[{"day":"14","article_processing_charge":"Yes","has_accepted_license":"1","scopus_import":"1","date_published":"2020-12-14T00:00:00Z","publication":"Journal of Computational Geometry","citation":{"chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182.","mla":"Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7.","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7","ista":"Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182.","ama":"Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7"},"article_type":"original","page":"162-182","abstract":[{"text":"Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context.","lang":"eng"}],"issue":"2","type":"journal_article","oa_version":"Published Version","file":[{"creator":"asandaue","file_size":1449234,"content_type":"application/pdf","file_name":"2020_JournalOfComputationalGeometry_Edelsbrunner.pdf","access_level":"open_access","date_updated":"2021-08-11T11:55:11Z","date_created":"2021-08-11T11:55:11Z","success":1,"checksum":"f02d0b2b3838e7891a6c417fc34ffdcd","file_id":"9882","relation":"main_file"}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","_id":"9630","status":"public","title":"Topological data analysis in information space","ddc":["510","000"],"intvolume":" 11","month":"12","publication_identifier":{"eissn":["1920180X"]},"doi":"10.20382/jocg.v11i2a7","language":[{"iso":"eng"}],"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"quality_controlled":"1","project":[{"name":"Discretization in Geometry and Dynamics","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","grant_number":"I4887"}],"file_date_updated":"2021-08-11T11:55:11Z","license":"https://creativecommons.org/licenses/by/3.0/","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2021-07-04T22:01:26Z","date_updated":"2021-08-11T12:26:34Z","volume":11,"acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2020","publication_status":"published","publisher":"Carleton University","department":[{"_id":"HeEd"}]},{"page":"45 - 57","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1608.03954v1","open_access":"1"}],"citation":{"ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","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","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","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.","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."},"oa":1,"publication":"Topology and its Applications","language":[{"iso":"eng"}],"doi":"10.1016/j.topol.2016.10.005","date_published":"2017-01-01T00:00:00Z","publication_identifier":{"issn":["01668641"]},"day":"01","month":"01","department":[{"_id":"HeEd"}],"publisher":"Elsevier","intvolume":" 215","status":"public","title":"Higson compactification and dimension raising","publication_status":"published","_id":"521","year":"2017","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","volume":215,"date_updated":"2021-01-12T08:01:21Z","date_created":"2018-12-11T11:46:56Z","author":[{"first_name":"Kyle","last_name":"Austin","full_name":"Austin, Kyle"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","publist_id":"7299","abstract":[{"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.","lang":"eng"}]},{"day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2017-11-01T00:00:00Z","publication":"Topology and its Applications","citation":{"short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","mla":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.","chicago":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications. Elsevier, 2017. https://doi.org/10.1016/j.topol.2017.09.015.","ama":"Virk Z, Zastrow A. A new topology on the universal path space. Topology and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015","apa":"Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2017.09.015","ieee":"Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology and its Applications, vol. 231. Elsevier, pp. 186–196, 2017.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196."},"page":"186 - 196","abstract":[{"text":"We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.","lang":"eng"}],"type":"journal_article","oa_version":"None","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"737","title":"A new topology on the universal path space","status":"public","intvolume":" 231","month":"11","publication_identifier":{"issn":["01668641"]},"doi":"10.1016/j.topol.2017.09.015","language":[{"iso":"eng"}],"external_id":{"isi":["000413889100012"]},"isi":1,"quality_controlled":"1","publist_id":"6930","author":[{"id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk","full_name":"Virk, Ziga"},{"last_name":"Zastrow","first_name":"Andreas","full_name":"Zastrow, Andreas"}],"date_created":"2018-12-11T11:48:14Z","date_updated":"2023-09-27T12:53:01Z","volume":231,"year":"2017","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Elsevier"}]