[{"status":"public","type":"journal_article","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","full_name":"Pausinger, Florian"}],"month":"01","day":"10","oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2018-12-12T10:12:10Z","date_updated":"2020-07-14T12:45:10Z","file_id":"4928","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","checksum":"f8869ec110c35c852ef6a37425374af7","content_type":"application/pdf","file_size":248985,"relation":"main_file","access_level":"open_access","creator":"system"}],"language":[{"iso":"eng"}],"publication":"Advances in Mathematics","pubrep_id":"774","date_updated":"2023-09-07T11:41:25Z","oa":1,"title":"Approximation and convergence of the intrinsic volume","has_accepted_license":"1","intvolume":"       287","scopus_import":1,"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"publisher":"Academic Press","date_published":"2016-01-10T00:00:00Z","page":"674 - 703","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":287,"publication_status":"published","ddc":["004"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"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"}],"file_date_updated":"2020-07-14T12:45:10Z","_id":"1662","doi":"10.1016/j.aim.2015.10.004","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","publist_id":"5488","citation":{"apa":"Edelsbrunner, H., &#38; Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. <i>Advances in Mathematics</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">https://doi.org/10.1016/j.aim.2015.10.004</a>","chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” <i>Advances in Mathematics</i>. Academic Press, 2016. <a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">https://doi.org/10.1016/j.aim.2015.10.004</a>.","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” <i>Advances in Mathematics</i>, vol. 287, Academic Press, 2016, pp. 674–703, doi:<a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">10.1016/j.aim.2015.10.004</a>.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","ama":"Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. <i>Advances in Mathematics</i>. 2016;287:674-703. doi:<a href=\"https://doi.org/10.1016/j.aim.2015.10.004\">10.1016/j.aim.2015.10.004</a>","ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” <i>Advances in Mathematics</i>, vol. 287. Academic Press, pp. 674–703, 2016."},"date_created":"2018-12-11T11:53:20Z","ec_funded":1,"related_material":{"record":[{"id":"1399","relation":"dissertation_contains","status":"public"}]}},{"publication":"Proceedings of the American Mathematical Society","language":[{"iso":"eng"}],"scopus_import":1,"intvolume":"       144","title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","issue":"10","article_processing_charge":"No","date_updated":"2021-01-12T06:50:09Z","oa":1,"status":"public","type":"journal_article","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1401.0442","open_access":"1"}],"day":"01","month":"10","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"full_name":"Balitskiy, Alexey","first_name":"Alexey","last_name":"Balitskiy"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"},{"full_name":"Sharipova, Anastasia","first_name":"Anastasia","last_name":"Sharipova"}],"doi":"10.1090/proc/13062","_id":"1360","ec_funded":1,"date_created":"2018-12-11T11:51:34Z","publist_id":"5885","citation":{"chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/proc/13062\">https://doi.org/10.1090/proc/13062</a>.","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:<a href=\"https://doi.org/10.1090/proc/13062\">10.1090/proc/13062</a>.","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.","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. <i>Proceedings of the American Mathematical Society</i>. 2016;144(10):4501-4513. doi:<a href=\"https://doi.org/10.1090/proc/13062\">10.1090/proc/13062</a>","apa":"Akopyan, A., Balitskiy, A., Karasev, R., &#38; Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/13062\">https://doi.org/10.1090/proc/13062</a>"},"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).","quality_controlled":"1","volume":144,"page":"4501 - 4513","department":[{"_id":"HeEd"}],"date_published":"2016-10-01T00:00:00Z","publisher":"American Mathematical Society","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"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"}],"publication_status":"published"},{"page":"126 - 164","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"quality_controlled":"1","volume":56,"publisher":"Springer","date_published":"2016-07-01T00:00:00Z","project":[{"grant_number":"M01980","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Robust invariants of Nonlinear Systems"},{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"abstract":[{"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.","lang":"eng"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","doi":"10.1007/s00454-016-9794-2","file_date_updated":"2020-07-14T12:44:53Z","_id":"1408","ec_funded":1,"related_material":{"record":[{"status":"public","id":"1510","relation":"earlier_version"}]},"citation":{"apa":"Franek, P., &#38; Krcál, M. (2016). On computability and triviality of well groups. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-016-9794-2\">https://doi.org/10.1007/s00454-016-9794-2</a>","ama":"Franek P, Krcál M. On computability and triviality of well groups. <i>Discrete &#38; Computational Geometry</i>. 2016;56(1):126-164. doi:<a href=\"https://doi.org/10.1007/s00454-016-9794-2\">10.1007/s00454-016-9794-2</a>","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” <i>Discrete &#38; Computational Geometry</i>, vol. 56, no. 1. Springer, pp. 126–164, 2016.","short":"P. Franek, M. Krcál, Discrete &#38; Computational Geometry 56 (2016) 126–164.