--- _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 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' ... --- _id: '718' abstract: - lang: eng text: Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4. author: - 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: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 - first_name: Matthias full_name: Reitzner, Matthias last_name: Reitzner citation: ama: Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 2017;49(3):745-767. doi:10.1017/apr.2017.20 apa: Edelsbrunner, H., Nikitenko, A., & Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. Cambridge University Press. https://doi.org/10.1017/apr.2017.20 chicago: Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability. Cambridge University Press, 2017. https://doi.org/10.1017/apr.2017.20. ieee: H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” Advances in Applied Probability, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017. ista: Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767. mla: Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20. short: H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767. date_created: 2018-12-11T11:48:07Z date_published: 2017-09-01T00:00:00Z date_updated: 2023-09-07T12:07:12Z day: '01' department: - _id: HeEd doi: 10.1017/apr.2017.20 ec_funded: 1 external_id: arxiv: - '1607.05915' intvolume: ' 49' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1607.05915 month: '09' oa: 1 oa_version: Preprint page: 745 - 767 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Advances in Applied Probability publication_identifier: issn: - '00018678' publication_status: published publisher: Cambridge University Press publist_id: '6962' quality_controlled: '1' related_material: record: - id: '6287' relation: dissertation_contains status: public scopus_import: 1 status: public title: Expected sizes of poisson Delaunay mosaics and their discrete Morse functions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 49 year: '2017' ... --- _id: '6287' abstract: - lang: eng text: The main objects considered in the present work are simplicial and CW-complexes with vertices forming a random point cloud. In particular, we consider a Poisson point process in R^n and study Delaunay and Voronoi complexes of the first and higher orders and weighted Delaunay complexes obtained as sections of Delaunay complexes, as well as the Čech complex. Further, we examine theDelaunay complex of a Poisson point process on the sphere S^n, as well as of a uniform point cloud, which is equivalent to the convex hull, providing a connection to the theory of random polytopes. Each of the complexes in question can be endowed with a radius function, which maps its cells to the radii of appropriately chosen circumspheres, called the radius of the cell. Applying and developing discrete Morse theory for these functions, joining it together with probabilistic and sometimes analytic machinery, and developing several integral geometric tools, we aim at getting the distributions of circumradii of typical cells. For all considered complexes, we are able to generalize and obtain up to constants the distribution of radii of typical intervals of all types. In low dimensions the constants can be computed explicitly, thus providing the explicit expressions for the expected numbers of cells. In particular, it allows to find the expected density of simplices of every dimension for a Poisson point process in R^4, whereas the result for R^3 was known already in 1970's. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Nikitenko A. Discrete Morse theory for random complexes . 2017. doi:10.15479/AT:ISTA:th_873 apa: Nikitenko, A. (2017). Discrete Morse theory for random complexes . Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_873 chicago: Nikitenko, Anton. “Discrete Morse Theory for Random Complexes .” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_873. ieee: A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017. ista: Nikitenko A. 2017. Discrete Morse theory for random complexes . Institute of Science and Technology Austria. mla: Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_873. short: A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017. date_created: 2019-04-09T15:04:32Z date_published: 2017-10-27T00:00:00Z date_updated: 2023-09-15T12:10:34Z day: '27' ddc: - '514' - '516' - '519' degree_awarded: PhD department: - _id: HeEd doi: 10.15479/AT:ISTA:th_873 file: - access_level: open_access checksum: ece7e598a2f060b263c2febf7f3fe7f9 content_type: application/pdf creator: dernst date_created: 2019-04-09T14:54:51Z date_updated: 2020-07-14T12:47:26Z file_id: '6289' file_name: 2017_Thesis_Nikitenko.pdf file_size: 2324870 relation: main_file - access_level: closed checksum: 99b7ad76e317efd447af60f91e29b49b content_type: application/zip creator: dernst date_created: 2019-04-09T14:54:51Z date_updated: 2020-07-14T12:47:26Z file_id: '6290' file_name: 2017_Thesis_Nikitenko_source.zip file_size: 2863219 relation: source_file file_date_updated: 2020-07-14T12:47:26Z has_accepted_license: '1' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '86' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria pubrep_id: '873' related_material: record: - id: '718' relation: part_of_dissertation status: public - id: '5678' relation: part_of_dissertation status: public - id: '87' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: 'Discrete Morse theory for random complexes ' 