--- _id: '2177' 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. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Salman full_name: Parsa, Salman id: 4BDBD4F2-F248-11E8-B48F-1D18A9856A87 last_name: Parsa citation: ama: 'Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM; 2014:152-160. doi:10.1137/1.9781611973402.11' apa: 'Edelsbrunner, H., & Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 152–160). Portland, USA: SIAM. https://doi.org/10.1137/1.9781611973402.11' 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. 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.' 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. conference: end_date: 2014-01-07 location: Portland, USA name: 'SODA: Symposium on Discrete Algorithms' start_date: 2014-01-05 date_created: 2018-12-11T11:56:09Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T06:55:48Z day: '01' department: - _id: HeEd doi: 10.1137/1.9781611973402.11 language: - iso: eng month: '01' oa_version: None page: 152 - 160 publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms publication_status: published publisher: SIAM publist_id: '4805' quality_controlled: '1' scopus_import: 1 status: public title: On the computational complexity of betti numbers reductions from matrix rank type: conference user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '2184' 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.' 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). article_number: '17 ' author: - first_name: Martin full_name: Čadek, Martin last_name: Čadek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál - first_name: Jiří full_name: Matoušek, Jiří last_name: Matoušek - first_name: Francis full_name: Sergeraert, Francis last_name: Sergeraert - first_name: Lukáš full_name: Vokřínek, Lukáš last_name: Vokřínek - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. Journal of the ACM. 2014;61(3). doi:10.1145/2597629 apa: Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., & Wagner, U. (2014). Computing all maps into a sphere. Journal of the ACM. ACM. https://doi.org/10.1145/2597629 chicago: Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere.” Journal of the ACM. ACM, 2014. https://doi.org/10.1145/2597629. 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. mla: Čadek, Martin, et al. “Computing All Maps into a Sphere.” Journal of the ACM, vol. 61, no. 3, 17, ACM, 2014, doi:10.1145/2597629. short: M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014). date_created: 2018-12-11T11:56:12Z date_published: 2014-05-01T00:00:00Z date_updated: 2021-01-12T06:55:50Z day: '01' department: - _id: UlWa - _id: HeEd doi: 10.1145/2597629 intvolume: ' 61' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1105.6257 month: '05' oa: 1 oa_version: Preprint publication: Journal of the ACM publication_status: published publisher: ACM publist_id: '4797' quality_controlled: '1' scopus_import: 1 status: public title: Computing all maps into a sphere type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 61 year: '2014' ... --- _id: '2905' abstract: - lang: eng text: "Persistent homology is a recent grandchild of homology that has found use in\r\nscience and engineering as well as in mathematics. This paper surveys the method as well\r\nas the applications, neglecting completeness in favor of highlighting ideas and directions." 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. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Dmitriy full_name: Morozovy, Dmitriy last_name: Morozovy citation: 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' 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' 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.' 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.' ista: 'Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.' mla: 'Edelsbrunner, Herbert, and Dmitriy Morozovy. Persistent Homology: Theory and Practice. European Mathematical Society Publishing House, 2014, pp. 31–50, doi:10.4171/120-1/3.' short: H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society Publishing House, 2014, pp. 31–50. conference: end_date: 2012-07-07 location: Kraków, Poland name: 'ECM: European Congress of Mathematics' start_date: 2012-07-02 date_created: 2018-12-11T12:00:16Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T07:00:36Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.4171/120-1/3 file: - access_level: open_access checksum: 1d4a046f1af945c407c5c4d411d4c5e4 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:43Z date_updated: 2020-07-14T12:45:52Z file_id: '5232' file_name: IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf file_size: 435320 relation: main_file file_date_updated: 2020-07-14T12:45:52Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Submitted Version page: 31 - 50 publication_status: published publisher: European Mathematical Society Publishing House publist_id: '3842' pubrep_id: '544' quality_controlled: '1' status: public title: 'Persistent homology: Theory and practice' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '10892' 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." 