[{"publication":"Annals of Applied Probability","day":"01","year":"2018","isi":1,"date_created":"2018-12-11T11:44:33Z","doi":"10.1214/18-AAP1389","date_published":"2018-10-01T00:00:00Z","page":"3215 - 3238","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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.","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","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","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.","short":"H. Edelsbrunner, A. Nikitenko, Annals of Applied Probability 28 (2018) 3215–3238."},"title":"Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics","article_processing_charge":"No","external_id":{"isi":["000442893500018"],"arxiv":["1705.02870"]},"publist_id":"7967","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko"}],"project":[{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"5","related_material":{"record":[{"status":"public","id":"6287","relation":"dissertation_contains"}]},"volume":28,"oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"intvolume":" 28","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1705.02870","open_access":"1"}],"scopus_import":"1","date_updated":"2023-09-15T12:10:35Z","department":[{"_id":"HeEd"}],"_id":"87","status":"public","article_type":"original","type":"journal_article"},{"oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"month":"05","intvolume":" 6","file":[{"date_created":"2019-04-30T06:14:58Z","file_name":"2018_ForumMahtematics_Akopyan.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:28Z","file_size":249246,"file_id":"6356","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2050-5094"]},"publication_status":"published","volume":6,"related_material":{"record":[{"id":"8156","status":"public","relation":"dissertation_contains"}]},"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"_id":"6355","status":"public","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-09-19T14:50:12Z","file_date_updated":"2020-07-14T12:47:28Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"publisher":"Cambridge University Press","quality_controlled":"1","oa":1,"day":"31","publication":"Forum of Mathematics, Sigma","isi":1,"has_accepted_license":"1","year":"2018","doi":"10.1017/fms.2018.7","date_published":"2018-05-31T00:00:00Z","date_created":"2019-04-30T06:09:57Z","article_number":"e7","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","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.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","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.","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","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","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."},"title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","last_name":"Avvakumov","full_name":"Avvakumov, Sergey"}],"article_processing_charge":"No","external_id":{"isi":["000433915500001"],"arxiv":["1712.10205"]}},{"publication":"Discrete & Computational Geometry","day":"01","year":"2018","has_accepted_license":"1","isi":1,"date_created":"2018-12-11T11:49:57Z","date_published":"2018-06-01T00:00:00Z","doi":"10.1007/s00454-017-9883-x","page":"1001-1009","oa":1,"quality_controlled":"1","publisher":"Springer","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete & Computational Geometry 59 (2018) 1001–1009.","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","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","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.","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."},"title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","external_id":{"isi":["000432205500011"]},"article_processing_charge":"Yes (via OA deal)","publist_id":"6324","author":[{"orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy"},{"first_name":"Alexey","full_name":"Balitskiy, Alexey","last_name":"Balitskiy"},{"first_name":"Mikhail","last_name":"Grigorev","full_name":"Grigorev, Mikhail"}],"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"5844","success":1,"date_updated":"2019-01-18T09:27:36Z","file_size":482518,"creator":"dernst","date_created":"2019-01-18T09:27:36Z","file_name":"2018_DiscreteComp_Akopyan.pdf"}],"publication_status":"published","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"ec_funded":1,"volume":59,"issue":"4","oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"intvolume":" 59","month":"06","scopus_import":"1","ddc":["516","000"],"date_updated":"2023-09-20T12:08:51Z","department":[{"_id":"HeEd"}],"file_date_updated":"2019-01-18T09:27:36Z","_id":"1064","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article"},{"status":"public","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"type":"preprint","article_number":"1804.03057","_id":"75","department":[{"_id":"HeEd"},{"_id":"JaMa"}],"title":"Convex fair partitions into arbitrary number of pieces","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan"},{"first_name":"Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","last_name":"Avvakumov"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"external_id":{"arxiv":["1804.03057"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-12-18T10:51:02Z","citation":{"ieee":"A. Akopyan, S. Avvakumov, and R. Karasev, “Convex fair partitions into arbitrary number of pieces.” arXiv, 2018.","short":"A. Akopyan, S. Avvakumov, R. Karasev, (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","ama":"Akopyan A, Avvakumov S, Karasev R. Convex fair partitions into arbitrary number of pieces. 