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Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds.","lang":"eng"}],"page":"441 - 455","scopus_import":1,"language":[{"iso":"eng"}],"intvolume":" 150","publication":"Acta Mathematica Hungarica","doi":"10.1007/s10474-016-0648-4","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.","author":[{"first_name":"Sebastian","last_name":"Durst","full_name":"Durst, Sebastian"},{"full_name":"Kegel, Marc","last_name":"Kegel","first_name":"Marc"},{"first_name":"Mirko D","id":"34927512-F248-11E8-B48F-1D18A9856A87","last_name":"Klukas","full_name":"Klukas, Mirko D"}],"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","ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","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.","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.","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.","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","short":"S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455."},"publication_status":"published","type":"journal_article","volume":150,"status":"public","department":[{"_id":"HeEd"}],"_id":"1292","date_published":"2016-12-01T00:00:00Z","month":"12","date_updated":"2021-01-12T06:49:40Z","year":"2016","day":"01"},{"publication":"Israel Journal of Mathematics","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.","doi":"10.1007/s11856-016-1429-z","intvolume":" 216","language":[{"iso":"eng"}],"publist_id":"5938","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"}],"citation":{"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.","short":"A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845.","apa":"Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 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Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z.","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."},"type":"journal_article","volume":216,"status":"public","publication_status":"published","department":[{"_id":"HeEd"}],"_id":"1330","date_published":"2016-10-15T00:00:00Z","month":"10","year":"2016","date_updated":"2021-01-12T06:49:56Z","day":"15","oa":1,"date_created":"2018-12-11T11:51:24Z","ec_funded":1,"issue":"2","main_file_link":[{"url":"https://arxiv.org/abs/1506.06014","open_access":"1"}],"title":"Billiards in convex bodies with acute angles","publisher":"Springer","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","quality_controlled":"1","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"}],"page":"833 - 845","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"scopus_import":1},{"publist_id":"5885","author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"},{"last_name":"Sharipova","first_name":"Anastasia","full_name":"Sharipova, Anastasia"}],"publication":"Proceedings of the American Mathematical Society","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).","doi":"10.1090/proc/13062","intvolume":" 144","language":[{"iso":"eng"}],"volume":144,"type":"journal_article","status":"public","publication_status":"published","citation":{"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.","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","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 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","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.","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.","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."},"date_published":"2016-10-01T00:00:00Z","month":"10","department":[{"_id":"HeEd"}],"_id":"1360","day":"01","year":"2016","date_updated":"2021-01-12T06:50:09Z","date_created":"2018-12-11T11:51:34Z","ec_funded":1,"oa":1,"title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"American Mathematical Society","quality_controlled":"1","oa_version":"Preprint","issue":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1401.0442"}],"page":"4501 - 4513","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"}],"article_processing_charge":"No","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"scopus_import":1},{"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.","short":"P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164.","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.","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."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"volume":56,"type":"journal_article","status":"public","publication_status":"published","pubrep_id":"614","publication":"Discrete & Computational Geometry","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","doi":"10.1007/s00454-016-9794-2","intvolume":" 56","language":[{"iso":"eng"}],"publist_id":"5799","file_date_updated":"2020-07-14T12:44:53Z","author":[{"last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek"}],"year":"2016","date_updated":"2023-02-23T10:02:11Z","day":"01","related_material":{"record":[{"relation":"earlier_version","id":"1510","status":"public"}]},"department":[{"_id":"UlWa"},{"_id":"HeEd"}],"_id":"1408","date_published":"2016-07-01T00:00:00Z","month":"07","issue":"1","title":"On computability and triviality of well groups","publisher":"Springer","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","quality_controlled":"1","ddc":["510"],"oa":1,"date_created":"2018-12-11T11:51:51Z","ec_funded":1,"scopus_import":1,"license":"https://creativecommons.org/licenses/by/4.0/","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"}],"has_accepted_license":"1","page":"126 - 164","file":[{"content_type":"application/pdf","file_id":"4846","date_created":"2018-12-12T10:10:55Z","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","file_size":905303,"relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:44:53Z","checksum":"e0da023abf6b72abd8c6a8c76740d53c","creator":"system"}],"article_processing_charge":"Yes (via OA deal)","project":[{"_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","grant_number":"M01980","call_identifier":"FWF","name":"Robust invariants of Nonlinear Systems"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"date_updated":"2023-02-23T10:04:40Z","year":"2016","related_material":{"record":[{"id":"1568","relation":"earlier_version","status":"public"}]},"day":"01","department":[{"_id":"HeEd"}],"_id":"1289","date_published":"2016-11-01T00:00:00Z","month":"11","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"citation":{"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","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.","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.","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.","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.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22.","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"},"publication_status":"published","pubrep_id":"975","volume":83,"type":"journal_article","status":"public","intvolume":" 83","language":[{"iso":"eng"}],"publication":"Pattern Recognition Letters","doi":"10.1016/j.patrec.2015.12.012","file_date_updated":"2020-07-14T12:44:42Z","author":[{"first_name":"Olga","last_name":"Dunaeva","full_name":"Dunaeva, Olga"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Lukyanov","first_name":"Anton","full_name":"Lukyanov, Anton"},{"first_name":"Michael","last_name":"Machin","full_name":"Machin, Michael"},{"first_name":"Daria","last_name":"Malkova","full_name":"Malkova, Daria"},{"full_name":"Kuvaev, Roman","last_name":"Kuvaev","first_name":"Roman"},{"full_name":"Kashin, Sergey","last_name":"Kashin","first_name":"Sergey"}],"publist_id":"6027","scopus_import":1,"article_processing_charge":"No","abstract":[{"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.","lang":"eng"}],"file":[{"content_type":"application/pdf","file_id":"6334","file_name":"2016-Edelsbrunner_The_classification.pdf","date_created":"2019-04-17T07:55:51Z","checksum":"33458bbb8c32a339e1adeca6d5a1112d","creator":"dernst","date_updated":"2020-07-14T12:44:42Z","relation":"main_file","access_level":"open_access","file_size":1921113}],"has_accepted_license":"1","page":"13 - 22","issue":"1","oa_version":"Submitted Version","quality_controlled":"1","title":"The classification of endoscopy images with persistent homology","publisher":"Elsevier","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["004","514"],"oa":1,"date_created":"2018-12-11T11:51:10Z"},{"main_file_link":[{"url":"http://arxiv.org/abs/1510.00251","open_access":"1"}],"citation":{"ista":"Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216.","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","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.","ieee":"F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,” Journal of Complexity, vol. 33. Academic Press, pp. 199–216, 2016.","short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.","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"},"status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Academic Press","title":"On the discrepancy of jittered sampling","volume":33,"type":"journal_article","publication_status":"published","oa_version":"Submitted Version","quality_controlled":"1","acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition.","doi":"10.1016/j.jco.2015.11.003","publication":"Journal of Complexity","oa":1,"language":[{"iso":"eng"}],"intvolume":" 33","publist_id":"5549","date_created":"2018-12-11T11:53:03Z","author":[{"orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian"},{"full_name":"Steinerberger, Stefan","last_name":"Steinerberger","first_name":"Stefan"}],"year":"2016","date_updated":"2021-01-12T06:52:02Z","day":"01","scopus_import":1,"page":"199 - 216","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"}],"_id":"1617","department":[{"_id":"HeEd"}],"month":"04","date_published":"2016-04-01T00:00:00Z"},{"year":"2016","date_updated":"2022-01-28T08:10:11Z","day":"09","department":[{"_id":"HeEd"}],"_id":"5806","date_published":"2016-04-09T00:00:00Z","month":"04","alternative_title":["LNCS"],"place":"Cham","citation":{"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","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.","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.","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.","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.","short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, 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"},"volume":9647,"type":"conference","status":"public","conference":{"end_date":"2016-04-20","start_date":"2016-04-18","location":"Nantes, France","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery"},"publication_status":"published","publication":"Discrete Geometry for Computer Imagery","doi":"10.1007/978-3-319-32360-2_20","language":[{"iso":"eng"}],"extern":"1","intvolume":" 9647","publication_identifier":{"eisbn":["978-3-319-32360-2"],"isbn":["978-3-319-32359-6"],"issn":["0302-9743","1611-3349"]},"author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"}],"page":"256-267","abstract":[{"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.","lang":"eng"}],"article_processing_charge":"No","title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","publisher":"Springer Nature","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","quality_controlled":"1","oa_version":"None","date_created":"2019-01-08T20:44:37Z"},{"date_created":"2019-01-08T20:44:24Z","title":"On some local topological properties of naive discrete sphere","publisher":"Springer Nature","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"None","quality_controlled":"1","abstract":[{"lang":"eng","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."