[{"abstract":[{"text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1016/j.comgeo.2015.01.004","_id":"1584","external_id":{"isi":["000351967400008"]},"publication_status":"published","publisher":"Elsevier","author":[{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"first_name":"Stefan","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kaaser, Dominik","first_name":"Dominik","last_name":"Kaaser"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}],"day":"01","ddc":["000"],"date_updated":"2025-09-29T11:06:25Z","has_accepted_license":"1","month":"07","file_date_updated":"2020-07-14T12:45:03Z","oa_version":"Published Version","pubrep_id":"475","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">https://doi.org/10.1016/j.comgeo.2015.01.004</a>.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">https://doi.org/10.1016/j.comgeo.2015.01.004</a>","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.","mla":"Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">10.1016/j.comgeo.2015.01.004</a>.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. 2015;48(5):429-442. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">10.1016/j.comgeo.2015.01.004</a>","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442."},"volume":48,"status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2018-12-11T11:52:51Z","related_material":{"record":[{"status":"public","id":"1582","relation":"other"}]},"scopus_import":"1","quality_controlled":"1","language":[{"iso":"eng"}],"file":[{"checksum":"5b33719a86f7f4c8e5dc62c1b6893f49","file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf","file_size":508379,"relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:45:03Z","date_created":"2018-12-12T10:17:36Z","access_level":"open_access","file_id":"5292","creator":"system"}],"title":"Reprint of: Weighted straight skeletons in the plane","publication":"Computational Geometry: Theory and Applications","type":"journal_article","year":"2015","issue":"5","page":"429 - 442","date_published":"2015-07-01T00:00:00Z","publist_id":"5587","intvolume":"        48","department":[{"_id":"HeEd"}],"isi":1},{"department":[{"_id":"HeEd"}],"publication_identifier":{"isbn":["978-3-319-27260-3"],"eisbn":["978-3-319-27261-0"]},"isi":1,"publist_id":"5581","intvolume":"      9411","arxiv":1,"page":"335 - 347","date_published":"2015-11-27T00:00:00Z","alternative_title":["LNCS"],"type":"book_chapter","year":"2015","language":[{"iso":"eng"}],"title":"Representing directed trees as straight skeletons","publication":"Graph Drawing and Network Visualization","date_created":"2018-12-11T11:52:54Z","scopus_import":"1","quality_controlled":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: <i>Graph Drawing and Network Visualization</i>. Vol 9411. Springer Nature; 2015:335-347. doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>","mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>.","ista":"Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.","short":"O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.","chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In <i>Graph Drawing and Network Visualization</i>, 9411:335–47. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>.","ieee":"O. Aichholzer <i>et al.</i>, “Representing directed trees as straight skeletons,” in <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–347.","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., &#38; Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In <i>Graph Drawing and Network Visualization</i> (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>"},"volume":9411,"status":"public","oa":1,"oa_version":"Preprint","date_updated":"2025-09-23T10:35:07Z","month":"11","main_file_link":[{"url":"http://arxiv.org/abs/1508.01076","open_access":"1"}],"publisher":"Springer Nature","_id":"1590","publication_status":"published","author":[{"first_name":"Oswin","full_name":"Aichholzer, Oswin","last_name":"Aichholzer"},{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"first_name":"Thomas","full_name":"Hackl, Thomas","last_name":"Hackl"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"},{"last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit","first_name":"Birgit"}],"external_id":{"isi":["000373628600028"],"arxiv":["1508.01076"]},"conference":{"end_date":"2015-09-26","location":"Los Angeles, CA, United States","start_date":"2015-09-24","name":"GD: Graph Drawing and Network Visualization"},"day":"27","abstract":[{"text":"The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1007/978-3-319-27261-0_28"},{"type":"journal_article","year":"2015","issue":"4","corr_author":"1","publication":"Journal of the ACM","title":"Robust satisfiability of systems of equations","language":[{"iso":"eng"}],"quality_controlled":"1","scopus_import":"1","date_created":"2018-12-11T11:53:27Z","status":"public","volume":62,"citation":{"ama":"Franek P, Krcál M. Robust satisfiability of systems of equations. <i>Journal of the ACM</i>. 2015;62(4). doi:<a href=\"https://doi.org/10.1145/2751524\">10.1145/2751524</a>","mla":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” <i>Journal of the ACM</i>, vol. 62, no. 4, 26, ACM, 2015, doi:<a href=\"https://doi.org/10.1145/2751524\">10.1145/2751524</a>.","ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26.","short":"P. Franek, M. Krcál, Journal of the ACM 62 (2015).","chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” <i>Journal of the ACM</i>. ACM, 2015. <a href=\"https://doi.org/10.1145/2751524\">https://doi.org/10.1145/2751524</a>.","ieee":"P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” <i>Journal of the ACM</i>, vol. 62, no. 4. ACM, 2015.","apa":"Franek, P., &#38; Krcál, M. (2015). Robust satisfiability of systems of equations. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2751524\">https://doi.org/10.1145/2751524</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"intvolume":"        62","publist_id":"5466","article_number":"26","date_published":"2015-08-01T00:00:00Z","arxiv":1,"day":"01","_id":"1682","publication_status":"published","external_id":{"isi":["000361200500001"],"arxiv":["1402.0858"]},"author":[{"first_name":"Peter","full_name":"Franek, Peter","last_name":"Franek"},{"full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál"}],"publisher":"ACM","doi":"10.1145/2751524","abstract":[{"text":"We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α &gt; 0, it holds that each function g: K → ℝn such that ||g - f || ∞ &lt; α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K &gt; 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.","lang":"eng"}],"article_processing_charge":"No","oa":1,"oa_version":"Preprint","month":"08","date_updated":"2025-09-23T10:38:46Z","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}]},{"isi":1,"department":[{"_id":"HeEd"}],"publist_id":"5423","intvolume":"        47","page":"2754 - 2769","arxiv":1,"date_published":"2015-07-14T00:00:00Z","issue":"4","type":"journal_article","year":"2015","language":[{"iso":"eng"}],"publication":"Society for Industrial and Applied Mathematics","title":"Minimal resistance of curves under the single impact assumption","date_created":"2018-12-11T11:53:36Z","scopus_import":"1","quality_controlled":"1","citation":{"chicago":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” <i>Society for Industrial and Applied Mathematics</i>. SIAM, 2015. <a href=\"https://doi.org/10.1137/140993843\">https://doi.org/10.1137/140993843</a>.","apa":"Akopyan, A., &#38; Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. <i>Society for Industrial and Applied Mathematics</i>. SIAM. <a href=\"https://doi.org/10.1137/140993843\">https://doi.org/10.1137/140993843</a>","ieee":"A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” <i>Society for Industrial and Applied Mathematics</i>, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015.","mla":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” <i>Society for Industrial and Applied Mathematics</i>, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:<a href=\"https://doi.org/10.1137/140993843\">10.1137/140993843</a>.","ama":"Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. <i>Society for Industrial and Applied Mathematics</i>. 2015;47(4):2754-2769. doi:<a href=\"https://doi.org/10.1137/140993843\">10.1137/140993843</a>","ista":"Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.","short":"A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","volume":47,"oa":1,"oa_version":"Preprint","date_updated":"2025-09-23T09:35:36Z","month":"07","main_file_link":[{"url":"http://arxiv.org/abs/1410.3736","open_access":"1"}],"ec_funded":1,"_id":"1710","external_id":{"isi":["000360691500009"],"arxiv":["1410.3736"]},"publisher":"SIAM","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexander","full_name":"Plakhov, Alexander","last_name":"Plakhov"}],"publication_status":"published","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"}],"day":"14","doi":"10.1137/140993843","abstract":[{"text":"We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) &lt; 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) &lt; 0 for 0 ≤ ξ &lt; 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.","lang":"eng"}],"article_processing_charge":"No"},{"abstract":[{"lang":"eng","text":"We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2."}],"article_processing_charge":"No","doi":"10.1016/j.physleta.2014.12.010","day":"06","_id":"1938","publication_status":"published","author":[{"first_name":"Florian","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger"},{"full_name":"Steinerberger, Stefan","first_name":"Stefan","last_name":"Steinerberger"}],"external_id":{"isi":["000349586000006"]},"publisher":"Elsevier","oa_version":"None","acknowledgement":"F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. ","month":"03","date_updated":"2025-09-23T09:44:12Z","title":"On the distribution of local extrema in quantum chaos","corr_author":"1","publication":"Physics Letters, Section A","language":[{"iso":"eng"}],"year":"2015","type":"journal_article","issue":"6","volume":379,"status":"public","citation":{"chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">https://doi.org/10.1016/j.physleta.2014.12.010</a>.","apa":"Pausinger, F., &#38; Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. <i>Physics Letters, Section A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">https://doi.org/10.1016/j.physleta.2014.12.010</a>","ieee":"F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” <i>Physics Letters, Section A</i>, vol. 379, no. 6. Elsevier, pp. 535–541, 2015.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:<a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">10.1016/j.physleta.2014.12.010</a>.","ama":"Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. <i>Physics Letters, Section A</i>. 