2018. doi:10.48550/arXiv.1804.03057","mla":"Akopyan, Arseniy, et al. Convex Fair Partitions into Arbitrary Number of Pieces. 1804.03057, arXiv, 2018, doi:10.48550/arXiv.1804.03057.","ista":"Akopyan A, Avvakumov S, Karasev R. 2018. Convex fair partitions into arbitrary number of pieces. 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."},"month":"09","publisher":"arXiv","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.03057"}],"oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"related_material":{"record":[{"status":"public","id":"8156","relation":"dissertation_contains"}]},"doi":"10.48550/arXiv.1804.03057","date_published":"2018-09-13T00:00:00Z","ec_funded":1,"date_created":"2018-12-11T11:44:30Z","day":"13","language":[{"iso":"eng"}],"year":"2018","publication_status":"published"},{"related_material":{"record":[{"id":"10892","status":"public","relation":"earlier_version"}]},"volume":26,"issue":"3-4","publication_status":"published","file":[{"file_size":769296,"date_updated":"2020-07-14T12:46:35Z","creator":"system","file_name":"IST-2018-949-v1+1_2016_huber_PLanar_matchings.pdf","date_created":"2018-12-12T10:09:34Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4758","checksum":"f79e8558bfe4b368dfefeb8eec2e3a5e"}],"language":[{"iso":"eng"}],"scopus_import":1,"month":"04","intvolume":" 26","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","file_date_updated":"2020-07-14T12:46:35Z","department":[{"_id":"HeEd"}],"date_updated":"2023-02-21T16:06:22Z","ddc":["004","514","516"],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"949","_id":"481","page":"211 - 229","doi":"10.1142/S0218195916600050","date_published":"2017-04-13T00:00:00Z","date_created":"2018-12-11T11:46:43Z","has_accepted_license":"1","year":"2017","day":"13","publication":"International Journal of Computational Geometry and Applications","publisher":"World Scientific Publishing","quality_controlled":"1","oa":1,"acknowledgement":"Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research supported by Austrian Science Fund (FWF): P25816-N15.","publist_id":"7338","author":[{"first_name":"Therese","full_name":"Biedl, Therese","last_name":"Biedl"},{"first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","full_name":"Huber, Stefan","last_name":"Huber"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"}],"title":"Planar matchings for weighted straight skeletons","citation":{"short":"T. Biedl, S. Huber, P. Palfrader, International Journal of Computational Geometry and Applications 26 (2017) 211–229.","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.","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","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","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.","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.","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."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"oa_version":"Submitted Version","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"}],"intvolume":" 215","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.03954v1"}],"oa":1,"quality_controlled":"1","publisher":"Elsevier","language":[{"iso":"eng"}],"publication":"Topology and its Applications","day":"01","publication_status":"published","year":"2017","publication_identifier":{"issn":["01668641"]},"date_created":"2018-12-11T11:46:56Z","doi":"10.1016/j.topol.2016.10.005","date_published":"2017-01-01T00:00:00Z","volume":215,"page":"45 - 57","_id":"521","status":"public","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","apa":"Austin, K., & Virk, Z. (2017). Higson compactification and dimension raising. Topology and Its Applications. Elsevier. https://doi.org/10.1016/j.topol.2016.10.005","ama":"Austin K, Virk Z. Higson compactification and dimension raising. Topology and its Applications. 2017;215:45-57. doi:10.1016/j.topol.2016.10.005","short":"K. Austin, Z. Virk, Topology and Its Applications 215 (2017) 45–57.","ieee":"K. Austin and Z. Virk, “Higson compactification and dimension raising,” Topology and its Applications, vol. 215. Elsevier, pp. 45–57, 2017.","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.","ista":"Austin K, Virk Z. 2017. Higson compactification and dimension raising. Topology and its Applications. 215, 45–57."