[{"project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1705.02870","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1705.02870"],"isi":["000442893500018"]},"language":[{"iso":"eng"}],"doi":"10.1214/18-AAP1389","month":"10","department":[{"_id":"HeEd"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","year":"2018","volume":28,"date_created":"2018-12-11T11:44:33Z","date_updated":"2023-09-15T12:10:35Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6287"}]},"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Nikitenko","first_name":"Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton"}],"publist_id":"7967","page":"3215 - 3238","article_type":"original","citation":{"ama":"Edelsbrunner H, Nikitenko A. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 2018;28(5):3215-3238. doi:10.1214/18-AAP1389","ieee":"H. Edelsbrunner and A. Nikitenko, “Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics,” Annals of Applied Probability, vol. 28, no. 5. Institute of Mathematical Statistics, pp. 3215–3238, 2018.","apa":"Edelsbrunner, H., & Nikitenko, A. (2018). Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AAP1389","ista":"Edelsbrunner H, Nikitenko A. 2018. Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics. Annals of Applied Probability. 28(5), 3215–3238.","short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability, vol. 28, no. 5, Institute of Mathematical Statistics, 2018, pp. 3215–38, doi:10.1214/18-AAP1389.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics.” Annals of Applied Probability. Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/18-AAP1389."},"publication":"Annals of Applied Probability","date_published":"2018-10-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","intvolume":" 28","status":"public","title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","_id":"87","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","type":"journal_article","issue":"5","abstract":[{"lang":"eng","text":"Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics."}]},{"date_published":"2018-05-31T00:00:00Z","publication":"Forum of Mathematics, Sigma","citation":{"mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7.","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018.","apa":"Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7"},"day":"31","has_accepted_license":"1","article_processing_charge":"No","file":[{"checksum":"5a71b24ba712a3eb2e46165a38fbc30a","date_updated":"2020-07-14T12:47:28Z","date_created":"2019-04-30T06:14:58Z","relation":"main_file","file_id":"6356","content_type":"application/pdf","file_size":249246,"creator":"dernst","access_level":"open_access","file_name":"2018_ForumMahtematics_Akopyan.pdf"}],"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"6355","status":"public","title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","ddc":["510"],"intvolume":" 6","abstract":[{"lang":"eng","text":"We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle."}],"type":"journal_article","doi":"10.1017/fms.2018.7","language":[{"iso":"eng"}],"external_id":{"isi":["000433915500001"],"arxiv":["1712.10205"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"month":"05","publication_identifier":{"issn":["2050-5094"]},"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"date_updated":"2023-09-19T14:50:12Z","date_created":"2019-04-30T06:09:57Z","volume":6,"year":"2018","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Cambridge University Press","file_date_updated":"2020-07-14T12:47:28Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","article_number":"e7"},{"author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Balitskiy, Alexey","last_name":"Balitskiy","first_name":"Alexey"},{"full_name":"Grigorev, Mikhail","last_name":"Grigorev","first_name":"Mikhail"}],"date_created":"2018-12-11T11:49:57Z","date_updated":"2023-09-20T12:08:51Z","volume":59,"year":"2018","publication_status":"published","publisher":"Springer","department":[{"_id":"HeEd"}],"file_date_updated":"2019-01-18T09:27:36Z","ec_funded":1,"publist_id":"6324","doi":"10.1007/s00454-017-9883-x","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000432205500011"]},"isi":1,"quality_controlled":"1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"month":"06","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"file":[{"relation":"main_file","file_id":"5844","date_updated":"2019-01-18T09:27:36Z","date_created":"2019-01-18T09:27:36Z","success":1,"file_name":"2018_DiscreteComp_Akopyan.pdf","access_level":"open_access","content_type":"application/pdf","file_size":482518,"creator":"dernst"}],"oa_version":"Published Version","_id":"1064","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["516","000"],"title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","status":"public","intvolume":" 59","abstract":[{"text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets.","lang":"eng"}],"issue":"4","type":"journal_article","date_published":"2018-06-01T00:00:00Z","publication":"Discrete & Computational Geometry","citation":{"chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry. Springer, 2018. https://doi.org/10.1007/s00454-017-9883-x.","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009.","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” Discrete & Computational Geometry, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:10.1007/s00454-017-9883-x.","apa":"Akopyan, A., Balitskiy, A., & Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-017-9883-x","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” Discrete & Computational Geometry, vol. 59, no. 4. Springer, pp. 1001–1009, 2018.","ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 59(4), 1001–1009.","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete & Computational Geometry. 2018;59(4):1001-1009. doi:10.1007/s00454-017-9883-x"},"article_type":"original","page":"1001-1009","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1"},{"date_created":"2018-12-11T11:44:30Z","date_updated":"2023-12-18T10:51:02Z","oa_version":"Preprint","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"last_name":"Avvakumov","first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"8156"}]},"status":"public","title":"Convex fair partitions into arbitrary number of pieces","publication_status":"published","publisher":"arXiv","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"75","year":"2018","abstract":[{"text":"We prove that any convex body in the plane can be partitioned into m convex parts of equal areas and perimeters for any integer m≥2; this result was previously known for prime powers m=pk. We also give a higher-dimensional generalization.","lang":"eng"}],"ec_funded":1,"article_number":"1804.03057","type":"preprint","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1804.03057","open_access":"1"}],"citation":{"ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","apa":"Akopyan, A., Avvakumov, S., & Karasev, R. (2018). Convex fair partitions into arbitrary number of pieces. arXiv. https://doi.org/10.48550/arXiv.1804.03057","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 1804.03057.","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","chicago":"Akopyan, Arseniy, Sergey Avvakumov, and Roman Karasev. “Convex Fair Partitions into Arbitrary Number of Pieces.” arXiv, 2018. https://doi.org/10.48550/arXiv.1804.03057.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (2018).","mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057."},"external_id":{"arxiv":["1804.03057"]},"month":"09","day":"13","article_processing_charge":"No"},{"doi":"10.1142/S0218195916600050","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","month":"04","author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan","last_name":"Huber","full_name":"Huber, Stefan"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10892"}]},"date_updated":"2023-02-21T16:06:22Z","date_created":"2018-12-11T11:46:43Z","volume":26,"year":"2017","acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","publication_status":"published","publisher":"World Scientific Publishing","department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:46:35Z","publist_id":"7338","date_published":"2017-04-13T00:00:00Z","publication":"International Journal of Computational Geometry and Applications","citation":{"mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4, World Scientific Publishing, 2017, pp. 211–29, doi:10.1142/S0218195916600050.","short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” International Journal of Computational Geometry and Applications. World Scientific Publishing, 2017. https://doi.org/10.1142/S0218195916600050.","ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 2017;26(3-4):211-229. doi:10.1142/S0218195916600050","ista":"Biedl T, Huber S, Palfrader P. 2017. Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. 26(3–4), 211–229.","apa":"Biedl, T., Huber, S., & Palfrader, P. (2017). Planar matchings for weighted straight skeletons. International Journal of Computational Geometry and Applications. World Scientific Publishing. https://doi.org/10.1142/S0218195916600050","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” International Journal of Computational Geometry and Applications, vol. 26, no. 3–4. World Scientific Publishing, pp. 211–229, 2017."},"page":"211 - 229","day":"13","has_accepted_license":"1","scopus_import":1,"pubrep_id":"949","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"4758","date_created":"2018-12-12T10:09:34Z","date_updated":"2020-07-14T12:46:35Z","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","access_level":"open_access","content_type":"application/pdf","file_size":769296,"creator":"system"}],"_id":"481","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Planar matchings for weighted straight skeletons","ddc":["004","514","516"],"intvolume":" 26","abstract":[{"lang":"eng","text":"We introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent. By translating the planar matching problem into a corresponding stable roommates problem we show that such matchings always exist. Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process. We present a generalized and unified approach to treat structural changes in the wavefront that focuses on the restoration of weak planarity by finding planar matchings."}],"issue":"3-4","type":"journal_article"},{"status":"public","title":"Higson compactification and dimension raising","publication_status":"published","department":[{"_id":"HeEd"}],"intvolume":" 215","publisher":"Elsevier","_id":"521","year":"2017","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:01:21Z","date_created":"2018-12-11T11:46:56Z","oa_version":"Submitted Version","volume":215,"author":[{"last_name":"Austin","first_name":"Kyle","full_name":"Austin, Kyle"},{"full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","last_name":"Virk","first_name":"Ziga"}],"type":"journal_article","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"}],"publist_id":"7299","quality_controlled":"1","page":"45 - 57","publication":"Topology and its Applications","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"citation":{"short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 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.","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.","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","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."},"oa":1,"language":[{"iso":"eng"}],"date_published":"2017-01-01T00:00:00Z","doi":"10.1016/j.topol.2016.10.005","day":"01","month":"01","publication_identifier":{"issn":["01668641"]}},{"publist_id":"7246","ec_funded":1,"author":[{"full_name":"Franek, Peter","last_name":"Franek","first_name":"Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"volume":19,"date_updated":"2021-01-12T08:03:12Z","date_created":"2018-12-11T11:47:14Z","year":"2017","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"International Press","publication_status":"published","publication_identifier":{"issn":["15320073"]},"month":"01","doi":"10.4310/HHA.2017.v19.n2.a16","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1507.04310","open_access":"1"}],"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"},{"name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425","grant_number":"701309"}],"quality_controlled":"1","issue":"2","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)."}],"type":"journal_article","oa_version":"Submitted Version","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"568","intvolume":" 19","title":"Persistence of zero sets","status":"public","day":"01","scopus_import":1,"date_published":"2017-01-01T00:00:00Z","citation":{"ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","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","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","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.","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."