2015;379(6):535-541. doi:<a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">10.1016/j.physleta.2014.12.010</a>","ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:54:49Z","department":[{"_id":"HeEd"}],"isi":1,"date_published":"2015-03-06T00:00:00Z","page":"535 - 541","intvolume":"       379","publist_id":"5152"},{"department":[{"_id":"HeEd"}],"isi":1,"date_published":"2015-10-01T00:00:00Z","page":"1213 - 1244","intvolume":"        15","publist_id":"5022","title":"The persistent homology of a self-map","publication":"Foundations of Computational Mathematics","language":[{"iso":"eng"}],"file":[{"creator":"system","file_id":"4670","access_level":"open_access","content_type":"application/pdf","date_created":"2018-12-12T10:08:10Z","date_updated":"2020-07-14T12:45:26Z","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","checksum":"3566f3a8b0c1bc550e62914a88c584ff","file_size":1317546,"relation":"main_file"}],"year":"2015","issue":"5","type":"journal_article","volume":15,"status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","apa":"Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2015). The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>.","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. 2015;15(5):1213-1244. doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>."},"scopus_import":"1","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2018-12-11T11:55:20Z","pubrep_id":"486","file_date_updated":"2020-07-14T12:45:26Z","oa_version":"Published Version","oa":1,"acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the Polish National Science Center under Grant No. N201 419639.","month":"10","date_updated":"2025-09-23T14:08:54Z","has_accepted_license":"1","ec_funded":1,"ddc":["000"],"abstract":[{"text":"Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n","lang":"eng"}],"article_processing_charge":"No","doi":"10.1007/s10208-014-9223-y","day":"01","project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7"}],"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"4483EF78-F248-11E8-B48F-1D18A9856A87","last_name":"Jablonski","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866"},{"last_name":"Mrozek","first_name":"Marian","full_name":"Mrozek, Marian"}],"_id":"2035","external_id":{"isi":["000360862900004"]},"publication_status":"published","publisher":"Springer"},{"day":"01","author":[{"last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","first_name":"Florian"},{"full_name":"Svane, Anne","first_name":"Anne","last_name":"Svane"}],"_id":"1792","external_id":{"isi":["000362926900001"]},"publication_status":"published","publisher":"Academic Press","doi":"10.1016/j.jco.2015.06.002","article_processing_charge":"No","abstract":[{"text":"Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology.","lang":"eng"}],"month":"12","date_updated":"2026-04-09T14:26:05Z","acknowledgement":"F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation.","oa_version":"None","quality_controlled":"1","scopus_import":"1","related_material":{"record":[{"id":"1399","status":"public","relation":"dissertation_contains"}]},"date_created":"2018-12-11T11:54:02Z","status":"public","volume":31,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” <i>Journal of Complexity</i>, vol. 31, no. 6. Academic Press, pp. 773–797, 2015.","apa":"Pausinger, F., &#38; Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">https://doi.org/10.1016/j.jco.2015.06.002</a>","chicago":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>. Academic Press, 2015. <a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">https://doi.org/10.1016/j.jco.2015.06.002</a>.","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","ama":"Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. 2015;31(6):773-797. doi:<a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">10.1016/j.jco.2015.06.002</a>","mla":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:<a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">10.1016/j.jco.2015.06.002</a>."},"type":"journal_article","issue":"6","year":"2015","corr_author":"1","publication":"Journal of Complexity","title":"A Koksma-Hlawka inequality for general discrepancy systems","language":[{"iso":"eng"}],"intvolume":"        31","publist_id":"5320","date_published":"2015-12-01T00:00:00Z","page":"773 - 797","isi":1,"department":[{"_id":"HeEd"}]},{"month":"06","date_updated":"2025-09-23T08:30:43Z","has_accepted_license":"1","oa":1,"pubrep_id":"454","oa_version":"Published Version","file_date_updated":"2020-07-14T12:45:16Z","day":"01","external_id":{"isi":["000356630900069"]},"_id":"1793","publication_status":"published","author":[{"orcid":"0000-0003-2012-9947","full_name":"Symonova, Olga","first_name":"Olga","last_name":"Symonova","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Christopher","full_name":"Topp, Christopher","last_name":"Topp"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"}],"publisher":"Public Library of Science","abstract":[{"lang":"eng","text":"We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth."}],"article_processing_charge":"No","doi":"10.1371/journal.pone.0127657","ddc":["000"],"intvolume":"        10","publist_id":"5318","date_published":"2015-06-01T00:00:00Z","article_number":"e0127657","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"isi":1,"related_material":{"record":[{"status":"public","id":"9737","relation":"research_data"}]},"scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:54:02Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"volume":10,"status":"public","citation":{"ista":"Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","mla":"Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” <i>PLoS One</i>, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657\">10.1371/journal.pone.0127657</a>.","ama":"Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. <i>PLoS One</i>. 