineering"},"doi":"10.1109/ISVD.2013.11","date_published":"2013-12-01T00:00:00Z","scopus_import":1,"month":"12","day":"01","publication_identifier":{"eisbn":["978-0-7695-5037-4 "]},"status":"public","publication_status":"published","title":"Recognizing straight skeletons and Voronoi diagrams and reconstructing their input","department":[{"_id":"HeEd"}],"publisher":"IEEE","_id":"2209","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:56:20Z","date_updated":"2021-01-12T06:56:00Z","oa_version":"None","author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan"}],"alternative_title":["2013 10th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2013) "],"type":"conference","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"}],"publist_id":"4763"},{"date_updated":"2021-01-12T06:56:00Z","date_created":"2018-12-11T11:56:21Z","oa_version":"Submitted Version","author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"full_name":"Huber, Stefan","last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87"}],"title":"Reconstructing polygons from embedded straight skeletons","publication_status":"published","status":"public","publisher":"TU Braunschweig","department":[{"_id":"HeEd"}],"_id":"2210","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013","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. 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."}],"publist_id":"4762","type":"conference","language":[{"iso":"eng"}],"conference":{"start_date":"2013-03-17","location":"Braunschweig, Germany","end_date":"2013-03-20","name":"EuroCG: European Workshop on Computational Geometry"},"date_published":"2013-03-01T00:00:00Z","page":"95 - 98","publication":"29th European Workshop on Computational Geometry","oa":1,"main_file_link":[{"url":"http://www.ibr.cs.tu-bs.de/alg/eurocg13/booklet_eurocg13.pdf","open_access":"1"}],"citation":{"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.","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.","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.","mla":"Biedl, Therese, et al. “Reconstructing Polygons from Embedded Straight Skeletons.” 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 95–98.","short":"T. Biedl, M. Held, S. Huber, in:, 29th European Workshop on Computational Geometry, TU Braunschweig, 2013, pp. 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."},"day":"01","month":"03"},{"author":[{"full_name":"Pausinger, Florian","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger"}],"volume":43,"oa_version":"None","date_updated":"2021-01-12T06:56:39Z","date_created":"2018-12-11T11:56:53Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2304","acknowledgement":"This research is supported by the Graduate school of IST Austria (Institute of Science and Technology Austria).","year":"2013","publisher":"Elsevier","intvolume":" 43","department":[{"_id":"HeEd"}],"publication_status":"published","title":"Van der Corput sequences and linear permutations","status":"public","publist_id":"4623","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."}],"type":"journal_article","doi":"10.1016/j.endm.2013.07.008","date_published":"2013-09-05T00:00:00Z","language":[{"iso":"eng"}],"citation":{"short":"F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.","mla":"Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” Electronic Notes in Discrete Mathematics, vol. 43, Elsevier, 2013, pp. 43–50, doi:10.1016/j.endm.2013.07.008.","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.","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","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","ista":"Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic Notes in Discrete Mathematics. 43, 43–50."},"publication":"Electronic Notes in Discrete Mathematics","page":"43 - 50","quality_controlled":"1","month":"09","day":"05","scopus_import":1},{"file":[{"file_id":"5081","relation":"main_file","date_updated":"2020-07-14T12:45:48Z","date_created":"2018-12-12T10:14:29Z","checksum":"06c2ce5c1135fbc1f71ca15eeb242dcf","file_name":"IST-2016-533-v1+1_Extending_continuous_maps_polynomiality_and_undecidability.pdf","access_level":"open_access","creator":"system","file_size":447945,"content_type":"application/pdf"}],"oa_version":"Submitted Version","pubrep_id":"533","ddc":["510"],"status":"public","title":"Extending continuous maps: Polynomiality and undecidability","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2807","abstract":[{"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. ","lang":"eng"}],"type":"conference","date_published":"2013-06-01T00:00:00Z","page":"595 - 604","citation":{"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.","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.","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.","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","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.","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.","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"},"publication":"45th Annual ACM Symposium on theory of