},"publication":"Homology, Homotopy and Applications","page":"313 - 342"},{"citation":{"short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 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.","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.","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","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."},"publication":"Combinatorial image analysis","page":"93-104","date_published":"2017-05-17T00:00:00Z","article_processing_charge":"No","day":"17","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"5803","intvolume":" 10256","title":"Construction of persistent Voronoi diagram on 3D digital plane","status":"public","oa_version":"None","type":"book_chapter","alternative_title":["LNCS"],"abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","doi":"10.1007/978-3-319-59108-7_8","conference":{"end_date":"2017-06-21","location":"Plovdiv, Bulgaria","start_date":"2017-06-19","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"month":"05","year":"2017","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"}],"volume":10256,"date_created":"2019-01-08T20:42:56Z","date_updated":"2022-01-28T07:48:24Z","place":"Cham","extern":"1"},{"publication_identifier":{"issn":["18688969"]},"month":"06","language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.SoCG.2017.39","conference":{"name":"Symposium on Computational Geometry, SoCG","location":"Brisbane, Australia","start_date":"2017-07-04","end_date":"2017-07-07"},"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"publist_id":"7021","file_date_updated":"2020-07-14T12:47:42Z","volume":77,"date_created":"2018-12-11T11:47:56Z","date_updated":"2021-01-12T08:09:26Z","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Hubert"}],"department":[{"_id":"HeEd"},{"_id":"UlWa"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","year":"2017","has_accepted_license":"1","day":"01","scopus_import":1,"date_published":"2017-06-01T00:00:00Z","page":"391-3916","citation":{"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.","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.","ista":"Edelsbrunner H, Wagner H. 2017. Topological data analysis with Bregman divergences. Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","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.","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","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"},"abstract":[{"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. 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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","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.","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","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.","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 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.","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."},"publication":"Bulletin of the London Mathematical Society","date_published":"2017-08-01T00:00:00Z","type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"We answer a question of M. Gromov on the waist of the unit ball."}],"intvolume":" 49","status":"public","title":"A tight estimate for the waist of the ball ","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"707","oa_version":"Preprint"},{"department":[{"_id":"HeEd"}],"publisher":"Cambridge University Press","publication_status":"published","year":"2017","volume":49,"date_updated":"2023-09-07T12:07:12Z","date_created":"2018-12-11T11:48:07Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6287"}]},"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"},{"last_name":"Reitzner","first_name":"Matthias","full_name":"Reitzner, Matthias"}],"ec_funded":1,"publist_id":"6962","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35"}],"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1607.05915","open_access":"1"}],"external_id":{"arxiv":["1607.05915"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1017/apr.2017.20","publication_identifier":{"issn":["00018678"]},"month":"09","intvolume":" 49","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"718","oa_version":"Preprint","type":"journal_article","issue":"3","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."}],"page":"745 - 767","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","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.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 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.","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."},"publication":"Advances in Applied Probability","date_published":"2017-09-01T00:00:00Z","scopus_import":1,"day":"01"},{"related_material":{"record":[{"id":"718","relation":"part_of_dissertation","status":"public"},{"id":"5678","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"87"}]},"author":[{"full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","first_name":"Anton","last_name":"Nikitenko"}],"date_created":"2019-04-09T15:04:32Z","date_updated":"2023-09-15T12:10:34Z","year":"2017","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"publication_status":"published","file_date_updated":"2020-07-14T12:47:26Z","doi":"10.15479/AT:ISTA:th_873","language":[{"iso":"eng"}],"supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"degree_awarded":"PhD","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publication_identifier":{"issn":["2663-337X"]},"month":"10","pubrep_id":"873","file":[{"file_size":2324870,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2017_Thesis_Nikitenko.pdf","checksum":"ece7e598a2f060b263c2febf7f3fe7f9","date_created":"2019-04-09T14:54:51Z","date_updated":"2020-07-14T12:47:26Z","relation":"main_file","file_id":"6289"},{"file_id":"6290","relation":"source_file","checksum":"99b7ad76e317efd447af60f91e29b49b","date_updated":"2020-07-14T12:47:26Z","date_created":"2019-04-09T14:54:51Z","access_level":"closed","file_name":"2017_Thesis_Nikitenko_source.zip","creator":"dernst","file_size":2863219,"content_type":"application/zip"}],"oa_version":"Published Version","_id":"6287","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Discrete Morse theory for random complexes ","ddc":["514","516","519"],"abstract":[{"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.","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"date_published":"2017-10-27T00:00:00Z","citation":{"short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","mla":"Nikitenko, Anton. Discrete Morse Theory for Random Complexes . Institute of Science and Technology Austria, 2017, doi: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.","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","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."},"page":"86","article_processing_charge":"No","has_accepted_license":"1","day":"27"},{"page":"76 - 90","article_type":"original","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","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","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.","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","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.","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."},"publication":"Journal of Symbolic Computation","date_published":"2017-01-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","intvolume":" 78","status":"public","title":"Phat - Persistent homology algorithms toolbox","_id":"1433","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Published Version","type":"journal_article","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."}],"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7"}],"isi":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"oa":1,"external_id":{"isi":["000384396000005"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.jsc.2016.03.008","publication_identifier":{"issn":[" 07477171"]},"month":"01","publisher":"Academic Press","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2017","volume":78,"date_updated":"2023-09-20T09:42:40Z","date_created":"2018-12-11T11:51:59Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10894"}]},"author":[{"first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"full_name":"Kerber, Michael","first_name":"Michael","last_name":"Kerber"},{"last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"},{"id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert","full_name":"Wagner, Hubert"}],"publist_id":"5765","ec_funded":1},{"date_published":"2017-02-21T00:00:00Z","citation":{"short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 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.","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.","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","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."},"publication":"Advances in Mathematics","page":"627 - 644","article_processing_charge":"No","day":"21","scopus_import":"1","oa_version":"Submitted Version","_id":"1180","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 308","title":"Algebraic vertices of non-convex polyhedra","status":"public","abstract":[{"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.","lang":"eng"}],"type":"journal_article","doi":"10.1016/j.aim.2016.12.026","language":[{"iso":"eng"}],"external_id":{"isi":["000409292900015"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["00018708"]},"month":"02","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Bárány, Imre","first_name":"Imre","last_name":"Bárány"},{"full_name":"Robins, Sinai","first_name":"Sinai","last_name":"Robins"}],"volume":308,"date_updated":"2023-09-20T11:21:27Z","date_created":"2018-12-11T11:50:34Z","year":"2017","department":[{"_id":"HeEd"}],"publisher":"Academic Press","publication_status":"published","ec_funded":1,"publist_id":"6173"},{"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1411.6337","open_access":"1"}],"external_id":{"isi":["000418056000005"]},"quality_controlled":"1","isi":1,"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"doi":"10.1007/s00493-016-3308-y","language":[{"iso":"eng"}],"month":"10","publication_identifier":{"issn":["02099683"]},"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.","year":"2017","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Glazyrin, Alexey","last_name":"Glazyrin","first_name":"Alexey"},{"last_name":"Musin","first_name":"Oleg","full_name":"Musin, Oleg"},{"last_name":"Nikitenko","first_name":"Anton","orcid":"0000-0002-0659-3201","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton"}],"date_updated":"2023-09-20T11:23:53Z","date_created":"2018-12-11T11:50:32Z","volume":37,"ec_funded":1,"publist_id":"6182","publication":"Combinatorica","citation":{"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.","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.","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","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.","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","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."},"page":"887 - 910","date_published":"2017-10-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1173","status":"public","title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","intvolume":" 37","oa_version":"Submitted Version","type":"journal_article","abstract":[{"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.","lang":"eng"}],"issue":"5"},{"type":"journal_article","issue":"5","abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field."}],"intvolume":" 369","status":"public","title":"The Morse theory of Čech and delaunay complexes","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1072","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","page":"3741 - 3762","article_type":"original","citation":{"chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society. American Mathematical Society, 2017. https://doi.org/10.1090/tran/6991.","short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Complexes.” Transactions of the American Mathematical Society, vol. 369, no. 5, American Mathematical Society, 2017, pp. 3741–62, doi:10.1090/tran/6991.","ieee":"U. Bauer and H. Edelsbrunner, “The Morse theory of Čech and delaunay complexes,” Transactions of the American Mathematical Society, vol. 369, no. 5. American Mathematical Society, pp. 3741–3762, 2017.","apa":"Bauer, U., & Edelsbrunner, H. (2017). The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6991","ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762.","ama":"Bauer U, Edelsbrunner H. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 2017;369(5):3741-3762. doi:10.1090/tran/6991"},"publication":"Transactions of the American Mathematical Society","date_published":"2017-05-01T00:00:00Z","ec_funded":1,"publist_id":"6311","publisher":"American Mathematical Society","department":[{"_id":"HeEd"}],"publication_status":"published","acknowledgement":"This research has been supported by the EU project Toposys(FP7-ICT-318493-STREP), by ESF under the ACAT Research Network Programme, by the Russian Government under mega project 11.G34.31.0053, and by the DFG Collaborative Research Center SFB/TRR 109 “Discretization in Geometry and Dynamics”.","year":"2017","volume":369,"date_updated":"2023-09-20T12:05:56Z","date_created":"2018-12-11T11:49:59Z","author":[{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"}],"month":"05","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000398030400024"],"arxiv":["1312.1231"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.1231"}],"language":[{"iso":"eng"}],"doi":"10.1090/tran/6991"},{"department":[{"_id":"KrCh"},{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","year":"2017","volume":122,"date_updated":"2023-09-20T12:08:18Z","date_created":"2018-12-11T11:49:57Z","author":[{"first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F"}],"publist_id":"6323","ec_funded":1,"file_date_updated":"2019-10-15T07:44:51Z","project":[{"name":"Modern Graph Algorithmic Techniques in Formal Verification","call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23"},{"name":"Game Theory","call_identifier":"FWF","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"isi":["000399506600005"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.ipl.2017.02.003","publication_identifier":{"issn":["00200190"]},"month":"06","intvolume":" 122","ddc":["000"],"title":"Pushdown reachability with constant treewidth","status":"public","_id":"1065","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"file_id":"4998","relation":"main_file","date_updated":"2019-10-15T07:44:51Z","date_created":"2018-12-12T10:13:17Z","access_level":"open_access","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","creator":"system","content_type":"application/pdf","file_size":247657}],"oa_version":"Submitted Version","pubrep_id":"991","type":"journal_article","abstract":[{"lang":"eng","text":"We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs."}],"page":"25 - 29","citation":{"apa":"Chatterjee, K., & Osang, G. F. (2017). Pushdown reachability with constant treewidth. Information Processing Letters. Elsevier. https://doi.org/10.1016/j.ipl.2017.02.003","ieee":"K. Chatterjee and G. F. Osang, “Pushdown reachability with constant treewidth,” Information Processing Letters, vol. 122. Elsevier, pp. 25–29, 2017.","ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29.","ama":"Chatterjee K, Osang GF. Pushdown reachability with constant treewidth. Information Processing Letters. 2017;122:25-29. doi:10.1016/j.ipl.2017.02.003","chicago":"Chatterjee, Krishnendu, and Georg F Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters. Elsevier, 2017. https://doi.org/10.1016/j.ipl.2017.02.003.","short":"K. Chatterjee, G.F. Osang, Information Processing Letters 122 (2017) 25–29.","mla":"Chatterjee, Krishnendu, and Georg F. Osang. “Pushdown Reachability with Constant Treewidth.” Information Processing Letters, vol. 122, Elsevier, 2017, pp. 25–29, doi:10.1016/j.ipl.2017.02.003."},"publication":"Information Processing Letters","date_published":"2017-06-01T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"No","day":"01"},{"publication":"Monthly Notices of the Royal Astronomical Society","citation":{"ista":"Pranav P, Edelsbrunner H, Van De Weygaert R, Vegter G, Kerber M, Jones B, Wintraecken M. 2017. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 465(4), 4281–4310.","ieee":"P. Pranav et al., “The topology of the cosmic web in terms of persistent Betti numbers,” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4. Oxford University Press, pp. 4281–4310, 2017.","apa":"Pranav, P., Edelsbrunner, H., Van De Weygaert, R., Vegter, G., Kerber, M., Jones, B., & Wintraecken, M. (2017). The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. Oxford University Press. https://doi.org/10.1093/mnras/stw2862","ama":"Pranav P, Edelsbrunner H, Van De Weygaert R, et al. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society. 2017;465(4):4281-4310. doi:10.1093/mnras/stw2862","chicago":"Pranav, Pratyush, Herbert Edelsbrunner, Rien Van De Weygaert, Gert Vegter, Michael Kerber, Bernard Jones, and Mathijs Wintraecken. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society. Oxford University Press, 2017. https://doi.org/10.1093/mnras/stw2862.","mla":"Pranav, Pratyush, et al. “The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.” Monthly Notices of the Royal Astronomical Society, vol. 465, no. 4, Oxford University Press, 2017, pp. 4281–310, doi:10.1093/mnras/stw2862.","short":"P. Pranav, H. Edelsbrunner, R. Van De Weygaert, G. Vegter, M. Kerber, B. Jones, M. Wintraecken, Monthly Notices of the Royal Astronomical Society 465 (2017) 4281–4310."},"page":"4281 - 4310","date_published":"2017-01-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1022","title":"The topology of the cosmic web in terms of persistent Betti numbers","status":"public","intvolume":" 465","oa_version":"Submitted Version","type":"journal_article","abstract":[{"text":"We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys.","lang":"eng"}],"issue":"4","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.04519"}],"oa":1,"external_id":{"isi":["000395170200039"]},"quality_controlled":"1","isi":1,"doi":"10.1093/mnras/stw2862","language":[{"iso":"eng"}],"month":"01","publication_identifier":{"issn":["00358711"]},"year":"2017","acknowledgement":"Part of this work has been supported by the 7th Framework Programme for Research of the European Commission, under FETOpen grant number 255827 (CGL Computational Geometry Learning) and ERC advanced grant, URSAT (Understanding Random Systems via Algebraic Topology) number 320422.","publication_status":"published","publisher":"Oxford University Press","department":[{"_id":"HeEd"}],"author":[{"full_name":"Pranav, Pratyush","last_name":"Pranav","first_name":"Pratyush"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"last_name":"Van De Weygaert","first_name":"Rien","full_name":"Van De Weygaert, Rien"},{"last_name":"Vegter","first_name":"Gert","full_name":"Vegter, Gert"},{"last_name":"Kerber","first_name":"Michael","full_name":"Kerber, Michael"},{"last_name":"Jones","first_name":"Bernard","full_name":"Jones, Bernard"},{"full_name":"Wintraecken, Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken"}],"date_created":"2018-12-11T11:49:44Z","date_updated":"2023-09-22T09:40:55Z","volume":465,"publist_id":"6373"},{"author":[{"full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk"},{"first_name":"Andreas","last_name":"Zastrow","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","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publist_id":"6930","doi":"10.1016/j.topol.2017.09.015","language":[{"iso":"eng"}],"external_id":{"isi":["000413889100012"]},"quality_controlled":"1","isi":1,"month":"11","publication_identifier":{"issn":["01668641"]},"oa_version":"None","_id":"737","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"A new topology on the universal path space","intvolume":" 231","abstract":[{"lang":"eng","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."}],"type":"journal_article","date_published":"2017-11-01T00:00:00Z","publication":"Topology and its Applications","citation":{"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.","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.","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.","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.","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"},"page":"186 - 196","day":"01","article_processing_charge":"No","scopus_import":"1"},{"month":"07","publication_identifier":{"isbn":["978-331956930-7"]},"conference":{"end_date":"2015-07-23","start_date":"2015-07-20","location":"Kalamata, Greece","name":"ACA: Applications of Computer Algebra"},"doi":"10.1007/978-3-319-56932-1_8","language":[{"iso":"eng"}],"external_id":{"isi":["000434088200008"]},"quality_controlled":"1","isi":1,"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"publist_id":"6812","ec_funded":1,"author":[{"last_name":"Ethier","first_name":"Marc","full_name":"Ethier, Marc"},{"last_name":"Jablonski","first_name":"Grzegorz","orcid":"0000-0002-3536-9866","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","full_name":"Jablonski, Grzegorz"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"date_updated":"2023-09-26T15:50:52Z","date_created":"2018-12-11T11:48:46Z","volume":198,"year":"2017","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","day":"27","article_processing_charge":"No","scopus_import":"1","date_published":"2017-07-27T00:00:00Z","publication":"Special Sessions in Applications of Computer Algebra","citation":{"chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In Special Sessions in Applications of Computer Algebra, 198:119–36. Springer, 2017. https://doi.org/10.1007/978-3-319-56932-1_8.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136.","mla":"Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” Special Sessions in Applications of Computer Algebra, vol. 198, Springer, 2017, pp. 119–36, doi:10.1007/978-3-319-56932-1_8.","apa":"Ethier, M., Jablonski, G., & Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In Special Sessions in Applications of Computer Algebra (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. https://doi.org/10.1007/978-3-319-56932-1_8","ieee":"M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps with the Kronecker canonical form,” in Special Sessions in Applications of Computer Algebra, Kalamata, Greece, 2017, vol. 198, pp. 119–136.","ista":"Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with the Kronecker canonical form. Special Sessions in Applications of Computer Algebra. ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.","ama":"Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: Special Sessions in Applications of Computer Algebra. Vol 198. Springer; 2017:119-136. doi:10.1007/978-3-319-56932-1_8"},"page":"119 - 136","abstract":[{"text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.","lang":"eng"}],"type":"conference","alternative_title":["PROMS"],"oa_version":"None","_id":"836","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Finding eigenvalues of self-maps with the Kronecker canonical form","intvolume":" 198"},{"publication_identifier":{"issn":["03029743"]},"month":"07","doi":"10.1007/978-3-319-64689-3_32","conference":{"location":"Ystad, Sweden","start_date":"2017-08-22","end_date":"2017-08-24","name":"CAIP: Computer Analysis of Images and Patterns"},"language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000432085900032"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.02045"}],"quality_controlled":"1","isi":1,"publist_id":"6815","author":[{"orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","first_name":"Teresa","full_name":"Heiss, Teresa"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert","last_name":"Wagner"}],"volume":10424,"date_created":"2018-12-11T11:48:45Z","date_updated":"2023-09-26T16:10:03Z","year":"2017","editor":[{"first_name":"Michael","last_name":"Felsberg","full_name":"Felsberg, Michael"},{"first_name":"Anders","last_name":"Heyden","full_name":"Heyden, Anders"},{"full_name":"Krüger, Norbert","first_name":"Norbert","last_name":"Krüger"}],"department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","article_processing_charge":"No","day":"28","scopus_import":"1","date_published":"2017-07-28T00:00:00Z","citation":{"short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","mla":"Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32.","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:10.1007/978-3-319-64689-3_32","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.","apa":"Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409."},"page":"397 - 409","abstract":[{"lang":"eng","text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams."}],"type":"conference","alternative_title":["LNCS"],"oa_version":"Submitted Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"833","intvolume":" 10424","status":"public","title":"Streaming algorithm for Euler characteristic curves of multidimensional images"},{"article_processing_charge":"No","publication_identifier":{"eisbn":["9781498711425"]},"month":"11","day":"09","scopus_import":"1","series_title":"Handbook of Discrete and Computational Geometry","doi":"10.1201/9781315119601","date_published":"2017-11-09T00:00:00Z","language":[{"iso":"eng"}],"citation":{"ama":"Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational Geometry, Third Edition. Handbook of Discrete and Computational Geometry. Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601","ista":"Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735.","apa":"Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor & Francis. https://doi.org/10.1201/9781315119601","ieee":"H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in Handbook of Discrete and Computational Geometry, Third Edition, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735.","mla":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35, doi:10.1201/9781315119601.","short":"H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis, 2017, pp. 1709–1735.","chicago":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601."