2015;10(6). doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657\">10.1371/journal.pone.0127657</a>","apa":"Symonova, O., Topp, C., &#38; Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. <i>PLoS One</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0127657\">https://doi.org/10.1371/journal.pone.0127657</a>","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” <i>PLoS One</i>, vol. 10, no. 6. Public Library of Science, 2015.","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” <i>PLoS One</i>. Public Library of Science, 2015. <a href=\"https://doi.org/10.1371/journal.pone.0127657\">https://doi.org/10.1371/journal.pone.0127657</a>."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","type":"journal_article","year":"2015","issue":"6","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","publication":"PLoS One","corr_author":"1","language":[{"iso":"eng"}],"file":[{"file_id":"5150","access_level":"open_access","creator":"system","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","checksum":"d20f26461ca575276ad3ed9ce4bfc787","relation":"main_file","file_size":1850825,"content_type":"application/pdf","date_created":"2018-12-12T10:15:30Z","date_updated":"2020-07-14T12:45:16Z"}]},{"OA_place":"publisher","department":[{"_id":"HeEd"}],"isi":1,"page":"606 - 621","date_published":"2015-06-03T00:00:00Z","publist_id":"5305","intvolume":"        48","language":[{"iso":"eng"}],"title":"Homological reconstruction and simplification in R3","publication":"Computational Geometry: Theory and Applications","corr_author":"1","type":"journal_article","issue":"8","year":"2015","citation":{"ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. <i>Computational Geometry: Theory and Applications</i>. 2015;48(8):606-621. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">10.1016/j.comgeo.2014.08.010</a>","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">10.1016/j.comgeo.2014.08.010</a>.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">https://doi.org/10.1016/j.comgeo.2014.08.010</a>.","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., &#38; Lieutier, A. (2015). Homological reconstruction and simplification in R3. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">https://doi.org/10.1016/j.comgeo.2014.08.010</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":48,"status":"public","date_created":"2018-12-11T11:54:06Z","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2812"}]},"quality_controlled":"1","scopus_import":"1","oa_version":"Published Version","article_type":"original","oa":1,"main_file_link":[{"url":"https://doi.org/10.1016/j.comgeo.2014.08.010","open_access":"1"}],"OA_type":"free access","date_updated":"2026-06-18T17:57:28Z","month":"06","ec_funded":1,"ddc":["500"],"abstract":[{"lang":"eng","text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard."}],"article_processing_charge":"No","doi":"10.1016/j.comgeo.2014.08.010","publication_status":"published","_id":"1805","external_id":{"isi":["000357353200006"]},"publisher":"Elsevier","author":[{"last_name":"Attali","full_name":"Attali, Dominique","first_name":"Dominique"},{"first_name":"Ulrich","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer"},{"first_name":"Olivier","full_name":"Devillers, Olivier","last_name":"Devillers"},{"first_name":"Marc","full_name":"Glisse, Marc","last_name":"Glisse"},{"first_name":"André","full_name":"Lieutier, André","last_name":"Lieutier"}],"day":"03","project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493"}]},{"type":"journal_article","year":"2015","issue":"1","corr_author":"1","publication":"Journal of Statistical Physics","title":"Invariant measures of genetic recombination process","language":[{"iso":"eng"}],"scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:54:14Z","status":"public","volume":160,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ieee":"A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” <i>Journal of Statistical Physics</i>, vol. 160, no. 1. Springer, pp. 163–167, 2015.","apa":"Akopyan, A., Pirogov, S., &#38; Rybko, A. (2015). Invariant measures of genetic recombination process. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-015-1238-5\">https://doi.org/10.1007/s10955-015-1238-5</a>","chicago":"Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” <i>Journal of Statistical Physics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s10955-015-1238-5\">https://doi.org/10.1007/s10955-015-1238-5</a>.","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","ista":"Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167.","ama":"Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. <i>Journal of Statistical Physics</i>. 2015;160(1):163-167. doi:<a href=\"https://doi.org/10.1007/s10955-015-1238-5\">10.1007/s10955-015-1238-5</a>","mla":"Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” <i>Journal of Statistical Physics</i>, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:<a href=\"https://doi.org/10.1007/s10955-015-1238-5\">10.1007/s10955-015-1238-5</a>."