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00454-016-9794-2\">https://doi.org/10.1007/s00454-016-9794-2</a>.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” <i>Discrete &#38; Computational Geometry</i>, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:<a href=\"https://doi.org/10.1007/s00454-016-9794-2\">10.1007/s00454-016-9794-2</a>.","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete &#38; Computational Geometry. 56(1), 126–164."},"date_created":"2018-12-11T11:51:51Z","publist_id":"5799","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","year":"2016","status":"public","type":"journal_article","oa_version":"Published Version","day":"01","file":[{"access_level":"open_access","relation":"main_file","file_size":905303,"content_type":"application/pdf","creator":"system","date_created":"2018-12-12T10:10:55Z","date_updated":"2020-07-14T12:44:53Z","checksum":"e0da023abf6b72abd8c6a8c76740d53c","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","file_id":"4846"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"07","author":[{"full_name":"Franek, Peter","first_name":"Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","last_name":"Franek"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál","full_name":"Krcál, Marek","first_name":"Marek"}],"publication":"Discrete & Computational Geometry","language":[{"iso":"eng"}],"has_accepted_license":"1","scopus_import":1,"intvolume":"        56","title":"On computability and triviality of well groups","date_updated":"2023-02-23T10:02:11Z","oa":1,"pubrep_id":"614","article_processing_charge":"Yes (via OA deal)","issue":"1"},{"intvolume":"      9667","date_updated":"2022-01-28T08:01:22Z","article_processing_charge":"No","title":"On some local topological properties of naive discrete sphere","publication":"Computational Topology in Image Context","language":[{"iso":"eng"}],"conference":{"location":"Marseille, France","end_date":"2016-06-17","name":"CTIC: Computational Topology in Image Context","start_date":"2016-06-15"},"publication_identifier":{"issn":["0302-9743"],"eisbn":["978-3-319-39441-1"],"eissn":["1611-3349"],"isbn":["978-3-319-39440-4"]},"month":"06","oa_version":"None","day":"02","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"first_name":"Nabhasmita","full_name":"Sen, Nabhasmita","last_name":"Sen"},{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","full_name":"Biswas, Ranita","first_name":"Ranita"},{"first_name":"Partha","full_name":"Bhowmick, Partha","last_name":"Bhowmick"}],"alternative_title":["LNCS"],"status":"public","type":"book_chapter","year":"2016","date_created":"2019-01-08T20:44:24Z","citation":{"mla":"Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” <i>Computational Topology in Image Context</i>, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">10.1007/978-3-319-39441-1_23</a>.","chicago":"Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In <i>Computational Topology in Image Context</i>, 9667:253–64. Cham: Springer Nature, 2016. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">https://doi.org/10.1007/978-3-319-39441-1_23</a>.","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 <i>Computational Topology in Image Context</i>, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.","ama":"Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: <i>Computational Topology in Image Context</i>. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:<a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">10.1007/978-3-319-39441-1_23</a>","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264.","apa":"Sen, N., Biswas, R., &#38; Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In <i>Computational Topology in Image Context</i> (Vol. 9667, pp. 253–264). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-39441-1_23\">https://doi.org/10.1007/978-3-319-39441-1_23</a>"},"doi":"10.1007/978-3-319-39441-1_23","_id":"5805","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"}],"place":"Cham","publication_status":"published","publisher":"Springer Nature","date_published":"2016-06-02T00:00:00Z","extern":"1","department":[{"_id":"HeEd"}],"page":"253-264","volume":9667,"quality_controlled":"1"},{"publication":"Discrete Geometry for Computer Imagery","language":[{"iso":"eng"}],"intvolume":"      9647","date_updated":"2022-01-28T08:10:11Z","article_processing_charge":"No","title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","alternative_title":["LNCS"],"status":"public","type":"conference","conference":{"end_date":"2016-04-20","location":"Nantes, France","start_date":"2016-04-18","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery"},"publication_identifier":{"issn":["0302-9743","1611-3349"],"eisbn":["978-3-319-32360-2"],"isbn":["978-3-319-32359-6"]},"month":"04","oa_version":"None","day":"09","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","author":[{"orcid":"0000-0002-5372-7890","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"}],"doi":"10.1007/978-3-319-32360-2_20","_id":"5806","year":"2016","date_created":"2019-01-08T20:44:37Z","citation":{"short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267.","ieee":"R. Biswas and P. Bhowmick, “On functionality of quadraginta octants of naive sphere with application to circle drawing,” in <i>Discrete Geometry for Computer Imagery</i>, Nantes, France, 2016, vol. 9647, pp. 256–267.","ama":"Biswas R, Bhowmick P. On functionality of quadraginta octants of naive sphere with application to circle drawing. In: <i>Discrete Geometry for Computer Imagery</i>. Vol 9647. Cham: Springer Nature; 2016:256-267. doi:<a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">10.1007/978-3-319-32360-2_20</a>","mla":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” <i>Discrete Geometry for Computer Imagery</i>, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:<a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">10.1007/978-3-319-32360-2_20</a>.","chicago":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In <i>Discrete Geometry for Computer Imagery</i>, 9647:256–67. Cham: Springer Nature, 2016. <a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">https://doi.org/10.1007/978-3-319-32360-2_20</a>.","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.","apa":"Biswas, R., &#38; Bhowmick, P. (2016). On functionality of quadraginta octants of naive sphere with application to circle drawing. In <i>Discrete Geometry for Computer Imagery</i> (Vol. 9647, pp. 256–267). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-32360-2_20\">https://doi.org/10.1007/978-3-319-32360-2_20</a>"},"publisher":"Springer Nature","date_published":"2016-04-09T00:00:00Z","page":"256-267","extern":"1","department":[{"_id":"HeEd"}],"volume":9647,"quality_controlled":"1","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."}],"place":"Cham","publication_status":"published"},{"department":[{"_id":"HeEd"}],"extern":"1","page":"86-100","volume":9448,"quality_controlled":"1","publisher":"Springer Nature","status":"public","type":"book_chapter","date_published":"2016-01-06T00:00:00Z","day":"06","oa_version":"None","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."}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","conference":{"location":"Kolkata, India","end_date":"2015-11-27","name":"IWCIA: International Workshop on Combinatorial Image Analysis","start_date":"2015-11-24"},"month":"01","publication_identifier":{"issn":["0302-9743"],"isbn":["978-3-319-26144-7"],"eisbn":["978-3-319-26145-4"],"eissn":["1611-3349"]},"publication_status":"published","author":[{"last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","full_name":"Biswas, Ranita"},{"last_name":"Bhowmick","full_name":"Bhowmick, Partha","first_name":"Partha"},{"first_name":"Valentin E.","full_name":"Brimkov, Valentin E.","last_name":"Brimkov"}],"place":"Cham","doi":"10.1007/978-3-319-26145-4_7","publication":"Combinatorial image analysis","language":[{"iso":"eng"}],"_id":"5809","intvolume":"      9448","date_created":"2019-01-08T20:45:19Z","citation":{"mla":"Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” <i>Combinatorial Image Analysis</i>, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:<a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">10.1007/978-3-319-26145-4_7</a>.","chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In <i>Combinatorial Image Analysis</i>, 9448:86–100. Cham: Springer Nature, 2016. <a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">https://doi.org/10.1007/978-3-319-26145-4_7</a>.","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.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100.","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in <i>Combinatorial image analysis</i>, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.","ama":"Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: <i>Combinatorial Image Analysis</i>. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:<a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">10.1007/978-3-319-26145-4_7</a>","apa":"Biswas, R., Bhowmick, P., &#38; Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In <i>Combinatorial image analysis</i> (Vol. 9448, pp. 86–100). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-26145-4_7\">https://doi.org/10.1007/978-3-319-26145-4_7</a>"},"title":"On the connectivity and smoothness of discrete spherical circles","date_updated":"2022-01-28T08:13:03Z","article_processing_charge":"No","year":"2016"},{"publist_id":"6209","date_created":"2018-12-11T11:50:25Z","title":"A study of rigorous ODE integrators for multi scale set oriented computations","citation":{"mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” <i>Applied Numerical Mathematics</i>, vol. 107, Elsevier, 2016, pp. 34–47, doi:<a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">10.1016/j.apnum.2016.04.005</a>.","chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” <i>Applied Numerical Mathematics</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">https://doi.org/10.1016/j.apnum.2016.04.005</a>.","ista":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47.","ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” <i>Applied Numerical Mathematics</i>, vol. 107. Elsevier, pp. 34–47, 2016.","ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. <i>Applied Numerical Mathematics</i>. 2016;107:34-47. doi:<a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">10.1016/j.apnum.2016.04.005</a>","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47.","apa":"Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., &#38; Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. <i>Applied Numerical Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.apnum.2016.04.005\">https://doi.org/10.1016/j.apnum.2016.04.005</a>"},"year":"2016","date_updated":"2021-01-12T06:48:38Z","acknowledgement":"MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch 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); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper.","scopus_import":1,"intvolume":"       107","ec_funded":1,"language":[{"iso":"eng"}],"_id":"1149","doi":"10.1016/j.apnum.2016.04.005","publication":"Applied Numerical Mathematics","publication_status":"published","author":[{"last_name":"Miyaji","first_name":"Tomoyuki","full_name":"Miyaji, Tomoyuki"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Gameiro","full_name":"Gameiro, Marcio","first_name":"Marcio"},{"full_name":"Kokubu, Hiroshi","first_name":"Hiroshi","last_name":"Kokubu"},{"last_name":"Mischaikow","full_name":"Mischaikow, Konstantin","first_name":"Konstantin"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved."}],"oa_version":"None","day":"01","month":"09","project":[{"call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033"}],"quality_controlled":"1","volume":107,"page":"34 - 47","department":[{"_id":"HeEd"}],"type":"journal_article","date_published":"2016-09-01T00:00:00Z","status":"public","publisher":"Elsevier"},{"publisher":"IEEE","date_published":"2015-10-14T00:00:00Z","status":"public","type":"conference","department":[{"_id":"HeEd"}],"page":"4741 - 4748","publication_status":"published","author":[{"last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","first_name":"Jan"},{"first_name":"Stefan","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"last_name":"Kwitt","full_name":"Kwitt, Roland","first_name":"Roland"}],"conference":{"end_date":"2015-06-12","location":"Boston, MA, USA","start_date":"2015-06-07","name":"CVPR: Computer Vision and Pattern Recognition"},"month":"10","publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"oa_version":"Preprint","day":"14","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"_id":"1483","doi":"10.1109/CVPR.2015.7299106","oa":1,"date_updated":"2021-01-12T06:51:03Z","year":"2015","date_created":"2018-12-11T11:52:17Z","citation":{"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.","mla":"Reininghaus, Jan, et al. <i>A Stable Multi-Scale Kernel for Topological Machine Learning</i>. IEEE, 2015, pp. 4741–48, doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>.","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>.","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 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.","ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>","apa":"Reininghaus, J., Huber, S., Bauer, U., &#38; 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. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>"},"title":"A stable multi-scale kernel for topological machine learning","publist_id":"5709","scopus_import":1},{"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","volume":"2015-August","department":[{"_id":"HeEd"}],"page":"128-135","status":"public","date_published":"2015-08-01T00:00:00Z","type":"conference","publisher":"Queen's University","publication_status":"published","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel","first_name":"Mabel"},{"last_name":"Kurlin","first_name":"Vitaliy","full_name":"Kurlin, Vitaliy"}],"abstract":[{"lang":"eng","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. "}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1505.03402"}],"day":"01","month":"08","conference":{"location":"Ontario, Canada","end_date":"2015-08-12","name":"CCCG: Canadian Conference on Computational Geometry","start_date":"2015-08-10"},"_id":"1495","language":[{"iso":"eng"}],"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","citation":{"ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>. Vol 2015-August. Queen’s University; 2015:128-135.","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.","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.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, 2015–August:128–35. Queen’s University, 2015.","mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, vol. 2015–August, Queen’s University, 2015, pp. 128–35.","apa":"Edelsbrunner, H., Iglesias Ham, M., &#38; Kurlin, V. (2015). Relaxed disk packing. In <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i> (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University."},"publist_id":"5684","date_created":"2018-12-11T11:52:21Z","title":"Relaxed disk packing","year":"2015","oa":1,"date_updated":"2021-01-12T06:51:09Z","scopus_import":1,"ec_funded":1},{"type":"conference","status":"public","alternative_title":["LIPIcs"],"author":[{"first_name":"Peter","full_name":"Franek, Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","last_name":"Franek"},{"full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","last_name":"Krcál"}],"month":"06","conference":{"end_date":"2015-06-25","location":"Eindhoven, Netherlands","start_date":"2015-06-22","name":"SoCG: Symposium on Computational Geometry"},"file":[{"file_name":"IST-2016-503-v1+1_32.pdf","file_id":"5001","checksum":"49eb5021caafaabe5356c65b9c5f8c9c","date_updated":"2020-07-14T12:44:59Z","date_created":"2018-12-12T10:13:19Z","creator":"system","access_level":"open_access","file_size":623563,"content_type":"application/pdf","relation":"main_file"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"11","language":[{"iso":"eng"}],"oa":1,"date_updated":"2023-02-21T17:02:57Z","pubrep_id":"503","title":"On computability and triviality of well groups","has_accepted_license":"1","scopus_import":1,"intvolume":"        34","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"date_published":"2015-06-11T00:00:00Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","volume":34,"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"page":"842 - 856","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"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 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 &gt; 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 &lt; 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. "}],"_id":"1510","file_date_updated":"2020-07-14T12:44:59Z","doi":"10.4230/LIPIcs.SOCG.2015.842","year":"2015","publist_id":"5667","date_created":"2018-12-11T11:52:26Z","citation":{"apa":"Franek, P., &#38; 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. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 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:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>","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.","mla":"Franek, Peter, and Marek Krcál. <i>On Computability and Triviality of Well Groups</i>. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>.","ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>."},"related_material":{"record":[{"relation":"later_version","id":"1408","status":"public"}]},"ec_funded":1},{"volume":40,"quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"257 - 267","date_published":"2015-01-01T00:00:00Z","publisher":"Springer","publication_status":"published","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."}],"_id":"1531","doi":"10.1007/978-3-319-15090-1_13","publist_id":"5640","date_created":"2018-12-11T11:52:33Z","citation":{"apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz &#38; T. Schultz (Eds.), <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i> (1st ed., Vol. 40, pp. 257–267). Springer. <a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">https://doi.org/10.1007/978-3-319-15090-1_13</a>","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.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>. Vol 40. 1st ed. Springer; 2015:257-267. doi:<a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">10.1007/978-3-319-15090-1_13</a>","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","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.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. <a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">https://doi.org/10.1007/978-3-319-15090-1_13</a>.","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:<a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">10.1007/978-3-319-15090-1_13</a>."},"year":"2015","edition":"1","type":"book_chapter","status":"public","alternative_title":["Mathematics and Visualization"],"author":[{"full_name":"Zobel, Valentin","first_name":"Valentin","last_name":"Zobel"},{"full_name":"Reininghaus, Jan","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"None","month":"01","publication_identifier":{"isbn":["978-3-319-15089-5"]},"language":[{"iso":"eng"}],"publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","article_processing_charge":"No","date_updated":"2022-06-10T09:50:14Z","intvolume":"        40","scopus_import":"1","editor":[{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"last_name":"Schultz","full_name":"Schultz, Thomas","first_name":"Thomas"}]},{"month":"01","publication_identifier":{"eissn":["1536-0040"]},"main_file_link":[{"url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf","open_access":"1"}],"oa_version":"Published Version","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Knipl","full_name":"Knipl, Diána","first_name":"Diána"},{"last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","full_name":"Pilarczyk, Pawel"},{"full_name":"Röst, Gergely","first_name":"Gergely","last_name":"Röst"}],"status":"public","type":"journal_article","scopus_import":1,"intvolume":"        14","date_updated":"2021-01-12T06:51:34Z","oa":1,"article_processing_charge":"No","issue":"2","title":"Rich bifurcation structure in a two patch vaccination model","publication":"SIAM Journal on Applied Dynamical Systems","language":[{"iso":"eng"}],"ddc":["510"],"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"}],"publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","date_published":"2015-01-01T00:00:00Z","department":[{"_id":"HeEd"}],"page":"980 - 1017","quality_controlled":"1","volume":14,"project":[{"grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps"}],"ec_funded":1,"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.","year":"2015","publist_id":"5616","citation":{"ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. <i>SIAM Journal on Applied Dynamical Systems</i>. 2015;14(2):980-1017. doi:<a href=\"https://doi.org/10.1137/140993934\">10.1137/140993934</a>","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.","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.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:<a href=\"https://doi.org/10.1137/140993934\">10.1137/140993934</a>.","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.","chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” <i>SIAM Journal on Applied Dynamical Systems</i>. Society for Industrial and Applied Mathematics , 2015. <a href=\"https://doi.org/10.1137/140993934\">https://doi.org/10.1137/140993934</a>.","apa":"Knipl, D., Pilarczyk, P., &#38; Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. <i>SIAM Journal on Applied Dynamical Systems</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/140993934\">https://doi.org/10.1137/140993934</a>"},"date_created":"2018-12-11T11:52:42Z","doi":"10.1137/140993934","_id":"1555","article_type":"original"},{"publication":"Topological Methods in Nonlinear Analysis","doi":"10.12775/TMNA.2015.014","_id":"1563","language":[{"iso":"eng"}],"intvolume":"        45","scopus_import":1,"date_updated":"2021-01-12T06:51:37Z","issue":"1","year":"2015","date_created":"2018-12-11T11:52:44Z","publist_id":"5608","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.","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.