},"publication":"Handbook of Discrete and Computational Geometry, Third Edition","page":"1709 - 1735","quality_controlled":"1","publist_id":"7970","abstract":[{"text":"The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind.","lang":"eng"}],"type":"book_chapter","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Koehl","first_name":"Patrice","full_name":"Koehl, Patrice"}],"oa_version":"None","date_updated":"2023-10-16T11:15:22Z","date_created":"2018-12-11T11:44:32Z","year":"2017","_id":"84","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"editor":[{"first_name":"Csaba","last_name":"Toth","full_name":"Toth, Csaba"},{"full_name":"O'Rourke, Joseph","first_name":"Joseph","last_name":"O'Rourke"},{"last_name":"Goodman","first_name":"Jacob","full_name":"Goodman, Jacob"}],"publisher":"Taylor & Francis","publication_status":"published","status":"public","title":"Computational topology for structural molecular biology"},{"oa_version":"Submitted Version","_id":"909","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 124","status":"public","title":"On the lengths of curves passing through boundary points of a planar convex shape","issue":"7","abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"type":"journal_article","date_published":"2017-01-01T00:00:00Z","citation":{"ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596. doi:10.4169/amer.math.monthly.124.7.588","ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","apa":"Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” The American Mathematical Monthly, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017.","mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:10.4169/amer.math.monthly.124.7.588.","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588."},"publication":"The American Mathematical Monthly","page":"588 - 596","article_type":"original","article_processing_charge":"No","day":"01","scopus_import":"1","author":[{"full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vysotsky, Vladislav","last_name":"Vysotsky","first_name":"Vladislav"}],"volume":124,"date_updated":"2023-10-17T11:24:57Z","date_created":"2018-12-11T11:49:09Z","year":"2017","publisher":"Mathematical Association of America","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"publist_id":"6534","doi":"10.4169/amer.math.monthly.124.7.588","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1605.07997","open_access":"1"}],"external_id":{"isi":["000413947300002"],"arxiv":["1605.07997"]},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["00029890"]},"month":"01"},{"language":[{"iso":"eng"}],"doi":"10.1016/j.apnum.2016.04.005","date_published":"2016-09-01T00:00:00Z","quality_controlled":"1","page":"34 - 47","project":[{"grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps"}],"publication":"Applied Numerical Mathematics","citation":{"ista":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47.","ieee":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” Applied Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016.","apa":"Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005","ama":"Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005","chicago":"Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005.","mla":"Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier, 2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005.","short":"T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47."},"month":"09","day":"01","scopus_import":1,"date_created":"2018-12-11T11:50:25Z","date_updated":"2021-01-12T06:48:38Z","oa_version":"None","volume":107,"author":[{"full_name":"Miyaji, Tomoyuki","first_name":"Tomoyuki","last_name":"Miyaji"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel"},{"last_name":"Gameiro","first_name":"Marcio","full_name":"Gameiro, Marcio"},{"full_name":"Kokubu, Hiroshi","first_name":"Hiroshi","last_name":"Kokubu"},{"first_name":"Konstantin","last_name":"Mischaikow","full_name":"Mischaikow, Konstantin"}],"status":"public","publication_status":"published","title":"A study of rigorous ODE integrators for multi scale set oriented computations","publisher":"Elsevier","department":[{"_id":"HeEd"}],"intvolume":" 107","acknowledgement":"MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper.","_id":"1149","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2016","abstract":[{"lang":"eng","text":"We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved."}],"ec_funded":1,"publist_id":"6209","type":"journal_article"},{"quality_controlled":"1","page":"55 - 80","publication":"Archives of Mechanics","citation":{"ieee":"J. Kasten et al., “Acceleration feature points of unsteady shear flows,” Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016.","apa":"Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., & Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives of Mechanics. Polish Academy of Sciences Publishing House.","ista":"Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M. 2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 68(1), 55–80.","ama":"Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 2016;68(1):55-80.","chicago":"Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House, 2016.","short":"J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80.","mla":"Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80."},"main_file_link":[{"open_access":"1","url":"http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf"}],"oa":1,"language":[{"iso":"eng"}],"date_published":"2016-01-01T00:00:00Z","scopus_import":1,"day":"01","month":"01","status":"public","publication_status":"published","title":"Acceleration feature points of unsteady shear flows","department":[{"_id":"HeEd"}],"publisher":"Polish Academy of Sciences Publishing House","intvolume":" 68","_id":"1216","acknowledgement":"The authors acknowledge funding of the German Re-\r\nsearch Foundation (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence 'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM) of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics Foundation for additional support. A part of this\r\nwork was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2016","date_updated":"2021-01-12T06:49:09Z","date_created":"2018-12-11T11:50:46Z","oa_version":"Published Version","volume":68,"author":[{"full_name":"Kasten, Jens","first_name":"Jens","last_name":"Kasten"},{"full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"full_name":"Hege, Hans","last_name":"Hege","first_name":"Hans"},{"first_name":"Bernd","last_name":"Noack","full_name":"Noack, Bernd"},{"full_name":"Daviller, Guillaume","last_name":"Daviller","first_name":"Guillaume"},{"full_name":"Morzyński, Marek","first_name":"Marek","last_name":"Morzyński"}],"type":"journal_article","abstract":[{"text":"A framework fo r extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of acceleration zeros) are extracted and discriminated into vortices and saddle points, based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These feature points are tracked in time with a robust algorithm for tracking features. Thus, a space-time hierarchy of the minima is built and vortex merging events are detected. We apply the acceleration feature extraction strategy to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure field and minima of λ2.","lang":"eng"}],"publist_id":"6118","issue":"1"},{"abstract":[{"lang":"eng","text":"We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is interesting due to a practical reason—the problem of “super resolution of images.” We have found optimal arrangements for N=6, 7 and 8 circles. Surprisingly, for the case N=7 there are three different optimal arrangements. Our proof is based on a computer enumeration of toroidal irreducible contact graphs."}],"issue":"1","type":"journal_article","oa_version":"Preprint","_id":"1222","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Optimal packings of congruent circles on a square flat torus","intvolume":" 55","day":"01","scopus_import":1,"date_published":"2016-01-01T00:00:00Z","publication":"Discrete & Computational Geometry","citation":{"ista":"Musin O, Nikitenko A. 2016. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 55(1), 1–20.","ieee":"O. Musin and A. Nikitenko, “Optimal packings of congruent circles on a square flat torus,” Discrete & Computational Geometry, vol. 55, no. 1. Springer, pp. 1–20, 2016.","apa":"Musin, O., & Nikitenko, A. (2016). Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-015-9742-6","ama":"Musin O, Nikitenko A. Optimal packings of congruent circles on a square flat torus. Discrete & Computational Geometry. 2016;55(1):1-20. doi:10.1007/s00454-015-9742-6","chicago":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry. Springer, 2016. https://doi.org/10.1007/s00454-015-9742-6.","mla":"Musin, Oleg, and Anton Nikitenko. “Optimal Packings of Congruent Circles on a Square Flat Torus.” Discrete & Computational Geometry, vol. 55, no. 1, Springer, 2016, pp. 1–20, doi:10.1007/s00454-015-9742-6.","short":"O. Musin, A. Nikitenko, Discrete & Computational Geometry 55 (2016) 1–20."},"page":"1 - 20","publist_id":"6111","author":[{"full_name":"Musin, Oleg","first_name":"Oleg","last_name":"Musin"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:50:48Z","date_updated":"2021-01-12T06:49:11Z","volume":55,"year":"2016","acknowledgement":"We wish to thank Alexey Tarasov, Vladislav Volkov and Brittany Fasy for some useful comments and remarks, and especially Thom Sulanke for modifying surftri to suit our purposes. Oleg R. Musin was partially supported by the NSF Grant DMS-1400876 and by the RFBR Grant 15-01-99563. Anton V. Nikitenko was supported by the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government Grant 11.G34.31.0026.","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer","month":"01","doi":"10.1007/s00454-015-9742-6","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1212.0649"}],"quality_controlled":"1"},{"author":[{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál","full_name":"Krcál, Marek"},{"full_name":"Pilarczyk, Pawel","first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T06:49:18Z","date_created":"2018-12-11T11:50:52Z","volume":9667,"year":"2016","acknowledgement":"The research conducted by both authors has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreements no. 291734 (for M. K.) and no. 622033 (for P. P.).","publication_status":"published","publisher":"Springer","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"ec_funded":1,"publist_id":"6096","conference":{"location":"Marseille, France","start_date":"2016-06-15","end_date":"2016-06-17","name":"CTIC: Computational Topology in Image Context"},"doi":"10.1007/978-3-319-39441-1_13","language":[{"iso":"eng"}],"quality_controlled":"1","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"},{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","call_identifier":"FP7","name":"Persistent Homology - Images, Data and Maps"}],"month":"06","oa_version":"None","_id":"1237","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","title":"Computation of cubical Steenrod squares","status":"public","intvolume":" 9667","abstract":[{"lang":"eng","text":"Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in ℝm. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher than 3. If such an operation is determined at the level of simplicial chains [see e.g. González-Díaz, Real, Homology, Homotopy Appl, 2003, 83-93], then it is effectively computable. However, decomposing a cubical complex into a simplicial one deleteriously affects the efficiency of such an approach. In order to avoid this overhead, a direct cubical approach was applied in [Pilarczyk, Real, Adv. Comput. Math., 2015, 253-275] for the cup product in cohomology, and implemented in the ChainCon software package [http://www.pawelpilarczyk.com/chaincon/]. We establish a formula for the Steenrod square operations [see Steenrod, Annals of Mathematics. Second Series, 1947, 290-320] directly at the level of cubical chains, and we prove the correctness of this formula. An implementation of this formula is programmed in C++ within the ChainCon software framework. We provide a few examples and discuss the effectiveness of this approach. One specific application follows from the fact that Steenrod squares yield tests for the topological extension problem: Can a given map A → Sd to a sphere Sd be extended to a given super-complex X of A? In particular, the ROB-SAT problem, which is to decide for a given function f: X → ℝm and a value r > 0 whether every g: X → ℝm with ∥g - f ∥∞ ≤ r has a root, reduces to the extension problem."