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.' alternative_title: - LNCS article_processing_charge: No author: - first_name: Therese full_name: Biedl, Therese last_name: Biedl - first_name: Stefan full_name: Huber, Stefan id: 4700A070-F248-11E8-B48F-1D18A9856A87 last_name: Huber orcid: 0000-0002-8871-5814 - first_name: Peter full_name: Palfrader, Peter last_name: Palfrader citation: 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' 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. 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.' 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. conference: end_date: 2014-12-17 location: Jeonju, Korea name: 'ISAAC: International Symposium on Algorithms and Computation' start_date: 2014-12-15 date_created: 2022-03-21T07:09:03Z date_published: 2014-11-08T00:00:00Z date_updated: 2023-02-23T12:20:55Z day: '08' department: - _id: HeEd doi: 10.1007/978-3-319-13075-0_10 intvolume: ' 8889' language: - iso: eng month: '11' oa_version: None page: 117-127 publication: 25th International Symposium, ISAAC 2014 publication_identifier: eisbn: - '9783319130750' eissn: - 1611-3349 isbn: - '9783319130743' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '481' relation: later_version status: public scopus_import: '1' status: public title: Planar matchings for weighted straight skeletons type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8889 year: '2014' ... --- _id: '6853' 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. alternative_title: - SpringerBriefs in Applied Sciences and Technology article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: 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' 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.' ieee: 'H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed. Cham: Springer Nature, 2014.' ista: 'Edelsbrunner H. 2014. A Short Course in Computational Geometry and Topology 1st ed., Cham: Springer Nature, IX, 110p.' mla: Edelsbrunner, Herbert. A Short Course in Computational Geometry and Topology. 1st ed., Springer Nature, 2014, doi:10.1007/978-3-319-05957-0. short: H. Edelsbrunner, A Short Course in Computational Geometry and Topology, 1st ed., Springer Nature, Cham, 2014. date_created: 2019-09-06T09:22:33Z date_published: 2014-01-01T00:00:00Z date_updated: 2022-03-04T07:47:54Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-319-05957-0 edition: '1' language: - iso: eng month: '01' oa_version: None page: IX, 110 place: Cham publication_identifier: eisbn: - 9-783-3190-5957-0 eissn: - 2191-5318 isbn: - 9-783-3190-5956-3 issn: - 2191-530X publication_status: published publisher: Springer Nature quality_controlled: '1' 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 scopus_import: '1' series_title: SpringerBriefs in Applied Sciences and Technology status: public title: A Short Course in Computational Geometry and Topology type: book user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '10886' 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. acknowledgement: This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP. alternative_title: - Mathematics and Visualization article_processing_charge: No author: - first_name: Valentin full_name: Zobel, Valentin last_name: Zobel - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz citation: 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. 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. ista: Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262. mla: Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–62, doi:10.1007/978-3-319-04099-8_16. short: V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262. date_created: 2022-03-18T13:05:39Z date_published: 2014-03-19T00:00:00Z date_updated: 2023-09-05T14:13:16Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_16 language: - iso: eng month: '03' oa_version: None page: 249-262 publication: 'Topological Methods in Data Analysis and Visualization III ' publication_identifier: eisbn: - '9783319040998' eissn: - 2197-666X isbn: - '9783319040981' issn: - 1612-3786 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2014' ... --- _id: '10817' abstract: - lang: eng text: The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption. acknowledgement: This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC. article_processing_charge: No author: - first_name: David full_name: Günther, David last_name: Günther - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Hans-Peter full_name: Seidel, Hans-Peter last_name: Seidel - first_name: Tino full_name: Weinkauf, Tino last_name: Weinkauf citation: 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' 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.' 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.' 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. 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. date_created: 2022-03-04T08:33:57Z date_published: 2014-03-19T00:00:00Z date_updated: 2023-09-05T15:33:45Z day: '19' department: - _id: HeEd doi: 10.1007/978-3-319-04099-8_9 ec_funded: 1 editor: - first_name: Peer-Timo full_name: Bremer, Peer-Timo last_name: Bremer - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Valerio full_name: Pascucci, Valerio last_name: Pascucci - first_name: Ronald full_name: Peikert, Ronald last_name: Peikert language: - iso: eng month: '03' oa_version: None page: 135-150 place: Cham project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Topological Methods in Data Analysis and Visualization III. publication_identifier: eisbn: - '9783319040998' eissn: - 2197-666X isbn: - '9783319040981' issn: - 1612-3786 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: Mathematics and Visualization status: public title: Notes on the simplification of the Morse-Smale complex type: book_chapter user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2014' ... --- _id: '2255' 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. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: 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 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. 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. 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. short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177. date_created: 2018-12-11T11:56:36Z date_published: 2014-09-01T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '01' ddc: - '000' department: - _id: HeEd doi: 10.1007/s10851-013-0468-x ec_funded: 1 file: - access_level: open_access checksum: 2f93f3e63a38a85cd4404d7953913b14 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:18Z date_updated: 2020-07-14T12:45:35Z file_id: '5204' file_name: IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf file_size: 3941391 relation: main_file file_date_updated: 2020-07-14T12:45:35Z has_accepted_license: '1' intvolume: ' 50' issue: '1' language: - iso: eng month: '09' oa: 1 oa_version: Submitted Version page: 164 - 177 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Journal of Mathematical Imaging and Vision publication_identifier: issn: - '09249907' publication_status: published publisher: Springer publist_id: '4691' pubrep_id: '549' quality_controlled: '1' related_material: record: - id: '2843' relation: earlier_version status: public - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: Stable length estimates of tube-like shapes type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 50 year: '2014' ... --- _id: '10894' abstract: - lang: eng text: PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations. article_processing_charge: No author: - first_name: Ulrich full_name: Bauer, Ulrich id: 2ADD483A-F248-11E8-B48F-1D18A9856A87 last_name: Bauer orcid: 0000-0002-9683-0724 - first_name: Michael full_name: Kerber, Michael last_name: Kerber - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Hubert full_name: Wagner, Hubert last_name: Wagner citation: ama: 'Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: ICMS 2014: International Congress on Mathematical Software. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:10.1007/978-3-662-44199-2_24' apa: 'Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In ICMS 2014: International Congress on Mathematical Software (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_24' 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.' 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.' 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.' 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.' conference: end_date: 2014-08-09 location: Seoul, South Korea name: 'ICMS: International Congress on Mathematical Software' start_date: 2014-08-05 date_created: 2022-03-21T07:12:16Z date_published: 2014-09-01T00:00:00Z date_updated: 2023-09-20T09:42:40Z day: '01' department: - _id: HeEd doi: 10.1007/978-3-662-44199-2_24 intvolume: ' 8592' language: - iso: eng month: '09' oa_version: None page: 137-143 place: Berlin, Heidelberg publication: 'ICMS 2014: International Congress on Mathematical Software' publication_identifier: eisbn: - '9783662441992' eissn: - 1611-3349 isbn: - '9783662441985' issn: - 0302-9743 publication_status: published publisher: Springer Berlin Heidelberg quality_controlled: '1' related_material: record: - id: '1433' relation: later_version status: public scopus_import: '1' series_title: LNCS status: public title: PHAT – Persistent Homology Algorithms Toolbox type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 8592 year: '2014' ... --- _id: '2012' 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. 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_number: '1401.0468' article_processing_charge: No author: - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham - first_name: Michael full_name: Kerber, Michael last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Caroline full_name: Uhler, Caroline id: 49ADD78E-F248-11E8-B48F-1D18A9856A87 last_name: Uhler orcid: 0000-0002-7008-0216 citation: ama: Iglesias Ham M, Kerber M, Uhler C. Sphere packing with limited overlap. arXiv. 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 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. 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. mla: Iglesias Ham, Mabel, et al. “Sphere Packing with Limited Overlap.” ArXiv, 1401.0468, doi:10.48550/arXiv.1401.0468. short: M. Iglesias Ham, M. Kerber, C. Uhler, ArXiv (n.d.). date_created: 2018-12-11T11:55:12Z date_published: 2014-01-01T00:00:00Z date_updated: 2023-10-18T08:06:45Z day: '01' department: - _id: HeEd - _id: CaUh doi: 10.48550/arXiv.1401.0468 external_id: arxiv: - '1401.0468' language: - iso: eng main_file_link: - open_access: '1' url: http://cccg.ca/proceedings/2014/papers/paper23.pdf month: '01' oa: 1 oa_version: Submitted Version publication: arXiv publication_status: submitted publist_id: '5064' status: public title: Sphere packing with limited overlap type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2014' ...