},"isi":1,"department":[{"_id":"HeEd"}],"intvolume":"       160","publist_id":"5276","date_published":"2015-07-01T00:00:00Z","arxiv":1,"page":"163 - 167","ec_funded":1,"project":[{"call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"day":"01","author":[{"first_name":"Arseniy","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pirogov, Sergey","first_name":"Sergey","last_name":"Pirogov"},{"first_name":"Aleksandr","full_name":"Rybko, Aleksandr","last_name":"Rybko"}],"_id":"1828","publisher":"Springer","publication_status":"published","external_id":{"isi":["000356579000009"],"arxiv":["1406.5313"]},"doi":"10.1007/s10955-015-1238-5","abstract":[{"text":"We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory.","lang":"eng"}],"article_processing_charge":"No","oa":1,"oa_version":"Preprint","month":"07","date_updated":"2025-09-23T09:23:53Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1406.5313","open_access":"1"}]},{"related_material":{"record":[{"id":"1793","status":"public","relation":"used_in_publication"}]},"day":"01","author":[{"id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","last_name":"Symonova","first_name":"Olga","full_name":"Symonova, Olga","orcid":"0000-0003-2012-9947"},{"full_name":"Topp, Christopher","first_name":"Christopher","last_name":"Topp"},{"first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"_id":"9737","publisher":"Public Library of Science","date_created":"2021-07-28T06:20:13Z","article_processing_charge":"No","status":"public","doi":"10.1371/journal.pone.0127657.s001","citation":{"chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">https://doi.org/10.1371/journal.pone.0127657.s001</a>.","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015.","apa":"Symonova, O., Topp, C., &#38; Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">https://doi.org/10.1371/journal.pone.0127657.s001</a>","ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>","mla":"Symonova, Olga, et al. <i>Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2</i>. Public Library of Science, 2015, doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>."},"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","type":"research_data_reference","year":"2015","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","month":"06","date_updated":"2025-09-23T08:30:43Z","date_published":"2015-06-01T00:00:00Z","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"oa_version":"Published Version"},{"editor":[{"last_name":"Bremer","full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"first_name":"Ronald","full_name":"Peikert, Ronald","last_name":"Peikert"}],"oa_version":"None","month":"03","date_updated":"2025-04-15T08:37:54Z","acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","ec_funded":1,"day":"19","project":[{"call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems"}],"_id":"10817","publication_status":"published","author":[{"full_name":"Günther, David","first_name":"David","last_name":"Günther"},{"first_name":"Jan","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus"},{"full_name":"Seidel, Hans-Peter","first_name":"Hans-Peter","last_name":"Seidel"},{"first_name":"Tino","full_name":"Weinkauf, Tino","last_name":"Weinkauf"}],"publisher":"Springer Nature","article_processing_charge":"No","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"}],"doi":"10.1007/978-3-319-04099-8_9","place":"Cham","publication_identifier":{"eissn":["2197-666X"],"eisbn":["9783319040998"],"isbn":["9783319040981"],"issn":["1612-3786"]},"department":[{"_id":"HeEd"}],"date_published":"2014-03-19T00:00:00Z","page":"135-150","type":"book_chapter","year":"2014","title":"Notes on the simplification of the Morse-Smale complex","publication":"Topological Methods in Data Analysis and Visualization III.","language":[{"iso":"eng"}],"series_title":"Mathematics and Visualization","quality_controlled":"1","scopus_import":"1","date_created":"2022-03-04T08:33:57Z","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in <i>Topological Methods in Data Analysis and Visualization III.</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., &#38; Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III.</i> (pp. 135–150). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>.","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.","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.","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. <i>Topological Methods in Data Analysis and Visualization III.</i> Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>","mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>."}},{"language":[{"iso":"eng"}],"publication":"Topological Methods in Data Analysis and Visualization III ","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","year":"2014","type":"conference","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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: <i>Topological Methods in Data Analysis and Visualization III </i>. Springer; 2014:249-262. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” <i>Topological Methods in Data Analysis and Visualization III </i>, Springer, 2014, pp. 249–62, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>.","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in <i>Topological Methods in Data Analysis and Visualization III </i>, 2014, pp. 249–262.","apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In <i>Topological Methods in Data Analysis and Visualization III </i> (pp. 249–262). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In <i>Topological Methods in Data Analysis and Visualization III </i>, 249–62. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>."