},"date_updated":"2021-01-12T08:01:21Z","title":"Higson compactification and dimension raising","department":[{"_id":"HeEd"}],"author":[{"full_name":"Austin, Kyle","last_name":"Austin","first_name":"Kyle"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7299"},{"type":"journal_article","status":"public","_id":"568","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_updated":"2021-01-12T08:03:12Z","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"month":"01","intvolume":" 19","abstract":[{"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).","lang":"eng"}],"oa_version":"Submitted Version","volume":19,"issue":"2","ec_funded":1,"publication_identifier":{"issn":["15320073"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"},{"grant_number":"701309","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425"}],"publist_id":"7246","author":[{"last_name":"Franek","full_name":"Franek, Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"},{"first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","last_name":"Krcál"}],"title":"Persistence of zero sets","citation":{"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.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” Homology, Homotopy and Applications, vol. 19, no. 2. International Press, pp. 313–342, 2017.","ama":"Franek P, Krcál M. Persistence of zero sets. Homology, Homotopy and Applications. 2017;19(2):313-342. doi:10.4310/HHA.2017.v19.n2.a16","apa":"Franek, P., & Krcál, M. (2017). Persistence of zero sets. Homology, Homotopy and Applications. International Press. https://doi.org/10.4310/HHA.2017.v19.n2.a16","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” Homology, Homotopy and Applications. International Press, 2017. https://doi.org/10.4310/HHA.2017.v19.n2.a16.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publisher":"International Press","quality_controlled":"1","oa":1,"page":"313 - 342","date_published":"2017-01-01T00:00:00Z","doi":"10.4310/HHA.2017.v19.n2.a16","date_created":"2018-12-11T11:47:14Z","year":"2017","day":"01","publication":"Homology, Homotopy and Applications"},{"alternative_title":["LNCS"],"intvolume":" 10256","month":"05","place":"Cham","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"}],"oa_version":"None","volume":10256,"publication_status":"published","publication_identifier":{"isbn":["978-3-319-59107-0","978-3-319-59108-7"],"issn":["0302-9743","1611-3349"]},"language":[{"iso":"eng"}],"conference":{"name":"IWCIA: International Workshop on Combinatorial Image Analysis","location":"Plovdiv, Bulgaria","end_date":"2017-06-21","start_date":"2017-06-19"},"type":"book_chapter","status":"public","_id":"5803","department":[{"_id":"HeEd"}],"date_updated":"2022-01-28T07:48:24Z","extern":"1","quality_controlled":"1","publisher":"Springer Nature","page":"93-104","date_created":"2019-01-08T20:42:56Z","doi":"10.1007/978-3-319-59108-7_8","date_published":"2017-05-17T00:00:00Z","year":"2017","publication":"Combinatorial image analysis","day":"17","article_processing_charge":"No","author":[{"id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","last_name":"Biswas"},{"first_name":"Partha","full_name":"Bhowmick, Partha","last_name":"Bhowmick"}],"title":"Construction of persistent Voronoi diagram on 3D digital plane","citation":{"ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In Combinatorial Image Analysis, 10256:93–104. Cham: Springer Nature, 2017. https://doi.org/10.1007/978-3-319-59108-7_8.","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in Combinatorial image analysis, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","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). 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Symposium on Computational Geometry, SoCG, LIPIcs, vol. 77, 391–3916.","mla":"Edelsbrunner, Herbert, and Hubert Wagner. Topological Data Analysis with Bregman Divergences. Vol. 77, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916, doi:10.4230/LIPIcs.SoCG.2017.39.","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.","short":"H. Edelsbrunner, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017, pp. 391–3916.","ama":"Edelsbrunner H, Wagner H. Topological data analysis with Bregman divergences. In: Vol 77. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2017:391-3916. doi:10.4230/LIPIcs.SoCG.2017.39","apa":"Edelsbrunner, H., & Wagner, H. (2017). Topological data analysis with Bregman divergences (Vol. 77, pp. 391–3916). Presented at the Symposium on Computational Geometry, SoCG, Brisbane, Australia: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.39"},"title":"Topological data analysis with Bregman divergences","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Wagner, Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert"}],"publist_id":"7021","file":[{"file_name":"IST-2017-895-v1+1_LIPIcs-SoCG-2017-39.pdf","date_created":"2018-12-12T10:11:03Z","file_size":990546,"date_updated":"2020-07-14T12:47:42Z","creator":"system","file_id":"4856","checksum":"067ab0cb3f962bae6c3af6bf0094e0f3","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["18688969"]},"publication_status":"published","volume":77,"oa_version":"Published Version","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. ","lang":"eng"}],"month":"06","intvolume":" 77","alternative_title":["LIPIcs"],"scopus_import":1,"ddc":["514","516"],"date_updated":"2021-01-12T08:09:26Z","file_date_updated":"2020-07-14T12:47:42Z","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"_id":"688","status":"public","pubrep_id":"895","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"conference":{"name":"Symposium on Computational Geometry, SoCG","location":"Brisbane, Australia","end_date":"2017-07-07","start_date":"2017-07-04"}},{"scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1608.06279","open_access":"1"}],"month":"08","intvolume":" 49","abstract":[{"lang":"eng","text":"We answer a question of M. Gromov on the waist of the unit ball."}],"oa_version":"Preprint","volume":49,"issue":"4","ec_funded":1,"publication_identifier":{"issn":["00246093"]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"707","department":[{"_id":"HeEd"}],"date_updated":"2021-01-12T08:11:41Z","publisher":"Wiley-Blackwell","quality_controlled":"1","oa":1,"page":"690 - 693","date_published":"2017-08-01T00:00:00Z","doi":"10.1112/blms.12062","date_created":"2018-12-11T11:48:02Z","year":"2017","day":"01","publication":"Bulletin of the London Mathematical Society","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"publist_id":"6982","author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","last_name":"Akopyan"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"title":"A tight estimate for the waist of the ball ","citation":{"chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” Bulletin of the London Mathematical Society. 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Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"year":"2017","day":"01","publication":"Advances in Applied Probability","page":"745 - 767","date_published":"2017-09-01T00:00:00Z","doi":"10.1017/apr.2017.20","date_created":"2018-12-11T11:48:07Z","quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"citation":{"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.","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767.","mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” Advances in Applied Probability, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:10.1017/apr.2017.20.","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","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.","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. 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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."}],"oa_version":"Preprint","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1607.05915"}],"month":"09","intvolume":" 49","date_updated":"2023-09-07T12:07:12Z","department":[{"_id":"HeEd"}],"_id":"718","type":"journal_article","status":"public"},{"article_processing_charge":"No","author":[{"orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87"}],"title":"Discrete Morse theory for random complexes ","citation":{"short":"A. Nikitenko, Discrete Morse Theory for Random Complexes , Institute of Science and Technology Austria, 2017.","ieee":"A. Nikitenko, “Discrete Morse theory for random complexes ,” Institute of Science and Technology Austria, 2017.","apa":"Nikitenko, A. (2017). Discrete Morse theory for random complexes . 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Institute of Science and Technology Austria.","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"86","date_created":"2019-04-09T15:04:32Z","date_published":"2017-10-27T00:00:00Z","doi":"10.15479/AT:ISTA:th_873","year":"2017","has_accepted_license":"1","day":"27","oa":1,"publisher":"Institute of Science and Technology Austria","file_date_updated":"2020-07-14T12:47:26Z","department":[{"_id":"HeEd"}],"date_updated":"2023-09-15T12:10:34Z","supervisor":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"ddc":["514","516","519"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","pubrep_id":"873","status":"public","_id":"6287","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"718"},{"relation":"part_of_dissertation","id":"5678","status":"public"},{"id":"87","status":"public","relation":"part_of_dissertation"}]},"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2019-04-09T14:54:51Z","file_name":"2017_Thesis_Nikitenko.pdf","creator":"dernst","date_updated":"2020-07-14T12:47:26Z","file_size":2324870,"checksum":"ece7e598a2f060b263c2febf7f3fe7f9","file_id":"6289","access_level":"open_access","relation":"main_file","content_type":"application/pdf"},{"date_updated":"2020-07-14T12:47:26Z","file_size":2863219,"creator":"dernst","date_created":"2019-04-09T14:54:51Z","file_name":"2017_Thesis_Nikitenko_source.zip","content_type":"application/zip","access_level":"closed","relation":"source_file","file_id":"6290","checksum":"99b7ad76e317efd447af60f91e29b49b"}],"alternative_title":["ISTA