[{"title":"On the distribution of local extrema in quantum chaos","abstract":[{"lang":"eng","text":"We numerically investigate the distribution of extrema of 'chaotic' Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy, which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2."}],"status":"public","publication":"Physics Letters, Section A","publication_status":"published","oa_version":"None","day":"06","date_updated":"2025-09-23T09:44:12Z","date_published":"2015-03-06T00:00:00Z","article_processing_charge":"No","publisher":"Elsevier","volume":379,"intvolume":"       379","quality_controlled":"1","page":"535 - 541","external_id":{"isi":["000349586000006"]},"month":"03","type":"journal_article","citation":{"short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.","mla":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:<a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">10.1016/j.physleta.2014.12.010</a>.","ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","chicago":"Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">https://doi.org/10.1016/j.physleta.2014.12.010</a>.","ieee":"F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” <i>Physics Letters, Section A</i>, vol. 379, no. 6. Elsevier, pp. 535–541, 2015.","apa":"Pausinger, F., &#38; Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. <i>Physics Letters, Section A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">https://doi.org/10.1016/j.physleta.2014.12.010</a>","ama":"Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. <i>Physics Letters, Section A</i>. 2015;379(6):535-541. doi:<a href=\"https://doi.org/10.1016/j.physleta.2014.12.010\">10.1016/j.physleta.2014.12.010</a>"},"corr_author":"1","language":[{"iso":"eng"}],"publist_id":"5152","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"year":"2015","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","last_name":"Pausinger","full_name":"Pausinger, Florian","first_name":"Florian","orcid":"0000-0002-8379-3768"},{"first_name":"Stefan","last_name":"Steinerberger","full_name":"Steinerberger, Stefan"}],"date_created":"2018-12-11T11:54:49Z","department":[{"_id":"HeEd"}],"issue":"6","acknowledgement":"F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm. ","scopus_import":"1","_id":"1938","doi":"10.1016/j.physleta.2014.12.010"},{"file":[{"relation":"main_file","file_size":1317546,"access_level":"open_access","date_updated":"2020-07-14T12:45:26Z","checksum":"3566f3a8b0c1bc550e62914a88c584ff","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","file_id":"4670","creator":"system","date_created":"2018-12-12T10:08:10Z","content_type":"application/pdf"}],"citation":{"ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","chicago":"Edelsbrunner, Herbert, Grzegorz Jablonski, and Marian Mrozek. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>.","ieee":"H. Edelsbrunner, G. Jablonski, and M. Mrozek, “The persistent homology of a self-map,” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5. Springer, pp. 1213–1244, 2015.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 1213–1244.","mla":"Edelsbrunner, Herbert, et al. “The Persistent Homology of a Self-Map.” <i>Foundations of Computational Mathematics</i>, vol. 15, no. 5, Springer, 2015, pp. 1213–44, doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>.","ama":"Edelsbrunner H, Jablonski G, Mrozek M. The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. 2015;15(5):1213-1244. doi:<a href=\"https://doi.org/10.1007/s10208-014-9223-y\">10.1007/s10208-014-9223-y</a>","apa":"Edelsbrunner, H., Jablonski, G., &#38; Mrozek, M. (2015). The persistent homology of a self-map. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-014-9223-y\">https://doi.org/10.1007/s10208-014-9223-y</a>"},"project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"intvolume":"        15","publisher":"Springer","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"volume":15,"external_id":{"isi":["000360862900004"]},"type":"journal_article","month":"10","page":"1213 - 1244","quality_controlled":"1","status":"public","publication":"Foundations of Computational Mathematics","publication_status":"published","article_processing_charge":"No","date_published":"2015-10-01T00:00:00Z","day":"01","date_updated":"2025-09-23T14:08:54Z","oa_version":"Published Version","ddc":["000"],"title":"The persistent homology of a self-map","abstract":[{"text":"Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.\r\n","lang":"eng"}],"ec_funded":1,"scopus_import":"1","acknowledgement":"This research is partially supported by the Toposys project 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 Polish National Science Center under Grant No. N201 419639.","issue":"5","has_accepted_license":"1","doi":"10.1007/s10208-014-9223-y","_id":"2035","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:55:20Z","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-3536-9866","first_name":"Grzegorz","full_name":"Jablonski, Grzegorz","last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian"}],"publist_id":"5022","year":"2015","isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file_date_updated":"2020-07-14T12:45:26Z","language":[{"iso":"eng"}],"pubrep_id":"486"},{"title":"Root traits computed by DynamicRoots for the maize root shown in fig 2","status":"public","article_processing_charge":"No","related_material":{"record":[{"relation":"used_in_publication","id":"1793","status":"public"}]},"date_published":"2015-06-01T00:00:00Z","year":"2015","date_updated":"2025-09-23T08:30:43Z","day":"01","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa_version":"Published Version","publisher":"Public Library of Science","department":[{"_id":"MaJö"},{"_id":"HeEd"}],"month":"06","type":"research_data_reference","date_created":"2021-07-28T06:20:13Z","author":[{"first_name":"Olga","orcid":"0000-0003-2012-9947","last_name":"Symonova","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","full_name":"Symonova, Olga"},{"full_name":"Topp, Christopher","last_name":"Topp","first_name":"Christopher"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833"}],"citation":{"ama":"Symonova O, Topp C, Edelsbrunner H. Root traits computed by DynamicRoots for the maize root shown in fig 2. 2015. doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>","apa":"Symonova, O., Topp, C., &#38; Edelsbrunner, H. (2015). Root traits computed by DynamicRoots for the maize root shown in fig 2. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">https://doi.org/10.1371/journal.pone.0127657.s001</a>","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. Root traits computed by DynamicRoots for the maize root shown in fig 2, Public Library of Science, <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>.","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2.” Public Library of Science, 2015. <a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">https://doi.org/10.1371/journal.pone.0127657.s001</a>.","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “Root traits computed by DynamicRoots for the maize root shown in fig 2.” Public Library of Science, 2015.","short":"O. Symonova, C. Topp, H. Edelsbrunner, (2015).","mla":"Symonova, Olga, et al. <i>Root Traits Computed by DynamicRoots for the Maize Root Shown in Fig 2</i>. Public Library of Science, 2015, doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657.s001\">10.1371/journal.pone.0127657.s001</a>."