--- _id: '1292' abstract: - lang: eng text: We give explicit formulas and algorithms for the computation of the Thurston–Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on Heegaard surfaces in convex position. Furthermore, we extend the results to rationally nullhomologous knots in arbitrary 3-manifolds. 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 full_name: Durst, Sebastian last_name: Durst - first_name: Marc full_name: Kegel, Marc last_name: Kegel - first_name: Mirko D full_name: Klukas, Mirko D id: 34927512-F248-11E8-B48F-1D18A9856A87 last_name: Klukas citation: ama: Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4 apa: Durst, S., Kegel, M., & Klukas, M. D. (2016). Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. Springer. https://doi.org/10.1007/s10474-016-0648-4 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. ieee: S. Durst, M. Kegel, and M. D. Klukas, “Computing the Thurston–Bennequin invariant in open books,” Acta Mathematica Hungarica, vol. 150, no. 2. Springer, pp. 441–455, 2016. ista: Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455. 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. short: S. Durst, M. Kegel, M.D. Klukas, Acta Mathematica Hungarica 150 (2016) 441–455. date_created: 2018-12-11T11:51:11Z date_published: 2016-12-01T00:00:00Z date_updated: 2021-01-12T06:49:40Z day: '01' department: - _id: HeEd doi: 10.1007/s10474-016-0648-4 intvolume: ' 150' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1605.00794 month: '12' oa: 1 oa_version: Preprint page: 441 - 455 publication: Acta Mathematica Hungarica publication_status: published publisher: Springer publist_id: '6023' quality_controlled: '1' scopus_import: 1 status: public title: Computing the Thurston–Bennequin invariant in open books type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 150 year: '2016' ... --- _id: '1330' abstract: - lang: eng 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. 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. author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy citation: ama: Akopyan A, Balitskiy A. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 2016;216(2):833-845. doi:10.1007/s11856-016-1429-z apa: Akopyan, A., & Balitskiy, A. (2016). Billiards in convex bodies with acute angles. Israel Journal of Mathematics. Springer. https://doi.org/10.1007/s11856-016-1429-z chicago: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics. Springer, 2016. https://doi.org/10.1007/s11856-016-1429-z. 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. ista: Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845. mla: Akopyan, Arseniy, and Alexey Balitskiy. “Billiards in Convex Bodies with Acute Angles.” Israel Journal of Mathematics, vol. 216, no. 2, Springer, 2016, pp. 833–45, doi:10.1007/s11856-016-1429-z. short: A. Akopyan, A. Balitskiy, Israel Journal of Mathematics 216 (2016) 833–845. date_created: 2018-12-11T11:51:24Z date_published: 2016-10-15T00:00:00Z date_updated: 2021-01-12T06:49:56Z day: '15' department: - _id: HeEd doi: 10.1007/s11856-016-1429-z ec_funded: 1 intvolume: ' 216' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1506.06014 month: '10' oa: 1 oa_version: Preprint page: 833 - 845 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Israel Journal of Mathematics publication_status: published publisher: Springer publist_id: '5938' quality_controlled: '1' scopus_import: 1 status: public title: Billiards in convex bodies with acute angles type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 216 year: '2016' ... --- _id: '1360' abstract: - lang: eng 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. ' 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). article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Alexey full_name: Balitskiy, Alexey last_name: Balitskiy - first_name: Roman full_name: Karasev, Roman last_name: Karasev - first_name: Anastasia full_name: Sharipova, Anastasia last_name: Sharipova citation: 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 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 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. ieee: A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” Proceedings of the American Mathematical Society, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016. ista: Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513. 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. short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513. date_created: 2018-12-11T11:51:34Z date_published: 2016-10-01T00:00:00Z date_updated: 2021-01-12T06:50:09Z day: '01' department: - _id: HeEd doi: 10.1090/proc/13062 ec_funded: 1 intvolume: ' 144' issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1401.0442 month: '10' oa: 1 oa_version: Preprint page: 4501 - 4513 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Proceedings of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5885' quality_controlled: '1' scopus_import: 1 status: public title: Elementary approach to closed billiard trajectories in asymmetric normed spaces type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 144 year: '2016' ... --- _id: '1408' abstract: - lang: eng text: 'The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.' acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). ' article_processing_charge: Yes (via OA deal) author: - first_name: Peter full_name: Franek, Peter id: 473294AE-F248-11E8-B48F-1D18A9856A87 last_name: Franek - first_name: Marek full_name: Krcál, Marek id: 33E21118-F248-11E8-B48F-1D18A9856A87 last_name: Krcál citation: 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 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 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. 