[{"publist_id":"6111","acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","year":"2016","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","author":[{"full_name":"Musin, Oleg","last_name":"Musin","first_name":"Oleg"},{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton"}],"volume":55,"date_updated":"2021-01-12T06:49:11Z","date_created":"2018-12-11T11:50:48Z","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1212.0649","open_access":"1"}],"oa":1,"quality_controlled":"1","doi":"10.1007/s00454-015-9742-6","language":[{"iso":"eng"}],"type":"journal_article","issue":"1","abstract":[{"text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs.","lang":"eng"}],"_id":"1222","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 55","status":"public","title":"Optimal packings of congruent circles on a square flat torus","oa_version":"Preprint","scopus_import":1,"day":"01","citation":{"ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6","ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer, pp. 1–20, 2016.","apa":"Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-015-9742-6","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.","short":"O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20.","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-015-9742-6."},"publication":"Discrete & Computational Geometry","page":"1 - 20","date_published":"2016-01-01T00:00:00Z"},{"ec_funded":1,"publist_id":"6096","author":[{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pilarczyk, Pawel","last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"volume":9667,"date_created":"2018-12-11T11:50:52Z","date_updated":"2021-01-12T06:49:18Z","acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","year":"2016","publisher":"Springer","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","month":"06","doi":"10.1007/978-3-319-39441-1_13","conference":{"start_date":"2016-06-15","location":"Marseille, France","end_date":"2016-06-17","name":"CTIC: Computational Topology in Image Context"},"language":[{"iso":"eng"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps"}],"quality_controlled":"1","abstract":[{"text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem.","lang":"eng"}],"type":"conference","alternative_title":["LNCS"],"oa_version":"None","_id":"1237","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 9667","status":"public","title":"Computation of cubical Steenrod squares","day":"02","scopus_import":1,"date_published":"2016-06-02T00:00:00Z","citation":{"short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","mla":"Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13.","ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13","apa":"Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13","ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151."},"page":"140 - 151"},{"oa_version":"Preprint","intvolume":" 144","status":"public","title":"Inducing a map on homology from a correspondence","_id":"1252","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"4","abstract":[{"text":"We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points.","lang":"eng"}],"type":"journal_article","date_published":"2016-04-01T00:00:00Z","page":"1787 - 1801","article_type":"original","citation":{"ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801. doi:10.1090/proc/12812","ista":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 144(4), 1787–1801.","apa":"Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/12812","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” Proceedings of the American Mathematical Society, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801.","chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812."},"publication":"Proceedings of the American Mathematical Society","article_processing_charge":"No","day":"01","scopus_import":"1","volume":144,"date_created":"2018-12-11T11:50:57Z","date_updated":"2022-05-24T09:35:58Z","author":[{"first_name":"Shaun","last_name":"Harker","full_name":"Harker, Shaun"},{"last_name":"Kokubu","first_name":"Hiroshi","full_name":"Kokubu, Hiroshi"},{"last_name":"Mischaikow","first_name":"Konstantin","full_name":"Mischaikow, Konstantin"},{"last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"}],"publisher":"American Mathematical Society","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"The authors gratefully acknowledge the support of the Lorenz Center which\r\nprovided an opportunity for us to discuss in depth the work of this paper. Research leading to these results has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033 (supporting PP). The work of the first and third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019, 1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029), Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan.","year":"2016","ec_funded":1,"publist_id":"6075","language":[{"iso":"eng"}],"doi":"10.1090/proc/12812","project":[{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps"}],"quality_controlled":"1","external_id":{"arxiv":["1411.7563"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1411.7563"}],"publication_identifier":{"issn":["1088-6826"]},"month":"04"},{"date_published":"2016-04-02T00:00:00Z","page":"116 - 124","citation":{"ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124. doi:10.1080/10586458.2015.1048011","apa":"Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” Experimental Mathematics, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.","ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124.","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124.","mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.","chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics. Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011."},"publication":"Experimental Mathematics","day":"02","scopus_import":1,"oa_version":"Preprint","intvolume":" 25","status":"public","title":"Uniform expansivity outside a critical neighborhood in the quadratic family","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1254","issue":"2","abstract":[{"lang":"eng","text":"We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critical neighborhood outside which the map is uniformly expanding. This radius is taken as small as possible, yet large enough for our numerical procedure to succeed in proving that the expansivity exponent outside this neighborhood is positive. Then, for each of the intervals, we compute a lower bound for this expansivity exponent, valid for all the parameters in that interval. We illustrate and study the distribution of the radii and the expansivity exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1080/10586458.2015.1048011","project":[{"call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033"}],"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1504.00116","open_access":"1"}],"oa":1,"month":"04","volume":25,"date_created":"2018-12-11T11:50:58Z","date_updated":"2021-01-12T06:49:25Z","author":[{"full_name":"Golmakani, Ali","first_name":"Ali","last_name":"Golmakani"},{"first_name":"Stefano","last_name":"Luzzatto","full_name":"Luzzatto, Stefano"},{"full_name":"Pilarczyk, Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","last_name":"Pilarczyk"}],"publisher":"Taylor and Francis","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"AG and PP were partially supported by Abdus Salam International Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS, and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics of Kyoto University for providing access\r\nto their server for conducting computations for this\r\nproject.","year":"2016","publist_id":"6071","ec_funded":1},{"abstract":[{"text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams.","lang":"eng"}],"issue":"5","type":"journal_article","file":[{"checksum":"c746f3a48edb62b588d92ea5d0fd2c0e","date_created":"2018-12-12T10:16:20Z","date_updated":"2020-07-14T12:44:42Z","relation":"main_file","file_id":"5206","content_type":"application/pdf","file_size":1678369,"creator":"system","access_level":"open_access","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf"}],"oa_version":"Published Version","pubrep_id":"694","ddc":["004","516"],"status":"public","title":"Generalized offsetting of planar structures using skeletons","intvolume":" 13","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1272","day":"02","has_accepted_license":"1","scopus_import":1,"date_published":"2016-09-02T00:00:00Z","page":"712 - 721","publication":"Computer-Aided Design and Applications","citation":{"ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721. doi:10.1080/16864360.2016.1150718","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” Computer-Aided Design and Applications, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","apa":"Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721.","short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.","chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications. Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718."},"file_date_updated":"2020-07-14T12:44:42Z","publist_id":"6048","date_updated":"2021-01-12T06:49:32Z","date_created":"2018-12-11T11:51:04Z","volume":13,"author":[{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"full_name":"Huber, Stefan","first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"publication_status":"published","publisher":"Taylor and Francis","department":[{"_id":"HeEd"}],"year":"2016","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","month":"09","language":[{"iso":"eng"}],"doi":"10.1080/16864360.2016.1150718","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1},{"abstract":[{"lang":"eng","text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls."}],"publist_id":"5976","ec_funded":1,"type":"journal_article","date_updated":"2021-01-12T06:49:41Z","date_created":"2018-12-11T11:51:12Z","oa_version":"None","volume":54,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"}],"publication_status":"published","title":"Multiple covers with balls II: Weighted averages","status":"public","department":[{"_id":"HeEd"}],"publisher":"Elsevier","intvolume":" 54","_id":"1295","year":"2016","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"01","month":"10","scopus_import":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.endm.2016.09.030","date_published":"2016-10-01T00:00:00Z","quality_controlled":"1","page":"169 - 174","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"publication":"Electronic Notes in Discrete Mathematics","citation":{"apa":"Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2016.09.030","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier, pp. 169–174, 2016.","ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.endm.2016.09.030.","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol. 54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030."}},{"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.00794"}],"quality_controlled":"1","doi":"10.1007/s10474-016-0648-4","language":[{"iso":"eng"}],"month":"12","year":"2016","acknowledgement":"The authors are veryg rateful to Hansj ̈org Geiges \r\nfor fruitful discussions and advice and Christian Evers for helpful remarks on a draft version.","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","author":[{"full_name":"Durst, Sebastian","first_name":"Sebastian","last_name":"Durst"},{"full_name":"Kegel, Marc","first_name":"Marc","last_name":"Kegel"},{"id":"34927512-F248-11E8-B48F-1D18A9856A87","last_name":"Klukas","first_name":"Mirko D","full_name":"Klukas, Mirko D"}],"volume":150,"date_created":"2018-12-11T11:51:11Z","date_updated":"2021-01-12T06:49:40Z","publist_id":"6023","citation":{"ama":"Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4","apa":"Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4","ieee":"S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer, pp. 441–455, 2016.","ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","short":"S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455.","mla":"Durst, Sebastian, et al. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica, vol. 150, no. 2, Springer, 2016, pp. 441–55, doi:10.1007/s10474-016-0648-4.","chicago":"Durst, Sebastian, Marc Kegel, and Mirko D Klukas. “Computing the Thurston–Bennequin Invariant in Open Books.” Acta Mathematica Hungarica. Springer, 2016. https://doi.org/10.1007/s10474-016-0648-4."