}],"page":"253-264","article_processing_charge":"No","publication":"Computational Topology in Image Context","doi":"10.1007/978-3-319-39441-1_23","language":[{"iso":"eng"}],"intvolume":" 9667","extern":"1","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"eisbn":["978-3-319-39441-1"],"isbn":["978-3-319-39440-4"]},"author":[{"full_name":"Sen, Nabhasmita","first_name":"Nabhasmita","last_name":"Sen"},{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas"},{"first_name":"Partha","last_name":"Bhowmick","full_name":"Bhowmick, Partha"}],"citation":{"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.","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","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.","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.","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., & 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"},"volume":9667,"type":"book_chapter","status":"public","conference":{"location":"Marseille, France","start_date":"2016-06-15","name":"CTIC: Computational Topology in Image Context","end_date":"2016-06-17"},"publication_status":"published","department":[{"_id":"HeEd"}],"_id":"5805","date_published":"2016-06-02T00:00:00Z","month":"06","alternative_title":["LNCS"],"place":"Cham","year":"2016","date_updated":"2022-01-28T08:01:22Z","day":"02"},{"citation":{"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","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.","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.","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.","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","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100."},"type":"book_chapter","volume":9448,"title":"On the connectivity and smoothness of discrete spherical circles","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publisher":"Springer Nature","status":"public","conference":{"start_date":"2015-11-24","location":"Kolkata, India","name":"IWCIA: International Workshop on Combinatorial Image Analysis","end_date":"2015-11-27"},"quality_controlled":"1","oa_version":"None","publication_status":"published","publication":"Combinatorial image analysis","doi":"10.1007/978-3-319-26145-4_7","language":[{"iso":"eng"}],"intvolume":" 9448","extern":"1","publication_identifier":{"issn":["0302-9743"],"isbn":["978-3-319-26144-7"],"eisbn":["978-3-319-26145-4"],"eissn":["1611-3349"]},"date_created":"2019-01-08T20:45:19Z","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"},{"first_name":"Valentin E.","last_name":"Brimkov","full_name":"Brimkov, Valentin E."}],"year":"2016","date_updated":"2022-01-28T08:13:03Z","day":"06","page":"86-100","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."}],"department":[{"_id":"HeEd"}],"article_processing_charge":"No","_id":"5809","date_published":"2016-01-06T00:00:00Z","month":"01","place":"Cham"},{"day":"10","related_material":{"record":[{"relation":"dissertation_contains","id":"1399","status":"public"}]},"year":"2016","date_updated":"2023-09-07T11:41:25Z","date_published":"2016-01-10T00:00:00Z","month":"01","department":[{"_id":"HeEd"}],"_id":"1662","type":"journal_article","volume":287,"status":"public","publication_status":"published","pubrep_id":"774","citation":{"ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016.","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","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","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."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"publist_id":"5488","file_date_updated":"2020-07-14T12:45:10Z","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-8379-3768","full_name":"Pausinger, Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","first_name":"Florian"}],"publication":"Advances in Mathematics","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.","doi":"10.1016/j.aim.2015.10.004","language":[{"iso":"eng"}],"intvolume":" 287","scopus_import":1,"has_accepted_license":"1","page":"674 - 703","abstract":[{"lang":"eng","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."}],"file":[{"file_size":248985,"relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:45:10Z","creator":"system","checksum":"f8869ec110c35c852ef6a37425374af7","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf","date_created":"2018-12-12T10:12:10Z","file_id":"4928","content_type":"application/pdf"}],"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"title":"Approximation and convergence of the intrinsic volume","publisher":"Academic Press","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","quality_controlled":"1","date_created":"2018-12-11T11:53:20Z","ec_funded":1,"ddc":["004"],"oa":1}]