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. ista: Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164. mla: Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” Discrete & Computational Geometry, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:10.1007/s00454-016-9794-2. short: P. Franek, M. Krcál, Discrete & Computational Geometry 56 (2016) 126–164. date_created: 2018-12-11T11:51:51Z date_published: 2016-07-01T00:00:00Z date_updated: 2023-02-23T10:02:11Z day: '01' ddc: - '510' department: - _id: UlWa - _id: HeEd doi: 10.1007/s00454-016-9794-2 ec_funded: 1 file: - access_level: open_access checksum: e0da023abf6b72abd8c6a8c76740d53c content_type: application/pdf creator: system date_created: 2018-12-12T10:10:55Z date_updated: 2020-07-14T12:44:53Z file_id: '4846' file_name: IST-2016-614-v1+1_s00454-016-9794-2.pdf file_size: 905303 relation: main_file file_date_updated: 2020-07-14T12:44:53Z has_accepted_license: '1' intvolume: ' 56' issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '07' oa: 1 oa_version: Published Version page: 126 - 164 project: - _id: 25F8B9BC-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M01980 name: Robust invariants of Nonlinear Systems - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Discrete & Computational Geometry publication_status: published publisher: Springer publist_id: '5799' pubrep_id: '614' quality_controlled: '1' related_material: record: - id: '1510' relation: earlier_version status: public scopus_import: 1 status: public title: On computability and triviality of well groups tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 56 year: '2016' ... --- _id: '1289' abstract: - lang: eng text: 'Aiming at the automatic diagnosis of tumors using narrow band imaging (NBI) magnifying endoscopic (ME) images of the stomach, we combine methods from image processing, topology, geometry, and machine learning to classify patterns into three classes: oval, tubular and irregular. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions.' article_processing_charge: No 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 - first_name: Michael full_name: Machin, Michael last_name: Machin - first_name: Daria full_name: Malkova, Daria last_name: Malkova - first_name: Roman full_name: Kuvaev, Roman last_name: Kuvaev - first_name: Sergey full_name: Kashin, Sergey last_name: Kashin 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 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 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. ieee: O. Dunaeva et al., “The classification of endoscopy images with persistent homology,” Pattern Recognition Letters, vol. 83, no. 1. Elsevier, pp. 13–22, 2016. ista: Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D, Kuvaev R, Kashin S. 2016. The classification of endoscopy images with persistent homology. Pattern Recognition Letters. 83(1), 13–22. 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. short: O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 13–22. date_created: 2018-12-11T11:51:10Z date_published: 2016-11-01T00:00:00Z date_updated: 2023-02-23T10:04:40Z day: '01' ddc: - '004' - '514' department: - _id: HeEd doi: 10.1016/j.patrec.2015.12.012 file: - access_level: open_access checksum: 33458bbb8c32a339e1adeca6d5a1112d content_type: application/pdf creator: dernst date_created: 2019-04-17T07:55:51Z date_updated: 2020-07-14T12:44:42Z file_id: '6334' file_name: 2016-Edelsbrunner_The_classification.pdf file_size: 1921113 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 83' issue: '1' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version page: 13 - 22 publication: Pattern Recognition Letters publication_status: published publisher: Elsevier publist_id: '6027' pubrep_id: '975' quality_controlled: '1' related_material: record: - id: '1568' relation: earlier_version status: public scopus_import: 1 status: public title: The classification of endoscopy images with persistent homology tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 83 year: '2016' ... --- _id: '1617' abstract: - lang: eng 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.' acknowledgement: We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition. author: - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 - first_name: Stefan full_name: Steinerberger, Stefan last_name: Steinerberger citation: ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. Journal of Complexity. 2016;33:199-216. doi:10.1016/j.jco.2015.11.003 apa: Pausinger, F., & Steinerberger, S. (2016). On the discrepancy of jittered sampling. Journal of Complexity. Academic Press. https://doi.org/10.1016/j.jco.2015.11.003 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. ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling. Journal of Complexity. 33, 199–216. mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered Sampling.” Journal of Complexity, vol. 33, Academic Press, 2016, pp. 199–216, doi:10.1016/j.jco.2015.11.003. short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216. date_created: 2018-12-11T11:53:03Z date_published: 2016-04-01T00:00:00Z date_updated: 2021-01-12T06:52:02Z day: '01' department: - _id: HeEd doi: 10.1016/j.jco.2015.11.003 intvolume: ' 33' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1510.00251 month: '04' oa: 1 oa_version: Submitted Version page: 199 - 216 publication: Journal of Complexity publication_status: published publisher: Academic Press publist_id: '5549' quality_controlled: '1' scopus_import: 1 status: public title: On the discrepancy of jittered sampling type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2016' ... --- _id: '5806' 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. alternative_title: - LNCS article_processing_charge: No author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick 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' 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' 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. 