},"publication":"Acta Mathematica Hungarica","page":"441 - 455","date_published":"2016-12-01T00:00:00Z","scopus_import":1,"day":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1292","intvolume":" 150","title":"Computing the Thurston–Bennequin invariant in open books","status":"public","oa_version":"Preprint","type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds."}]},{"citation":{"ama":"Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z","ieee":"A. Akopyan and A. Balitskiy, “Billiards in convex bodies with acute angles,” Israel Journal of Mathematics, vol. 216, no. 2. Springer, pp. 833–845, 2016.","apa":"Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.","mla":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:10.1007/s11856-016-1429-z.","chicago":"Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z."},"publication":"Israel Journal of Mathematics","page":"833 - 845","date_published":"2016-10-15T00:00:00Z","scopus_import":1,"day":"15","_id":"1330","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 216","status":"public","title":"Billiards in convex bodies with acute angles","oa_version":"Preprint","type":"journal_article","issue":"2","abstract":[{"text":"In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}],"oa":1,"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","doi":"10.1007/s11856-016-1429-z","language":[{"iso":"eng"}],"month":"10","year":"2016","acknowledgement":"Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734]. Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"last_name":"Balitskiy","first_name":"Alexey","full_name":"Balitskiy, Alexey"}],"volume":216,"date_created":"2018-12-11T11:51:24Z","date_updated":"2021-01-12T06:49:56Z","ec_funded":1,"publist_id":"5938"},{"ec_funded":1,"publist_id":"5885","year":"2016","acknowledgement":"The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved).","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexey","last_name":"Balitskiy","full_name":"Balitskiy, Alexey"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"},{"full_name":"Sharipova, Anastasia","last_name":"Sharipova","first_name":"Anastasia"}],"date_updated":"2021-01-12T06:50:09Z","date_created":"2018-12-11T11:51:34Z","volume":144,"month":"10","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1401.0442"}],"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"doi":"10.1090/proc/13062","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"text":"We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. ","lang":"eng"}],"issue":"10","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1360","status":"public","title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","intvolume":" 144","oa_version":"Preprint","scopus_import":1,"day":"01","article_processing_charge":"No","publication":"Proceedings of the American Mathematical Society","citation":{"apa":"Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13062","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016.","ista":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062","chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062.","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” Proceedings of the American Mathematical Society, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062."},"page":"4501 - 4513","date_published":"2016-10-01T00:00:00Z"},{"month":"07","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"name":"Robust invariants of Nonlinear Systems","call_identifier":"FWF","grant_number":"M01980","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425"},{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"doi":"10.1007/s00454-016-9794-2","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:44:53Z","ec_funded":1,"publist_id":"5799","year":"2016","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"Springer","author":[{"full_name":"Franek, Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","last_name":"Franek","first_name":"Peter"},{"full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"1510"}]},"date_created":"2018-12-11T11:51:51Z","date_updated":"2023-02-23T10:02:11Z","volume":56,"scopus_import":1,"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","publication":"Discrete & Computational Geometry","citation":{"ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” Discrete & Computational Geometry, vol. 56, no. 1. Springer, pp. 126–164, 2016.","apa":"Franek, P., & Krcál, M. (2016). On computability and triviality of well groups. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-016-9794-2","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164.","ama":"Franek P, Krcál M. On computability and triviality of well groups. Discrete & Computational Geometry. 2016;56(1):126-164. doi:10.1007/s00454-016-9794-2","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-016-9794-2.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2."},"page":"126 - 164","date_published":"2016-07-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status."}],"issue":"1","_id":"1408","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"On computability and triviality of well groups","ddc":["510"],"intvolume":" 56","pubrep_id":"614","file":[{"file_id":"4846","relation":"main_file","date_updated":"2020-07-14T12:44:53Z","date_created":"2018-12-12T10:10:55Z","checksum":"e0da023abf6b72abd8c6a8c76740d53c","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","access_level":"open_access","creator":"system","file_size":905303,"content_type":"application/pdf"}],"oa_version":"Published Version"},{"publist_id":"6027","file_date_updated":"2020-07-14T12:44:42Z","related_material":{"record":[{"id":"1568","relation":"earlier_version","status":"public"}]},"author":[{"full_name":"Dunaeva, Olga","last_name":"Dunaeva","first_name":"Olga"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Lukyanov","first_name":"Anton","full_name":"Lukyanov, Anton"},{"last_name":"Machin","first_name":"Michael","full_name":"Machin, Michael"},{"last_name":"Malkova","first_name":"Daria","full_name":"Malkova, Daria"},{"first_name":"Roman","last_name":"Kuvaev","full_name":"Kuvaev, Roman"},{"full_name":"Kashin, Sergey","last_name":"Kashin","first_name":"Sergey"}],"volume":83,"date_updated":"2023-02-23T10:04:40Z","date_created":"2018-12-11T11:51:10Z","year":"2016","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","month":"11","doi":"10.1016/j.patrec.2015.12.012","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"quality_controlled":"1","issue":"1","abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI) magnifying endoscopic (ME) images of the stomach, we combine methods from image processing, topology, geometry, and machine learning to classify patterns into three classes: oval, tubular and irregular. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"type":"journal_article","pubrep_id":"975","file":[{"file_id":"6334","relation":"main_file","date_created":"2019-04-17T07:55:51Z","date_updated":"2020-07-14T12:44:42Z","checksum":"33458bbb8c32a339e1adeca6d5a1112d","file_name":"2016-Edelsbrunner_The_classification.pdf","access_level":"open_access","creator":"dernst","file_size":1921113,"content_type":"application/pdf"}],"oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1289","intvolume":" 83","status":"public","ddc":["004","514"],"title":"The classification of endoscopy images with persistent homology","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":1,"date_published":"2016-11-01T00:00:00Z","citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria Malkova, Roman Kuvaev, and Sergey Kashin. “The Classification of Endoscopy Images with Persistent Homology.” Pattern Recognition Letters. Elsevier, 2016. https://doi.org/10.1016/j.patrec.2015.12.012.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Pattern Recognition Letters, vol. 83, no. 1, Elsevier, 2016, pp. 13–22, doi:10.1016/j.patrec.2015.12.012.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., Malkova, D., Kuvaev, R., & Kashin, S. (2016). The classification of endoscopy images with persistent homology. Pattern Recognition Letters. Elsevier. https://doi.org/10.1016/j.patrec.2015.12.012","ieee":"O. Dunaeva et al., “The classification of endoscopy images with persistent homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22, 2016.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin S. 2016. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 83(1), 13–22.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, et al. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 2016;83(1):13-22. doi:10.1016/j.patrec.2015.12.012"},"publication":"Pattern Recognition Letters","page":"13 - 22"},{"month":"04","day":"01","scopus_import":1,"doi":"10.1016/j.jco.2015.11.003","date_published":"2016-04-01T00:00:00Z","language":[{"iso":"eng"}],"citation":{"short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216, doi:10.1016/j.jco.2015.11.003.","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity. Academic Press, 2016. https://doi.org/10.1016/j.jco.2015.11.003.","ama":"Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003","apa":"Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003","ieee":"F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.","ista":"Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216."},"main_file_link":[{"url":"http://arxiv.org/abs/1510.00251","open_access":"1"}],"oa":1,"publication":"Journal of Complexity","page":"199 - 216","quality_controlled":"1","publist_id":"5549","abstract":[{"text":"We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of equal measure and placing a random point inside each of the N=md cubes. We prove that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d, where the upper bound with an unspecified constant Cd was proven earlier by Beck. Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality and a suitably taylored Bernstein inequality; we have reasons to believe that the upper bound has the sharp scaling in N. Additional heuristics suggest that jittered sampling should be able to improve known bounds on the inverse of the star-discrepancy in the regime N≳dd. We also prove a partition principle showing that every partition of [0,1]d combined with a jittered sampling construction gives rise to a set whose expected squared L2-discrepancy is smaller than that of purely random points.","lang":"eng"}],"type":"journal_article","author":[{"first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian"},{"last_name":"Steinerberger","first_name":"Stefan","full_name":"Steinerberger, Stefan"}],"volume":33,"oa_version":"Submitted Version","date_created":"2018-12-11T11:53:03Z","date_updated":"2021-01-12T06:52:02Z","_id":"1617","acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2016","intvolume":" 33","publisher":"Academic Press","department":[{"_id":"HeEd"}],"title":"On the discrepancy of jittered sampling","publication_status":"published","status":"public"},{"day":"09","article_processing_charge":"No","publication":"Discrete Geometry for Computer Imagery","citation":{"chicago":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20.","mla":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.","short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267.","ista":"Biswas R, Bhowmick P. 2016. On functionality of quadraginta octants of naive sphere with application to circle drawing. Discrete Geometry for Computer Imagery. DGCI: International Conference on Discrete Geometry for Computer Imagery, LNCS, vol. 9647, 256–267.","ieee":"R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive sphere with application to circle drawing,” in Discrete Geometry for Computer Imagery, Nantes, France, 2016, vol. 9647, pp. 256–267.","apa":"Biswas, R., & Bhowmick, P. (2016). On functionality of quadraginta octants of naive sphere with application to circle drawing. In Discrete Geometry for Computer Imagery (Vol. 9647, pp. 256–267). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-32360-2_20","ama":"Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere with application to circle drawing. In: Discrete Geometry for Computer Imagery. Vol 9647. Cham: Springer Nature; 2016:256-267. doi:10.1007/978-3-319-32360-2_20"},"page":"256-267","date_published":"2016-04-09T00:00:00Z","type":"conference","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane."}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"5806","title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","status":"public","intvolume":" 9647","oa_version":"None","month":"04","publication_identifier":{"isbn":["978-3-319-32359-6"],"issn":["0302-9743","1611-3349"],"eisbn":["978-3-319-32360-2"]},"quality_controlled":"1","conference":{"start_date":"2016-04-18","location":"Nantes, France","end_date":"2016-04-20","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery"},"doi":"10.1007/978-3-319-32360-2_20","language":[{"iso":"eng"}],"place":"Cham","extern":"1","year":"2016","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita"},{"first_name":"Partha","last_name":"Bhowmick","full_name":"Bhowmick, Partha"}],"date_updated":"2022-01-28T08:10:11Z","date_created":"2019-01-08T20:44:37Z","volume":9647},{"abstract":[{"text":"Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy.","lang":"eng"}],"alternative_title":["LNCS"],"type":"book_chapter","oa_version":"None","status":"public","title":"On some local topological properties of naive discrete sphere","intvolume":" 9667","_id":"5805","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","day":"02","article_processing_charge":"No","date_published":"2016-06-02T00:00:00Z","page":"253-264","publication":"Computational Topology in Image Context","citation":{"chicago":"Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In Computational Topology in Image Context, 9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.","mla":"Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264.","ista":"Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.","ieee":"N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties of naive discrete sphere,” in Computational Topology in Image Context, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.","apa":"Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In Computational Topology in Image Context (Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23","ama":"Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23"},"extern":"1","place":"Cham","date_updated":"2022-01-28T08:01:22Z","date_created":"2019-01-08T20:44:24Z","volume":9667,"author":[{"full_name":"Sen, Nabhasmita","first_name":"Nabhasmita","last_name":"Sen"},{"full_name":"Biswas, Ranita","last_name":"Biswas","first_name":"Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"}],"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"year":"2016","month":"06","publication_identifier":{"eisbn":["978-3-319-39441-1"],"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["978-3-319-39440-4"]},"language":[{"iso":"eng"}],"conference":{"name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15","location":"Marseille, France","end_date":"2016-06-17"},"doi":"10.1007/978-3-319-39441-1_23","quality_controlled":"1"},{"type":"book_chapter","place":"Cham","abstract":[{"lang":"eng","text":"A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness."}],"extern":"1","_id":"5809","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","year":"2016","department":[{"_id":"HeEd"}],"intvolume":" 9448","publisher":"Springer Nature","title":"On the connectivity and smoothness of discrete spherical circles","status":"public","publication_status":"published","author":[{"full_name":"Biswas, Ranita","first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"},{"full_name":"Brimkov, Valentin E.","first_name":"Valentin E.","last_name":"Brimkov"}],"volume":9448,"oa_version":"None","date_updated":"2022-01-28T08:13:03Z","date_created":"2019-01-08T20:45:19Z","article_processing_charge":"No","publication_identifier":{"isbn":["978-3-319-26144-7"],"eissn":["1611-3349"],"eisbn":["978-3-319-26145-4"],"issn":["0302-9743"]},"month":"01","day":"06","citation":{"chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis, 9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100.","mla":"Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:10.1007/978-3-319-26145-4_7.","apa":"Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In Combinatorial image analysis (Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.","ista":"Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.","ama":"Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7"},"publication":"Combinatorial image analysis","page":"86-100","quality_controlled":"1","date_published":"2016-01-06T00:00:00Z","doi":"10.1007/978-3-319-26145-4_7","conference":{"start_date":"2015-11-24","location":"Kolkata, India","end_date":"2015-11-27","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"language":[{"iso":"eng"}]},{"doi":"10.1016/j.aim.2015.10.004","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1,"quality_controlled":"1","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"month":"01","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Pausinger, Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger","first_name":"Florian"}],"related_material":{"record":[{"id":"1399","status":"public","relation":"dissertation_contains"}]},"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:53:20Z","volume":287,"acknowledgement":"This research is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne Marie Svane for her comments on an early version of this paper. The second author wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for enlightening discussions and their kind hospitality during a visit of their department in 2014.","year":"2016","publication_status":"published","publisher":"Academic Press","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:45:10Z","publist_id":"5488","ec_funded":1,"date_published":"2016-01-10T00:00:00Z","publication":"Advances in Mathematics","citation":{"ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","apa":"Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004","ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016.","ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703."},"page":"674 - 703","day":"10","has_accepted_license":"1","scopus_import":1,"pubrep_id":"774","file":[{"file_size":248985,"content_type":"application/pdf","creator":"system","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","access_level":"open_access","date_created":"2018-12-12T10:12:10Z","date_updated":"2020-07-14T12:45:10Z","checksum":"f8869ec110c35c852ef6a37425374af7","relation":"main_file","file_id":"4928"}],"oa_version":"Published Version","_id":"1662","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","title":"Approximation and convergence of the intrinsic volume","status":"public","ddc":["004"],"intvolume":" 287","abstract":[{"text":"We introduce a modification of the classic notion of intrinsic volume using persistence moments of height functions. Evaluating the modified first intrinsic volume on digital approximations of a compact body with smoothly embedded boundary in Rn, we prove convergence to the first intrinsic volume of the body as the resolution of the approximation improves. We have weaker results for the other modified intrinsic volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional unit ball.","lang":"eng"}],"type":"journal_article"},{"day":"01","month":"12","main_file_link":[{"open_access":"1","url":"https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective"}],"oa":1,"citation":{"chicago":"Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems, 2015.","mla":"Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective. Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78.","short":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems, 2015, pp. 3070–3078.","ista":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078.","ieee":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.","apa":"Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems.","ama":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems; 2015:3070-3078."},"quality_controlled":"1","page":"3070 - 3078","conference":{"location":"Montreal, Canada","start_date":"2015-12-07","end_date":"2015-12-12","name":"NIPS: Neural Information Processing Systems"},"date_published":"2015-12-01T00:00:00Z","language":[{"iso":"eng"}],"type":"conference","alternative_title":["Advances in Neural Information Processing Systems"],"abstract":[{"text":"We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data.","lang":"eng"}],"publist_id":"5782","_id":"1424","year":"2015","acknowledgement":"This work was partially supported by the Austrian Science FUnd, project no. KLI 00012.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_status":"published","title":"Statistical topological data analysis-A kernel perspective","intvolume":" 28","department":[{"_id":"HeEd"}],"publisher":"Neural Information Processing Systems","author":[{"full_name":"Kwitt, Roland","last_name":"Kwitt","first_name":"Roland"},{"full_name":"Huber, Stefan","first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"},{"first_name":"Marc","last_name":"Niethammer","full_name":"Niethammer, Marc"},{"last_name":"Lin","first_name":"Weili","full_name":"Lin, Weili"},{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich"}],"date_updated":"2021-01-12T06:50:38Z","date_created":"2018-12-11T11:51:56Z","oa_version":"Submitted Version","volume":28},{"month":"10","day":"14","publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"scopus_import":1,"language":[{"iso":"eng"}],"conference":{"name":"CVPR: Computer Vision and Pattern Recognition","start_date":"2015-06-07","location":"Boston, MA, USA","end_date":"2015-06-12"},"doi":"10.1109/CVPR.2015.7299106","date_published":"2015-10-14T00:00:00Z","page":"4741 - 4748","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"citation":{"ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106","ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","apa":"Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106","mla":"Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106."},"oa":1,"abstract":[{"text":"Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.","lang":"eng"}],"publist_id":"5709","type":"conference","date_updated":"2021-01-12T06:51:03Z","date_created":"2018-12-11T11:52:17Z","oa_version":"Preprint","author":[{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"first_name":"Roland","last_name":"Kwitt","full_name":"Kwitt, Roland"}],"publication_status":"published","title":"A stable multi-scale kernel for topological machine learning","status":"public","publisher":"IEEE","department":[{"_id":"HeEd"}],"_id":"1483","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015"},{"type":"conference","abstract":[{"text":"Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. ","lang":"eng"}],"publist_id":"5684","ec_funded":1,"status":"public","publication_status":"published","title":"Relaxed disk packing","department":[{"_id":"HeEd"}],"publisher":"Queen's University","_id":"1495","year":"2015","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:51:09Z","date_created":"2018-12-11T11:52:21Z","oa_version":"Submitted Version","volume":"2015-August","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel"},{"full_name":"Kurlin, Vitaliy","last_name":"Kurlin","first_name":"Vitaliy"}],"scopus_import":1,"day":"01","month":"08","quality_controlled":"1","page":"128-135","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","citation":{"ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings of the 27th Canadian Conference on Computational Geometry. Vol 2015-August. Queen’s University; 2015:128-135.","ista":"Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135.","ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in Proceedings of the 27th Canadian Conference on Computational Geometry, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","apa":"Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk packing. In Proceedings of the 27th Canadian Conference on Computational Geometry (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.","mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the 27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s University, 2015, pp. 128–35.","short":"H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational Geometry, 2015–August:128–35. Queen’s University, 2015."