},"status":"public","doi":"10.1007/978-3-319-04099-8_16","article_processing_charge":"No","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"}],"author":[{"first_name":"Valentin","full_name":"Zobel, Valentin","last_name":"Zobel"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan","first_name":"Jan"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"}],"_id":"10886","publisher":"Springer","date_created":"2022-03-18T13:05:39Z","publication_status":"published","scopus_import":"1","quality_controlled":"1","day":"19","oa_version":"None","publication_identifier":{"eisbn":["9783319040998"],"eissn":["2197-666X"],"issn":["1612-3786"],"isbn":["9783319040981"]},"department":[{"_id":"HeEd"}],"page":"249-262","alternative_title":["Mathematics and Visualization"],"date_published":"2014-03-19T00:00:00Z","acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","date_updated":"2023-09-05T14:13:16Z","month":"03"},{"oa_version":"None","month":"11","date_updated":"2025-09-29T13:22:55Z","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.","day":"08","conference":{"location":"Jeonju, Korea","start_date":"2014-12-15","name":"ISAAC: International Symposium on Algorithms and Computation","end_date":"2014-12-17"},"publisher":"Springer Nature","_id":"10892","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Stefan","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"publication_status":"published","external_id":{"isi":["000354865900010"]},"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."}],"article_processing_charge":"No","doi":"10.1007/978-3-319-13075-0_10","publication_identifier":{"issn":["0302-9743"],"isbn":["9783319130743"],"eisbn":["9783319130750"],"eissn":["1611-3349"]},"department":[{"_id":"HeEd"}],"isi":1,"intvolume":"      8889","date_published":"2014-11-08T00:00:00Z","alternative_title":["LNCS"],"page":"117-127","year":"2014","type":"conference","title":"Planar matchings for weighted straight skeletons","publication":"25th International Symposium, ISAAC 2014","corr_author":"1","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"481"}]},"quality_controlled":"1","scopus_import":"1","date_created":"2022-03-21T07:09:03Z","volume":8889,"status":"public","citation":{"chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In <i>25th International Symposium, ISAAC 2014</i>, 8889:117–27. Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">https://doi.org/10.1007/978-3-319-13075-0_10</a>.","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in <i>25th International Symposium, ISAAC 2014</i>, Jeonju, Korea, 2014, vol. 8889, pp. 117–127.","apa":"Biedl, T., Huber, S., &#38; Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In <i>25th International Symposium, ISAAC 2014</i> (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">https://doi.org/10.1007/978-3-319-13075-0_10</a>","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: <i>25th International Symposium, ISAAC 2014</i>. Vol 8889. Springer Nature; 2014:117-127. doi:<a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">10.1007/978-3-319-13075-0_10</a>","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” <i>25th International Symposium, ISAAC 2014</i>, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:<a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">10.1007/978-3-319-13075-0_10</a>.","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.","short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"date_created":"2022-03-21T07:11:23Z","series_title":"Mathematics and Visualization","quality_controlled":"1","scopus_import":"1","citation":{"chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>.","apa":"Kasten, J., Reininghaus, J., Reich, W., &#38; Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III </i> (Vol. 1, pp. 55–69). Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>","ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in <i>Topological Methods in Data Analysis and Visualization III </i>, vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69.","mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>.","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III </i>. Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>","short":"J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69.","ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":1,"status":"public","type":"book_chapter","year":"2014","language":[{"iso":"eng"}],"title":"Toward the extraction of saddle periodic orbits","publication":"Topological Methods in Data Analysis and Visualization III ","intvolume":"         1","page":"55-69","date_published":"2014-03-19T00:00:00Z","department":[{"_id":"HeEd"}],"publication_identifier":{"eissn":["2197-666X"],"eisbn":["9783319040998"],"isbn":["9783319040981"],"issn":["1612-3786"]},"_id":"10893","publisher":"Springer","author":[{"last_name":"Kasten","first_name":"Jens","full_name":"Kasten, Jens"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Reich","full_name":"Reich, Wieland","first_name":"Wieland"},{"full_name":"Scheuermann, Gerik","first_name":"Gerik","last_name":"Scheuermann"}],"publication_status":"published","day":"19","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7"}],"place":"Cham","abstract":[{"text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1007/978-3-319-04099-8_4","ec_funded":1,"date_updated":"2025-04-15T08:37:54Z","month":"03","acknowledgement":"First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program.","oa_version":"None","editor":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo","last_name":"Bremer"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"first_name":"Ronald","full_name":"Peikert, Ronald","last_name":"Peikert"}]},{"_id":"10894","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","first_name":"Ulrich"},{"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"},{"last_name":"Wagner","full_name":"Wagner, Hubert","first_name":"Hubert"}],"publication_status":"published","publisher":"Springer Berlin Heidelberg","conference":{"name":"ICMS: International Congress on Mathematical Software","location":"Seoul, South