computing","has_accepted_license":"1","day":"01","scopus_import":1,"date_updated":"2021-01-12T06:59:51Z","date_created":"2018-12-11T11:59:42Z","author":[{"first_name":"Martin","last_name":"Čadek","full_name":"Čadek, Martin"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","first_name":"Marek"},{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"full_name":"Vokřínek, Lukáš","last_name":"Vokřínek","first_name":"Lukáš"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli"}],"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","publication_status":"published","year":"2013","publist_id":"4078","file_date_updated":"2020-07-14T12:45:48Z","language":[{"iso":"eng"}],"doi":"10.1145/2488608.2488683","conference":{"name":"STOC: Symposium on the Theory of Computing","location":"Palo Alto, CA, United States","start_date":"2013-06-01","end_date":"2013-06-04"},"quality_controlled":"1","oa":1,"month":"06"},{"publist_id":"4072","abstract":[{"text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in 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.","lang":"eng"}],"type":"conference","oa_version":"Submitted Version","date_created":"2018-12-11T11:59:44Z","date_updated":"2023-02-23T10:15:15Z","related_material":{"record":[{"id":"1805","status":"public","relation":"later_version"}]},"author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"full_name":"Devillers, Olivier","last_name":"Devillers","first_name":"Olivier"},{"full_name":"Glisse, Marc","first_name":"Marc","last_name":"Glisse"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"}],"publisher":"ACM","department":[{"_id":"HeEd"}],"title":"Homological reconstruction and simplification in R3","publication_status":"published","status":"public","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).","_id":"2812","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2013","month":"06","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"doi":"10.1145/2462356.2462373","date_published":"2013-06-01T00:00:00Z","conference":{"end_date":"2013-06-20","location":"Rio de Janeiro, Brazil","start_date":"2013-06-17","name":"SoCG: Symposium on Computational Geometry"},"page":"117 - 125","quality_controlled":"1","main_file_link":[{"url":"http://hal.archives-ouvertes.fr/hal-00833791/","open_access":"1"}],"oa":1,"citation":{"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","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.","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","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.","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.","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.","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."},"publication":"Proceedings of the 29th annual symposium on Computational Geometry"},{"month":"04","quality_controlled":"1","external_id":{"pmid":["25673779"]},"main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4378147/","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1073/pnas.1304354110","publist_id":"3979","publisher":"National Academy of Sciences","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publication_status":"published","pmid":1,"year":"2013","volume":110,"date_updated":"2021-01-12T06:59:58Z","date_created":"2018-12-11T11:59:47Z","author":[{"last_name":"Topp","first_name":"Christopher","full_name":"Topp, Christopher"},{"full_name":"Iyer Pascuzzi, Anjali","last_name":"Iyer Pascuzzi","first_name":"Anjali"},{"last_name":"Anderson","first_name":"Jill","full_name":"Anderson, Jill"},{"last_name":"Lee","first_name":"Cheng","full_name":"Lee, Cheng"},{"last_name":"Zurek","first_name":"Paul","full_name":"Zurek, Paul"},{"last_name":"Symonova","first_name":"Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","full_name":"Symonova, Olga"},{"last_name":"Zheng","first_name":"Ying","full_name":"Zheng, Ying"},{"first_name":"Alexander","last_name":"Bucksch","full_name":"Bucksch, Alexander"},{"full_name":"Mileyko, Yuriy","first_name":"Yuriy","last_name":"Mileyko"},{"last_name":"Galkovskyi","first_name":"Taras","full_name":"Galkovskyi, Taras"},{"full_name":"Moore, Brad","last_name":"Moore","first_name":"Brad"},{"full_name":"Harer, John","first_name":"John","last_name":"Harer"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Mitchell Olds","first_name":"Thomas","full_name":"Mitchell Olds, Thomas"},{"full_name":"Weitz, Joshua","first_name":"Joshua","last_name":"Weitz"},{"full_name":"Benfey, Philip","last_name":"Benfey","first_name":"Philip"}],"scopus_import":1,"day":"30","page":"E1695 - E1704","citation":{"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.","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.","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.","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.","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","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.","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"},"publication":"PNAS","date_published":"2013-04-30T00:00:00Z","type":"journal_article","issue":"18","abstract":[{"lang":"eng","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."