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:<a href=\"https://doi.org/10.12775/TMNA.2015.014\">10.12775/TMNA.2015.014</a>.","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.” <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies, 2015. <a href=\"https://doi.org/10.12775/TMNA.2015.014\">https://doi.org/10.12775/TMNA.2015.014</a>.","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","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,” <i>Topological Methods in Nonlinear Analysis</i>, 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. <i>Topological Methods in Nonlinear Analysis</i>. 2015;45(1):273-286. doi:<a href=\"https://doi.org/10.12775/TMNA.2015.014\">10.12775/TMNA.2015.014</a>","apa":"Graff, G., &#38; Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies. <a href=\"https://doi.org/10.12775/TMNA.2015.014\">https://doi.org/10.12775/TMNA.2015.014</a>"},"title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","publisher":"Juliusz Schauder Center for Nonlinear Studies","status":"public","date_published":"2015-03-01T00:00:00Z","type":"journal_article","department":[{"_id":"HeEd"}],"page":"273 - 286","quality_controlled":"1","volume":45,"month":"03","oa_version":"None","day":"01","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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","author":[{"first_name":"Grzegorz","full_name":"Graff, Grzegorz","last_name":"Graff"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk","first_name":"Pawel","full_name":"Pilarczyk, Pawel"}]},{"volume":9411,"quality_controlled":"1","department":[{"_id":"HeEd"}],"type":"conference","status":"public","date_published":"2015-01-01T00:00:00Z","alternative_title":["LNCS"],"publisher":"Springer Nature","abstract":[{"lang":"eng","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."}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","day":"01","oa_version":"None","month":"01","conference":{"name":"GD: Graph Drawing and Network Visualization","start_date":"2015-09-24","location":"Los Angeles, CA, United States","end_date":"2015-09-26"},"author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","publication":"23rd International Symposium","language":[{"iso":"eng"}],"_id":"1567","intvolume":"      9411","scopus_import":"1","date_created":"2018-12-11T11:52:46Z","citation":{"short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: <i>23rd International Symposium</i>. Vol 9411. Springer Nature; 2015.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in <i>23rd International Symposium</i>, Los Angeles, CA, United States, 2015, vol. 9411.","chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In <i>23rd International Symposium</i>, Vol. 9411. Springer Nature, 2015.","ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” <i>23rd International Symposium</i>, vol. 9411, Springer Nature, 2015.","apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In <i>23rd International Symposium</i> (Vol. 9411). Los Angeles, CA, United States: Springer Nature."},"publist_id":"5604","title":"Shape, homology, persistence, and stability","year":"2015","article_processing_charge":"No","date_updated":"2022-01-28T08:25:00Z"},{"type":"conference","date_published":"2015-02-05T00:00:00Z","status":"public","publisher":"IEEE","quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"7034731","month":"02","conference":{"name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing","start_date":"2014-09-22","location":"Timisoara, Romania","end_date":"2014-09-25"},"abstract":[{"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.","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"05","oa_version":"None","publication_status":"published","author":[{"first_name":"Olga","full_name":"Dunaeva, Olga","last_name":"Dunaeva"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"first_name":"Anton","full_name":"Lukyanov, Anton","last_name":"Lukyanov"},{"last_name":"Machin","full_name":"Machin, Michael","first_name":"Michael"},{"last_name":"Malkova","full_name":"Malkova, Daria","first_name":"Daria"}],"publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","doi":"10.1109/SYNASC.2014.81","language":[{"iso":"eng"}],"_id":"1568","related_material":{"record":[{"status":"public","id":"1289","relation":"later_version"}]},"scopus_import":1,"year":"2015","date_updated":"2023-02-21T16:57:29Z","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","title":"The classification of endoscopy images with persistent homology","date_created":"2018-12-11T11:52:46Z","publist_id":"5603","citation":{"chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, 7034731. IEEE, 2015. <a href=\"https://doi.org/10.1109/SYNASC.2014.81\">https://doi.org/10.1109/SYNASC.2014.81</a>.","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, IEEE, 2015, p. 7034731, doi:<a href=\"https://doi.org/10.1109/SYNASC.2014.81\">10.1109/SYNASC.2014.81</a>.","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: <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>. IEEE; 2015:7034731. doi:<a href=\"https://doi.org/10.1109/SYNASC.2014.81\">10.1109/SYNASC.2014.81</a>","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, Timisoara, Romania, 2015, p. 7034731.","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.