Thesis"],"month":"10","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"}],"oa_version":"Published Version"},{"article_type":"original","type":"journal_article","status":"public","_id":"1433","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T09:42:40Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jsc.2016.03.008"}],"month":"01","intvolume":" 78","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","volume":78,"related_material":{"record":[{"relation":"earlier_version","id":"10894","status":"public"}]},"ec_funded":1,"publication_identifier":{"issn":[" 07477171"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","grant_number":"318493"}],"publist_id":"5765","author":[{"first_name":"Ulrich","full_name":"Bauer, Ulrich","last_name":"Bauer"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan"},{"last_name":"Wagner","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","first_name":"Hubert"}],"article_processing_charge":"No","external_id":{"isi":["000384396000005"]},"title":"Phat - Persistent homology algorithms toolbox","citation":{"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.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” Journal of Symbolic Computation, vol. 78, Academic Press, 2017, pp. 76–90, doi:10.1016/j.jsc.2016.03.008.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","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.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 2017;78:76-90. doi:10.1016/j.jsc.2016.03.008","apa":"Bauer, U., Kerber, M., Reininghaus, J., & Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. Academic Press. https://doi.org/10.1016/j.jsc.2016.03.008"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","quality_controlled":"1","publisher":"Academic Press","oa":1,"page":"76 - 90","doi":"10.1016/j.jsc.2016.03.008","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:51:59Z","isi":1,"year":"2017","day":"01","publication":"Journal of Symbolic Computation"},{"oa":1,"publisher":"Academic Press","quality_controlled":"1","page":"627 - 644","date_created":"2018-12-11T11:50:34Z","doi":"10.1016/j.aim.2016.12.026","date_published":"2017-02-21T00:00:00Z","year":"2017","isi":1,"publication":"Advances in Mathematics","day":"21","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"external_id":{"isi":["000409292900015"]},"article_processing_charge":"No","publist_id":"6173","author":[{"last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Bárány, Imre","last_name":"Bárány","first_name":"Imre"},{"last_name":"Robins","full_name":"Robins, Sinai","first_name":"Sinai"}],"title":"Algebraic vertices of non-convex polyhedra","citation":{"ista":"Akopyan A, Bárány I, Robins S. 2017. Algebraic vertices of non-convex polyhedra. Advances in Mathematics. 308, 627–644.","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.","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","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","short":"A. Akopyan, I. Bárány, S. Robins, Advances in Mathematics 308 (2017) 627–644.","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.","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1508.07594"}],"scopus_import":"1","intvolume":" 308","month":"02","abstract":[{"lang":"eng","text":"In this article we define an algebraic vertex of a generalized polyhedron and show that the set of algebraic vertices is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope P is a linear combination of indicator functions of simplices whose vertices are algebraic vertices of P. We also show that the indicator function of any generalized polyhedron is a linear combination, with integer coefficients, of indicator functions of cones with apices at algebraic vertices and line-cones. The concept of an algebraic vertex is closely related to the Fourier–Laplace transform. We show that a point v is an algebraic vertex of a generalized polyhedron P if and only if the tangent cone of P, at v, has non-zero Fourier–Laplace transform."}],"oa_version":"Submitted Version","ec_funded":1,"volume":308,"publication_status":"published","publication_identifier":{"issn":["00018708"]},"language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1180","department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T11:21:27Z"},{"_id":"1173","status":"public","type":"journal_article","date_updated":"2023-09-20T11:23:53Z","department":[{"_id":"HeEd"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions."}],"intvolume":" 37","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1411.6337","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["02099683"]},"ec_funded":1,"issue":"5","volume":37,"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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.","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.","short":"H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017) 887–910.","ama":"Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. 