},"doi":"10.1371/journal.pone.0127657.s001","_id":"9737"},{"status":"public","publication_status":"published","publication":"PLoS One","oa_version":"Published Version","day":"01","date_updated":"2025-09-23T08:30:43Z","date_published":"2015-06-01T00:00:00Z","article_processing_charge":"No","title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","ddc":["000"],"abstract":[{"lang":"eng","text":"We present a software platform for reconstructing and analyzing the growth of a plant root system from a time-series of 3D voxelized shapes. It aligns the shapes with each other, constructs a geometric graph representation together with the function that records the time of growth, and organizes the branches into a hierarchy that reflects the order of creation. The software includes the automatic computation of structural and dynamic traits for each root in the system enabling the quantification of growth on fine-scale. These are important advances in plant phenotyping with applications to the study of genetic and environmental influences on growth."}],"citation":{"apa":"Symonova, O., Topp, C., &#38; Edelsbrunner, H. (2015). DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. <i>PLoS One</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pone.0127657\">https://doi.org/10.1371/journal.pone.0127657</a>","ama":"Symonova O, Topp C, Edelsbrunner H. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. <i>PLoS One</i>. 2015;10(6). doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657\">10.1371/journal.pone.0127657</a>","mla":"Symonova, Olga, et al. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” <i>PLoS One</i>, vol. 10, no. 6, e0127657, Public Library of Science, 2015, doi:<a href=\"https://doi.org/10.1371/journal.pone.0127657\">10.1371/journal.pone.0127657</a>.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","ieee":"O. Symonova, C. Topp, and H. Edelsbrunner, “DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots,” <i>PLoS One</i>, vol. 10, no. 6. Public Library of Science, 2015.","ista":"Symonova O, Topp C, Edelsbrunner H. 2015. DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots. PLoS One. 10(6), e0127657.","chicago":"Symonova, Olga, Christopher Topp, and Herbert Edelsbrunner. “DynamicRoots: A Software Platform for the Reconstruction and Analysis of Growing Plant Roots.” <i>PLoS One</i>. Public Library of Science, 2015. <a href=\"https://doi.org/10.1371/journal.pone.0127657\">https://doi.org/10.1371/journal.pone.0127657</a>."},"file":[{"creator":"system","date_created":"2018-12-12T10:15:30Z","content_type":"application/pdf","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","checksum":"d20f26461ca575276ad3ed9ce4bfc787","file_id":"5150","file_size":1850825,"access_level":"open_access","date_updated":"2020-07-14T12:45:16Z","relation":"main_file"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Public Library of Science","oa":1,"volume":10,"intvolume":"        10","quality_controlled":"1","type":"journal_article","external_id":{"isi":["000356630900069"]},"month":"06","publist_id":"5318","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"article_number":"e0127657","year":"2015","related_material":{"record":[{"id":"9737","relation":"research_data","status":"public"}]},"corr_author":"1","file_date_updated":"2020-07-14T12:45:16Z","pubrep_id":"454","language":[{"iso":"eng"}],"issue":"6","scopus_import":"1","_id":"1793","has_accepted_license":"1","doi":"10.1371/journal.pone.0127657","author":[{"first_name":"Olga","orcid":"0000-0003-2012-9947","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","last_name":"Symonova","full_name":"Symonova, Olga"},{"last_name":"Topp","full_name":"Topp, Christopher","first_name":"Christopher"},{"orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"}],"department":[{"_id":"MaJö"},{"_id":"HeEd"}],"date_created":"2018-12-11T11:54:02Z"},{"OA_place":"publisher","intvolume":"        48","volume":48,"publisher":"Elsevier","oa":1,"page":"606 - 621","type":"journal_article","month":"06","external_id":{"isi":["000357353200006"]},"quality_controlled":"1","citation":{"short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">10.1016/j.comgeo.2014.08.010</a>.","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">https://doi.org/10.1016/j.comgeo.2014.08.010</a>.","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., &#38; Lieutier, A. (2015). Homological reconstruction and simplification in R3. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">https://doi.org/10.1016/j.comgeo.2014.08.010</a>","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. <i>Computational Geometry: Theory and Applications</i>. 2015;48(8):606-621. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">10.1016/j.comgeo.2014.08.010</a>"},"article_type":"original","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"title":"Homological reconstruction and simplification in R3","ddc":["500"],"abstract":[{"lang":"eng","text":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard."}],"ec_funded":1,"publication_status":"published","publication":"Computational Geometry: Theory and Applications","status":"public","article_processing_charge":"No","date_published":"2015-06-03T00:00:00Z","oa_version":"Published Version","date_updated":"2026-06-18T17:57:28Z","day":"03","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:54:06Z","author":[{"first_name":"Dominique","last_name":"Attali","full_name":"Attali, Dominique"},{"orcid":"0000-0002-9683-0724","first_name":"Ulrich","full_name":"Bauer, Ulrich","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Olivier","last_name":"Devillers","full_name":"Devillers, Olivier"},{"full_name":"Glisse, Marc","last_name":"Glisse","first_name":"Marc"},{"first_name":"André","full_name":"Lieutier, André","last_name":"Lieutier"}],"scopus_import":"1","issue":"8","doi":"10.1016/j.comgeo.2014.08.010","_id":"1805","corr_author":"1","OA_type":"free access","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.comgeo.2014.08.010"}],"publist_id":"5305","related_material":{"record":[{"relation":"earlier_version","id":"2812","status":"public"}]},"year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1},{"_id":"1828","doi":"10.1007/s10955-015-1238-5","issue":"1","scopus_import":"1","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","first_name":"Arseniy"},{"last_name":"Pirogov","full_name":"Pirogov, Sergey","first_name":"Sergey"},{"last_name":"Rybko","full_name":"Rybko, Aleksandr","first_name":"Aleksandr"}],"date_created":"2018-12-11T11:54:14Z","department":[{"_id":"HeEd"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"year":"2015","publist_id":"5276","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1406.5313"}],"corr_author":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"citation":{"short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","mla":"Akopyan, Arseniy, et al. “Invariant Measures of Genetic Recombination Process.” <i>Journal of Statistical Physics</i>, vol. 160, no. 1, Springer, 2015, pp. 163–67, doi:<a href=\"https://doi.org/10.1007/s10955-015-1238-5\">10.1007/s10955-015-1238-5</a>.","ista":"Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167.","chicago":"Akopyan, Arseniy, Sergey Pirogov, and Aleksandr Rybko. “Invariant Measures of Genetic Recombination Process.” <i>Journal of Statistical Physics</i>. Springer, 2015. <a href=\"https://doi.org/10.1007/s10955-015-1238-5\">https://doi.org/10.1007/s10955-015-1238-5</a>.","ieee":"A. Akopyan, S. Pirogov, and A. Rybko, “Invariant measures of genetic recombination process,” <i>Journal of Statistical Physics</i>, vol. 160, no. 1. Springer, pp. 163–167, 2015.","apa":"Akopyan, A., Pirogov, S., &#38; Rybko, A. (2015). Invariant measures of genetic recombination process. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-015-1238-5\">https://doi.org/10.1007/s10955-015-1238-5</a>","ama":"Akopyan A, Pirogov S, Rybko A. Invariant measures of genetic recombination process. <i>Journal of Statistical Physics</i>. 