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Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 484–490.","short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","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","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). 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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"}],"oa_version":"Submitted Version","main_file_link":[{"url":"http://arxiv.org/abs/1312.1231","open_access":"1"}],"scopus_import":1,"month":"06","date_updated":"2021-01-12T06:55:38Z","department":[{"_id":"HeEd"}],"_id":"2155","conference":{"start_date":"2014-06-08","location":"Kyoto, Japan","end_date":"2014-06-11","name":"SoCG: Symposium on Computational Geometry"},"type":"conference","status":"public"},{"month":"01","publisher":"SIAM","quality_controlled":"1","scopus_import":1,"oa_version":"None","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."}],"doi":"10.1137/1.9781611973402.11","date_published":"2014-01-01T00:00:00Z","date_created":"2018-12-11T11:56:09Z","page":"152 - 160","day":"01","language":[{"iso":"eng"}],"publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","year":"2014","publication_status":"published","status":"public","type":"conference","conference":{"start_date":"2014-01-05","end_date":"2014-01-07","location":"Portland, USA","name":"SODA: Symposium on Discrete Algorithms"},"_id":"2177","department":[{"_id":"HeEd"}],"title":"On the computational complexity of betti numbers reductions from matrix rank","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Salman","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87","full_name":"Parsa, Salman","last_name":"Parsa"}],"publist_id":"4805","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:55:48Z","citation":{"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.","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.","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.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160.","ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Portland, USA, 2014, pp. 152–160.","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","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"}},{"doi":"10.1145/2597629","date_published":"2014-05-01T00:00:00Z","date_created":"2018-12-11T11:56:12Z","year":"2014","day":"01","publication":"Journal of the ACM","quality_controlled":"1","publisher":"ACM","oa":1,"acknowledgement":"The research by M. K. was supported by project GAUK 49209. The research by M. K. was also supported by project 1M0545 by the Ministry of Education of the Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague (project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).","publist_id":"4797","author":[{"last_name":"Čadek","full_name":"Čadek, Martin","first_name":"Martin"},{"last_name":"Krcál","full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jiří","full_name":"Matoušek, Jiří","last_name":"Matoušek"},{"first_name":"Francis","full_name":"Sergeraert, Francis","last_name":"Sergeraert"},{"last_name":"Vokřínek","full_name":"Vokřínek, Lukáš","first_name":"Lukáš"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","last_name":"Wagner","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568"}],"title":"Computing all maps into a sphere","citation":{"short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014).","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” Journal of the ACM, vol. 61, no. 3. ACM, 2014.","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","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","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.","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.","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."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","article_number":"17 ","volume":61,"issue":"3","publication_status":"published","language":[{"iso":"eng"}],"scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1105.6257","open_access":"1"}],"month":"05","intvolume":" 61","abstract":[{"lang":"eng","text":"Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable."}],"oa_version":"Preprint","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T06:55:50Z","type":"journal_article","status":"public","_id":"2184"},{"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:52Z","date_updated":"2021-01-12T07:00:36Z","ddc":["000"],"conference":{"end_date":"2012-07-07","location":"Kraków, Poland","start_date":"2012-07-02","name":"ECM: European Congress of Mathematics"},"type":"conference","pubrep_id":"544","status":"public","_id":"2905","publication_status":"published","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"1d4a046f1af945c407c5c4d411d4c5e4","file_id":"5232","creator":"system","date_updated":"2020-07-14T12:45:52Z","file_size":435320,"date_created":"2018-12-12T10:16:43Z","file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf"}],"month":"01","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"}],"oa_version":"Submitted Version","article_processing_charge":"No","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Dmitriy","full_name":"Morozovy, Dmitriy","last_name":"Morozovy"}],"publist_id":"3842","title":"Persistent homology: Theory and practice","citation":{"ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","chicago":"Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory and Practice,” 31–50. European Mathematical Society Publishing House, 2014. https://doi.org/10.4171/120-1/3.","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 31–50.","ieee":"H. 