2017;37(5):887-910. doi:10.1007/s00493-016-3308-y","apa":"Edelsbrunner, H., Glazyrin, A., Musin, O., & Nikitenko, A. (2017). The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica. Springer. https://doi.org/10.1007/s00493-016-3308-y","chicago":"Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko. “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.” Combinatorica. Springer, 2017. https://doi.org/10.1007/s00493-016-3308-y.","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."},"title":"The Voronoi functional is maximized by the Delaunay triangulation in the plane","article_processing_charge":"No","external_id":{"isi":["000418056000005"]},"publist_id":"6182","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"last_name":"Glazyrin","full_name":"Glazyrin, Alexey","first_name":"Alexey"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton","orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","last_name":"Nikitenko"}],"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.","oa":1,"publisher":"Springer","quality_controlled":"1","publication":"Combinatorica","day":"01","year":"2017","isi":1,"date_created":"2018-12-11T11:50:32Z","doi":"10.1007/s00493-016-3308-y","date_published":"2017-10-01T00:00:00Z","page":"887 - 910"},{"doi":"10.1090/tran/6991","date_published":"2017-05-01T00:00:00Z","date_created":"2018-12-11T11:49:59Z","page":"3741 - 3762","day":"01","publication":"Transactions of the American Mathematical Society","isi":1,"year":"2017","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"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”.","title":"The Morse theory of Čech and delaunay complexes","publist_id":"6311","author":[{"full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"article_processing_charge":"No","external_id":{"arxiv":["1312.1231"],"isi":["000398030400024"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"U. Bauer, H. Edelsbrunner, Transactions of the American Mathematical Society 369 (2017) 3741–3762.","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","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","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.","ista":"Bauer U, Edelsbrunner H. 2017. The Morse theory of Čech and delaunay complexes. Transactions of the American Mathematical Society. 369(5), 3741–3762.","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."},"project":[{"grant_number":"318493","name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"volume":369,"issue":"5","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"05","intvolume":" 369","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.1231"}],"oa_version":"Preprint","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."}],"department":[{"_id":"HeEd"}],"date_updated":"2023-09-20T12:05:56Z","status":"public","article_type":"original","type":"journal_article","_id":"1072"},{"file_date_updated":"2019-10-15T07:44:51Z","department":[{"_id":"KrCh"},{"_id":"HeEd"}],"date_updated":"2023-09-20T12:08:18Z","ddc":["000"],"type":"journal_article","pubrep_id":"991","status":"public","_id":"1065","ec_funded":1,"volume":122,"publication_status":"published","publication_identifier":{"issn":["00200190"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4998","file_size":247657,"date_updated":"2019-10-15T07:44:51Z","creator":"system","file_name":"IST-2018-991-v1+2_2018_Chatterjee_Pushdown_PREPRINT.pdf","date_created":"2018-12-12T10:13:17Z"}],"scopus_import":"1","intvolume":" 122","month":"06","abstract":[{"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.","lang":"eng"}],"oa_version":"Submitted Version","article_processing_charge":"No","external_id":{"isi":["000399506600005"]},"author":[{"orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu"},{"last_name":"Osang","orcid":"0000-0002-8882-5116","full_name":"Osang, Georg F","first_name":"Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6323","title":"Pushdown reachability with constant treewidth","citation":{"ista":"Chatterjee K, Osang GF. 2017. Pushdown reachability with constant treewidth. Information Processing Letters. 