Korea","start_date":"2014-08-05","end_date":"2014-08-09"},"day":"01","place":"Berlin, Heidelberg","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","doi":"10.1007/978-3-662-44199-2_24","oa_version":"None","date_updated":"2026-06-18T17:35:15Z","month":"09","year":"2014","type":"conference","language":[{"iso":"eng"}],"title":"PHAT – Persistent Homology Algorithms Toolbox","publication":"ICMS 2014: International Congress on Mathematical Software","date_created":"2022-03-21T07:12:16Z","related_material":{"record":[{"relation":"later_version","id":"1433","status":"public"}]},"series_title":"LNCS","quality_controlled":"1","scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in <i>ICMS 2014: International Congress on Mathematical Software</i>, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","apa":"Bauer, U., Kerber, M., Reininghaus, J., &#38; Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In <i>ICMS 2014: International Congress on Mathematical Software</i> (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">https://doi.org/10.1007/978-3-662-44199-2_24</a>","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In <i>ICMS 2014: International Congress on Mathematical Software</i>, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. <a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">https://doi.org/10.1007/978-3-662-44199-2_24</a>.","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.","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.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: <i>ICMS 2014: International Congress on Mathematical Software</i>. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:<a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">10.1007/978-3-662-44199-2_24</a>","mla":"Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” <i>ICMS 2014: International Congress on Mathematical Software</i>, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:<a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">10.1007/978-3-662-44199-2_24</a>."},"volume":8592,"status":"public","department":[{"_id":"HeEd"}],"publication_identifier":{"eisbn":["9783662441992"],"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783662441985"]},"intvolume":"      8592","page":"137-143","date_published":"2014-09-01T00:00:00Z"},{"ec_funded":1,"ddc":["000"],"doi":"10.1007/s10851-013-0468-x","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."}],"article_processing_charge":"No","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493"}],"day":"01","_id":"2255","publisher":"Springer","external_id":{"isi":["000339823000012"]},"publication_status":"published","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Florian","full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger"}],"pubrep_id":"549","file_date_updated":"2020-07-14T12:45:35Z","oa_version":"Submitted Version","oa":1,"month":"09","has_accepted_license":"1","date_updated":"2026-04-16T10:09:04Z","publication":"Journal of Mathematical Imaging and Vision","corr_author":"1","title":"Stable length estimates of tube-like shapes","file":[{"creator":"system","access_level":"open_access","file_id":"5204","content_type":"application/pdf","date_updated":"2020-07-14T12:45:35Z","date_created":"2018-12-12T10:16:18Z","checksum":"2f93f3e63a38a85cd4404d7953913b14","file_name":"IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf","relation":"main_file","file_size":3941391}],"language":[{"iso":"eng"}],"issue":"1","year":"2014","type":"journal_article","status":"public","volume":50,"citation":{"ama":"Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. <i>Journal of Mathematical Imaging and Vision</i>. 2014;50(1):164-177. doi:<a href=\"https://doi.org/10.1007/s10851-013-0468-x\">10.1007/s10851-013-0468-x</a>","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” <i>Journal of Mathematical Imaging and Vision</i>, vol. 50, no. 1, Springer, 2014, pp. 164–77, doi:<a href=\"https://doi.org/10.1007/s10851-013-0468-x\">10.1007/s10851-013-0468-x</a>.","ista":"Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes. Journal of Mathematical Imaging and Vision. 50(1), 164–177.","short":"H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision 50 (2014) 164–177.","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like Shapes.” <i>Journal of Mathematical Imaging and Vision</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s10851-013-0468-x\">https://doi.org/10.1007/s10851-013-0468-x</a>.","ieee":"H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,” <i>Journal of Mathematical Imaging and Vision</i>, vol. 50, no. 1. Springer, pp. 164–177, 2014.","apa":"Edelsbrunner, H., &#38; Pausinger, F. (2014). Stable length estimates of tube-like shapes. <i>Journal of Mathematical Imaging and Vision</i>. Springer. <a href=\"https://doi.org/10.1007/s10851-013-0468-x\">https://doi.org/10.1007/s10851-013-0468-x</a>"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","quality_controlled":"1","scopus_import":"1","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2843"},{"relation":"dissertation_contains","id":"1399","status":"public"}]},"date_created":"2018-12-11T11:56:36Z","isi":1,"department":[{"_id":"HeEd"}],"publication_identifier":{"issn":["0924-9907"]},"date_published":"2014-09-01T00:00:00Z","page":"164 - 177","intvolume":"        50","publist_id":"4691"},{"date_created":"2018-12-11T12:00:16Z","quality_controlled":"1","citation":{"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.","apa":"Edelsbrunner, H., &#38; Morozovy, D. (2014). Persistent homology: Theory and practice (pp. 31–50). Presented at the ECM: European Congress of Mathematics, Kraków, Poland: European Mathematical Society. <a href=\"https://doi.org/10.4171/120-1/3\">https://doi.org/10.4171/120-1/3</a>","chicago":"Edelsbrunner, Herbert, and