}],"intvolume":" 110","title":"3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2822","oa_version":"Submitted Version"},{"_id":"2843","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","intvolume":" 7749","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Stable length estimates of tube-like shapes","related_material":{"record":[{"relation":"later_version","status":"public","id":"2255"}]},"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian"}],"oa_version":"None","volume":7749,"date_created":"2018-12-11T11:59:53Z","date_updated":"2023-02-23T10:35:00Z","type":"conference","alternative_title":["LNCS"],"publist_id":"3952","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"}],"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.","short":"H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Springer, 2013, pp. 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.","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.","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","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.","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"},"publication":"17th IAPR International Conference on Discrete Geometry for Computer Imagery","page":"XV - XIX","quality_controlled":"1","doi":"10.1007/978-3-642-37067-0","date_published":"2013-02-21T00:00:00Z","conference":{"start_date":"2013-03-20","location":"Seville, Spain","end_date":"2013-03-22","name":"DGCI: Discrete Geometry for Computer Imagery"},"language":[{"iso":"eng"}],"scopus_import":1,"month":"02","day":"21"},{"external_id":{"arxiv":["1102.3389"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1102.3389v1"}],"oa":1,"quality_controlled":"1","doi":"10.4310/HHA.2013.v15.n1.a3","language":[{"iso":"eng"}],"month":"05","year":"2013","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"International Press","author":[{"id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","first_name":"Paul","last_name":"Bendich","full_name":"Bendich, Paul"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Morozov, Dmitriy","last_name":"Morozov","first_name":"Dmitriy"},{"full_name":"Patel, Amit","first_name":"Amit","last_name":"Patel","id":"34A254A0-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T07:00:18Z","date_created":"2018-12-11T11:59:58Z","volume":15,"publist_id":"3930","publication":"Homology, Homotopy and Applications","citation":{"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.","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.","short":"P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, Homology, Homotopy and Applications 15 (2013) 51–72.","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.","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.","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"},"page":"51 - 72","date_published":"2013-05-01T00:00:00Z","scopus_import":1,"day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2859","title":"Homology and robustness of level and interlevel sets","status":"public","intvolume":" 15","oa_version":"Preprint","type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"1"},{"day":"12","article_processing_charge":"No","scopus_import":1,"date_published":"2013-02-12T00:00:00Z","article_type":"original","page":"2670 - 2675","publication":"PNAS","citation":{"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.","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.","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.","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.","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","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.","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"},"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"}],"issue":"7","type":"journal_article","oa_version":"Published Version","status":"public","title":"Genotypic recognition and spatial responses by rice roots","intvolume":" 110","_id":"2887","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02","language":[{"iso":"eng"}],"doi":"10.1073/pnas.1222821110","quality_controlled":"1","external_id":{"pmid":["23362379"]},"main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574932/"}],"oa":1,"publist_id":"3872","date_updated":"2021-01-12T07:00:29Z","date_created":"2018-12-11T12:00:09Z","volume":110,"author":[{"full_name":"Fang, Suqin","last_name":"Fang","first_name":"Suqin"},{"full_name":"Clark, Randy","first_name":"Randy","last_name":"Clark"},{"last_name":"Zheng","first_name":"Ying","full_name":"Zheng, Ying"},{"last_name":"Iyer Pascuzzi","first_name":"Anjali","full_name":"Iyer Pascuzzi, Anjali"},{"last_name":"Weitz","first_name":"Joshua","full_name":"Weitz, Joshua"},{"first_name":"Leon","last_name":"Kochian","full_name":"Kochian, Leon"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Liao, Hong","first_name":"Hong","last_name":"Liao"},{"last_name":"Benfey","first_name":"Philip","full_name":"Benfey, Philip"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"National Academy of Sciences","year":"2013","pmid":1}]