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., &#38; Malkova, D. (2015). The classification of endoscopy images with persistent homology. In <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i> (p. 7034731). Timisoara, Romania: IEEE. <a href=\"https://doi.org/10.1109/SYNASC.2014.81\">https://doi.org/10.1109/SYNASC.2014.81</a>"}},{"month":"08","day":"01","oa_version":"None","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","author":[{"full_name":"Cao, Thanhtung","first_name":"Thanhtung","last_name":"Cao"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"full_name":"Tan, Tiowseng","first_name":"Tiowseng","last_name":"Tan"}],"publisher":"Elsevier","type":"journal_article","date_published":"2015-08-01T00:00:00Z","status":"public","department":[{"_id":"HeEd"}],"page":"507 - 519","volume":48,"quality_controlled":"1","intvolume":"        48","scopus_import":1,"date_updated":"2021-01-12T06:51:43Z","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","year":"2015","issue":"7","date_created":"2018-12-11T11:52:49Z","title":"Triangulations from topologically correct digital Voronoi diagrams","publist_id":"5593","citation":{"mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” <i>Computational Geometry</i>, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>.","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” <i>Computational Geometry</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. 2015;48(7):507-519. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” <i>Computational Geometry</i>, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","apa":"Cao, T., Edelsbrunner, H., &#38; Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>"},"publication":"Computational Geometry","doi":"10.1016/j.comgeo.2015.04.001","language":[{"iso":"eng"}],"_id":"1578"},{"doi":"10.1016/j.comgeo.2014.08.006","file_date_updated":"2020-07-14T12:45:02Z","_id":"1582","related_material":{"record":[{"relation":"other","id":"1584","status":"public"}]},"year":"2015","publist_id":"5589","date_created":"2018-12-11T11:52:51Z","citation":{"mla":"Biedl, Therese, et al. “Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 2, Elsevier, 2015, pp. 120–33, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">10.1016/j.comgeo.2014.08.006</a>.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">https://doi.org/10.1016/j.comgeo.2014.08.006</a>.","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.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 120–133.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. 2015;48(2):120-133. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">10.1016/j.comgeo.2014.08.006</a>","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Weighted straight skeletons in the plane,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 2. Elsevier, pp. 120–133, 2015.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.006\">https://doi.org/10.1016/j.comgeo.2014.08.006</a>"},"publisher":"Elsevier","date_published":"2015-02-01T00:00:00Z","page":"120 - 133","department":[{"_id":"HeEd"}],"volume":48,"quality_controlled":"1","ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"abstract":[{"text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.","lang":"eng"}],"publication_status":"published","publication":"Computational Geometry: Theory and Applications","language":[{"iso":"eng"}],"intvolume":"        48","scopus_import":1,"has_accepted_license":"1","oa":1,"date_updated":"2023-02-23T10:05:27Z","pubrep_id":"474","issue":"2","title":"Weighted straight skeletons in the plane","type":"journal_article","status":"public","month":"02","oa_version":"Published Version","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"checksum":"c1ef67f6ec925e12f73a96b8fe285ab4","file_name":"IST-2016-474-v1+1_1-s2.0-S0925772114000807-main.pdf","file_id":"5215","date_created":"2018-12-12T10:16:28Z","date_updated":"2020-07-14T12:45:02Z","creator":"system","content_type":"application/pdf","access_level":"open_access","file_size":505987,"relation":"main_file"}],"author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"first_name":"Stefan","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}]},{"doi":"10.1016/j.ipl.2014.09.021","file_date_updated":"2020-07-14T12:45:03Z","_id":"1583","citation":{"apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). A simple algorithm for computing positively weighted straight skeletons of monotone polygons. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">https://doi.org/10.1016/j.ipl.2014.09.021</a>","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” <i>Information Processing Letters</i>, 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. <i>Information Processing Letters</i>. 2015;115(2):243-247. doi:<a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">10.1016/j.ipl.2014.09.021</a>","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” <i>Information Processing Letters</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">https://doi.org/10.1016/j.ipl.2014.09.021</a>.","mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” <i>Information Processing Letters</i>, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:<a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">10.1016/j.ipl.2014.09.021</a>.","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."},"publist_id":"5588","date_created":"2018-12-11T11:52:51Z","year":"2015","department":[{"_id":"HeEd"}],"page":"243 - 247","volume":115,"quality_controlled":"1","publisher":"Elsevier","date_published":"2015-02-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","publication":"Information Processing Letters","language":[{"iso":"eng"}],"has_accepted_license":"1","scopus_import":1,"intvolume":"       115","title":"A simple algorithm for computing positively weighted straight skeletons of monotone polygons","oa":1,"pubrep_id":"473","date_updated":"2021-01-12T06:51:45Z","issue":"2","status":"public","type":"journal_article","day":"01","oa_version":"Published