122, 25–29.","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.","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","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.","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","grant_number":"P 23499-N23"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Game Theory","grant_number":"S11407"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"}],"page":"25 - 29","date_created":"2018-12-11T11:49:57Z","doi":"10.1016/j.ipl.2017.02.003","date_published":"2017-06-01T00:00:00Z","year":"2017","has_accepted_license":"1","isi":1,"publication":"Information Processing Letters","day":"01","oa":1,"quality_controlled":"1","publisher":"Elsevier"},{"date_updated":"2023-09-22T09:40:55Z","department":[{"_id":"HeEd"}],"_id":"1022","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_identifier":{"issn":["00358711"]},"publication_status":"published","issue":"4","volume":465,"oa_version":"Submitted Version","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"}],"month":"01","intvolume":" 465","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1608.04519","open_access":"1"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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","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","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.","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.","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.","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.","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."},"title":"The topology of the cosmic web in terms of persistent Betti numbers","author":[{"first_name":"Pratyush","last_name":"Pranav","full_name":"Pranav, Pratyush"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Van De Weygaert, Rien","last_name":"Van De Weygaert","first_name":"Rien"},{"last_name":"Vegter","full_name":"Vegter, Gert","first_name":"Gert"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"first_name":"Bernard","full_name":"Jones, Bernard","last_name":"Jones"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6373","external_id":{"isi":["000395170200039"]},"article_processing_charge":"No","day":"01","publication":"Monthly Notices of the Royal Astronomical Society","isi":1,"year":"2017","date_published":"2017-01-01T00:00:00Z","doi":"10.1093/mnras/stw2862","date_created":"2018-12-11T11:49:44Z","page":"4281 - 4310","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.","quality_controlled":"1","publisher":"Oxford University Press","oa":1},{"volume":231,"publication_status":"published","publication_identifier":{"issn":["01668641"]},"language":[{"iso":"eng"}],"scopus_import":"1","intvolume":" 231","month":"11","abstract":[{"text":"We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.","lang":"eng"}],"oa_version":"None","department":[{"_id":"HeEd"}],"date_updated":"2023-09-27T12:53:01Z","type":"journal_article","status":"public","_id":"737","page":"186 - 196","date_created":"2018-12-11T11:48:14Z","doi":"10.1016/j.topol.2017.09.015","date_published":"2017-11-01T00:00:00Z","year":"2017","isi":1,"publication":"Topology and its Applications","day":"01","quality_controlled":"1","publisher":"Elsevier","article_processing_charge":"No","external_id":{"isi":["000413889100012"]},"publist_id":"6930","author":[{"last_name":"Virk","full_name":"Virk, Ziga","first_name":"Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Andreas","last_name":"Zastrow","full_name":"Zastrow, Andreas"}],"title":"A new topology on the universal path space","citation":{"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","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","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.","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","mla":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.","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."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-331956930-7"]},"publication_status":"published","volume":198,"ec_funded":1,"oa_version":"None","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"}],"month":"07","intvolume":" 198","alternative_title":["PROMS"],"scopus_import":"1","date_updated":"2023-09-26T15:50:52Z","department":[{"_id":"HeEd"}],"_id":"836","status":"public","type":"conference","conference":{"name":"ACA: Applications of Computer Algebra","start_date":"2015-07-20","end_date":"2015-07-23","location":"Kalamata, Greece"},"day":"27","publication":"Special Sessions in Applications of Computer Algebra","isi":1,"year":"2017","date_published":"2017-07-27T00:00:00Z","doi":"10.1007/978-3-319-56932-1_8","date_created":"2018-12-11T11:48:46Z","page":"119 - 136","publisher":"Springer","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","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.","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","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","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.","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."},"title":"Finding eigenvalues of self-maps with the Kronecker canonical form","publist_id":"6812","author":[{"first_name":"Marc","full_name":"Ethier, Marc","last_name":"Ethier"},{"first_name":"Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","full_name":"Jablonski, Grzegorz","orcid":"0000-0002-3536-9866","last_name":"Jablonski"},{"first_name":"Marian","last_name":"Mrozek","full_name":"Mrozek, Marian"}],"article_processing_charge":"No","external_id":{"isi":["000434088200008"]},"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}]}]