--- _id: '521' abstract: - lang: eng text: Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension. author: - first_name: Kyle full_name: Austin, Kyle last_name: Austin - first_name: Ziga full_name: Virk, Ziga id: 2E36B656-F248-11E8-B48F-1D18A9856A87 last_name: Virk citation: ama: Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005 apa: Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005 chicago: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2016.10.005. ieee: K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017. ista: Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57. mla: Austin, Kyle, and Ziga Virk. “Higson Compactification and Dimension Raising.” Topology and Its Applications, vol. 215, Elsevier, 2017, pp. 45–57, doi:10.1016/j.topol.2016.10.005. short: K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57. date_created: 2018-12-11T11:46:56Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:01:21Z day: '01' department: - _id: HeEd doi: 10.1016/j.topol.2016.10.005 intvolume: ' 215' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.03954v1 month: '01' oa: 1 oa_version: Submitted Version page: 45 - 57 publication: Topology and its Applications publication_identifier: issn: - '01668641' publication_status: published publisher: Elsevier publist_id: '7299' quality_controlled: '1' status: public title: Higson compactification and dimension raising type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 215 year: '2017' ... --- _id: '568' abstract: - lang: eng text: 'We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).' 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. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16 apa: Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16 chicago: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16. ieee: P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017. ista: Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342. mla: Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:10.4310/HHA.2017.v19.n2.a16. short: P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342. date_created: 2018-12-11T11:47:14Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:03:12Z day: '01' department: - _id: UlWa - _id: HeEd doi: 10.4310/HHA.2017.v19.n2.a16 ec_funded: 1 intvolume: ' 19' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1507.04310 month: '01' oa: 1 oa_version: Submitted Version page: 313 - 342 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 2590DB08-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '701309' name: Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020) publication: Homology, Homotopy and Applications publication_identifier: issn: - '15320073' publication_status: published publisher: International Press publist_id: '7246' quality_controlled: '1' scopus_import: 1 status: public title: Persistence of zero sets type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2017' ... --- _id: '5803' abstract: - lang: eng text: Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept. 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. Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial Image Analysis. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:10.1007/978-3-319-59108-7_8' apa: 'Biswas, R., & Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In Combinatorial image analysis (Vol. 10256, pp. 93–104). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-59108-7_8' chicago: 'Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.' ieee: 'R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.' ista: 'Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.' mla: Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” Combinatorial Image Analysis, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:10.1007/978-3-319-59108-7_8. short: R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104. conference: end_date: 2017-06-21 location: Plovdiv, Bulgaria name: 'IWCIA: International Workshop on Combinatorial Image Analysis' start_date: 2017-06-19 date_created: 2019-01-08T20:42:56Z date_published: 2017-05-17T00:00:00Z date_updated: 2022-01-28T07:48:24Z day: '17' department: - _id: HeEd doi: 10.1007/978-3-319-59108-7_8 extern: '1' intvolume: ' 10256' language: - iso: eng month: '05' oa_version: None page: 93-104 place: Cham publication: Combinatorial image analysis publication_identifier: isbn: - 978-3-319-59107-0 - 978-3-319-59108-7 issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Construction of persistent Voronoi diagram on 3D digital plane type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 10256 year: '2017' ... --- _id: '688' abstract: - lang: eng text: 'We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. ' alternative_title: - LIPIcs author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: 'Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39' apa: 'Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39' chicago: Edelsbrunner, Herbert, and Hubert Wagner. “Topological Data Analysis with Bregman Divergences,” 77:391–3916. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. https://doi.org/10.4230/LIPIcs.SoCG.2017.39. ieee: H. Edelsbrunner and H. Wagner, “Topological data analysis with Bregman divergences,” presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia, 2017, vol. 77, pp. 391–3916. ista: Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916. mla: Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39. short: H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916. conference: end_date: 2017-07-07 location: Brisbane, Australia name: Symposium on Computational Geometry, SoCG start_date: 2017-07-04 date_created: 2018-12-11T11:47:56Z date_published: 2017-06-01T00:00:00Z date_updated: 2021-01-12T08:09:26Z day: '01' ddc: - '514' - '516' department: - _id: HeEd - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2017.39 file: - access_level: open_access checksum: 067ab0cb3f962bae6c3af6bf0094e0f3 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:03Z date_updated: 2020-07-14T12:47:42Z file_id: '4856' file_name: IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf file_size: 990546 relation: main_file file_date_updated: 2020-07-14T12:47:42Z has_accepted_license: '1' intvolume: ' 77' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version page: 391-3916 publication_identifier: issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7021' pubrep_id: '895' quality_controlled: '1' scopus_import: 1 status: public title: Topological data analysis with Bregman divergences 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: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 77 year: '2017' ... --- _id: '707' abstract: - lang: eng text: We answer a question of M. Gromov on the waist of the unit ball. author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Akopyan A, Karasev R. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 2017;49(4):690-693. doi:10.1112/blms.12062 apa: Akopyan, A., & Karasev, R. (2017). A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. Wiley-Blackwell. https://doi.org/10.1112/blms.12062 chicago: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. Wiley-Blackwell, 2017. https://doi.org/10.1112/blms.12062. ieee: A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” Bulletin of the London Mathematical Society, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017. ista: Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693. mla: Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society, vol. 49, no. 4, Wiley-Blackwell, 2017, pp. 690–93, doi:10.1112/blms.12062. short: A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693. date_created: 2018-12-11T11:48:02Z date_published: 2017-08-01T00:00:00Z date_updated: 2021-01-12T08:11:41Z day: '01' department: - _id: HeEd doi: 10.1112/blms.12062 ec_funded: 1 intvolume: ' 49' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.06279 month: '08' oa: 1 oa_version: Preprint page: 690 - 693 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Bulletin of the London Mathematical Society publication_identifier: issn: - '00246093' publication_status: published publisher: Wiley-Blackwell publist_id: '6982' quality_controlled: '1' scopus_import: 1 status: public title: 'A tight estimate for the waist of the ball ' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2017' ...