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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."}],"month":"11","intvolume":" 8889","alternative_title":["LNCS"],"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127.","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.","apa":"Biedl, T., Huber, S., & Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In 25th International Symposium, ISAAC 2014 (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. https://doi.org/10.1007/978-3-319-13075-0_10","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: 25th International Symposium, ISAAC 2014. Vol 8889. Springer Nature; 2014:117-127. doi:10.1007/978-3-319-13075-0_10","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.","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."},"title":"Planar matchings for weighted straight skeletons","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"article_processing_charge":"No","day":"08","publication":"25th International Symposium, ISAAC 2014","year":"2014","date_published":"2014-11-08T00:00:00Z","doi":"10.1007/978-3-319-13075-0_10","date_created":"2022-03-21T07:09:03Z","page":"117-127","acknowledgement":"T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.","publisher":"Springer Nature","quality_controlled":"1"},{"_id":"6853","series_title":"SpringerBriefs in Applied Sciences and Technology","status":"public","type":"book","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.","chicago":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed. SpringerBriefs in Applied Sciences and Technology. Cham: Springer Nature, 2014. https://doi.org/10.1007/978-3-319-05957-0.","short":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014.","ieee":"H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.","ama":"Edelsbrunner H. A Short Course in Computational Geometry and Topology. 1st ed. Cham: Springer Nature; 2014. doi:10.1007/978-3-319-05957-0","apa":"Edelsbrunner, H. (2014). A Short Course in Computational Geometry and Topology (1st ed.). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-05957-0","mla":"Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0."},"date_updated":"2022-03-04T07:47:54Z","department":[{"_id":"HeEd"}],"title":"A Short Course in Computational Geometry and Topology","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","oa_version":"None","abstract":[{"lang":"eng","text":"This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields."}],"place":"Cham","month":"01","publisher":"Springer Nature","alternative_title":["SpringerBriefs in Applied Sciences and Technology"],"scopus_import":"1","quality_controlled":"1","edition":"1","day":"01","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9-783-3190-5956-3"],"eissn":["2191-5318"],"issn":["2191-530X"],"eisbn":["9-783-3190-5957-0"]},"publication_status":"published","year":"2014","doi":"10.1007/978-3-319-05957-0","related_material":{"link":[{"description":"available as eBook via catalog IST BookList","relation":"other","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=356106"},{"description":"available via catalog IST BookList","relation":"other","url":"https://koha.app.ist.ac.at/cgi-bin/koha/opac-detail.pl?biblionumber=373842"}]},"date_published":"2014-01-01T00:00:00Z","date_created":"2019-09-06T09:22:33Z","page":"IX, 110"},{"page":"249-262","doi":"10.1007/978-3-319-04099-8_16","date_published":"2014-03-19T00:00:00Z","date_created":"2022-03-18T13:05:39Z","publication_identifier":{"eisbn":["9783319040998"],"issn":["1612-3786"],"isbn":["9783319040981"],"eissn":["2197-666X"]},"publication_status":"published","year":"2014","day":"19","language":[{"iso":"eng"}],"publication":"Topological Methods in Data Analysis and Visualization III ","alternative_title":["Mathematics and Visualization"],"scopus_import":"1","quality_controlled":"1","publisher":"Springer","month":"03","abstract":[{"text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set.","lang":"eng"}],"oa_version":"None","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","author":[{"first_name":"Valentin","last_name":"Zobel","full_name":"Zobel, Valentin"},{"last_name":"Reininghaus","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"}],"article_processing_charge":"No","department":[{"_id":"HeEd"}],"title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","citation":{"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.","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.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","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","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","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In Topological Methods in Data Analysis and Visualization III , 249–62. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_16.","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262."},"date_updated":"2023-09-05T14:13:16Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","type":"conference","status":"public","_id":"10886"},{"title":"Notes on the simplification of the Morse-Smale complex","editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"full_name":"Pascucci, Valerio","last_name":"Pascucci","first_name":"Valerio"},{"first_name":"Ronald","last_name":"Peikert","full_name":"Peikert, Ronald"}],"article_processing_charge":"No","author":[{"first_name":"David","last_name":"Günther","full_name":"Günther, David"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"last_name":"Seidel","full_name":"Seidel, Hans-Peter","first_name":"Hans-Peter"},{"full_name":"Weinkauf, Tino","last_name":"Weinkauf","first_name":"Tino"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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.","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","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.","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.","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."