}],"type":"conference","alternative_title":["LNCS"],"date_published":"2016-06-02T00:00:00Z","citation":{"ama":"Krcál M, Pilarczyk P. Computation of cubical Steenrod squares. In: Vol 9667. Springer; 2016:140-151. doi:10.1007/978-3-319-39441-1_13","ista":"Krcál M, Pilarczyk P. 2016. Computation of cubical Steenrod squares. CTIC: Computational Topology in Image Context, LNCS, vol. 9667, 140–151.","apa":"Krcál, M., & Pilarczyk, P. (2016). Computation of cubical Steenrod squares (Vol. 9667, pp. 140–151). Presented at the CTIC: Computational Topology in Image Context, Marseille, France: Springer. https://doi.org/10.1007/978-3-319-39441-1_13","ieee":"M. Krcál and P. Pilarczyk, “Computation of cubical Steenrod squares,” presented at the CTIC: Computational Topology in Image Context, Marseille, France, 2016, vol. 9667, pp. 140–151.","mla":"Krcál, Marek, and Pawel Pilarczyk. Computation of Cubical Steenrod Squares. Vol. 9667, Springer, 2016, pp. 140–51, doi:10.1007/978-3-319-39441-1_13.","short":"M. Krcál, P. Pilarczyk, in:, Springer, 2016, pp. 140–151.","chicago":"Krcál, Marek, and Pawel Pilarczyk. “Computation of Cubical Steenrod Squares,” 9667:140–51. Springer, 2016. https://doi.org/10.1007/978-3-319-39441-1_13."},"page":"140 - 151","day":"02","scopus_import":1},{"author":[{"full_name":"Harker, Shaun","last_name":"Harker","first_name":"Shaun"},{"full_name":"Kokubu, Hiroshi","last_name":"Kokubu","first_name":"Hiroshi"},{"full_name":"Mischaikow, Konstantin","first_name":"Konstantin","last_name":"Mischaikow"},{"first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"}],"volume":144,"date_created":"2018-12-11T11:50:57Z","date_updated":"2022-05-24T09:35:58Z","acknowledgement":"The authors gratefully acknowledge the support of the Lorenz Center which\r\nprovided an opportunity for us to discuss in depth the work of this paper. Research leading to these results has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Funda¸c˜ao para a Ciˆencia e a Tecnologia (FCT) in the framework of the research\r\nproject FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008),\r\nas well as from the People Programme (Marie Curie Actions) of the European\r\nUnion’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033 (supporting PP). The work of the first and third author has\r\nbeen partially supported by NSF grants NSF-DMS-0835621, 0915019, 1125174,\r\n1248071, and contracts from AFOSR and DARPA. The work of the second author\r\nwas supported by Grant-in-Aid for Scientific Research (No. 25287029), Ministry of\r\nEducation, Science, Technology, Culture and Sports, Japan.","year":"2016","publisher":"American Mathematical Society","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"publist_id":"6075","doi":"10.1090/proc/12812","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1411.7563"]},"main_file_link":[{"url":"https://arxiv.org/abs/1411.7563","open_access":"1"}],"project":[{"name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033"}],"quality_controlled":"1","publication_identifier":{"issn":["1088-6826"]},"month":"04","oa_version":"Preprint","_id":"1252","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 144","title":"Inducing a map on homology from a correspondence","status":"public","issue":"4","abstract":[{"lang":"eng","text":"We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points."}],"type":"journal_article","date_published":"2016-04-01T00:00:00Z","citation":{"chicago":"Harker, Shaun, Hiroshi Kokubu, Konstantin Mischaikow, and Pawel Pilarczyk. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/proc/12812.","mla":"Harker, Shaun, et al. “Inducing a Map on Homology from a Correspondence.” Proceedings of the American Mathematical Society, vol. 144, no. 4, American Mathematical Society, 2016, pp. 1787–801, doi:10.1090/proc/12812.","short":"S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk, Proceedings of the American Mathematical Society 144 (2016) 1787–1801.","ista":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. 2016. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 144(4), 1787–1801.","apa":"Harker, S., Kokubu, H., Mischaikow, K., & Pilarczyk, P. (2016). Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/12812","ieee":"S. Harker, H. Kokubu, K. Mischaikow, and P. Pilarczyk, “Inducing a map on homology from a correspondence,” Proceedings of the American Mathematical Society, vol. 144, no. 4. American Mathematical Society, pp. 1787–1801, 2016.","ama":"Harker S, Kokubu H, Mischaikow K, Pilarczyk P. Inducing a map on homology from a correspondence. Proceedings of the American Mathematical Society. 2016;144(4):1787-1801. doi:10.1090/proc/12812"},"publication":"Proceedings of the American Mathematical Society","page":"1787 - 1801","article_type":"original","article_processing_charge":"No","day":"01","scopus_import":"1"},{"date_published":"2016-04-02T00:00:00Z","page":"116 - 124","publication":"Experimental Mathematics","citation":{"ama":"Golmakani A, Luzzatto S, Pilarczyk P. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 2016;25(2):116-124. doi:10.1080/10586458.2015.1048011","ista":"Golmakani A, Luzzatto S, Pilarczyk P. 2016. Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. 25(2), 116–124.","ieee":"A. Golmakani, S. Luzzatto, and P. Pilarczyk, “Uniform expansivity outside a critical neighborhood in the quadratic family,” Experimental Mathematics, vol. 25, no. 2. Taylor and Francis, pp. 116–124, 2016.","apa":"Golmakani, A., Luzzatto, S., & Pilarczyk, P. (2016). Uniform expansivity outside a critical neighborhood in the quadratic family. Experimental Mathematics. Taylor and Francis. https://doi.org/10.1080/10586458.2015.1048011","mla":"Golmakani, Ali, et al. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics, vol. 25, no. 2, Taylor and Francis, 2016, pp. 116–24, doi:10.1080/10586458.2015.1048011.","short":"A. Golmakani, S. Luzzatto, P. Pilarczyk, Experimental Mathematics 25 (2016) 116–124.","chicago":"Golmakani, Ali, Stefano Luzzatto, and Pawel Pilarczyk. “Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family.” Experimental Mathematics. Taylor and Francis, 2016. https://doi.org/10.1080/10586458.2015.1048011."},"day":"02","scopus_import":1,"oa_version":"Preprint","title":"Uniform expansivity outside a critical neighborhood in the quadratic family","status":"public","intvolume":" 25","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1254","abstract":[{"text":"We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We first compute a radius of the critical neighborhood outside which the map is uniformly expanding. This radius is taken as small as possible, yet large enough for our numerical procedure to succeed in proving that the expansivity exponent outside this neighborhood is positive. Then, for each of the intervals, we compute a lower bound for this expansivity exponent, valid for all the parameters in that interval. We illustrate and study the distribution of the radii and the expansivity exponents. The results of our computations are mathematically rigorous. The source code of the software and the results of the computations are made publicly available at http://www.pawelpilarczyk.com/quadratic/.","lang":"eng"}],"issue":"2","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1080/10586458.2015.1048011","quality_controlled":"1","project":[{"_id":"255F06BE-B435-11E9-9278-68D0E5697425","grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1504.00116"}],"oa":1,"month":"04","date_updated":"2021-01-12T06:49:25Z","date_created":"2018-12-11T11:50:58Z","volume":25,"author":[{"full_name":"Golmakani, Ali","first_name":"Ali","last_name":"Golmakani"},{"last_name":"Luzzatto","first_name":"Stefano","full_name":"Luzzatto, Stefano"},{"first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"}],"publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Taylor and Francis","acknowledgement":"AG and PP were partially supported by Abdus Salam International Centre for Theoretical Physics (ICTP). Additionally, AG was supported by BREUDS, and research conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008); and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622033. The authors gratefully acknowledge the Department of\r\nMathematics of Kyoto University for providing access\r\nto their server for conducting computations for this\r\nproject.","year":"2016","ec_funded":1,"publist_id":"6071"},{"doi":"10.1080/16864360.2016.1150718","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"quality_controlled":"1","month":"09","author":[{"full_name":"Held, Martin","first_name":"Martin","last_name":"Held"},{"full_name":"Huber, Stefan","first_name":"Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"date_updated":"2021-01-12T06:49:32Z","date_created":"2018-12-11T11:51:04Z","volume":13,"year":"2016","acknowledgement":"This work was supported by Austrian Science Fund (FWF): P25816-N15.","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Taylor and Francis","file_date_updated":"2020-07-14T12:44:42Z","publist_id":"6048","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","date_published":"2016-09-02T00:00:00Z","publication":"Computer-Aided Design and Applications","citation":{"short":"M. Held, S. Huber, P. Palfrader, Computer-Aided Design and Applications 13 (2016) 712–721.","mla":"Held, Martin, et al. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications, vol. 13, no. 5, Taylor and Francis, 2016, pp. 712–21, doi:10.1080/16864360.2016.1150718.","chicago":"Held, Martin, Stefan Huber, and Peter Palfrader. “Generalized Offsetting of Planar Structures Using Skeletons.” Computer-Aided Design and Applications. Taylor and Francis, 2016. https://doi.org/10.1080/16864360.2016.1150718.","ama":"Held M, Huber S, Palfrader P. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 2016;13(5):712-721. doi:10.1080/16864360.2016.1150718","apa":"Held, M., Huber, S., & Palfrader, P. (2016). Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. Taylor and Francis. https://doi.org/10.1080/16864360.2016.1150718","ieee":"M. Held, S. Huber, and P. Palfrader, “Generalized offsetting of planar structures using skeletons,” Computer-Aided Design and Applications, vol. 13, no. 5. Taylor and Francis, pp. 712–721, 2016.","ista":"Held M, Huber S, Palfrader P. 2016. Generalized offsetting of planar structures using skeletons. Computer-Aided Design and Applications. 13(5), 712–721."},"page":"712 - 721","day":"02","has_accepted_license":"1","scopus_import":1,"pubrep_id":"694","file":[{"file_id":"5206","relation":"main_file","date_updated":"2020-07-14T12:44:42Z","date_created":"2018-12-12T10:16:20Z","checksum":"c746f3a48edb62b588d92ea5d0fd2c0e","file_name":"IST-2016-694-v1+1_Generalized_offsetting_of_planar_structures_using_skeletons.pdf","access_level":"open_access","creator":"system","file_size":1678369,"content_type":"application/pdf"}],"oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1272","status":"public","ddc":["004","516"],"title":"Generalized offsetting of planar structures using skeletons","intvolume":" 13","abstract":[{"text":"We study different means to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons, for which the orthogonal distance of offset elements to their respective input elements is constant and uniform over all input elements. Our main contribution is a new geometric structure, called variable-radius Voronoi diagram, which supports the computation of variable-radius offsets, i.e., offsets whose distance to the input is allowed to vary along the input. We discuss properties of this structure and sketch a prototype implementation that supports the computation of variable-radius offsets based on this new variant of Voronoi diagrams.","lang":"eng"}],"issue":"5","type":"journal_article"},{"doi":"10.1016/j.endm.2016.09.030","date_published":"2016-10-01T00:00:00Z","language":[{"iso":"eng"}],"citation":{"short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol. 54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.endm.2016.09.030.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier, pp. 169–174, 2016.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2016.09.030","ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174."},"publication":"Electronic Notes in Discrete Mathematics","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"page":"169 - 174","quality_controlled":"1","day":"01","month":"10","scopus_import":1,"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Iglesias Ham, Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","last_name":"Iglesias Ham"}],"volume":54,"oa_version":"None","date_updated":"2021-01-12T06:49:41Z","date_created":"2018-12-11T11:51:12Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1295","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","year":"2016","intvolume":" 54","department":[{"_id":"HeEd"}],"publisher":"Elsevier","title":"Multiple covers with balls II: Weighted averages","publication_status":"published","status":"public","ec_funded":1,"publist_id":"5976","abstract":[{"lang":"eng","text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls."}],"type":"journal_article"},{"issue":"2","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","intvolume":" 150","title":"Computing the Thurston–Bennequin invariant in open books","status":"public","_id":"1292","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"01","scopus_import":1,"date_published":"2016-12-01T00:00:00Z","page":"441 - 455","citation":{"ama":"Durst S, Kegel M, Klukas MD. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 2016;150(2):441-455. doi:10.1007/s10474-016-0648-4","ista":"Durst S, Kegel M, Klukas MD. 2016. Computing the Thurston–Bennequin invariant in open books. Acta Mathematica Hungarica. 150(2), 441–455.","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","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.","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.","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."},"publication":"Acta Mathematica Hungarica","publist_id":"6023","volume":150,"date_updated":"2021-01-12T06:49:40Z","date_created":"2018-12-11T11:51:11Z","author":[{"full_name":"Durst, Sebastian","first_name":"Sebastian","last_name":"Durst"},{"full_name":"Kegel, Marc","last_name":"Kegel","first_name":"Marc"},{"full_name":"Klukas, Mirko D","first_name":"Mirko D","last_name":"Klukas","id":"34927512-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2016","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.","month":"12","language":[{"iso":"eng"}],"doi":"10.1007/s10474-016-0648-4","quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.00794"}]},{"ec_funded":1,"publist_id":"5938","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.","year":"2016","publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"full_name":"Balitskiy, Alexey","first_name":"Alexey","last_name":"Balitskiy"}],"volume":216,"date_updated":"2021-01-12T06:49:56Z","date_created":"2018-12-11T11:51:24Z","month":"10","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1506.06014"}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1","doi":"10.1007/s11856-016-1429-z","language":[{"iso":"eng"}],"type":"journal_article","issue":"2","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."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1330","intvolume":" 216","status":"public","title":"Billiards in convex bodies with acute angles","oa_version":"Preprint","scopus_import":1,"day":"15","citation":{"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.","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.","ista":"Akopyan A, Balitskiy A. 2016. Billiards in convex bodies with acute angles. Israel Journal of Mathematics. 216(2), 833–845.","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.","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","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"},"publication":"Israel Journal of Mathematics","page":"833 - 845","date_published":"2016-10-15T00:00:00Z"},{"date_published":"2016-10-01T00:00:00Z","citation":{"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.","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.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 2016;144(10):4501-4513. doi:10.1090/proc/13062","ista":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513.","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","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."},"publication":"Proceedings of the American Mathematical Society","page":"4501 - 4513","article_processing_charge":"No","day":"01","scopus_import":1,"oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1360","intvolume":" 144","title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","status":"public","issue":"10","abstract":[{"text":"We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results. ","lang":"eng"}],"type":"journal_article","doi":"10.1090/proc/13062","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1401.0442","open_access":"1"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"quality_controlled":"1","month":"10","author":[{"full_name":"Akopyan, Arseniy","first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X"},{"last_name":"Balitskiy","first_name":"Alexey","full_name":"Balitskiy, Alexey"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"},{"first_name":"Anastasia","last_name":"Sharipova","full_name":"Sharipova, Anastasia"}],"volume":144,"date_updated":"2021-01-12T06:50:09Z","date_created":"2018-12-11T11:51:34Z","year":"2016","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).","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","publication_status":"published","ec_funded":1,"publist_id":"5885"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1408","title":"On computability and triviality of well groups","status":"public","ddc":["510"],"intvolume":" 56","pubrep_id":"614","file":[{"file_size":905303,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","checksum":"e0da023abf6b72abd8c6a8c76740d53c","date_created":"2018-12-12T10:10:55Z","date_updated":"2020-07-14T12:44:53Z","relation":"main_file","file_id":"4846"}],"oa_version":"Published Version","type":"journal_article","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."}],"issue":"1","publication":"Discrete & Computational Geometry","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","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete & Computational Geometry. 56(1), 126–164.","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.","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","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.","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."},"page":"126 - 164","date_published":"2016-07-01T00:00:00Z","scopus_import":1,"day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","year":"2016","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","publication_status":"published","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publisher":"Springer","author":[{"full_name":"Franek, Peter","first_name":"Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1510"}]},"date_updated":"2023-02-23T10:02:11Z","date_created":"2018-12-11T11:51:51Z","volume":56,"file_date_updated":"2020-07-14T12:44:53Z","publist_id":"5799","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"name":"Robust invariants of Nonlinear Systems","call_identifier":"FWF","grant_number":"M01980","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425"},{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"doi":"10.1007/s00454-016-9794-2","language":[{"iso":"eng"}],"month":"07"},{"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"1568"}]},"author":[{"full_name":"Dunaeva, Olga","first_name":"Olga","last_name":"Dunaeva"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Lukyanov","first_name":"Anton","full_name":"Lukyanov, Anton"},{"full_name":"Machin, Michael","first_name":"Michael","last_name":"Machin"},{"first_name":"Daria","last_name":"Malkova","full_name":"Malkova, Daria"},{"last_name":"Kuvaev","first_name":"Roman","full_name":"Kuvaev, Roman"},{"full_name":"Kashin, Sergey","last_name":"Kashin","first_name":"Sergey"}],"volume":83,"date_created":"2018-12-11T11:51:10Z","date_updated":"2023-02-23T10:04:40Z","year":"2016","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publication_status":"published","publist_id":"6027","file_date_updated":"2020-07-14T12:44:42Z","doi":"10.1016/j.patrec.2015.12.012","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1,"quality_controlled":"1","month":"11","pubrep_id":"975","file":[{"date_updated":"2020-07-14T12:44:42Z","date_created":"2019-04-17T07:55:51Z","checksum":"33458bbb8c32a339e1adeca6d5a1112d","file_id":"6334","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":1921113,"file_name":"2016-Edelsbrunner_The_classification.pdf","access_level":"open_access"}],"oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1289","intvolume":" 83","title":"The classification of endoscopy images with persistent homology","status":"public","ddc":["004","514"],"issue":"1","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."}],"type":"journal_article","date_published":"2016-11-01T00:00:00Z","citation":{"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.","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","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.","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","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.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, R. Kuvaev, S. Kashin, Pattern Recognition Letters 83 (2016) 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."},"publication":"Pattern Recognition Letters","page":"13 - 22","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":1},{"month":"04","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2016-04-01T00:00:00Z","doi":"10.1016/j.jco.2015.11.003","page":"199 - 216","quality_controlled":"1","main_file_link":[{"url":"http://arxiv.org/abs/1510.00251","open_access":"1"}],"citation":{"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","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.","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","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.","short":"F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 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."},"oa":1,"publication":"Journal of Complexity","publist_id":"5549","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."}],"type":"journal_article","volume":33,"oa_version":"Submitted Version","date_updated":"2021-01-12T06:52:02Z","date_created":"2018-12-11T11:53:03Z","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian","last_name":"Pausinger","full_name":"Pausinger, Florian"},{"full_name":"Steinerberger, Stefan","first_name":"Stefan","last_name":"Steinerberger"}],"department":[{"_id":"HeEd"}],"publisher":"Academic Press","intvolume":" 33","publication_status":"published","title":"On the discrepancy of jittered sampling","status":"public","_id":"1617","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2016","acknowledgement":"We are grateful to the referee whose suggestions greatly improved the quality and clarity of the exposition."},{"place":"Cham","extern":"1","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","year":"2016","date_updated":"2022-01-28T08:10:11Z","date_created":"2019-01-08T20:44:37Z","volume":9647,"author":[{"orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"}],"month":"04","publication_identifier":{"isbn":["978-3-319-32359-6"],"issn":["0302-9743","1611-3349"],"eisbn":["978-3-319-32360-2"]},"quality_controlled":"1","language":[{"iso":"eng"}],"conference":{"location":"Nantes, France","start_date":"2016-04-18","end_date":"2016-04-20","name":"DGCI: International Conference on Discrete Geometry for Computer Imagery"},"doi":"10.1007/978-3-319-32360-2_20","alternative_title":["LNCS"],"type":"conference","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."}],"title":"On functionality of quadraginta octants of naive sphere with application to circle drawing","status":"public","intvolume":" 9647","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"5806","oa_version":"None","day":"09","article_processing_charge":"No","page":"256-267","publication":"Discrete Geometry for Computer Imagery","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","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.","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","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.","short":"R. Biswas, P. Bhowmick, in:, Discrete Geometry for Computer Imagery, Springer Nature, Cham, 2016, pp. 256–267.","mla":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” Discrete Geometry for Computer Imagery, vol. 9647, Springer Nature, 2016, pp. 256–67, doi:10.1007/978-3-319-32360-2_20.","chicago":"Biswas, Ranita, and Partha Bhowmick. “On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing.” In Discrete Geometry for Computer Imagery, 9647:256–67. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-32360-2_20."},"date_published":"2016-04-09T00:00:00Z"},{"department":[{"_id":"HeEd"}],"publisher":"Springer Nature","publication_status":"published","year":"2016","volume":9667,"date_created":"2019-01-08T20:44:24Z","date_updated":"2022-01-28T08:01:22Z","author":[{"last_name":"Sen","first_name":"Nabhasmita","full_name":"Sen, Nabhasmita"},{"full_name":"Biswas, Ranita","first_name":"Ranita","last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890"},{"first_name":"Partha","last_name":"Bhowmick","full_name":"Bhowmick, Partha"}],"place":"Cham","extern":"1","quality_controlled":"1","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-39441-1_23","conference":{"name":"CTIC: Computational Topology in Image Context","end_date":"2016-06-17","location":"Marseille, France","start_date":"2016-06-15"},"publication_identifier":{"eisbn":["978-3-319-39441-1"],"issn":["0302-9743"],"isbn":["978-3-319-39440-4"],"eissn":["1611-3349"]},"month":"06","intvolume":" 9667","status":"public","title":"On some local topological properties of naive discrete sphere","_id":"5805","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"None","alternative_title":["LNCS"],"type":"book_chapter","abstract":[{"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.","lang":"eng"}],"page":"253-264","citation":{"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.","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","ista":"Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.","ama":"Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23","chicago":"Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In Computational Topology in Image Context, 9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.","short":"N. Sen, R. Biswas, P. Bhowmick, in:, Computational Topology in Image Context, Springer Nature, Cham, 2016, pp. 