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1505.03402"}],"oa":1,"language":[{"iso":"eng"}],"conference":{"start_date":"2015-08-10","location":"Ontario, Canada","end_date":"2015-08-12","name":"CCCG: Canadian Conference on Computational Geometry"},"date_published":"2015-08-01T00:00:00Z"},{"year":"2015","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","related_material":{"record":[{"id":"1408","relation":"later_version","status":"public"}]},"author":[{"first_name":"Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"volume":34,"date_updated":"2023-02-21T17:02:57Z","date_created":"2018-12-11T11:52:26Z","publist_id":"5667","ec_funded":1,"file_date_updated":"2020-07-14T12:44:59Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1","doi":"10.4230/LIPIcs.SOCG.2015.842","conference":{"location":"Eindhoven, Netherlands","start_date":"2015-06-22","end_date":"2015-06-25","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"month":"06","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1510","intvolume":" 34","ddc":["510"],"title":"On computability and triviality of well groups","status":"public","pubrep_id":"503","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"IST-2016-503-v1+1_32.pdf","content_type":"application/pdf","file_size":623563,"creator":"system","relation":"main_file","file_id":"5001","checksum":"49eb5021caafaabe5356c65b9c5f8c9c","date_created":"2018-12-12T10:13:19Z","date_updated":"2020-07-14T12:44:59Z"}],"type":"conference","alternative_title":["LIPIcs"],"abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r > 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. ","lang":"eng"}],"citation":{"apa":"Franek, P., & Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SOCG.2015.842","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856.","ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856.","mla":"Franek, Peter, and Marek Krcál. On Computability and Triviality of Well Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842."},"page":"842 - 856","date_published":"2015-06-11T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"11"},{"abstract":[{"lang":"eng","text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece."}],"type":"book_chapter","alternative_title":["Mathematics and Visualization"],"oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1531","intvolume":" 40","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","status":"public","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2015-01-01T00:00:00Z","citation":{"ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40. 1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13","ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13."},"publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","page":"257 - 267","publist_id":"5640","edition":"1","author":[{"full_name":"Zobel, Valentin","last_name":"Zobel","first_name":"Valentin"},{"first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"}],"volume":40,"date_created":"2018-12-11T11:52:33Z","date_updated":"2022-06-10T09:50:14Z","year":"2015","department":[{"_id":"HeEd"}],"editor":[{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"last_name":"Schultz","first_name":"Thomas","full_name":"Schultz, Thomas"}],"publisher":"Springer","publication_status":"published","publication_identifier":{"isbn":["978-3-319-15089-5"]},"month":"01","doi":"10.1007/978-3-319-15090-1_13","language":[{"iso":"eng"}],"quality_controlled":"1"},{"article_type":"original","page":"980 - 1017","publication":"SIAM Journal on Applied Dynamical Systems","citation":{"chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934.","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","mla":"Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.","apa":"Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934","ista":"Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.","ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017. doi:10.1137/140993934"},"date_published":"2015-01-01T00:00:00Z","scopus_import":1,"day":"01","article_processing_charge":"No","title":"Rich bifurcation structure in a two patch vaccination model","ddc":["510"],"status":"public","intvolume":" 14","_id":"1555","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","type":"journal_article","abstract":[{"text":"We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations.","lang":"eng"}],"issue":"2","quality_controlled":"1","project":[{"name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7","grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf"}],"language":[{"iso":"eng"}],"doi":"10.1137/140993934","month":"01","publication_identifier":{"eissn":["1536-0040"]},"publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"year":"2015","acknowledgement":"Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project.","date_created":"2018-12-11T11:52:42Z","date_updated":"2021-01-12T06:51:34Z","volume":14,"author":[{"last_name":"Knipl","first_name":"Diána","full_name":"Knipl, Diána"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"},{"full_name":"Röst, Gergely","first_name":"Gergely","last_name":"Röst"}],"publist_id":"5616","ec_funded":1},{"language":[{"iso":"eng"}],"conference":{"name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing","location":"Timisoara, Romania","start_date":"2014-09-22","end_date":"2014-09-25"},"doi":"10.1109/SYNASC.2014.81","date_published":"2015-02-05T00:00:00Z","quality_controlled":"1","page":"7034731","publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D. (2015). The classification of endoscopy images with persistent homology. In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2015, p. 7034731.","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE; 2015:7034731. doi:10.1109/SYNASC.2014.81"},"day":"05","month":"02","scopus_import":1,"date_created":"2018-12-11T11:52:46Z","date_updated":"2023-02-21T16:57:29Z","oa_version":"None","author":[{"full_name":"Dunaeva, Olga","last_name":"Dunaeva","first_name":"Olga"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anton","last_name":"Lukyanov","full_name":"Lukyanov, Anton"},{"first_name":"Michael","last_name":"Machin","full_name":"Machin, Michael"},{"first_name":"Daria","last_name":"Malkova","full_name":"Malkova, Daria"}],"related_material":{"record":[{"relation":"later_version","status":"public","id":"1289"}]},"status":"public","title":"The classification of endoscopy images with persistent homology","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"IEEE","_id":"1568","year":"2015","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","abstract":[{"lang":"eng","text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions."}],"publist_id":"5603","type":"conference"},{"scopus_import":"1","article_processing_charge":"No","day":"01","month":"01","citation":{"apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.","ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.","chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd International Symposium, vol. 9411, Springer Nature, 2015."},"publication":"23rd International Symposium","quality_controlled":"1","date_published":"2015-01-01T00:00:00Z","conference":{"name":"GD: Graph Drawing and Network Visualization","end_date":"2015-09-26","start_date":"2015-09-24","location":"Los Angeles, CA, United States"},"language":[{"iso":"eng"}],"type":"conference","alternative_title":["LNCS"],"publist_id":"5604","abstract":[{"text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations.","lang":"eng"}],"_id":"1567","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","year":"2015","intvolume":" 9411","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"status":"public","publication_status":"published","title":"Shape, homology, persistence, and stability","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"oa_version":"None","volume":9411,"date_updated":"2022-01-28T08:25:00Z","date_created":"2018-12-11T11:52:46Z"},{"department":[{"_id":"HeEd"}],"publisher":"Juliusz Schauder Center for Nonlinear Studies","intvolume":" 45","status":"public","publication_status":"published","title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","_id":"1563","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","oa_version":"None","volume":45,"date_created":"2018-12-11T11:52:44Z","date_updated":"2021-01-12T06:51:37Z","author":[{"full_name":"Graff, Grzegorz","first_name":"Grzegorz","last_name":"Graff"},{"last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"}],"type":"journal_article","issue":"1","publist_id":"5608","abstract":[{"text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}.","lang":"eng"}],"page":"273 - 286","quality_controlled":"1","citation":{"ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286.","apa":"Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014","chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286."},"publication":"Topological Methods in Nonlinear Analysis","language":[{"iso":"eng"}],"doi":"10.12775/TMNA.2015.014","date_published":"2015-03-01T00:00:00Z","scopus_import":1,"day":"01","month":"03"},{"scopus_import":1,"month":"08","day":"01","citation":{"mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:10.1016/j.comgeo.2015.04.001.","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” Computational Geometry. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.04.001.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 2015;48(7):507-519. doi:10.1016/j.comgeo.2015.04.001","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” Computational Geometry, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","apa":"Cao, T., Edelsbrunner, H., & Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. Elsevier. https://doi.org/10.1016/j.comgeo.2015.04.001"},"publication":"Computational Geometry","page":"507 - 519","quality_controlled":"1","date_published":"2015-08-01T00:00:00Z","doi":"10.1016/j.comgeo.2015.04.001","language":[{"iso":"eng"}],"type":"journal_article","issue":"7","publist_id":"5593","abstract":[{"lang":"eng","text":"We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations."}],"year":"2015","_id":"1578","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n","publisher":"Elsevier","department":[{"_id":"HeEd"}],"intvolume":" 48","status":"public","publication_status":"published","title":"Triangulations from topologically correct digital Voronoi diagrams","author":[{"full_name":"Cao, Thanhtung","last_name":"Cao","first_name":"Thanhtung"},{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Tan, Tiowseng","first_name":"Tiowseng","last_name":"Tan"}],"volume":48,"oa_version":"None","date_updated":"2021-01-12T06:51:43Z","date_created":"2018-12-11T11:52:49Z"},{"file_date_updated":"2020-07-14T12:45:03Z","publist_id":"5587","year":"2015","publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan"},{"first_name":"Dominik","last_name":"Kaaser","full_name":"Kaaser, Dominik"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"related_material":{"record":[{"id":"1582","status":"public","relation":"other"}]},"date_updated":"2023-02-23T10:05:22Z","date_created":"2018-12-11T11:52:51Z","volume":48,"month":"07","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.1016/j.comgeo.2015.01.004","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"lang":"eng","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."}],"issue":"5","_id":"1584","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"title":"Reprint of: Weighted straight skeletons in the plane","status":"public","intvolume":" 48","pubrep_id":"475","file":[{"file_id":"5292","relation":"main_file","date_updated":"2020-07-14T12:45:03Z","date_created":"2018-12-12T10:17:36Z","checksum":"5b33719a86f7f4c8e5dc62c1b6893f49","file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf","access_level":"open_access","creator":"system","content_type":"application/pdf","file_size":508379}],"oa_version":"Published Version","scopus_import":1,"day":"01","has_accepted_license":"1","publication":"Computational Geometry: Theory and Applications","citation":{"ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(5):429-442. doi:10.1016/j.comgeo.2015.01.004","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.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2015.01.004","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.","mla":"Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:10.1016/j.comgeo.2015.01.004.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2015.01.004."},"page":"429 - 442","date_published":"2015-07-01T00:00:00Z"},{"citation":{"ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 2015;48(2):120-133. doi:10.1016/j.comgeo.2014.08.006","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(2), 120–133.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” Computational Geometry: Theory and Applications, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.006","mla":"Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:10.1016/j.comgeo.2014.08.006.