2015;160(1):163-167. doi:<a href=\"https://doi.org/10.1007/s10955-015-1238-5\">10.1007/s10955-015-1238-5</a>"},"quality_controlled":"1","page":"163 - 167","external_id":{"isi":["000356579000009"],"arxiv":["1406.5313"]},"month":"07","type":"journal_article","publisher":"Springer","volume":160,"oa":1,"intvolume":"       160","oa_version":"Preprint","day":"01","date_updated":"2025-09-23T09:23:53Z","article_processing_charge":"No","date_published":"2015-07-01T00:00:00Z","status":"public","publication_status":"published","publication":"Journal of Statistical Physics","ec_funded":1,"abstract":[{"lang":"eng","text":"We construct a non-linear Markov process connected with a biological model of a bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory."}],"arxiv":1,"title":"Invariant measures of genetic recombination process"},{"project":[{"name":"Persistent Homology - Images, Data and Maps","_id":"255F06BE-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"622033"}],"article_type":"original","citation":{"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.” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 14, no. 2, Society for Industrial and Applied Mathematics, 2015, pp. 980–1017, doi:<a href=\"https://doi.org/10.1137/140993934\">10.1137/140993934</a>.","chicago":"Knipl, Diána, Pawel Pilarczyk, and Gergely Röst. “Rich Bifurcation Structure in a Two Patch Vaccination Model.” <i>SIAM Journal on Applied Dynamical Systems</i>. Society for Industrial and Applied Mathematics, 2015. <a href=\"https://doi.org/10.1137/140993934\">https://doi.org/10.1137/140993934</a>.","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.","ieee":"D. Knipl, P. Pilarczyk, and G. Röst, “Rich bifurcation structure in a two patch vaccination model,” <i>SIAM Journal on Applied Dynamical Systems</i>, vol. 14, no. 2. Society for Industrial and Applied Mathematics, pp. 980–1017, 2015.","apa":"Knipl, D., Pilarczyk, P., &#38; Röst, G. (2015). Rich bifurcation structure in a two patch vaccination model. <i>SIAM Journal on Applied Dynamical Systems</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/140993934\">https://doi.org/10.1137/140993934</a>","ama":"Knipl D, Pilarczyk P, Röst G. Rich bifurcation structure in a two patch vaccination model. <i>SIAM Journal on Applied Dynamical Systems</i>. 2015;14(2):980-1017. doi:<a href=\"https://doi.org/10.1137/140993934\">10.1137/140993934</a>"},"quality_controlled":"1","month":"01","type":"journal_article","external_id":{"isi":["000357310400015"]},"page":"980 - 1017","publisher":"Society for Industrial and Applied Mathematics","oa":1,"volume":14,"intvolume":"        14","publication_identifier":{"eissn":["1536-0040"]},"day":"01","date_updated":"2026-07-06T13:59:25Z","oa_version":"Published Version","date_published":"2015-01-01T00:00:00Z","article_processing_charge":"No","publication_status":"published","publication":"SIAM Journal on Applied Dynamical Systems","status":"public","ec_funded":1,"abstract":[{"lang":"eng","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."}],"ddc":["510"],"title":"Rich bifurcation structure in a two patch vaccination model","_id":"1555","doi":"10.1137/140993934","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.","issue":"2","scopus_import":"1","author":[{"full_name":"Knipl, Diána","last_name":"Knipl","first_name":"Diána"},{"first_name":"Pawel","last_name":"Pilarczyk","id":"3768D56A-F248-11E8-B48F-1D18A9856A87","full_name":"Pilarczyk, Pawel"},{"first_name":"Gergely","last_name":"Röst","full_name":"Röst, Gergely"}],"date_created":"2018-12-11T11:52:42Z","department":[{"_id":"HeEd"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","das_tickbox":"1","year":"2015","publist_id":"5616","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf"}]},{"citation":{"mla":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>, vol. 31, no. 6, Academic Press, 2015, pp. 773–97, doi:<a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">10.1016/j.jco.2015.06.002</a>.","short":"F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.","ieee":"F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy systems,” <i>Journal of Complexity</i>, vol. 31, no. 6. Academic Press, pp. 773–797, 2015.","chicago":"Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General Discrepancy Systems.” <i>Journal of Complexity</i>. Academic Press, 2015. <a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">https://doi.org/10.1016/j.jco.2015.06.002</a>.","ista":"Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity. 31(6), 773–797.","apa":"Pausinger, F., &#38; Svane, A. (2015). A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">https://doi.org/10.1016/j.jco.2015.06.002</a>","ama":"Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems. <i>Journal of Complexity</i>. 2015;31(6):773-797. doi:<a href=\"https://doi.org/10.1016/j.jco.2015.06.002\">10.1016/j.jco.2015.06.002</a>"},"volume":31,"publisher":"Academic Press","intvolume":"        31","quality_controlled":"1","page":"773 - 797","external_id":{"isi":["000362926900001"]},"month":"12","type":"journal_article","publication_status":"published","status":"public","publication":"Journal of Complexity","oa_version":"None","day":"01","date_updated":"2026-07-29T10:08:33Z","date_published":"2015-12-01T00:00:00Z","article_processing_charge":"No","title":"A Koksma-Hlawka inequality for general discrepancy systems","abstract":[{"lang":"eng","text":"Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology."}],"issue":"6","acknowledgement":"F.P. is supported by the Graduate School of IST Austria, A.M.S is supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum Foundation.","scopus_import":"1","_id":"1792","doi":"10.1016/j.jco.2015.06.002","author":[{"orcid":"0000-0002-8379-3768","first_name":"Florian","full_name":"Pausinger, Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Anne","last_name":"Svane","full_name":"Svane, Anne"}],"date_created":"2018-12-11T11:54:02Z","department":[{"_id":"HeEd"}],"publist_id":"5320","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"year":"2015","related_material":{"record":[{"status":"public","id":"1399","relation":"dissertation_contains"}]},"corr_author":"1","language":[{"iso":"eng"}]},{"page":"144","date_created":"2018-12-11T11:51:48Z","month":"06","type":"dissertation","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"author":[{"full_name":"Pausinger, Florian","last_name":"Pausinger","id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8379-3768","first_name":"Florian"}],"publication_identifier":{"issn":["2663-337X"]},"OA_place":"publisher","publisher":"Institute of Science and Technology Austria","_id":"1399","citation":{"apa":"Pausinger, F. (2015). <i>On the approximation of intrinsic volumes</i>. Institute of Science and Technology Austria.","ama":"Pausinger F. On the approximation of intrinsic volumes. 2015.","mla":"Pausinger, Florian. <i>On the Approximation of Intrinsic Volumes</i>. Institute of Science and Technology Austria, 2015.","short":"F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science and Technology Austria, 2015.","ieee":"F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science and Technology Austria, 2015.","chicago":"Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute of Science and Technology Austria, 2015.","ista":"Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of Science and Technology Austria."},"abstract":[{"lang":"eng","text":"This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold."}],"language":[{"iso":"eng"}],"title":"On the approximation of intrinsic volumes","corr_author":"1","related_material":{"record":[{"id":"1662","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"1792","status":"public"},{"status":"public","id":"2255","relation":"part_of_dissertation"}]},"year":"2015","date_published":"2015-06-01T00:00:00Z","article_processing_charge":"No","supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"None","date_updated":"2026-07-29T10:08:34Z","alternative_title":["ISTA Thesis"],"day":"01","publist_id":"5808","status":"public","degree_awarded":"PhD","publication_status":"published","doi_confirm":"1"},{"doi":"10.1007/978-3-319-04099-8_9","_id":"10817","scopus_import":"1","acknowledgement":"This research is supported and funded by the Digiteo unTopoVis project, the TOPOSYS project FP7-ICT-318493-STREP, and MPC-VCC.","department":[{"_id":"HeEd"}],"date_created":"2022-03-04T08:33:57Z","author":[{"first_name":"David","last_name":"Günther","full_name":"Günther, David"},{"first_name":"Jan","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus"},{"full_name":"Seidel, Hans-Peter","last_name":"Seidel","first_name":"Hans-Peter"},{"last_name":"Weinkauf","full_name":"Weinkauf, Tino","first_name":"Tino"}],"year":"2014","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"editor":[{"last_name":"Bremer","full_name":"Bremer, Peer-Timo","first_name":"Peer-Timo"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"last_name":"Pascucci","full_name":"Pascucci, Valerio","first_name":"Valerio"},{"last_name":"Peikert","full_name":"Peikert, Ronald","first_name":"Ronald"}],"series_title":"Mathematics and Visualization","project":[{"call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems"}],"citation":{"ieee":"D. Günther, J. Reininghaus, H.-P. Seidel, and T. Weinkauf, “Notes on the simplification of the Morse-Smale complex,” in <i>Topological Methods in Data Analysis and Visualization III.</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer Nature, 2014, pp. 135–150.","chicago":"Günther, David, Jan Reininghaus, Hans-Peter Seidel, and Tino Weinkauf. “Notes on the Simplification of the Morse-Smale Complex.” In <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 135–50. Mathematics and Visualization. Cham: Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>.","ista":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. 2014.Notes on the simplification of the Morse-Smale complex. In: Topological Methods in Data Analysis and Visualization III. , 135–150.","mla":"Günther, David, et al. “Notes on the Simplification of the Morse-Smale Complex.” <i>Topological Methods in Data Analysis and Visualization III.</i>, edited by Peer-Timo Bremer et al., Springer Nature, 2014, pp. 135–50, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>.","short":"D. Günther, J. Reininghaus, H.-P. Seidel, T. Weinkauf, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III., Springer Nature, Cham, 2014, pp. 135–150.","ama":"Günther D, Reininghaus J, Seidel H-P, Weinkauf T. Notes on the simplification of the Morse-Smale complex. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III.</i> Mathematics and Visualization. Cham: Springer Nature; 2014:135-150. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">10.1007/978-3-319-04099-8_9</a>","apa":"Günther, D., Reininghaus, J., Seidel, H.-P., &#38; Weinkauf, T. (2014). Notes on the simplification of the Morse-Smale complex. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III.</i> (pp. 135–150). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_9\">https://doi.org/10.1007/978-3-319-04099-8_9</a>"},"page":"135-150","month":"03","type":"book_chapter","quality_controlled":"1","publication_identifier":{"eissn":["2197-666X"],"isbn":["9783319040981"],"eisbn":["9783319040998"],"issn":["1612-3786"]},"publisher":"Springer Nature","place":"Cham","date_published":"2014-03-19T00:00:00Z","article_processing_charge":"No","oa_version":"None","date_updated":"2025-04-15T08:37:54Z","day":"19","publication":"Topological Methods in Data Analysis and Visualization III.","publication_status":"published","status":"public","abstract":[{"lang":"eng","text":"The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption."}],"ec_funded":1,"title":"Notes on the simplification of the Morse-Smale complex"},{"status":"public","publication_status":"published","publication":"Topological Methods in Data Analysis and Visualization III ","year":"2014","article_processing_charge":"No","date_published":"2014-03-19T00:00:00Z","oa_version":"None","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-05T14:13:16Z","alternative_title":["Mathematics and Visualization"],"day":"19","title":"Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature","abstract":[{"lang":"eng","text":"We propose a method for visualizing two-dimensional symmetric positive definite tensor fields using the Heat Kernel Signature (HKS). The HKS is derived from the heat kernel and was originally introduced as an isometry invariant shape signature. Each positive definite tensor field defines a Riemannian manifold by considering the tensor field as a Riemannian metric. On this Riemmanian manifold we can apply the definition of the HKS. The resulting scalar quantity is used for the visualization of tensor fields. The HKS is closely related to the Gaussian curvature of the Riemannian manifold and the time parameter of the heat kernel allows a multiscale analysis in a natural way. In this way, the HKS represents field related scale space properties, enabling a level of detail analysis of tensor fields. This makes the HKS an interesting new scalar quantity for tensor fields, which differs significantly from usual tensor invariants like the trace or the determinant. A method for visualization and a numerical realization of the HKS for tensor fields is proposed in this chapter. To validate the approach we apply it to some illustrating simple examples as isolated critical points and to a medical diffusion tensor data set."}],"language":[{"iso":"eng"}],"scopus_import":"1","citation":{"ama":"Zobel V, Reininghaus J, Hotz I. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In: <i>Topological Methods in Data Analysis and Visualization III </i>. Springer; 2014:249-262. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>","apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2014). Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. In <i>Topological Methods in Data Analysis and Visualization III </i> (pp. 249–262). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” In <i>Topological Methods in Data Analysis and Visualization III </i>, 249–62. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">https://doi.org/10.1007/978-3-319-04099-8_16</a>.","ista":"Zobel V, Reininghaus J, Hotz I. 2014. Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature. Topological Methods in Data Analysis and Visualization III . , Mathematics and Visualization, , 249–262.","ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualization of two-dimensional symmetric positive definite tensor fields using the heat kernel signature,” in <i>Topological Methods in Data Analysis and Visualization III </i>, 2014, pp. 249–262.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, Topological Methods in Data Analysis and Visualization III , Springer, 2014, pp. 249–262.","mla":"Zobel, Valentin, et al. “Visualization of Two-Dimensional Symmetric Positive Definite Tensor Fields Using the Heat Kernel Signature.” <i>Topological Methods in Data Analysis and Visualization III </i>, Springer, 2014, pp. 249–62, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_16\">10.1007/978-3-319-04099-8_16</a>."