Dmitriy Morozovy. “Persistent Homology: Theory and Practice,” 31–50. European Mathematical Society, 2014. <a href=\"https://doi.org/10.4171/120-1/3\">https://doi.org/10.4171/120-1/3</a>.","short":"H. Edelsbrunner, D. Morozovy, in:, European Mathematical Society, 2014, pp. 31–50.","ista":"Edelsbrunner H, Morozovy D. 2014. Persistent homology: Theory and practice. ECM: European Congress of Mathematics, 31–50.","ama":"Edelsbrunner H, Morozovy D. Persistent homology: Theory and practice. In: European Mathematical Society; 2014:31-50. doi:<a href=\"https://doi.org/10.4171/120-1/3\">10.4171/120-1/3</a>","mla":"Edelsbrunner, Herbert, and Dmitriy Morozovy. <i>Persistent Homology: Theory and Practice</i>. European Mathematical Society, 2014, pp. 31–50, doi:<a href=\"https://doi.org/10.4171/120-1/3\">10.4171/120-1/3</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","year":"2014","type":"conference","language":[{"iso":"eng"}],"file":[{"file_name":"IST-2016-544-v1+1_2012-P-11-PHTheoryPractice.pdf","checksum":"1d4a046f1af945c407c5c4d411d4c5e4","relation":"main_file","file_size":435320,"content_type":"application/pdf","date_created":"2018-12-12T10:16:43Z","date_updated":"2020-07-14T12:45:52Z","access_level":"open_access","file_id":"5232","creator":"system"}],"title":"Persistent homology: Theory and practice","corr_author":"1","publist_id":"3842","page":"31 - 50","date_published":"2014-01-01T00:00:00Z","department":[{"_id":"HeEd"}],"_id":"2905","publication_status":"published","author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"first_name":"Dmitriy","full_name":"Morozovy, Dmitriy","last_name":"Morozovy"}],"publisher":"European Mathematical Society","conference":{"end_date":"2012-07-07","name":"ECM: European Congress of Mathematics","location":"Kraków, Poland","start_date":"2012-07-02"},"day":"01","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."}],"article_processing_charge":"No","doi":"10.4171/120-1/3","ddc":["000"],"date_updated":"2025-06-03T11:46:59Z","has_accepted_license":"1","month":"01","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.","oa":1,"oa_version":"Submitted Version","file_date_updated":"2020-07-14T12:45:52Z","pubrep_id":"544"},{"language":[{"iso":"eng"}],"title":"Induced matchings of barcodes and the algebraic stability of persistence","publication":"Proceedings of the Annual Symposium on Computational Geometry","type":"conference","year":"2014","citation":{"chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 355–64. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>.","apa":"Bauer, U., &#38; Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 355–364). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 355–364.","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 355–64, doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>.","ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:355-364. doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>","ista":"Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_created":"2018-12-11T11:56:01Z","quality_controlled":"1","scopus_import":"1","department":[{"_id":"HeEd"}],"arxiv":1,"page":"355 - 364","date_published":"2014-06-01T00:00:00Z","publist_id":"4853","ec_funded":1,"abstract":[{"text":"We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s).","lang":"eng"}],"article_processing_charge":"No","doi":"10.1145/2582112.2582168","external_id":{"arxiv":["1311.3681"]},"_id":"2153","author":[{"orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Lesnick","first_name":"Michael","full_name":"Lesnick, Michael"}],"publisher":"ACM","publication_status":"published","day":"01","conference":{"end_date":"2014-06-11","location":"Kyoto, Japan","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7"}],"oa_version":"Submitted Version","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.3681"}],"date_updated":"2025-06-11T07:57:54Z","month":"06"},{"project":[{"call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"day":"01","conference":{"end_date":"2014-06-11","location":"Kyoto, Japan","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry"},"_id":"2155","external_id":{"arxiv":["1312.1231"]},"publication_status":"published","author":[{"orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"publisher":"ACM","doi":"10.1145/2582112.2582167","abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s)."}],"article_processing_charge":"No","ec_funded":1,"month":"06","date_updated":"2025-06-11T07:58:27Z","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","main_file_link":[{"url":"http://arxiv.org/abs/1312.1231","open_access":"1"}],"oa":1,"oa_version":"Submitted Version","scopus_import":"1","quality_controlled":"1","date_created":"2018-12-11T11:56:01Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 484–90. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>.","ieee":"U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 484–490.","apa":"Bauer, U., &#38; Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 484–490). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>","ama":"Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. 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Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490."},"type":"conference","year":"2014","publication":"Proceedings of the Annual Symposium on Computational Geometry","corr_author":"1","title":"The morse theory of Čech and Delaunay filtrations","language":[{"iso":"eng"}],"publist_id":"4851","date_published":"2014-06-01T00:00:00Z","page":"484 - 490","arxiv":1,"department":[{"_id":"HeEd"}]}]