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. short: R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267. conference: end_date: 2016-04-20 location: Nantes, France name: 'DGCI: International Conference on Discrete Geometry for Computer Imagery' start_date: 2016-04-18 date_created: 2019-01-08T20:44:37Z date_published: 2016-04-09T00:00:00Z date_updated: 2022-01-28T08:10:11Z day: '09' department: - _id: HeEd doi: 10.1007/978-3-319-32360-2_20 extern: '1' intvolume: ' 9647' language: - iso: eng month: '04' oa_version: None page: 256-267 place: Cham publication: Discrete Geometry for Computer Imagery publication_identifier: eisbn: - 978-3-319-32360-2 isbn: - 978-3-319-32359-6 issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: On functionality of quadraginta octants of naive sphere with application to circle drawing type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9647 year: '2016' ... --- _id: '5805' 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. alternative_title: - LNCS article_processing_charge: No author: - first_name: Nabhasmita full_name: Sen, Nabhasmita last_name: Sen - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick citation: 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' 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' 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.' 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.' 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.' mla: Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.” Computational Topology in Image Context, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23. short: N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 253–264. conference: end_date: 2016-06-17 location: Marseille, France name: 'CTIC: Computational Topology in Image Context' start_date: 2016-06-15 date_created: 2019-01-08T20:44:24Z date_published: 2016-06-02T00:00:00Z date_updated: 2022-01-28T08:01:22Z day: '02' department: - _id: HeEd doi: 10.1007/978-3-319-39441-1_23 extern: '1' intvolume: ' 9667' language: - iso: eng month: '06' oa_version: None page: 253-264 place: Cham publication: Computational Topology in Image Context publication_identifier: eisbn: - 978-3-319-39441-1 eissn: - 1611-3349 isbn: - 978-3-319-39440-4 issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: On some local topological properties of naive discrete sphere type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9667 year: '2016' ... --- _id: '5809' 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. article_processing_charge: No author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Partha full_name: Bhowmick, Partha last_name: Bhowmick - first_name: Valentin E. full_name: Brimkov, Valentin E. last_name: Brimkov citation: 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' 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' 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.' ieee: 'R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.' ista: 'Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.' 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. short: R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100. conference: end_date: 2015-11-27 location: Kolkata, India name: 'IWCIA: International Workshop on Combinatorial Image Analysis' start_date: 2015-11-24 date_created: 2019-01-08T20:45:19Z date_published: 2016-01-06T00:00:00Z date_updated: 2022-01-28T08:13:03Z day: '06' department: - _id: HeEd doi: 10.1007/978-3-319-26145-4_7 extern: '1' intvolume: ' 9448' language: - iso: eng month: '01' oa_version: None page: 86-100 place: Cham publication: Combinatorial image analysis publication_identifier: eisbn: - 978-3-319-26145-4 eissn: - 1611-3349 isbn: - 978-3-319-26144-7 issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: On the connectivity and smoothness of discrete spherical circles type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 9448 year: '2016' ... --- _id: '1662' 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. 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." author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Florian full_name: Pausinger, Florian id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87 last_name: Pausinger orcid: 0000-0002-8379-3768 citation: ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 2016;287:674-703. doi:10.1016/j.aim.2015.10.004 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 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. ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016. 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.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004. short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703. date_created: 2018-12-11T11:53:20Z date_published: 2016-01-10T00:00:00Z date_updated: 2023-09-07T11:41:25Z day: '10' ddc: - '004' department: - _id: HeEd doi: 10.1016/j.aim.2015.10.004 ec_funded: 1 file: - access_level: open_access checksum: f8869ec110c35c852ef6a37425374af7 content_type: application/pdf creator: system 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 file_size: 248985 relation: main_file file_date_updated: 2020-07-14T12:45:10Z has_accepted_license: '1' intvolume: ' 287' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 674 - 703 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Advances in Mathematics publication_status: published publisher: Academic Press publist_id: '5488' pubrep_id: '774' quality_controlled: '1' related_material: record: - id: '1399' relation: dissertation_contains status: public scopus_import: 1 status: public title: Approximation and convergence of the intrinsic volume tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 287 year: '2016' ...