},"acknowledgement":"This research is partially supported by the TOPOSYS project FP7-ICT-318493-STREP.","doi":"10.1007/978-3-319-04099-8_16","_id":"10886","publication_identifier":{"isbn":["9783319040981"],"eissn":["2197-666X"],"issn":["1612-3786"],"eisbn":["9783319040998"]},"publisher":"Springer","page":"249-262","month":"03","type":"conference","department":[{"_id":"HeEd"}],"date_created":"2022-03-18T13:05:39Z","quality_controlled":"1","author":[{"full_name":"Zobel, Valentin","last_name":"Zobel","first_name":"Valentin"},{"first_name":"Jan","last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan"},{"first_name":"Ingrid","full_name":"Hotz, Ingrid","last_name":"Hotz"}]},{"doi":"10.1007/978-3-319-13075-0_10","_id":"10892","scopus_import":"1","acknowledgement":"T. Biedl was supported by NSERC and the Ross and Muriel Cheriton Fellowship. P. Palfrader was supported by Austrian Science Fund (FWF): P25816-N15.","date_created":"2022-03-21T07:09:03Z","department":[{"_id":"HeEd"}],"author":[{"full_name":"Biedl, Therese","last_name":"Biedl","first_name":"Therese"},{"full_name":"Huber, Stefan","last_name":"Huber","id":"4700A070-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8871-5814","first_name":"Stefan"},{"last_name":"Palfrader","full_name":"Palfrader, Peter","first_name":"Peter"}],"related_material":{"record":[{"id":"481","relation":"later_version","status":"public"}]},"year":"2014","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"language":[{"iso":"eng"}],"corr_author":"1","citation":{"ama":"Biedl T, Huber S, Palfrader P. Planar matchings for weighted straight skeletons. In: <i>25th International Symposium, ISAAC 2014</i>. Vol 8889. Springer Nature; 2014:117-127. doi:<a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">10.1007/978-3-319-13075-0_10</a>","apa":"Biedl, T., Huber, S., &#38; Palfrader, P. (2014). Planar matchings for weighted straight skeletons. In <i>25th International Symposium, ISAAC 2014</i> (Vol. 8889, pp. 117–127). Jeonju, Korea: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">https://doi.org/10.1007/978-3-319-13075-0_10</a>","ieee":"T. Biedl, S. Huber, and P. Palfrader, “Planar matchings for weighted straight skeletons,” in <i>25th International Symposium, ISAAC 2014</i>, Jeonju, Korea, 2014, vol. 8889, pp. 117–127.","chicago":"Biedl, Therese, Stefan Huber, and Peter Palfrader. “Planar Matchings for Weighted Straight Skeletons.” In <i>25th International Symposium, ISAAC 2014</i>, 8889:117–27. Springer Nature, 2014. <a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">https://doi.org/10.1007/978-3-319-13075-0_10</a>.","ista":"Biedl T, Huber S, Palfrader P. 2014. Planar matchings for weighted straight skeletons. 25th International Symposium, ISAAC 2014. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 8889, 117–127.","mla":"Biedl, Therese, et al. “Planar Matchings for Weighted Straight Skeletons.” <i>25th International Symposium, ISAAC 2014</i>, vol. 8889, Springer Nature, 2014, pp. 117–27, doi:<a href=\"https://doi.org/10.1007/978-3-319-13075-0_10\">10.1007/978-3-319-13075-0_10</a>.","short":"T. Biedl, S. Huber, P. Palfrader, in:, 25th International Symposium, ISAAC 2014, Springer Nature, 2014, pp. 117–127."},"page":"117-127","external_id":{"isi":["000354865900010"]},"month":"11","type":"conference","quality_controlled":"1","publication_identifier":{"isbn":["9783319130743"],"eissn":["1611-3349"],"issn":["0302-9743"],"eisbn":["9783319130750"]},"intvolume":"      8889","conference":{"location":"Jeonju, Korea","end_date":"2014-12-17","name":"ISAAC: International Symposium on Algorithms and Computation","start_date":"2014-12-15"},"publisher":"Springer Nature","volume":8889,"article_processing_charge":"No","date_published":"2014-11-08T00:00:00Z","oa_version":"None","day":"08","alternative_title":["LNCS"],"date_updated":"2025-09-29T13:22:55Z","status":"public","publication_status":"published","publication":"25th International Symposium, ISAAC 2014","abstract":[{"lang":"eng","text":"In this paper, 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.\r\nUsing 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."}],"title":"Planar matchings for weighted straight skeletons"},{"publisher":"Springer","place":"Cham","volume":1,"intvolume":"         1","publication_identifier":{"issn":["1612-3786"],"eisbn":["9783319040998"],"isbn":["9783319040981"],"eissn":["2197-666X"]},"quality_controlled":"1","type":"book_chapter","month":"03","page":"55-69","citation":{"ieee":"J. Kasten, J. Reininghaus, W. Reich, and G. Scheuermann, “Toward the extraction of saddle periodic orbits,” in <i>Topological Methods in Data Analysis and Visualization III </i>, vol. 1, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Cham: Springer, 2014, pp. 55–69.","chicago":"Kasten, Jens, Jan Reininghaus, Wieland Reich, and Gerik Scheuermann. “Toward the Extraction of Saddle Periodic Orbits.” In <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 1:55–69. Mathematics and Visualization. Cham: Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>.","ista":"Kasten J, Reininghaus J, Reich W, Scheuermann G. 2014.Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III . vol. 1, 55–69.","mla":"Kasten, Jens, et al. “Toward the Extraction of Saddle Periodic Orbits.” <i>Topological Methods in Data Analysis and Visualization III </i>, edited by Peer-Timo Bremer et al., vol. 1, Springer, 2014, pp. 55–69, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>.","short":"J. Kasten, J. Reininghaus, W. Reich, G. Scheuermann, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III , Springer, Cham, 2014, pp. 55–69.","ama":"Kasten J, Reininghaus J, Reich W, Scheuermann G. Toward the extraction of saddle periodic orbits. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III </i>. Vol 1. Mathematics and Visualization. Cham: Springer; 2014:55-69. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">10.1007/978-3-319-04099-8_4</a>","apa":"Kasten, J., Reininghaus, J., Reich, W., &#38; Scheuermann, G. (2014). Toward the extraction of saddle periodic orbits. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III </i> (Vol. 1, pp. 55–69). Cham: Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_4\">https://doi.org/10.1007/978-3-319-04099-8_4</a>"},"project":[{"call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems"}],"title":"Toward the extraction of saddle periodic orbits","ec_funded":1,"abstract":[{"lang":"eng","text":"Saddle periodic orbits are an essential and stable part of the topological skeleton of a 3D vector field. Nevertheless, there is currently no efficient algorithm to robustly extract these features. In this chapter, we present a novel technique to extract saddle periodic orbits. Exploiting the analytic properties of such an orbit, we propose a scalar measure based on the finite-time Lyapunov exponent (FTLE) that indicates its presence. Using persistent homology, we can then extract the robust cycles of this field. These cycles thereby represent the saddle periodic orbits of the given vector field. We discuss the different existing FTLE approximation schemes regarding their applicability to this specific problem and propose an adapted version of FTLE called Normalized Velocity Separation. Finally, we evaluate our method using simple analytic vector field data."