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."},"publication":"Computational Topology in Image Context","date_published":"2016-06-02T00:00:00Z","article_processing_charge":"No","day":"02"},{"_id":"5809","year":"2016","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"publisher":"Springer Nature","intvolume":" 9448","title":"On the connectivity and smoothness of discrete spherical circles","status":"public","publication_status":"published","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-5372-7890","first_name":"Ranita","last_name":"Biswas","full_name":"Biswas, Ranita"},{"full_name":"Bhowmick, Partha","last_name":"Bhowmick","first_name":"Partha"},{"last_name":"Brimkov","first_name":"Valentin E.","full_name":"Brimkov, Valentin E."}],"volume":9448,"oa_version":"None","date_created":"2019-01-08T20:45:19Z","date_updated":"2022-01-28T08:13:03Z","type":"book_chapter","place":"Cham","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."}],"extern":"1","citation":{"ista":"Biswas R, Bhowmick P, Brimkov VE. 2016.On the connectivity and smoothness of discrete spherical circles. In: Combinatorial image analysis. vol. 9448, 86–100.","ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the connectivity and smoothness of discrete spherical circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer Nature, 2016, pp. 86–100.","apa":"Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the connectivity and smoothness of discrete spherical circles. In Combinatorial image analysis (Vol. 9448, pp. 86–100). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-26145-4_7","ama":"Biswas R, Bhowmick P, Brimkov VE. On the connectivity and smoothness of discrete spherical circles. In: Combinatorial Image Analysis. Vol 9448. Cham: Springer Nature; 2016:86-100. doi:10.1007/978-3-319-26145-4_7","chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis, 9448:86–100. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.","mla":"Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” Combinatorial Image Analysis, vol. 9448, Springer Nature, 2016, pp. 86–100, doi:10.1007/978-3-319-26145-4_7.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2016, pp. 86–100."},"publication":"Combinatorial image analysis","page":"86-100","quality_controlled":"1","date_published":"2016-01-06T00:00:00Z","doi":"10.1007/978-3-319-26145-4_7","conference":{"start_date":"2015-11-24","location":"Kolkata, India","end_date":"2015-11-27","name":"IWCIA: International Workshop on Combinatorial Image Analysis"},"language":[{"iso":"eng"}],"article_processing_charge":"No","publication_identifier":{"isbn":["978-3-319-26144-7"],"eissn":["1611-3349"],"eisbn":["978-3-319-26145-4"],"issn":["0302-9743"]},"month":"01","day":"06"},{"day":"10","has_accepted_license":"1","scopus_import":1,"date_published":"2016-01-10T00:00:00Z","page":"674 - 703","publication":"Advances in Mathematics","citation":{"chicago":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics. Academic Press, 2016. https://doi.org/10.1016/j.aim.2015.10.004.","mla":"Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence of the Intrinsic Volume.” Advances in Mathematics, vol. 287, Academic Press, 2016, pp. 674–703, doi:10.1016/j.aim.2015.10.004.","short":"H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.","ista":"Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic volume. Advances in Mathematics. 287, 674–703.","ieee":"H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic volume,” Advances in Mathematics, vol. 287. Academic Press, pp. 674–703, 2016.","apa":"Edelsbrunner, H., & Pausinger, F. (2016). Approximation and convergence of the intrinsic volume. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2015.10.004","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"},"abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"checksum":"f8869ec110c35c852ef6a37425374af7","date_created":"2018-12-12T10:12:10Z","date_updated":"2020-07-14T12:45:10Z","relation":"main_file","file_id":"4928","file_size":248985,"content_type":"application/pdf","creator":"system","access_level":"open_access","file_name":"IST-2017-774-v1+1_2016-J-03-FirstIntVolume.pdf"}],"pubrep_id":"774","ddc":["004"],"status":"public","title":"Approximation and convergence of the intrinsic volume","intvolume":" 287","_id":"1662","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"01","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2015.10.004","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1,"file_date_updated":"2020-07-14T12:45:10Z","publist_id":"5488","ec_funded":1,"date_updated":"2023-09-07T11:41:25Z","date_created":"2018-12-11T11:53:20Z","volume":287,"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Pausinger","first_name":"Florian","orcid":"0000-0002-8379-3768","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"1399"}]},"publication_status":"published","publisher":"Academic Press","department":[{"_id":"HeEd"}],"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.","year":"2016"},{"_id":"1424","year":"2015","acknowledgement":"This work was partially supported by the Austrian Science FUnd, project no. KLI 00012.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Neural Information Processing Systems","department":[{"_id":"HeEd"}],"intvolume":" 28","status":"public","publication_status":"published","title":"Statistical topological data analysis-A kernel perspective","author":[{"full_name":"Kwitt, Roland","last_name":"Kwitt","first_name":"Roland"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"},{"full_name":"Niethammer, Marc","first_name":"Marc","last_name":"Niethammer"},{"full_name":"Lin, Weili","first_name":"Weili","last_name":"Lin"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9683-0724","first_name":"Ulrich","last_name":"Bauer","full_name":"Bauer, Ulrich"}],"oa_version":"Submitted Version","volume":28,"date_updated":"2021-01-12T06:50:38Z","date_created":"2018-12-11T11:51:56Z","type":"conference","alternative_title":["Advances in Neural Information Processing Systems"],"publist_id":"5782","abstract":[{"lang":"eng","text":"We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data."}],"citation":{"ama":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. Statistical topological data analysis-A kernel perspective. In: Vol 28. Neural Information Processing Systems; 2015:3070-3078.","ieee":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, “Statistical topological data analysis-A kernel perspective,” presented at the NIPS: Neural Information Processing Systems, Montreal, Canada, 2015, vol. 28, pp. 3070–3078.","apa":"Kwitt, R., Huber, S., Niethammer, M., Lin, W., & Bauer, U. (2015). Statistical topological data analysis-A kernel perspective (Vol. 28, pp. 3070–3078). Presented at the NIPS: Neural Information Processing Systems, Montreal, Canada: Neural Information Processing Systems.","ista":"Kwitt R, Huber S, Niethammer M, Lin W, Bauer U. 2015. Statistical topological data analysis-A kernel perspective. NIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 28, 3070–3078.","short":"R. Kwitt, S. Huber, M. Niethammer, W. Lin, U. Bauer, in:, Neural Information Processing Systems, 2015, pp. 3070–3078.","mla":"Kwitt, Roland, et al. Statistical Topological Data Analysis-A Kernel Perspective. Vol. 28, Neural Information Processing Systems, 2015, pp. 3070–78.","chicago":"Kwitt, Roland, Stefan Huber, Marc Niethammer, Weili Lin, and Ulrich Bauer. “Statistical Topological Data Analysis-A Kernel Perspective,” 28:3070–78. Neural Information Processing Systems, 2015."},"oa":1,"main_file_link":[{"open_access":"1","url":"https://papers.nips.cc/paper/5887-statistical-topological-data-analysis-a-kernel-perspective"}],"page":"3070 - 3078","quality_controlled":"1","date_published":"2015-12-01T00:00:00Z","conference":{"location":"Montreal, Canada","start_date":"2015-12-07","end_date":"2015-12-12","name":"NIPS: Neural Information Processing Systems"},"language":[{"iso":"eng"}],"month":"12","day":"01"},{"type":"conference","publist_id":"5709","abstract":[{"lang":"eng","text":"Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1483","year":"2015","publisher":"IEEE","department":[{"_id":"HeEd"}],"publication_status":"published","title":"A stable multi-scale kernel for topological machine learning","status":"public","author":[{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-8871-5814","id":"4700A070-F248-11E8-B48F-1D18A9856A87","last_name":"Huber","first_name":"Stefan","full_name":"Huber, Stefan"},{"orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","first_name":"Ulrich","full_name":"Bauer, Ulrich"},{"first_name":"Roland","last_name":"Kwitt","full_name":"Kwitt, Roland"}],"oa_version":"Preprint","date_created":"2018-12-11T11:52:17Z","date_updated":"2021-01-12T06:51:03Z","scopus_import":1,"publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"day":"14","month":"10","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"citation":{"ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:10.1109/CVPR.2015.7299106","ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","apa":"Reininghaus, J., Huber, S., Bauer, U., & Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7299106","ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","mla":"Reininghaus, Jan, et al. A Stable Multi-Scale Kernel for Topological Machine Learning. IEEE, 2015, pp. 4741–48, doi:10.1109/CVPR.2015.7299106.","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7299106."},"oa":1,"page":"4741 - 4748","doi":"10.1109/CVPR.2015.7299106","date_published":"2015-10-14T00:00:00Z","conference":{"name":"CVPR: Computer Vision and Pattern Recognition","end_date":"2015-06-12","location":"Boston, MA, USA","start_date":"2015-06-07"},"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"date_published":"2015-08-01T00:00:00Z","conference":{"location":"Ontario, Canada","start_date":"2015-08-10","end_date":"2015-08-12","name":"CCCG: Canadian Conference on Computational Geometry"},"page":"128-135","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}],"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1505.03402"}],"citation":{"ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: Proceedings of the 27th Canadian Conference on Computational Geometry. Vol 2015-August. Queen’s University; 2015:128-135.","ista":"Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135.","apa":"Edelsbrunner, H., Iglesias Ham, M., & Kurlin, V. (2015). Relaxed disk packing. In Proceedings of the 27th Canadian Conference on Computational Geometry (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.","ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in Proceedings of the 27th Canadian Conference on Computational Geometry, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” Proceedings of the 27th Canadian Conference on Computational Geometry, vol. 2015–August, Queen’s University, 2015, pp. 128–35.","short":"H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In Proceedings of the 27th Canadian Conference on Computational Geometry, 2015–August:128–35. Queen’s University, 2015."},"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","day":"01","month":"08","scopus_import":1,"oa_version":"Submitted Version","volume":"2015-August","date_updated":"2021-01-12T06:51:09Z","date_created":"2018-12-11T11:52:21Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"},{"last_name":"Kurlin","first_name":"Vitaliy","full_name":"Kurlin, Vitaliy"}],"publisher":"Queen's University","department":[{"_id":"HeEd"}],"status":"public","title":"Relaxed disk packing","publication_status":"published","_id":"1495","year":"2015","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"publist_id":"5684","abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. "}],"type":"conference"},{"abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r > 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. 