Version","file":[{"date_created":"2018-12-12T10:18:45Z","date_updated":"2020-07-14T12:45:03Z","checksum":"2779a648610c9b5c86d0b51a62816d23","file_name":"IST-2016-473-v1+1_1-s2.0-S0020019014001987-main.pdf","file_id":"5367","file_size":270137,"content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"system"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"last_name":"Held","full_name":"Held, Martin","first_name":"Martin"},{"last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","full_name":"Huber, Stefan"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}]},{"issue":"5","pubrep_id":"475","oa":1,"date_updated":"2023-02-23T10:05:22Z","title":"Reprint of: Weighted straight skeletons in the plane","has_accepted_license":"1","intvolume":"        48","scopus_import":1,"language":[{"iso":"eng"}],"publication":"Computational Geometry: Theory and Applications","author":[{"last_name":"Biedl","full_name":"Biedl, Therese","first_name":"Therese"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","first_name":"Stefan"},{"last_name":"Kaaser","first_name":"Dominik","full_name":"Kaaser, Dominik"},{"first_name":"Peter","full_name":"Palfrader, Peter","last_name":"Palfrader"}],"month":"07","file":[{"file_name":"IST-2016-475-v1+1_1-s2.0-S092577211500005X-main.pdf","file_id":"5292","checksum":"5b33719a86f7f4c8e5dc62c1b6893f49","date_updated":"2020-07-14T12:45:03Z","date_created":"2018-12-12T10:17:36Z","creator":"system","access_level":"open_access","content_type":"application/pdf","file_size":508379,"relation":"main_file"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"01","type":"journal_article","status":"public","year":"2015","publist_id":"5587","citation":{"mla":"Biedl, Therese, et al. “Reprint of: Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 5, Elsevier, 2015, pp. 429–42, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">10.1016/j.comgeo.2015.01.004</a>.","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “Reprint of: Weighted Straight Skeletons in the Plane.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">https://doi.org/10.1016/j.comgeo.2015.01.004</a>.","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.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “Reprint of: Weighted straight skeletons in the plane,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 5. Elsevier, pp. 429–442, 2015.","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. Reprint of: Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. 2015;48(5):429-442. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">10.1016/j.comgeo.2015.01.004</a>","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Computational Geometry: Theory and Applications 48 (2015) 429–442.","apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2015.01.004\">https://doi.org/10.1016/j.comgeo.2015.01.004</a>"},"date_created":"2018-12-11T11:52:51Z","related_material":{"record":[{"status":"public","id":"1582","relation":"other"}]},"_id":"1584","file_date_updated":"2020-07-14T12:45:03Z","doi":"10.1016/j.comgeo.2015.01.004","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["000"],"abstract":[{"text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.","lang":"eng"}],"date_published":"2015-07-01T00:00:00Z","publisher":"Elsevier","quality_controlled":"1","volume":48,"department":[{"_id":"HeEd"}],"page":"429 - 442"},{"doi":"10.1007/978-3-319-27261-0_28","_id":"1590","year":"2015","citation":{"chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In <i>Graph Drawing and Network Visualization</i>, 9411:335–47. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>.","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.","mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>.","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.","ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: <i>Graph Drawing and Network Visualization</i>. Vol 9411. Springer Nature; 2015:335-347. doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>","ieee":"O. Aichholzer <i>et al.</i>, “Representing directed trees as straight skeletons,” in <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–347.","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., &#38; Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In <i>Graph Drawing and Network Visualization</i> (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>"},"publist_id":"5581","date_created":"2018-12-11T11:52:54Z","date_published":"2015-11-27T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":9411,"department":[{"_id":"HeEd"}],"page":"335 - 347","abstract":[{"text":"The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed.","lang":"eng"}],"publication_status":"published","publication":"Graph Drawing and Network Visualization","language":[{"iso":"eng"}],"intvolume":"      9411","scopus_import":"1","article_processing_charge":"No","oa":1,"date_updated":"2022-01-28T09:10:37Z","title":"Representing directed trees as straight skeletons","type":"book_chapter","status":"public","alternative_title":["LNCS"],"publication_identifier":{"eisbn":["978-3-319-27261-0"],"isbn":["978-3-319-27260-3"]},"month":"11","conference":{"end_date":"2015-09-26","location":"Los Angeles, CA, United States","start_date":"2015-09-24","name":"GD: International Symposium on Graph Drawing"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","day":"27","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.01076"}],"author":[{"last_name":"Aichholzer","full_name":"Aichholzer, Oswin","first_name":"Oswin"},{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"last_name":"Hackl","full_name":"Hackl, Thomas","first_name":"Thomas"},{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","orcid":"0000-0002-8871-5814","first_name":"Stefan","full_name":"Huber, Stefan"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"},{"last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit","first_name":"Birgit"}]}]