}],"publication":"Topological Methods in Data Analysis and Visualization III ","publication_status":"published","status":"public","date_updated":"2025-04-15T08:37:54Z","day":"19","oa_version":"None","date_published":"2014-03-19T00:00:00Z","article_processing_charge":"No","author":[{"first_name":"Jens","last_name":"Kasten","full_name":"Kasten, Jens"},{"last_name":"Reininghaus","id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","first_name":"Jan"},{"first_name":"Wieland","last_name":"Reich","full_name":"Reich, Wieland"},{"full_name":"Scheuermann, Gerik","last_name":"Scheuermann","first_name":"Gerik"}],"date_created":"2022-03-21T07:11:23Z","department":[{"_id":"HeEd"}],"acknowledgement":"First, we thank the reviewers of this paper for their ideas and critical comments. In addition, we thank Ronny Peikert and Filip Sadlo for a fruitful discussions. This research is supported by the European Commission under the TOPOSYS project FP7-ICT-318493-STREP, the European Social Fund (ESF App. No. 100098251), and the European Science Foundation under the ACAT Research Network Program.","scopus_import":"1","_id":"10893","doi":"10.1007/978-3-319-04099-8_4","series_title":"Mathematics and Visualization","editor":[{"first_name":"Peer-Timo","last_name":"Bremer","full_name":"Bremer, Peer-Timo"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"first_name":"Valerio","full_name":"Pascucci, Valerio","last_name":"Pascucci"},{"first_name":"Ronald","full_name":"Peikert, Ronald","last_name":"Peikert"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2014"},{"series_title":"LNCS","language":[{"iso":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","year":"2014","related_material":{"record":[{"id":"1433","relation":"later_version","status":"public"}]},"author":[{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","orcid":"0000-0002-9683-0724","first_name":"Ulrich"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"first_name":"Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","full_name":"Reininghaus, Jan"},{"first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner"}],"department":[{"_id":"HeEd"}],"date_created":"2022-03-21T07:12:16Z","scopus_import":"1","_id":"10894","doi":"10.1007/978-3-662-44199-2_24","title":"PHAT – Persistent Homology Algorithms Toolbox","abstract":[{"text":"PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations.","lang":"eng"}],"publication_status":"published","status":"public","publication":"ICMS 2014: International Congress on Mathematical Software","day":"01","date_updated":"2026-06-18T17:35:15Z","oa_version":"None","date_published":"2014-09-01T00:00:00Z","article_processing_charge":"No","place":"Berlin, Heidelberg","volume":8592,"publisher":"Springer Berlin Heidelberg","intvolume":"      8592","conference":{"location":"Seoul, South Korea","start_date":"2014-08-05","name":"ICMS: International Congress on Mathematical Software","end_date":"2014-08-09"},"publication_identifier":{"issn":["0302-9743"],"eisbn":["9783662441992"],"eissn":["1611-3349"],"isbn":["9783662441985"]},"quality_controlled":"1","type":"conference","month":"09","page":"137-143","citation":{"ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “PHAT – Persistent Homology Algorithms Toolbox,” in <i>ICMS 2014: International Congress on Mathematical Software</i>, Seoul, South Korea, 2014, vol. 8592, pp. 137–143.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2014. PHAT – Persistent Homology Algorithms Toolbox. ICMS 2014: International Congress on Mathematical Software. ICMS: International Congress on Mathematical SoftwareLNCS vol. 8592, 137–143.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “PHAT – Persistent Homology Algorithms Toolbox.” In <i>ICMS 2014: International Congress on Mathematical Software</i>, 8592:137–43. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. <a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">https://doi.org/10.1007/978-3-662-44199-2_24</a>.","mla":"Bauer, Ulrich, et al. “PHAT – Persistent Homology Algorithms Toolbox.” <i>ICMS 2014: International Congress on Mathematical Software</i>, vol. 8592, Springer Berlin Heidelberg, 2014, pp. 137–43, doi:<a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">10.1007/978-3-662-44199-2_24</a>.","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, in:, ICMS 2014: International Congress on Mathematical Software, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 137–143.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. PHAT – Persistent Homology Algorithms Toolbox. In: <i>ICMS 2014: International Congress on Mathematical Software</i>. Vol 8592. LNCS. Berlin, Heidelberg: Springer Berlin Heidelberg; 2014:137-143. doi:<a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">10.1007/978-3-662-44199-2_24</a>","apa":"Bauer, U., Kerber, M., Reininghaus, J., &#38; Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In <i>ICMS 2014: International Congress on Mathematical Software</i> (Vol. 8592, pp. 137–143). Berlin, Heidelberg: Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-44199-2_24\">https://doi.org/10.1007/978-3-662-44199-2_24</a>"}},{"project":[{"call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","name":"Topological Complex Systems"}],"citation":{"mla":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 355–64, doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>.","short":"U. Bauer, M. Lesnick, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 355–364.","ieee":"U. Bauer and M. Lesnick, “Induced matchings of barcodes and the algebraic stability of persistence,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 355–364.","chicago":"Bauer, Ulrich, and Michael Lesnick. “Induced Matchings of Barcodes and the Algebraic Stability of Persistence.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 355–64. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>.","ista":"Bauer U, Lesnick M. 2014. Induced matchings of barcodes and the algebraic stability of persistence. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 355–364.","apa":"Bauer, U., &#38; Lesnick, M. (2014). Induced matchings of barcodes and the algebraic stability of persistence. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 355–364). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582168\">https://doi.org/10.1145/2582112.2582168</a>","ama":"Bauer U, Lesnick M. Induced matchings of barcodes and the algebraic stability of persistence. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:355-364. doi:<a href=\"https://doi.org/10.1145/2582112.2582168\">10.1145/2582112.2582168</a>"},"type":"conference","month":"06","external_id":{"arxiv":["1311.3681"]},"page":"355 - 364","quality_controlled":"1","conference":{"location":"Kyoto, Japan","start_date":"2014-06-08","name":"SoCG: Symposium on Computational Geometry","end_date":"2014-06-11"},"publisher":"ACM","oa":1,"article_processing_charge":"No","date_published":"2014-06-01T00:00:00Z","date_updated":"2025-06-11T07:57:54Z","day":"01","oa_version":"Submitted Version","publication":"Proceedings of the Annual Symposium on Computational Geometry","publication_status":"published","status":"public","arxiv":1,"abstract":[{"text":"We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the algebraic stability theorem for persistence barcodes [5, 9], a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a δ-interleaving morphism between two persistence modules induces a δ-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules. Copyright is held by the owner/author(s).","lang":"eng"}],"ec_funded":1,"title":"Induced matchings of barcodes and the algebraic stability of persistence","doi":"10.1145/2582112.2582168","_id":"2153","scopus_import":"1","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:56:01Z","author":[{"first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"first_name":"Michael","last_name":"Lesnick","full_name":"Lesnick, Michael"}],"year":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"4853","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1311.3681"}]},{"status":"public","publication_status":"published","publication":"Proceedings of the Annual Symposium on Computational Geometry","oa_version":"Submitted Version","date_updated":"2025-06-11T07:58:27Z","day":"01","date_published":"2014-06-01T00:00:00Z","article_processing_charge":"No","title":"The morse theory of Čech and Delaunay filtrations","ec_funded":1,"abstract":[{"lang":"eng","text":"Given a finite set of points in Rn and a positive radius, we study the Čech, Delaunay-Čech, alpha, and wrap complexes as instances of a generalized discrete Morse theory. We prove that the latter three complexes are simple-homotopy equivalent. Our results have applications in topological data analysis and in the reconstruction of shapes from sampled data. Copyright is held by the owner/author(s)."