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: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2017' ... --- _id: '1433' abstract: - lang: eng text: Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology. article_processing_charge: No article_type: original author: - first_name: Ulrich full_name: Bauer, Ulrich last_name: Bauer - first_name: Michael full_name: Kerber, Michael last_name: Kerber - first_name: Jan full_name: Reininghaus, Jan last_name: Reininghaus - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008 apa: Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008 chicago: Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation. Academic Press, 2017. https://doi.org/10.1016/j.jsc.2016.03.008. ieee: U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” Journal of Symbolic Computation, vol. 78. Academic Press, pp. 76–90, 2017. ista: Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90. mla: Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008. short: U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90. date_created: 2018-12-11T11:51:59Z date_published: 2017-01-01T00:00:00Z date_updated: 2023-09-20T09:42:40Z day: '01' department: - _id: HeEd doi: 10.1016/j.jsc.2016.03.008 ec_funded: 1 external_id: isi: - '000384396000005' intvolume: ' 78' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1016/j.jsc.2016.03.008 month: '01' oa: 1 oa_version: Published Version page: 76 - 90 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Journal of Symbolic Computation publication_identifier: issn: - ' 07477171' publication_status: published publisher: Academic Press publist_id: '5765' quality_controlled: '1' related_material: record: - id: '10894' relation: earlier_version status: public scopus_import: '1' status: public title: Phat - Persistent homology algorithms toolbox type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 78 year: '2017' ... --- _id: '1180' abstract: - lang: eng text: In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform. 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: Imre full_name: Bárány, Imre last_name: Bárány - first_name: Sinai full_name: Robins, Sinai last_name: Robins citation: ama: Akopyan A, Bárány I, Robins S. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 2017;308:627-644. doi:10.1016/j.aim.2016.12.026 apa: Akopyan, A., Bárány, I., & Robins, S. (2017). Algebraic vertices of non-convex polyhedra. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2016.12.026 chicago: Akopyan, Arseniy, Imre Bárány, and Sinai Robins. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2016.12.026. ieee: A. Akopyan, I. Bárány, and S. Robins, “Algebraic vertices of non-convex polyhedra,” Advances in Mathematics, vol. 308. Academic Press, pp. 627–644, 2017. ista: Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644. mla: Akopyan, Arseniy, et al. “Algebraic Vertices of Non-Convex Polyhedra.” Advances in Mathematics, vol. 308, Academic Press, 2017, pp. 627–44, doi:10.1016/j.aim.2016.12.026. short: A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644. date_created: 2018-12-11T11:50:34Z date_published: 2017-02-21T00:00:00Z date_updated: 2023-09-20T11:21:27Z day: '21' department: - _id: HeEd doi: 10.1016/j.aim.2016.12.026 ec_funded: 1 external_id: isi: - '000409292900015' intvolume: ' 308' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1508.07594 month: '02' oa: 1 oa_version: Submitted Version page: 627 - 644 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Advances in Mathematics publication_identifier: issn: - '00018708' publication_status: published publisher: Academic Press publist_id: '6173' quality_controlled: '1' scopus_import: '1' status: public title: Algebraic vertices of non-convex polyhedra type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 308 year: '2017' ... --- _id: '1173' abstract: - lang: eng text: We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions. acknowledgement: This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Glazyrin, Alexey last_name: Glazyrin - first_name: Oleg full_name: Musin, Oleg last_name: Musin - first_name: Anton full_name: Nikitenko, Anton id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87 last_name: Nikitenko orcid: 0000-0002-0659-3201 citation: ama: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y apa: Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y. ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane,” Combinatorica, vol. 37, no. 5. Springer, pp. 887–910, 2017. ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5), 887–910. mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica, vol. 37, no. 5, Springer, 2017, pp. 887–910, doi:10.1007/s00493-016-3308-y. short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910. date_created: 2018-12-11T11:50:32Z date_published: 2017-10-01T00:00:00Z date_updated: 2023-09-20T11:23:53Z day: '01' department: - _id: HeEd doi: 10.1007/s00493-016-3308-y ec_funded: 1 external_id: isi: - '000418056000005' intvolume: ' 37' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1411.6337 month: '10' oa: 1 oa_version: Submitted Version page: 887 - 910 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Combinatorica publication_identifier: issn: - '02099683' publication_status: published publisher: Springer publist_id: '6182' quality_controlled: '1' scopus_import: '1' status: public title: The Voronoi functional is maximized by the Delaunay triangulation in the plane type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 37 year: '2017' ...