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.006."},"publication":"Computational Geometry: Theory and Applications","page":"120 - 133","date_published":"2015-02-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1582","intvolume":" 48","status":"public","ddc":["000"],"title":"Weighted straight skeletons in the plane","pubrep_id":"474","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":505987,"creator":"system","access_level":"open_access","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf","checksum":"c1ef67f6ec925e12f73a96b8fe285ab4","date_created":"2018-12-12T10:16:28Z","date_updated":"2020-07-14T12:45:02Z","relation":"main_file","file_id":"5215"}],"type":"journal_article","issue":"2","abstract":[{"lang":"eng","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."}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.1016/j.comgeo.2014.08.006","language":[{"iso":"eng"}],"month":"02","year":"2015","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","related_material":{"record":[{"id":"1584","status":"public","relation":"other"}]},"author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan"},{"full_name":"Kaaser, Dominik","last_name":"Kaaser","first_name":"Dominik"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"volume":48,"date_updated":"2023-02-23T10:05:27Z","date_created":"2018-12-11T11:52:51Z","publist_id":"5589","file_date_updated":"2020-07-14T12:45:02Z"},{"oa_version":"Published Version","file":[{"file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","access_level":"open_access","file_size":270137,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5367","date_updated":"2020-07-14T12:45:03Z","date_created":"2018-12-12T10:18:45Z","checksum":"2779a648610c9b5c86d0b51a62816d23"}],"pubrep_id":"473","title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","status":"public","ddc":["000"],"intvolume":" 115","_id":"1583","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon."}],"issue":"2","type":"journal_article","date_published":"2015-02-01T00:00:00Z","page":"243 - 247","publication":"Information Processing Letters","citation":{"ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 115(2), 243–247.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., & Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2014.09.021","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” Information Processing Letters, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. Information Processing Letters. 2015;115(2):243-247. doi:10.1016/j.ipl.2014.09.021","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters. Elsevier, 2015. https://doi.org/10.1016/j.ipl.2014.09.021.","mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” Information Processing Letters, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:10.1016/j.ipl.2014.09.021.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247."},"day":"01","has_accepted_license":"1","scopus_import":1,"date_updated":"2021-01-12T06:51:45Z","date_created":"2018-12-11T11:52:51Z","volume":115,"author":[{"last_name":"Biedl","first_name":"Therese","full_name":"Biedl, Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"full_name":"Palfrader, Peter","first_name":"Peter","last_name":"Palfrader"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","year":"2015","file_date_updated":"2020-07-14T12:45:03Z","publist_id":"5588","language":[{"iso":"eng"}],"doi":"10.1016/j.ipl.2014.09.021","quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"month":"02"},{"publist_id":"5581","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2015","volume":9411,"date_created":"2018-12-11T11:52:54Z","date_updated":"2022-01-28T09:10:37Z","author":[{"full_name":"Aichholzer, Oswin","first_name":"Oswin","last_name":"Aichholzer"},{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"last_name":"Hackl","first_name":"Thomas","full_name":"Hackl, Thomas"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","last_name":"Huber","first_name":"Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"publication_identifier":{"isbn":["978-3-319-27260-3"],"eisbn":["978-3-319-27261-0"]},"month":"11","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.01076"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-27261-0_28","conference":{"location":"Los Angeles, CA, United States","start_date":"2015-09-24","end_date":"2015-09-26","name":"GD: International Symposium on Graph Drawing"},"alternative_title":["LNCS"],"type":"book_chapter","abstract":[{"lang":"eng","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."}],"intvolume":" 9411","status":"public","title":"Representing directed trees as straight skeletons","_id":"1590","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"27","page":"335 - 347","citation":{"ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28","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.","ieee":"O. Aichholzer et al., “Representing directed trees as straight skeletons,” in Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–347.","apa":"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 (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28","mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:10.1007/978-3-319-27261-0_28.","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 Graph Drawing and Network Visualization, 9411:335–47. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28."},"publication":"Graph Drawing and Network Visualization","date_published":"2015-11-27T00:00:00Z"},{"year":"2015","_id":"1682","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"ACM","intvolume":" 62","status":"public","title":"Robust satisfiability of systems of equations","publication_status":"published","author":[{"full_name":"Franek, Peter","last_name":"Franek","first_name":"Peter"},{"first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"}],"volume":62,"oa_version":"Preprint","date_created":"2018-12-11T11:53:27Z","date_updated":"2021-01-12T06:52:30Z","type":"journal_article","article_number":"26","publist_id":"5466","issue":"4","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 > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < 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 > 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"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}],"citation":{"short":"P. Franek, M. Krcál, Journal of the ACM 62 (2015).","mla":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM, vol. 62, no. 4, 26, ACM, 2015, doi:10.1145/2751524.","chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” Journal of the ACM. ACM, 2015. https://doi.org/10.1145/2751524.","ama":"Franek P, Krcál M. Robust satisfiability of systems of equations. Journal of the ACM. 2015;62(4). doi:10.1145/2751524","apa":"Franek, P., & Krcál, M. (2015). Robust satisfiability of systems of equations. Journal of the ACM. ACM. https://doi.org/10.1145/2751524","ieee":"P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” Journal of the ACM, vol. 62, no. 4. ACM, 2015.","ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26."},"publication":"Journal of the ACM","quality_controlled":"1","date_published":"2015-08-01T00:00:00Z","doi":"10.1145/2751524","language":[{"iso":"eng"}],"scopus_import":1,"month":"08","day":"01"},{"month":"07","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1410.3736"}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"quality_controlled":"1","doi":"10.1137/140993843","language":[{"iso":"eng"}],"ec_funded":1,"publist_id":"5423","year":"2015","department":[{"_id":"HeEd"}],"publisher":"SIAM","publication_status":"published","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Plakhov, Alexander","first_name":"Alexander","last_name":"Plakhov"}],"volume":47,"date_created":"2018-12-11T11:53:36Z","date_updated":"2021-01-12T06:52:41Z","scopus_import":1,"day":"14","citation":{"chicago":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics. SIAM, 2015. https://doi.org/10.1137/140993843.","mla":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” Society for Industrial and Applied Mathematics, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:10.1137/140993843.","short":"A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769.","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.","ieee":"A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” Society for Industrial and Applied Mathematics, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015.","apa":"Akopyan, A., & Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. SIAM. https://doi.org/10.1137/140993843","ama":"Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 2015;47(4):2754-2769. doi:10.1137/140993843"},"publication":"Society for Industrial and Applied Mathematics","page":"2754 - 2769","date_published":"2015-07-14T00:00:00Z","type":"journal_article","issue":"4","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) < 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) < 0 for 0 ≤ ξ < 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"}],"_id":"1710","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 47","title":"Minimal resistance of curves under the single impact assumption","status":"public","oa_version":"Preprint"},{"scopus_import":1,"day":"01","article_processing_charge":"No","page":"163 - 167","publication":"Journal of Statistical Physics","citation":{"mla":"Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:10.1007/s10955-015-1238-5.","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","chicago":"Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” Journal of Statistical Physics. Springer, 2015. https://doi.org/10.1007/s10955-015-1238-5.","ama":"Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. Journal of Statistical Physics. 2015;160(1):163-167. doi:10.1007/s10955-015-1238-5","ista":"Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167.","apa":"Akopyan, A., Pirogov, S., & Rybko, A. (2015). Invariant measures of genetic recombination process. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-015-1238-5","ieee":"A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” Journal of Statistical Physics, vol. 160, no. 1. Springer, pp. 163–167, 2015."},"date_published":"2015-07-01T00:00:00Z","type":"journal_article","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"}],"issue":"1","status":"public","title":"Invariant measures of genetic recombination process","intvolume":" 160","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1828","oa_version":"Preprint","month":"07","quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"main_file_link":[{"open_access":"1","url":"arxiv.org/abs/1406.5313"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s10955-015-1238-5","publist_id":"5276","ec_funded":1,"publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"year":"2015","date_created":"2018-12-11T11:54:14Z","date_updated":"2021-01-12T06:53:28Z","volume":160,"author":[{"last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy"},{"full_name":"Pirogov, Sergey","first_name":"Sergey","last_name":"Pirogov"},{"full_name":"Rybko, Aleksandr","last_name":"Rybko","first_name":"Aleksandr"}]},{"date_updated":"2021-01-12T06:54:12Z","date_created":"2018-12-11T11:54:49Z","oa_version":"None","volume":379,"author":[{"full_name":"Pausinger, Florian","first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768"},{"first_name":"Stefan","last_name":"Steinerberger","full_name":"Steinerberger, Stefan"}],"title":"On the distribution of local extrema in quantum chaos","publication_status":"published","status":"public","intvolume":" 379","department":[{"_id":"HeEd"}],"publisher":"Elsevier","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. ","_id":"1938","year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"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.","lang":"eng"}],"publist_id":"5152","issue":"6","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1016/j.physleta.2014.12.010","date_published":"2015-03-06T00:00:00Z","quality_controlled":"1","page":"535 - 541","publication":"Physics Letters, Section A","citation":{"ieee":"F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” Physics Letters, Section A, vol. 379, no. 6. Elsevier, pp. 535–541, 2015.","apa":"Pausinger, F., & Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. Physics Letters, Section A. Elsevier. https://doi.org/10.1016/j.physleta.2014.12.010","ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","ama":"Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A. Elsevier, 2015. https://doi.org/10.1016/j.physleta.2014.12.010.","short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010."