}],"arxiv":1,"citation":{"short":"U. Bauer, H. Edelsbrunner, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 484–490.","mla":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 484–90, doi:<a href=\"https://doi.org/10.1145/2582112.2582167\">10.1145/2582112.2582167</a>.","chicago":"Bauer, Ulrich, and Herbert Edelsbrunner. “The Morse Theory of Čech and Delaunay Filtrations.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 484–90. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>.","ista":"Bauer U, Edelsbrunner H. 2014. The morse theory of Čech and Delaunay filtrations. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 484–490.","ieee":"U. Bauer and H. Edelsbrunner, “The morse theory of Čech and Delaunay filtrations,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 484–490.","apa":"Bauer, U., &#38; Edelsbrunner, H. (2014). The morse theory of Čech and Delaunay filtrations. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 484–490). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582167\">https://doi.org/10.1145/2582112.2582167</a>","ama":"Bauer U, Edelsbrunner H. The morse theory of Čech and Delaunay filtrations. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:484-490. doi:<a href=\"https://doi.org/10.1145/2582112.2582167\">10.1145/2582112.2582167</a>"},"project":[{"name":"Topological Complex Systems","grant_number":"318493","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"publisher":"ACM","oa":1,"conference":{"location":"Kyoto, Japan","name":"SoCG: Symposium on Computational Geometry","end_date":"2014-06-11","start_date":"2014-06-08"},"quality_controlled":"1","page":"484 - 490","external_id":{"arxiv":["1312.1231"]},"month":"06","type":"conference","publist_id":"4851","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2014","corr_author":"1","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1312.1231"}],"acknowledgement":"This research is partially supported by ESF under the ACAT Research Network Programme, and by the Russian Government under mega project 11.G34.31.0053","scopus_import":"1","_id":"2155","doi":"10.1145/2582112.2582167","author":[{"first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","full_name":"Bauer, Ulrich"},{"first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"}],"department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:56:01Z"},{"publist_id":"4850","year":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1307.2839"}],"scopus_import":"1","acknowledgement":"National Science Foundation under grants CCF-1319406, CCF-1116258.","doi":"10.1145/2582112.2582169","_id":"2156","date_created":"2018-12-11T11:56:02Z","department":[{"_id":"HeEd"}],"author":[{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","full_name":"Bauer, Ulrich","first_name":"Ulrich","orcid":"0000-0002-9683-0724"},{"first_name":"Xiaoyin","last_name":"Ge","full_name":"Ge, Xiaoyin"},{"full_name":"Wang, Yusu","last_name":"Wang","first_name":"Yusu"}],"status":"public","publication_status":"published","publication":"Proceedings of the Annual Symposium on Computational Geometry","date_published":"2014-06-01T00:00:00Z","article_processing_charge":"No","day":"01","date_updated":"2025-06-11T07:58:42Z","oa_version":"Submitted Version","title":"Measuring distance between Reeb graphs","arxiv":1,"abstract":[{"lang":"eng","text":"We propose a metric for Reeb graphs, called the functional distortion distance. Under this distance, the Reeb graph is stable against small changes of input functions. At the same time, it remains discriminative at differentiating input functions. In particular, the main result is that the functional distortion distance between two Reeb graphs is bounded from below by the bottleneck distance between both the ordinary and extended persistence diagrams for appropriate dimensions. As an application of our results, we analyze a natural simplification scheme for Reeb graphs, and show that persistent features in Reeb graph remains persistent under simplification. Understanding the stability of important features of the Reeb graph under simplification is an interesting problem on its own right, and critical to the practical usage of Reeb graphs. Copyright is held by the owner/author(s)."}],"ec_funded":1,"citation":{"short":"U. Bauer, X. Ge, Y. Wang, in:, Proceedings of the Annual Symposium on Computational Geometry, ACM, 2014, pp. 464–473.","mla":"Bauer, Ulrich, et al. “Measuring Distance between Reeb Graphs.” <i>Proceedings of the Annual Symposium on Computational Geometry</i>, ACM, 2014, pp. 464–73, doi:<a href=\"https://doi.org/10.1145/2582112.2582169\">10.1145/2582112.2582169</a>.","chicago":"Bauer, Ulrich, Xiaoyin Ge, and Yusu Wang. “Measuring Distance between Reeb Graphs.” In <i>Proceedings of the Annual Symposium on Computational Geometry</i>, 464–73. ACM, 2014. <a href=\"https://doi.org/10.1145/2582112.2582169\">https://doi.org/10.1145/2582112.2582169</a>.","ista":"Bauer U, Ge X, Wang Y. 2014. Measuring distance between Reeb graphs. Proceedings of the Annual Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 464–473.","ieee":"U. Bauer, X. Ge, and Y. Wang, “Measuring distance between Reeb graphs,” in <i>Proceedings of the Annual Symposium on Computational Geometry</i>, Kyoto, Japan, 2014, pp. 464–473.","apa":"Bauer, U., Ge, X., &#38; Wang, Y. (2014). Measuring distance between Reeb graphs. In <i>Proceedings of the Annual Symposium on Computational Geometry</i> (pp. 464–473). Kyoto, Japan: ACM. <a href=\"https://doi.org/10.1145/2582112.2582169\">https://doi.org/10.1145/2582112.2582169</a>","ama":"Bauer U, Ge X, Wang Y. Measuring distance between Reeb graphs. In: <i>Proceedings of the Annual Symposium on Computational Geometry</i>. ACM; 2014:464-473. doi:<a href=\"https://doi.org/10.1145/2582112.2582169\">10.1145/2582112.2582169</a>"},"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"conference":{"name":"SoCG: Symposium on Computational Geometry","end_date":"2014-06-11","start_date":"2014-06-08","location":"Kyoto, Japan"},"publisher":"ACM","oa":1,"external_id":{"arxiv":["1307.2839"]},"month":"06","type":"conference","page":"464 - 473","quality_controlled":"1"},{"doi":"10.1137/1.9781611973402.11","_id":"2177","scopus_import":1,"citation":{"mla":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, SIAM, 2014, pp. 152–60, doi:<a href=\"https://doi.org/10.1137/1.9781611973402.11\">10.1137/1.9781611973402.11</a>.","short":"H. Edelsbrunner, S. Parsa, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2014, pp. 152–160.","ieee":"H. Edelsbrunner and S. Parsa, “On the computational complexity of betti numbers reductions from matrix rank,” in <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Portland, USA, 2014, pp. 152–160.","chicago":"Edelsbrunner, Herbert, and Salman Parsa. “On the Computational Complexity of Betti Numbers Reductions from Matrix Rank.” In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 152–60. SIAM, 2014. <a href=\"https://doi.org/10.1137/1.9781611973402.11\">https://doi.org/10.1137/1.9781611973402.11</a>.","ista":"Edelsbrunner H, Parsa S. 2014. On the computational complexity of betti numbers reductions from matrix rank. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 152–160.","apa":"Edelsbrunner, H., &#38; Parsa, S. (2014). On the computational complexity of betti numbers reductions from matrix rank. In <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 152–160). Portland, USA: SIAM. <a href=\"https://doi.org/10.1137/1.9781611973402.11\">https://doi.org/10.1137/1.9781611973402.11</a>","ama":"Edelsbrunner H, Parsa S. On the computational complexity of betti numbers reductions from matrix rank. In: <i>Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms</i>. SIAM; 2014:152-160. doi:<a href=\"https://doi.org/10.1137/1.9781611973402.11\">10.1137/1.9781611973402.11</a>"},"date_created":"2018-12-11T11:56:09Z","type":"conference","month":"01","department":[{"_id":"HeEd"}],"page":"152 - 160","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Salman","full_name":"Parsa, Salman","last_name":"Parsa","id":"4BDBD4F2-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","conference":{"name":"SODA: Symposium on Discrete Algorithms","start_date":"2014-01-05","end_date":"2014-01-07","location":"Portland, USA"},"publisher":"SIAM","date_published":"2014-01-01T00:00:00Z","year":"2014","day":"01","date_updated":"2024-10-09T20:55:33Z","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa_version":"None","publication":"Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms","status":"public","publication_status":"published","publist_id":"4805","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We give evidence for the difficulty of computing Betti numbers of simplicial complexes over a finite field. We do this by reducing the rank computation for sparse matrices with to non-zero entries to computing Betti numbers of simplicial complexes consisting of at most a constant times to simplices. Together with the known reduction in the other direction, this implies that the two problems have the same computational complexity."}],"corr_author":"1","title":"On the computational complexity of betti numbers reductions from matrix rank"},{"date_created":"2018-12-11T11:56:12Z","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"author":[{"first_name":"Martin","full_name":"Čadek, Martin","last_name":"Čadek"},{"last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","first_name":"Marek"},{"last_name":"Matoušek","full_name":"Matoušek, Jiří","first_name":"Jiří"},{"first_name":"Francis","full_name":"Sergeraert, Francis","last_name":"Sergeraert"},{"full_name":"Vokřínek, Lukáš","last_name":"Vokřínek","first_name":"Lukáš"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Wagner, Uli","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"doi":"10.1145/2597629","_id":"2184","scopus_import":"1","acknowledgement":"The research by M. K. was supported by project GAUK 49209. The research by M. K. was also supported by project 1M0545 by the Ministry of Education of the Czech Republic and by Center of Excellence { Inst. for Theor. Comput. Sci., Prague (project P202/12/G061 of GACR). The research by U. W. was supported by the Swiss National Science Foundation (SNF Projects 200021-125309, 200020-138230, and PP00P2-138948).","issue":"3","main_file_link":[{"url":"http://arxiv.org/abs/1105.6257","open_access":"1"}],"language":[{"iso":"eng"}],"year":"2014","article_number":"17 ","isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publist_id":"4797","type":"journal_article","month":"05","external_id":{"arxiv":["1105.6257"],"isi":["000337201400003"]},"quality_controlled":"1","intvolume":"        61","oa":1,"volume":61,"publisher":"ACM","citation":{"apa":"Čadek, M., Krcál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., &#38; Wagner, U. (2014). Computing all maps into a sphere. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2597629\">https://doi.org/10.1145/2597629</a>","ama":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. Computing all maps into a sphere. <i>Journal of the ACM</i>. 2014;61(3). doi:<a href=\"https://doi.org/10.1145/2597629\">10.1145/2597629</a>","short":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, U. Wagner, Journal of the ACM 61 (2014).","mla":"Čadek, Martin, et al. “Computing All Maps into a Sphere.” <i>Journal of the ACM</i>, vol. 61, no. 3, 17, ACM, 2014, doi:<a href=\"https://doi.org/10.1145/2597629\">10.1145/2597629</a>.","chicago":"Čadek, Martin, Marek Krcál, Jiří Matoušek, Francis Sergeraert, Lukáš Vokřínek, and Uli Wagner. “Computing All Maps into a Sphere.” <i>Journal of the ACM</i>. ACM, 2014. <a href=\"https://doi.org/10.1145/2597629\">https://doi.org/10.1145/2597629</a>.","ista":"Čadek M, Krcál M, Matoušek J, Sergeraert F, Vokřínek L, Wagner U. 2014. Computing all maps into a sphere. Journal of the ACM. 61(3), 17.","ieee":"M. Čadek, M. Krcál, J. Matoušek, F. Sergeraert, L. Vokřínek, and U. Wagner, “Computing all maps into a sphere,” <i>Journal of the ACM</i>, vol. 61, no. 3. ACM, 2014."},"arxiv":1,"abstract":[{"lang":"eng","text":"Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable."}],"title":"Computing all maps into a sphere","date_published":"2014-05-01T00:00:00Z","article_processing_charge":"No","date_updated":"2025-09-29T11:34:15Z","day":"01","oa_version":"Preprint","publication":"Journal of the ACM","publication_status":"published","status":"public"},{"abstract":[{"lang":"eng","text":"We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets."}],"arxiv":1,"title":"Functionals on triangulations of delaunay sets","date_published":"2014-07-01T00:00:00Z","article_processing_charge":"No","oa_version":"Submitted Version","day":"01","date_updated":"2025-07-10T11:51:26Z","publication_status":"published","status":"public","publication":"Moscow Mathematical Journal","page":"491 - 504","type":"journal_article","external_id":{"arxiv":["1211.7053"]},"month":"07","quality_controlled":"1","publication_identifier":{"issn":["1609-3321"]},"intvolume":"        14","oa":1,"volume":14,"publisher":"Independent University of Moscow","article_type":"original","citation":{"mla":"Dolbilin, Nikolai, et al. “Functionals on Triangulations of Delaunay Sets.” <i>Moscow Mathematical Journal</i>, vol. 14, no. 3, Independent University of Moscow, 2014, pp. 491–504, doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">10.17323/1609-4514-2014-14-3-491-504</a>.","short":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, O. Musin, Moscow Mathematical Journal 14 (2014) 491–504.","ieee":"N. Dolbilin, H. Edelsbrunner, A. Glazyrin, and O. Musin, “Functionals on triangulations of delaunay sets,” <i>Moscow Mathematical Journal</i>, vol. 14, no. 3. Independent University of Moscow, pp. 491–504, 2014.","ista":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. 2014. Functionals on triangulations of delaunay sets. Moscow Mathematical Journal. 14(3), 491–504.","chicago":"Dolbilin, Nikolai, Herbert Edelsbrunner, Alexey Glazyrin, and Oleg Musin. “Functionals on Triangulations of Delaunay Sets.” <i>Moscow Mathematical Journal</i>. Independent University of Moscow, 2014. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">https://doi.org/10.17323/1609-4514-2014-14-3-491-504</a>.","apa":"Dolbilin, N., Edelsbrunner, H., Glazyrin, A., &#38; Musin, O. (2014). Functionals on triangulations of delaunay sets. <i>Moscow Mathematical Journal</i>. Independent University of Moscow. <a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">https://doi.org/10.17323/1609-4514-2014-14-3-491-504</a>","ama":"Dolbilin N, Edelsbrunner H, Glazyrin A, Musin O. Functionals on triangulations of delaunay sets. <i>Moscow Mathematical Journal</i>. 2014;14(3):491-504. doi:<a href=\"https://doi.org/10.17323/1609-4514-2014-14-3-491-504\">10.17323/1609-4514-2014-14-3-491-504</a>"},"main_file_link":[{"url":"http://arxiv.org/abs/1211.7053","open_access":"1"}],"language":[{"iso":"eng"}],"year":"2014","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"5220","department":[{"_id":"HeEd"}],"date_created":"2018-12-11T11:54:29Z","author":[{"first_name":"Nikolai","last_name":"Dolbilin","full_name":"Dolbilin, Nikolai"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Alexey","last_name":"Glazyrin","full_name":"Glazyrin, Alexey"},{"last_name":"Musin","full_name":"Musin, Oleg","first_name":"Oleg"}],"doi":"10.17323/1609-4514-2014-14-3-491-504","_id":"1876","scopus_import":"1","issue":"3"}]