},"project":[{"grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_created":"2022-03-04T08:33:57Z","doi":"10.1007/978-3-319-04099-8_9","date_published":"2014-03-19T00:00:00Z","page":"135-150","publication":"Topological Methods in Data Analysis and Visualization III.","day":"19","year":"2014","quality_controlled":"1","publisher":"Springer Nature","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"}],"date_updated":"2023-09-05T15:33:45Z","status":"public","type":"book_chapter","series_title":"Mathematics and Visualization","_id":"10817","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eisbn":["9783319040998"],"isbn":["9783319040981"],"eissn":["2197-666X"],"issn":["1612-3786"]},"month":"03","place":"Cham","scopus_import":"1","oa_version":"None","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"}]},{"year":"2014","has_accepted_license":"1","publication":"Journal of Mathematical Imaging and Vision","day":"01","page":"164 - 177","date_created":"2018-12-11T11:56:36Z","date_published":"2014-09-01T00:00:00Z","doi":"10.1007/s10851-013-0468-x","oa":1,"publisher":"Springer","quality_controlled":"1","citation":{"short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” Journal of Mathematical Imaging and Vision, vol. 50, no. 1. Springer, pp. 164–177, 2014.","ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 2014;50(1):164-177. doi:10.1007/s10851-013-0468-x","apa":"Edelsbrunner, H., & Pausinger, F. (2014). Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. Springer. https://doi.org/10.1007/s10851-013-0468-x","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.","ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” Journal of Mathematical Imaging and Vision. Springer, 2014. https://doi.org/10.1007/s10851-013-0468-x."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian","last_name":"Pausinger","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian"}],"publist_id":"4691","title":"Stable length estimates of tube-like shapes","project":[{"name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publication_status":"published","publication_identifier":{"issn":["09249907"]},"language":[{"iso":"eng"}],"file":[{"file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","date_created":"2018-12-12T10:16:18Z","file_size":3941391,"date_updated":"2020-07-14T12:45:35Z","creator":"system","file_id":"5204","checksum":"2f93f3e63a38a85cd4404d7953913b14","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"ec_funded":1,"issue":"1","volume":50,"related_material":{"record":[{"id":"2843","status":"public","relation":"earlier_version"},{"relation":"dissertation_contains","status":"public","id":"1399"}]},"abstract":[{"text":"Motivated by applications in biology, we present an algorithm for estimating the length of tube-like shapes in 3-dimensional Euclidean space. In a first step, we combine the tube formula of Weyl with integral geometric methods to obtain an integral representation of the length, which we approximate using a variant of the Koksma-Hlawka Theorem. In a second step, we use tools from computational topology to decrease the dependence on small perturbations of the shape. We present computational experiments that shed light on the stability and the convergence rate of our algorithm.","lang":"eng"}],"oa_version":"Submitted Version","scopus_import":1,"intvolume":" 50","month":"09","date_updated":"2023-09-07T11:41:25Z","ddc":["000"],"file_date_updated":"2020-07-14T12:45:35Z","department":[{"_id":"HeEd"}],"_id":"2255","type":"journal_article","pubrep_id":"549","status":"public"},{"page":"137-143","date_created":"2022-03-21T07:12:16Z","date_published":"2014-09-01T00:00:00Z","doi":"10.1007/978-3-662-44199-2_24","year":"2014","publication":"ICMS 2014: International Congress on Mathematical Software","day":"01","publisher":"Springer Berlin Heidelberg","quality_controlled":"1","article_processing_charge":"No","author":[{"orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","last_name":"Bauer","first_name":"Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michael","full_name":"Kerber, Michael","last_name":"Kerber"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert"}],"title":"PHAT – Persistent Homology Algorithms Toolbox","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.","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","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","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in ICMS 2014: International Congress on Mathematical Software, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143.","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.","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"status":"public","id":"1433","relation":"later_version"}]},"volume":8592,"publication_status":"published","publication_identifier":{"isbn":["9783662441985"],"eissn":["1611-3349"],"issn":["0302-9743"],"eisbn":["9783662441992"]},"language":[{"iso":"eng"}],"scopus_import":"1","intvolume":" 8592","month":"09","place":"Berlin, Heidelberg","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"}],"oa_version":"None","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T09:42:40Z","conference":{"name":"ICMS: International Congress on Mathematical Software","start_date":"2014-08-05","location":"Seoul, South Korea","end_date":"2014-08-09"},"type":"conference","status":"public","_id":"10894","series_title":"LNCS"}]