},"day":"06","month":"03","scopus_import":1},{"year":"2015","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.","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Jablonski, Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","first_name":"Grzegorz","last_name":"Jablonski"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"volume":15,"date_updated":"2021-01-12T06:54:53Z","date_created":"2018-12-11T11:55:20Z","publist_id":"5022","ec_funded":1,"file_date_updated":"2020-07-14T12:45:26Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"quality_controlled":"1","doi":"10.1007/s10208-014-9223-y","language":[{"iso":"eng"}],"month":"10","_id":"2035","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 15","title":"The persistent homology of a self-map","ddc":["000"],"status":"public","pubrep_id":"486","oa_version":"Published Version","file":[{"checksum":"3566f3a8b0c1bc550e62914a88c584ff","date_created":"2018-12-12T10:08:10Z","date_updated":"2020-07-14T12:45:26Z","relation":"main_file","file_id":"4670","file_size":1317546,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf"}],"type":"journal_article","issue":"5","abstract":[{"lang":"eng","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"}],"citation":{"ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. Foundations of Computational Mathematics. 2015;15(5):1213-1244. doi:10.1007/s10208-014-9223-y","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” Foundations of Computational Mathematics, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","apa":"Edelsbrunner, H., Jablonski, G., & Mrozek, M. (2015). The persistent homology of a self-map. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-014-9223-y","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:10.1007/s10208-014-9223-y.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” Foundations of Computational Mathematics. Springer, 2015. https://doi.org/10.1007/s10208-014-9223-y."},"publication":"Foundations of Computational Mathematics","page":"1213 - 1244","date_published":"2015-10-01T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"01"},{"oa_version":"None","status":"public","title":"Homological reconstruction and simplification in R3","intvolume":" 48","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1805","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."}],"issue":"8","type":"journal_article","date_published":"2015-06-03T00:00:00Z","page":"606 - 621","publication":"Computational Geometry: Theory and Applications","citation":{"chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications. Elsevier, 2015. https://doi.org/10.1016/j.comgeo.2014.08.010.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” Computational Geometry: Theory and Applications, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:10.1016/j.comgeo.2014.08.010.","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” Computational Geometry: Theory and Applications, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., & Lieutier, A. (2015). Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2014.08.010","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.","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 2015;48(8):606-621. doi:10.1016/j.comgeo.2014.08.010"},"day":"03","scopus_import":1,"date_updated":"2023-02-23T10:59:19Z","date_created":"2018-12-11T11:54:06Z","volume":48,"author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"full_name":"Bauer, Ulrich","last_name":"Bauer","first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Devillers","first_name":"Olivier","full_name":"Devillers, Olivier"},{"last_name":"Glisse","first_name":"Marc","full_name":"Glisse, Marc"},{"first_name":"André","last_name":"Lieutier","full_name":"Lieutier, André"}],"related_material":{"record":[{"id":"2812","status":"public","relation":"earlier_version"}]},"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier","year":"2015","publist_id":"5305","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2014.08.010","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"month":"06"},{"scopus_import":1,"has_accepted_license":"1","day":"01","citation":{"ama":"Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 2015;10(6). doi:10.1371/journal.pone.0127657","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.","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” PLoS One, vol. 10, no. 6. Public Library of Science, 2015.","apa":"Symonova, O., Topp, C., & Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657","mla":"Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” PLoS One. Public Library of Science, 2015. https://doi.org/10.1371/journal.pone.0127657."},"publication":"PLoS One","date_published":"2015-06-01T00:00:00Z","type":"journal_article","issue":"6","abstract":[{"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.","lang":"eng"}],"_id":"1793","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 10","status":"public","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","ddc":["000"],"pubrep_id":"454","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"5150","checksum":"d20f26461ca575276ad3ed9ce4bfc787","date_updated":"2020-07-14T12:45:16Z","date_created":"2018-12-12T10:15:30Z","access_level":"open_access","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","content_type":"application/pdf","file_size":1850825,"creator":"system"}],"month":"06","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","doi":"10.1371/journal.pone.0127657","language":[{"iso":"eng"}],"article_number":"e0127657","publist_id":"5318","file_date_updated":"2020-07-14T12:45:16Z","year":"2015","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"publisher":"Public Library of Science","publication_status":"published","related_material":{"record":[{"relation":"research_data","status":"public","id":"9737"}]},"author":[{"full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","last_name":"Symonova","first_name":"Olga"},{"last_name":"Topp","first_name":"Christopher","full_name":"Topp, Christopher"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"volume":10,"date_created":"2018-12-11T11:54:02Z","date_updated":"2023-02-23T14:06:33Z"},{"month":"06","day":"01","article_processing_charge":"No","citation":{"ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:10.1371/journal.pone.0127657.s001","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, 10.1371/journal.pone.0127657.s001.","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., & Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. https://doi.org/10.1371/journal.pone.0127657.s001","mla":"Symonova, Olga, et al. Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2. Public Library of Science, 2015, doi:10.1371/journal.pone.0127657.s001.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","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. https://doi.org/10.1371/journal.pone.0127657.s001."},"doi":"10.1371/journal.pone.0127657.s001","date_published":"2015-06-01T00:00:00Z","type":"research_data_reference","_id":"9737","year":"2015","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","status":"public","publisher":"Public Library of Science","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"author":[{"full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga","last_name":"Symonova"},{"full_name":"Topp, Christopher","last_name":"Topp","first_name":"Christopher"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"}],"related_material":{"record":[{"id":"1793","relation":"used_in_publication","status":"public"}]},"date_created":"2021-07-28T06:20:13Z","date_updated":"2023-02-23T10:14:42Z","oa_version":"Published Version"},{"publist_id":"5320","issue":"6","abstract":[{"lang":"eng","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."}],"type":"journal_article","volume":31,"oa_version":"None","date_created":"2018-12-11T11:54:02Z","date_updated":"2023-09-07T11:41:25Z","related_material":{"record":[{"id":"1399","relation":"dissertation_contains","status":"public"}]},"author":[{"first_name":"Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian"},{"full_name":"Svane, Anne","first_name":"Anne","last_name":"Svane"}],"intvolume":" 31","publisher":"Academic Press","department":[{"_id":"HeEd"}],"title":"A Koksma-Hlawka inequality for general discrepancy systems","status":"public","publication_status":"published","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.","_id":"1792","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","month":"12","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.jco.2015.06.002","date_published":"2015-12-01T00:00:00Z","page":"773 - 797","quality_controlled":"1","citation":{"ama":"Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 2015;31(6):773-797. doi:10.1016/j.jco.2015.06.002","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","apa":"Pausinger, F., & Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.06.002","ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” Journal of Complexity, vol. 31, no. 6. Academic Press, pp. 773–797, 2015.","mla":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:10.1016/j.jco.2015.06.002.","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","chicago":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” Journal of Complexity. Academic Press, 2015. https://doi.org/10.1016/j.jco.2015.06.002."},"publication":"Journal of Complexity"},{"abstract":[{"lang":"eng","text":"This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold."}],"publist_id":"5808","type":"dissertation","alternative_title":["ISTA Thesis"],"author":[{"full_name":"Pausinger, Florian","last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1662"},{"status":"public","relation":"part_of_dissertation","id":"1792"},{"relation":"part_of_dissertation","status":"public","id":"2255"}]},"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:51:48Z","oa_version":"None","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1399","year":"2015","title":"On the approximation of intrinsic volumes","publication_status":"published","status":"public","department":[{"_id":"HeEd"}],"publisher":"Institute of Science and Technology Austria","month":"06","day":"01","article_processing_charge":"No","publication_identifier":{"issn":["2663-337X"]},"date_published":"2015-06-01T00:00:00Z","degree_awarded":"PhD","supervisor":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"language":[{"iso":"eng"}],"citation":{"chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","mla":"Pausinger, Florian. On the Approximation of Intrinsic Volumes. Institute of Science and Technology Austria, 2015.","short":"F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","apa":"Pausinger, F. (2015). On the approximation of intrinsic volumes. Institute of Science and Technology Austria.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015."},"page":"144"},{"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_4","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","publication_identifier":{"issn":["1612-3786"],"eisbn":["9783319040998"],"eissn":["2197-666X"],"isbn":["9783319040981"]},"month":"03","volume":1,"date_created":"2022-03-21T07:11:23Z","date_updated":"2022-06-21T12:01:47Z","author":[{"first_name":"Jens","last_name":"Kasten","full_name":"Kasten, Jens"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Reich, Wieland","first_name":"Wieland","last_name":"Reich"},{"last_name":"Scheuermann","first_name":"Gerik","full_name":"Scheuermann, Gerik"}],"publisher":"Springer","editor":[{"full_name":"Bremer, Peer-Timo","last_name":"Bremer","first_name":"Peer-Timo"},{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"},{"full_name":"Pascucci, Valerio","last_name":"Pascucci","first_name":"Valerio"},{"full_name":"Peikert, Ronald","first_name":"Ronald","last_name":"Peikert"}],"department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program.","year":"2014","ec_funded":1,"place":"Cham","date_published":"2014-03-19T00:00:00Z","page":"55-69","citation":{"mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:10.1007/978-3-319-04099-8_4.","short":"J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69.","chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In Topological Methods in Data Analysis and Visualization III , edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_4.","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III . Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:10.1007/978-3-319-04099-8_4","ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.","apa":"Kasten, J., Reininghaus, J., Reich, W., & Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (Vol. 1, pp. 55–69). Cham: Springer. https://doi.org/10.1007/978-3-319-04099-8_4","ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in Topological Methods in Data Analysis and Visualization III , vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69."},"publication":"Topological Methods in Data Analysis and Visualization III ","article_processing_charge":"No","day":"19","series_title":"Mathematics and Visualization","scopus_import":"1","oa_version":"None","intvolume":" 1","status":"public","title":"Toward the extraction of saddle periodic orbits","_id":"10893","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data.","lang":"eng"}],"type":"book_chapter"},{"page":"61 - 86","citation":{"ama":"Huber S, Held M, Meerwald P, Kwitt R. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 2014;24(1):61-86. doi:10.1142/S0218195914500034","ieee":"S. Huber, M. Held, P. Meerwald, and R. Kwitt, “Topology-preserving watermarking of vector graphics,” International Journal of Computational Geometry and Applications, vol. 24, no. 1. World Scientific Publishing, pp. 61–86, 2014.","apa":"Huber, S., Held, M., Meerwald, P., & Kwitt, R. (2014). Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195914500034","ista":"Huber S, Held M, Meerwald P, Kwitt R. 2014. Topology-preserving watermarking of vector graphics. International Journal of Computational Geometry and Applications. 24(1), 61–86.","short":"S. Huber, M. Held, P. Meerwald, R. Kwitt, International Journal of Computational Geometry and Applications 24 (2014) 61–86.","mla":"Huber, Stefan, et al. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications, vol. 24, no. 1, World Scientific Publishing, 2014, pp. 61–86, doi:10.1142/S0218195914500034.","chicago":"Huber, Stefan, Martin Held, Peter Meerwald, and Roland Kwitt. “Topology-Preserving Watermarking of Vector Graphics.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2014. https://doi.org/10.1142/S0218195914500034."},"publication":"International Journal of Computational Geometry and Applications","date_published":"2014-03-16T00:00:00Z","scopus_import":1,"has_accepted_license":"1","day":"16","intvolume":" 24","status":"public","title":"Topology-preserving watermarking of vector graphics","ddc":["000"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1816","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"4704","date_created":"2018-12-12T10:08:43Z","date_updated":"2020-07-14T12:45:17Z","checksum":"be45c133ab4d43351260e21beaa8f4b1","file_name":"IST-2016-443-v1+1_S0218195914500034.pdf","access_level":"open_access","content_type":"application/pdf","file_size":991734,"creator":"system"}],"pubrep_id":"443","type":"journal_article","issue":"1","abstract":[{"text":"Watermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques.","lang":"eng"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"doi":"10.1142/S0218195914500034","month":"03","department":[{"_id":"HeEd"}],"publisher":"World Scientific Publishing","publication_status":"published","acknowledgement":"Work by Martin Held and Stefan Huber was supported by Austrian Science Fund (FWF): L367-N15 and P25816-N15.","year":"2014","volume":24,"date_created":"2018-12-11T11:54:10Z","date_updated":"2021-01-12T06:53:23Z","author":[{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"full_name":"Meerwald, Peter","first_name":"Peter","last_name":"Meerwald"},{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"}],"publist_id":"5290","file_date_updated":"2020-07-14T12:45:17Z"},{"type":"journal_article","issue":"1","publist_id":"5260","abstract":[{"lang":"eng","text":"We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on 2n vertices are bounded by O(n3) and O(n10), in the convex and general case, respectively. We then apply similar methods to prove an (Formula presented.) upper bound on the Ramsey number of a path with n ordered vertices."}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"1842","year":"2014","acknowledgement":"Marek Krčál was supported by the ERC Advanced Grant No. 267165.","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"intvolume":" 53","publisher":"Springer","status":"public","title":"On the geometric ramsey number of outerplanar graphs","publication_status":"published","author":[{"first_name":"Josef","last_name":"Cibulka","full_name":"Cibulka, Josef"},{"first_name":"Pu","last_name":"Gao","full_name":"Gao, Pu"},{"first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"},{"full_name":"Valla, Tomáš","last_name":"Valla","first_name":"Tomáš"},{"last_name":"Valtr","first_name":"Pavel","full_name":"Valtr, Pavel"}],"volume":53,"oa_version":"Submitted Version","date_created":"2018-12-11T11:54:18Z","date_updated":"2021-01-12T06:53:33Z","scopus_import":1,"day":"14","month":"11","citation":{"ista":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. 2014. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 53(1), 64–79.","ieee":"J. Cibulka, P. Gao, M. Krcál, T. Valla, and P. Valtr, “On the geometric ramsey number of outerplanar graphs,” Discrete & Computational Geometry, vol. 53, no. 1. Springer, pp. 64–79, 2014.","apa":"Cibulka, J., Gao, P., Krcál, M., Valla, T., & Valtr, P. (2014). On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-014-9646-x","ama":"Cibulka J, Gao P, Krcál M, Valla T, Valtr P. On the geometric ramsey number of outerplanar graphs. Discrete & Computational Geometry. 2014;53(1):64-79. doi:10.1007/s00454-014-9646-x","chicago":"Cibulka, Josef, Pu Gao, Marek Krcál, Tomáš Valla, and Pavel Valtr. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-014-9646-x.","mla":"Cibulka, Josef, et al. “On the Geometric Ramsey Number of Outerplanar Graphs.” Discrete & Computational Geometry, vol. 53, no. 1, Springer, 2014, pp. 64–79, doi:10.1007/s00454-014-9646-x.","short":"J. Cibulka, P. Gao, M. Krcál, T. Valla, P. Valtr, Discrete & Computational Geometry 53 (2014) 64–79."},"main_file_link":[{"url":"http://arxiv.org/abs/1310.7004","open_access":"1"}],"oa":1,"publication":"Discrete & Computational Geometry","page":"64 - 79","doi":"10.1007/s00454-014-9646-x","date_published":"2014-11-14T00:00:00Z","language":[{"iso":"eng"}]},{"abstract":[{"text":"We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.","lang":"eng"}],"issue":"3","type":"journal_article","oa_version":"Submitted Version","title":"Functionals on triangulations of delaunay sets","status":"public","intvolume":" 14","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1876","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2014-07-01T00:00:00Z","article_type":"original","page":"491 - 504","publication":"Moscow Mathematical Journal","citation":{"chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-3-491-504.","mla":"Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” Moscow Mathematical Journal, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:10.17323/1609-4514-2014-14-3-491-504.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504.","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.","apa":"Dolbilin, N., Edelsbrunner, H., Glazyrin, A., & Musin, O. (2014). Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-3-491-504","ieee":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations of delaunay sets,” Moscow Mathematical Journal, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014.","ama":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 2014;14(3):491-504. doi:10.17323/1609-4514-2014-14-3-491-504"},"publist_id":"5220","date_created":"2018-12-11T11:54:29Z","date_updated":"2022-03-03T11:47:09Z","volume":14,"author":[{"last_name":"Dolbilin","first_name":"Nikolai","full_name":"Dolbilin, Nikolai"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Glazyrin, Alexey","first_name":"Alexey","last_name":"Glazyrin"},{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"}],"publication_status":"published","publisher":"Independent University of Moscow","department":[{"_id":"HeEd"}],"year":"2014","month":"07","publication_identifier":{"issn":["16093321"]},"language":[{"iso":"eng"}],"doi":"10.17323/1609-4514-2014-14-3-491-504","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1211.7053"}],"external_id":{"arxiv":["1211.7053"]},"oa":1},{"page":"754 - 760","article_type":"original","citation":{"short":"V.V. Alexeev, V.G. Bogaevskaya, M.M. Preobrazhenskaya, A.Y. Ukhalov, H. Edelsbrunner, O. Yakimova, Journal of Mathematical Sciences 203 (2014) 754–760.","mla":"Alexeev, V. V., et al. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences, vol. 203, no. 6, Springer, 2014, pp. 754–60, doi:10.1007/s10958-014-2165-8.","chicago":"Alexeev, V V, V G Bogaevskaya, M M Preobrazhenskaya, A Y Ukhalov, Herbert Edelsbrunner, and Olga Yakimova. “An Algorithm for Cartographic Generalization That Preserves Global Topology.” Journal of Mathematical Sciences. Springer, 2014. https://doi.org/10.1007/s10958-014-2165-8.","ama":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 2014;203(6):754-760. doi:10.1007/s10958-014-2165-8","apa":"Alexeev, V. V., Bogaevskaya, V. G., Preobrazhenskaya, M. M., Ukhalov, A. Y., Edelsbrunner, H., & Yakimova, O. (2014). An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. Springer. https://doi.org/10.1007/s10958-014-2165-8","ieee":"V. V. Alexeev, V. G. Bogaevskaya, M. M. Preobrazhenskaya, A. Y. Ukhalov, H. Edelsbrunner, and O. Yakimova, “An algorithm for cartographic generalization that preserves global topology,” Journal of Mathematical Sciences, vol. 203, no. 6. Springer, pp. 754–760, 2014.","ista":"Alexeev VV, Bogaevskaya VG, Preobrazhenskaya MM, Ukhalov AY, Edelsbrunner H, Yakimova O. 2014. An algorithm for cartographic generalization that preserves global topology. Journal of Mathematical Sciences. 203(6), 754–760."},"publication":"Journal of Mathematical Sciences","date_published":"2014-11-16T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"16","intvolume":" 203","title":"An algorithm for cartographic generalization that preserves global topology","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1929","oa_version":"None","type":"journal_article","issue":"6","abstract":[{"text":"We propose an algorithm for the generalization of cartographic objects that can be used to represent maps on different scales.","lang":"eng"}],"quality_controlled":"1","language":[{"iso":"eng"}],"doi":"10.1007/s10958-014-2165-8","publication_identifier":{"issn":["1072-3374"],"eissn":["1573-8795"]},"month":"11","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"We would like to offer our special thanks to students of the Department of Mathematics of Demidov Yaroslavl State University A. A. Gorokhov and V. N. Knyazev for participation in developing the program and assistance in preparation of test data. This work was supported by grant 11.G34.31.0053 from the government of the Russian Federation.","year":"2014","volume":203,"date_updated":"2022-05-24T10:39:06Z","date_created":"2018-12-11T11:54:46Z","author":[{"first_name":"V V","last_name":"Alexeev","full_name":"Alexeev, V V"},{"full_name":"Bogaevskaya, V G","last_name":"Bogaevskaya","first_name":"V G"},{"full_name":"Preobrazhenskaya, M M","first_name":"M M","last_name":"Preobrazhenskaya"},{"last_name":"Ukhalov","first_name":"A Y","full_name":"Ukhalov, A Y"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"first_name":"Olga","last_name":"Yakimova","full_name":"Yakimova, Olga"}],"publist_id":"5165"},{"language":[{"iso":"eng"}],"date_published":"2014-12-31T00:00:00Z","doi":"10.1109/TVCG.2014.2346432","page":"2585 - 2594","quality_controlled":"1","citation":{"ama":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 2014;20(12):2585-2594. doi:10.1109/TVCG.2014.2346432","ieee":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, and T. Weinkauf, “Fast and memory-efficient topological denoising of 2D and 3D scalar fields,” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12. IEEE, pp. 2585–2594, 2014.","apa":"Günther, D., Jacobson, A., Reininghaus, J., Seidel, H., Sorkine Hornung, O., & Weinkauf, T. (2014). Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2014.2346432","ista":"Günther D, Jacobson A, Reininghaus J, Seidel H, Sorkine Hornung O, Weinkauf T. 2014. Fast and memory-efficient topological denoising of 2D and 3D scalar fields. IEEE Transactions on Visualization and Computer Graphics. 20(12), 2585–2594.","short":"D. Günther, A. Jacobson, J. Reininghaus, H. Seidel, O. Sorkine Hornung, T. Weinkauf, IEEE Transactions on Visualization and Computer Graphics 20 (2014) 2585–2594.","mla":"Günther, David, et al. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 12, IEEE, 2014, pp. 2585–94, doi:10.1109/TVCG.2014.2346432.","chicago":"Günther, David, Alec Jacobson, Jan Reininghaus, Hans Seidel, Olga Sorkine Hornung, and Tino Weinkauf. “Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2014. https://doi.org/10.1109/TVCG.2014.2346432."},"publication":"IEEE Transactions on Visualization and Computer Graphics","day":"31","month":"12","scopus_import":1,"oa_version":"None","volume":20,"date_updated":"2021-01-12T06:54:09Z","date_created":"2018-12-11T11:54:46Z","author":[{"last_name":"Günther","first_name":"David","full_name":"Günther, David"},{"full_name":"Jacobson, Alec","last_name":"Jacobson","first_name":"Alec"},{"last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"first_name":"Hans","last_name":"Seidel","full_name":"Seidel, Hans"},{"last_name":"Sorkine Hornung","first_name":"Olga","full_name":"Sorkine Hornung, Olga"},{"full_name":"Weinkauf, Tino","first_name":"Tino","last_name":"Weinkauf"}],"department":[{"_id":"HeEd"}],"intvolume":" 20","publisher":"IEEE","publication_status":"published","title":"Fast and memory-efficient topological denoising of 2D and 3D scalar fields","status":"public","_id":"1930","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","year":"2014","acknowledgement":"RTRA Digiteoproject; ERC grant; SNF award; Intel Doctoral Fellowship; MPC-VCC","publist_id":"5164","issue":"12","abstract":[{"lang":"eng","text":"(Figure Presented) Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications."}],"type":"journal_article"},{"date_updated":"2021-01-12T06:54:56Z","date_created":"2018-12-11T11:55:23Z","author":[{"full_name":"Bauer, Ulrich","last_name":"Bauer","first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","first_name":"Michael"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Reininghaus"}],"editor":[{"full_name":" McGeoch, Catherine","first_name":"Catherine","last_name":" McGeoch"},{"full_name":"Meyer, Ulrich","last_name":"Meyer","first_name":"Ulrich"}],"department":[{"_id":"HeEd"}],"publisher":"Society of Industrial and Applied Mathematics","publication_status":"published","year":"2014","publist_id":"5008","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1137/1.9781611973198.4","conference":{"name":"ALENEX: Algorithm Engineering and Experiments","start_date":"2014-01-05","location":"Portland, USA","end_date":"2014-01-05"},"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1310.0710","open_access":"1"}],"oa":1,"month":"01","oa_version":"Submitted Version","status":"public","title":"Distributed computation of persistent homology","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2043","abstract":[{"lang":"eng","text":"Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically – as long as the algorithm does not exhaust the available memory. Following up on a recently presented parallel method for persistence computation on shared memory systems [1], we demonstrate that a simple adaption of the standard reduction algorithm leads to a variant for distributed systems. Our algorithmic design ensures that the data is distributed over the nodes without redundancy; this permits the computation of much larger instances than on a single machine. Moreover, we observe that the parallelism at least compensates for the overhead caused by communication between nodes, and often even speeds up the computation compared to sequential and even parallel shared memory algorithms. In our experiments, we were able to compute the persistent homology of filtrations with more than a billion (109) elements within seconds on a cluster with 32 nodes using less than 6GB of memory per node."}],"type":"conference","date_published":"2014-01-01T00:00:00Z","page":"31 - 38","citation":{"ista":"Bauer U, Kerber M, Reininghaus J. 2014. Distributed computation of persistent homology. Proceedings of the Workshop on Algorithm Engineering and Experiments. ALENEX: Algorithm Engineering and Experiments, 31–38.","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Distributed computation of persistent homology,” in Proceedings of the Workshop on Algorithm Engineering and Experiments, Portland, USA, 2014, pp. 31–38.","apa":"Bauer, U., Kerber, M., & Reininghaus, J. (2014). Distributed computation of persistent homology. In C. McGeoch & U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments (pp. 31–38). Portland, USA: Society of Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611973198.4","ama":"Bauer U, Kerber M, Reininghaus J. Distributed computation of persistent homology. In: McGeoch C, Meyer U, eds. Proceedings of the Workshop on Algorithm Engineering and Experiments. Society of Industrial and Applied Mathematics; 2014:31-38. doi:10.1137/1.9781611973198.4","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Distributed Computation of Persistent Homology.” In Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, 31–38. Society of Industrial and Applied Mathematics, 2014. https://doi.org/10.1137/1.9781611973198.4.","mla":"Bauer, Ulrich, et al. “Distributed Computation of Persistent Homology.” Proceedings of the Workshop on Algorithm Engineering and Experiments, edited by Catherine McGeoch and Ulrich Meyer, Society of Industrial and Applied Mathematics, 2014, pp. 31–38, doi:10.1137/1.9781611973198.4.","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, C. McGeoch, U. Meyer (Eds.), Proceedings of the Workshop on Algorithm Engineering and Experiments, Society of Industrial and Applied Mathematics, 2014, pp. 31–38."},"publication":"Proceedings of the Workshop on Algorithm Engineering and Experiments","day":"01","scopus_import":1},{"series_title":"Mathematics and Visualization","scopus_import":1,"day":"19","page":"103 - 117","publication":"Topological Methods in Data Analysis and Visualization III","citation":{"short":"U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117.","mla":"Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:10.1007/978-3-319-04099-8_7.","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In Topological Methods in Data Analysis and Visualization III, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. https://doi.org/10.1007/978-3-319-04099-8_7.","ama":"Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer; 2014:103-117. doi:10.1007/978-3-319-04099-8_7","ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in Topological Methods in Data Analysis and Visualization III, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.","apa":"Bauer, U., Kerber, M., & Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (pp. 103–117). Springer. https://doi.org/10.1007/978-3-319-04099-8_7","ista":"Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117."},"date_published":"2014-03-19T00:00:00Z","type":"book_chapter","abstract":[{"lang":"eng","text":"We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation."}],"title":"Clear and Compress: Computing Persistent Homology in Chunks","status":"public","_id":"2044","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","month":"03","quality_controlled":"1","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1303.0477","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-04099-8_7","publist_id":"5007","ec_funded":1,"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","editor":[{"full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo","last_name":"Bremer"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"full_name":"Pascucci, Valerio","first_name":"Valerio","last_name":"Pascucci"},{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"}],"year":"2014","date_updated":"2021-01-12T06:54:56Z","date_created":"2018-12-11T11:55:23Z","author":[{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber","first_name":"Michael"},{"last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"}]},{"status":"public","title":"Induced matchings of barcodes and the algebraic stability of persistence","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"ACM","year":"2014","_id":"2153","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:55:38Z","date_created":"2018-12-11T11:56:01Z","oa_version":"Submitted Version","author":[{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724"},{"full_name":"Lesnick, Michael","first_name":"Michael","last_name":"Lesnick"}],"type":"conference","abstract":[{"lang":"eng","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)."}],"publist_id":"4853","ec_funded":1,"quality_controlled":"1","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"page":"355 - 364","publication":"Proceedings of the Annual Symposium on Computational Geometry","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.3681"}],"citation":{"chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In Proceedings of the Annual Symposium on Computational Geometry, 355–64. ACM, 2014. https://doi.org/10.1145/2582112.2582168.","mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–64, doi:10.1145/2582112.2582168.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","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.","apa":"Bauer, U., & Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In Proceedings of the Annual Symposium on Computational Geometry (pp. 355–364). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582168","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 355–364.","ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:355-364. doi:10.1145/2582112.2582168"},"language":[{"iso":"eng"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2014-06-11","start_date":"2014-06-08","location":"Kyoto, Japan"},"date_published":"2014-06-01T00:00:00Z","doi":"10.1145/2582112.2582168","scopus_import":1,"day":"01","month":"06"},{"year":"2014","acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","publisher":"ACM","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"last_name":"Ge","first_name":"Xiaoyin","full_name":"Ge, Xiaoyin"},{"full_name":"Wang, Yusu","last_name":"Wang","first_name":"Yusu"}],"date_updated":"2021-01-12T06:55:39Z","date_created":"2018-12-11T11:56:02Z","publist_id":"4850","ec_funded":1,"main_file_link":[{"url":"http://arxiv.org/abs/1307.2839","open_access":"1"}],"oa":1,"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"quality_controlled":"1","doi":"10.1145/2582112.2582169","conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2014-06-11","location":"Kyoto, Japan","start_date":"2014-06-08"},"language":[{"iso":"eng"}],"month":"06","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2156","title":"Measuring distance between Reeb graphs","status":"public","oa_version":"Submitted Version","type":"conference","abstract":[{"text":"We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s).","lang":"eng"}],"citation":{"short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.","mla":"Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–73, doi:10.1145/2582112.2582169.","chicago":"Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In Proceedings of the Annual Symposium on Computational Geometry, 464–73. ACM, 2014. https://doi.org/10.1145/2582112.2582169.","ama":"Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: Proceedings of the Annual Symposium on Computational Geometry. ACM; 2014:464-473. doi:10.1145/2582112.2582169","ieee":"U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in Proceedings of the Annual Symposium on Computational Geometry, Kyoto, Japan, 2014, pp. 464–473.","apa":"Bauer, U., Ge, X., & Wang, Y. (2014). Measuring distance between Reeb graphs. In Proceedings of the Annual Symposium on Computational Geometry (pp. 464–473). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582169","ista":"Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473."},"publication":"Proceedings of the Annual Symposium on Computational Geometry","page":"464 - 473","date_published":"2014-06-01T00:00:00Z","scopus_import":1,"day":"01"}]