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 R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K < 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. ","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"pubrep_id":"503","oa_version":"Published Version","file":[{"file_id":"5001","relation":"main_file","date_created":"2018-12-12T10:13:19Z","date_updated":"2020-07-14T12:44:59Z","checksum":"49eb5021caafaabe5356c65b9c5f8c9c","file_name":"IST-2016-503-v1+1_32.pdf","access_level":"open_access","creator":"system","file_size":623563,"content_type":"application/pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1510","intvolume":" 34","status":"public","title":"On computability and triviality of well groups","ddc":["510"],"has_accepted_license":"1","day":"11","scopus_import":1,"date_published":"2015-06-11T00:00:00Z","citation":{"chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. https://doi.org/10.4230/LIPIcs.SOCG.2015.842.","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856.","mla":"Franek, Peter, and Marek Krcál. On Computability and Triviality of Well Groups. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:10.4230/LIPIcs.SOCG.2015.842.","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856.","apa":"Franek, P., & Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SOCG.2015.842","ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:10.4230/LIPIcs.SOCG.2015.842"},"page":"842 - 856","ec_funded":1,"publist_id":"5667","file_date_updated":"2020-07-14T12:44:59Z","related_material":{"record":[{"status":"public","relation":"later_version","id":"1408"}]},"author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál"}],"volume":34,"date_updated":"2023-02-21T17:02:57Z","date_created":"2018-12-11T11:52:26Z","year":"2015","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"publication_status":"published","month":"06","doi":"10.4230/LIPIcs.SOCG.2015.842","conference":{"end_date":"2015-06-25","location":"Eindhoven, Netherlands","start_date":"2015-06-22","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"quality_controlled":"1"},{"quality_controlled":"1","doi":"10.1007/978-3-319-15090-1_13","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-3-319-15089-5"]},"month":"01","year":"2015","department":[{"_id":"HeEd"}],"publisher":"Springer","editor":[{"last_name":"Hotz","first_name":"Ingrid","full_name":"Hotz, Ingrid"},{"full_name":"Schultz, Thomas","last_name":"Schultz","first_name":"Thomas"}],"publication_status":"published","edition":"1","author":[{"first_name":"Valentin","last_name":"Zobel","full_name":"Zobel, Valentin"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"},{"full_name":"Hotz, Ingrid","first_name":"Ingrid","last_name":"Hotz"}],"volume":40,"date_created":"2018-12-11T11:52:33Z","date_updated":"2022-06-10T09:50:14Z","publist_id":"5640","citation":{"mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:10.1007/978-3-319-15090-1_13.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. https://doi.org/10.1007/978-3-319-15090-1_13.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Vol 40. 1st ed. Springer; 2015:257-267. doi:10.1007/978-3-319-15090-1_13","ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","apa":"Zobel, V., Reininghaus, J., & Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz & T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data (1st ed., Vol. 40, pp. 257–267). Springer. https://doi.org/10.1007/978-3-319-15090-1_13","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267."},"publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","page":"257 - 267","date_published":"2015-01-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","_id":"1531","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 40","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","status":"public","oa_version":"None","type":"book_chapter","alternative_title":["Mathematics and Visualization"],"abstract":[{"lang":"eng","text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece."}]},{"language":[{"iso":"eng"}],"doi":"10.1137/140993934","project":[{"grant_number":"622033","_id":"255F06BE-B435-11E9-9278-68D0E5697425","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7"}],"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf"}],"publication_identifier":{"eissn":["1536-0040"]},"month":"01","volume":14,"date_updated":"2021-01-12T06:51:34Z","date_created":"2018-12-11T11:52:42Z","author":[{"last_name":"Knipl","first_name":"Diána","full_name":"Knipl, Diána"},{"last_name":"Pilarczyk","first_name":"Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"},{"last_name":"Röst","first_name":"Gergely","full_name":"Röst, Gergely"}],"publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2015","acknowledgement":"Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria (pawel.pilarczyk@ist.ac.at). This author’s work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 622033, by Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE—Programa Operacional Factores de Competitividade (POFC), by the Portuguese national funds through Funda ̧caoparaaCiˆencia e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (ref. FCT PTDC/MAT/098871/2008), and by European Research Council through StG 259559 in the framework of the EPIDELAY project.","publist_id":"5616","ec_funded":1,"date_published":"2015-01-01T00:00:00Z","page":"980 - 1017","article_type":"original","citation":{"ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 2015;14(2):980-1017. doi:10.1137/140993934","apa":"Knipl, D., Pilarczyk, P., & Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/140993934","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2. Society for Industrial and Applied Mathematics , pp. 980–1017, 2015.","ista":"Knipl D, Pilarczyk P, Röst G. 2015. Rich bifurcation structure in a two patch vaccination model. SIAM Journal on Applied Dynamical Systems. 14(2), 980–1017.","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","mla":"Knipl, Diána, et al. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, Society for Industrial and Applied Mathematics , 2015, pp. 980–1017, doi:10.1137/140993934.","chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” SIAM Journal on Applied Dynamical Systems. Society for Industrial and Applied Mathematics , 2015. https://doi.org/10.1137/140993934."},"publication":"SIAM Journal on Applied Dynamical Systems","article_processing_charge":"No","day":"01","scopus_import":1,"oa_version":"Published Version","intvolume":" 14","title":"Rich bifurcation structure in a two patch vaccination model","status":"public","ddc":["510"],"_id":"1555","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","abstract":[{"text":"We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible-infected-vaccinated-susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each subpopulation, both forward and backward bifurcations can occur. This implies that for disconnected regions the two-patch system may admit several steady states. We consider traveling between the regions and investigate the impact of spatial dispersal of individuals on the model dynamics. We establish conditions for the existence of multiple nontrivial steady states in the system, and we study the structure of the equilibria. The mathematical analysis reveals an unusually rich dynamical behavior, not normally found in the simple epidemic models. In addition to the disease-free equilibrium, eight endemic equilibria emerge from backward transcritical and saddle-node bifurcation points, forming an interesting bifurcation diagram. Stability of steady states, their bifurcations, and the global dynamics are investigated with analytical tools, numerical simulations, and rigorous set-oriented numerical computations.","lang":"eng"}],"type":"journal_article"},{"month":"02","day":"05","scopus_import":1,"conference":{"start_date":"2014-09-22","location":"Timisoara, Romania","end_date":"2014-09-25","name":"SYNASC: Symbolic and Numeric Algorithms for Scientific Computing"},"date_published":"2015-02-05T00:00:00Z","doi":"10.1109/SYNASC.2014.81","language":[{"iso":"eng"}],"publication":"Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","citation":{"mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731, doi:10.1109/SYNASC.2014.81.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 7034731. IEEE, 2015. https://doi.org/10.1109/SYNASC.2014.81.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE; 2015:7034731. doi:10.1109/SYNASC.2014.81","ista":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. 2015. The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, 2015, p. 7034731.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., & Malkova, D. (2015). The classification of endoscopy images with persistent homology. In Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (p. 7034731). Timisoara, Romania: IEEE. https://doi.org/10.1109/SYNASC.2014.81"},"quality_controlled":"1","page":"7034731","abstract":[{"text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. The analysis of the learning algorithm reveals that a handful of geometric and topological features are responsible for the overwhelming majority of decisions.","lang":"eng"}],"publist_id":"5603","type":"conference","author":[{"full_name":"Dunaeva, Olga","first_name":"Olga","last_name":"Dunaeva"},{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Lukyanov, Anton","first_name":"Anton","last_name":"Lukyanov"},{"first_name":"Michael","last_name":"Machin","full_name":"Machin, Michael"},{"last_name":"Malkova","first_name":"Daria","full_name":"Malkova, Daria"}],"related_material":{"record":[{"id":"1289","relation":"later_version","status":"public"}]},"date_updated":"2023-02-21T16:57:29Z","date_created":"2018-12-11T11:52:46Z","oa_version":"None","_id":"1568","year":"2015","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","title":"The classification of endoscopy images with persistent homology","status":"public","publication_status":"published","publisher":"IEEE","department":[{"_id":"HeEd"}]},{"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"1567","year":"2015","status":"public","publication_status":"published","title":"Shape, homology, persistence, and stability","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"intvolume":" 9411","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"date_created":"2018-12-11T11:52:46Z","date_updated":"2022-01-28T08:25:00Z","volume":9411,"oa_version":"None","type":"conference","alternative_title":["LNCS"],"abstract":[{"lang":"eng","text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations."}],"publist_id":"5604","publication":"23rd International Symposium","citation":{"ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in 23rd International Symposium, Los Angeles, CA, United States, 2015, vol. 9411.","apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In 23rd International Symposium (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: 23rd International Symposium. Vol 9411. Springer Nature; 2015.","chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In 23rd International Symposium, Vol. 9411. Springer Nature, 2015.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” 23rd International Symposium, vol. 9411, Springer Nature, 2015.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015."},"quality_controlled":"1","conference":{"name":"GD: Graph Drawing and Network Visualization","end_date":"2015-09-26","start_date":"2015-09-24","location":"Los Angeles, CA, United States"},"date_published":"2015-01-01T00:00:00Z","language":[{"iso":"eng"}],"scopus_import":"1","day":"01","month":"01","article_processing_charge":"No"},{"language":[{"iso":"eng"}],"date_published":"2015-03-01T00:00:00Z","doi":"10.12775/TMNA.2015.014","quality_controlled":"1","page":"273 - 286","publication":"Topological Methods in Nonlinear Analysis","citation":{"chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies, 2015. https://doi.org/10.12775/TMNA.2015.014.","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” Topological Methods in Nonlinear Analysis, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:10.12775/TMNA.2015.014.","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286.","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” Topological Methods in Nonlinear Analysis, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","apa":"Graff, G., & Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Juliusz Schauder Center for Nonlinear Studies. https://doi.org/10.12775/TMNA.2015.014","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 2015;45(1):273-286. doi:10.12775/TMNA.2015.014"},"month":"03","day":"01","scopus_import":1,"date_created":"2018-12-11T11:52:44Z","date_updated":"2021-01-12T06:51:37Z","volume":45,"oa_version":"None","author":[{"full_name":"Graff, Grzegorz","last_name":"Graff","first_name":"Grzegorz"},{"id":"3768D56A-F248-11E8-B48F-1D18A9856A87","last_name":"Pilarczyk","first_name":"Pawel","full_name":"Pilarczyk, Pawel"}],"publication_status":"published","title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","status":"public","department":[{"_id":"HeEd"}],"intvolume":" 45","publisher":"Juliusz Schauder Center for Nonlinear Studies","_id":"1563","year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}."}],"publist_id":"5608","issue":"1","type":"journal_article"}]