[{"intvolume":"        10","volume":10,"_id":"1793","scopus_import":"1","doi":"10.1371/journal.pone.0127657","date_created":"2018-12-11T11:54:02Z","author":[{"full_name":"Symonova, Olga","id":"3C0C7BC6-F248-11E8-B48F-1D18A9856A87","first_name":"Olga","last_name":"Symonova","orcid":"0000-0003-2012-9947"},{"full_name":"Topp, Christopher","first_name":"Christopher","last_name":"Topp"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2015-06-01T00:00:00Z","oa":1,"citation":{"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.","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.","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>","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>.","short":"O. Symonova, C. Topp, H. Edelsbrunner, PLoS One 10 (2015).","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>.","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>"},"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."}],"title":"DynamicRoots: A software platform for the reconstruction and analysis of growing plant roots","oa_version":"Published Version","publication_status":"published","quality_controlled":"1","file_date_updated":"2020-07-14T12:45:16Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"year":"2015","type":"journal_article","pubrep_id":"454","corr_author":"1","month":"06","publisher":"Public Library of Science","issue":"6","publist_id":"5318","day":"01","related_material":{"record":[{"status":"public","id":"9737","relation":"research_data"}]},"language":[{"iso":"eng"}],"ddc":["000"],"date_updated":"2025-09-23T08:30:43Z","file":[{"relation":"main_file","access_level":"open_access","creator":"system","file_name":"IST-2016-454-v1+1_journal.pone.0127657.pdf","file_id":"5150","date_created":"2018-12-12T10:15:30Z","checksum":"d20f26461ca575276ad3ed9ce4bfc787","content_type":"application/pdf","file_size":1850825,"date_updated":"2020-07-14T12:45:16Z"}],"status":"public","external_id":{"isi":["000356630900069"]},"article_number":"e0127657","publication":"PLoS One","isi":1,"department":[{"_id":"MaJö"},{"_id":"HeEd"}],"has_accepted_license":"1","article_processing_charge":"No"},{"intvolume":"        48","article_type":"original","volume":48,"scopus_import":"1","OA_place":"publisher","_id":"1805","author":[{"full_name":"Attali, Dominique","last_name":"Attali","first_name":"Dominique"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer","first_name":"Ulrich"},{"last_name":"Devillers","first_name":"Olivier","full_name":"Devillers, Olivier"},{"full_name":"Glisse, Marc","last_name":"Glisse","first_name":"Marc"},{"last_name":"Lieutier","first_name":"André","full_name":"Lieutier, André"}],"date_created":"2018-12-11T11:54:06Z","doi":"10.1016/j.comgeo.2014.08.010","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"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.","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.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 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>.","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>.","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>","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>"},"date_published":"2015-06-03T00:00:00Z","oa":1,"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."}],"oa_version":"Published Version","title":"Homological reconstruction and simplification in R3","publication_status":"published","main_file_link":[{"url":"https://doi.org/10.1016/j.comgeo.2014.08.010","open_access":"1"}],"page":"606 - 621","quality_controlled":"1","ec_funded":1,"year":"2015","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493"}],"type":"journal_article","month":"06","corr_author":"1","publisher":"Elsevier","OA_type":"free access","day":"03","issue":"8","publist_id":"5305","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"2812","status":"public","relation":"earlier_version"}]},"date_updated":"2025-09-23T09:18:30Z","status":"public","external_id":{"isi":["000357353200006"]},"department":[{"_id":"HeEd"}],"isi":1,"publication":"Computational Geometry: Theory and Applications","article_processing_charge":"No"},{"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","year":"2015","ec_funded":1,"day":"01","publist_id":"5276","issue":"1","publisher":"Springer","month":"07","corr_author":"1","date_updated":"2025-09-23T09:23:53Z","language":[{"iso":"eng"}],"article_processing_charge":"No","isi":1,"department":[{"_id":"HeEd"}],"publication":"Journal of Statistical Physics","external_id":{"arxiv":["1406.5313"],"isi":["000356579000009"]},"status":"public","volume":160,"intvolume":"       160","citation":{"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.","ista":"Akopyan A, Pirogov S, Rybko A. 2015. Invariant measures of genetic recombination process. Journal of Statistical Physics. 160(1), 163–167.","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>","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>.","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>.","short":"A. Akopyan, S. Pirogov, A. Rybko, Journal of Statistical Physics 160 (2015) 163–167.","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>"},"arxiv":1,"date_published":"2015-07-01T00:00:00Z","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1007/s10955-015-1238-5","date_created":"2018-12-11T11:54:14Z","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","first_name":"Arseniy","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"last_name":"Pirogov","first_name":"Sergey","full_name":"Pirogov, Sergey"},{"full_name":"Rybko, Aleksandr","last_name":"Rybko","first_name":"Aleksandr"}],"scopus_import":"1","_id":"1828","publication_status":"published","oa_version":"Preprint","title":"Invariant measures of genetic recombination process","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","page":"163 - 167","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1406.5313","open_access":"1"}]},{"ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493"}],"type":"journal_article","pubrep_id":"486","year":"2015","publisher":"Springer","month":"10","publist_id":"5022","day":"01","issue":"5","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:45:26Z","file_size":1317546,"access_level":"open_access","creator":"system","checksum":"3566f3a8b0c1bc550e62914a88c584ff","date_created":"2018-12-12T10:08:10Z","file_id":"4670","file_name":"IST-2016-486-v1+1_s10208-014-9223-y.pdf","relation":"main_file"}],"date_updated":"2025-09-23T14:08:54Z","ddc":["000"],"external_id":{"isi":["000360862900004"]},"status":"public","article_processing_charge":"No","publication":"Foundations of Computational Mathematics","has_accepted_license":"1","department":[{"_id":"HeEd"}],"isi":1,"intvolume":"        15","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.","volume":15,"doi":"10.1007/s10208-014-9223-y","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Jablonski, Grzegorz","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","first_name":"Grzegorz","last_name":"Jablonski","orcid":"0000-0002-3536-9866"},{"first_name":"Marian","last_name":"Mrozek","full_name":"Mrozek, Marian"}],"date_created":"2018-12-11T11:55:20Z","_id":"2035","scopus_import":"1","oa":1,"date_published":"2015-10-01T00:00:00Z","citation":{"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.","ista":"Edelsbrunner H, Jablonski G, Mrozek M. 2015. The persistent homology of a self-map. Foundations of Computational Mathematics. 15(5), 1213–1244.","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>","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>.","short":"H. Edelsbrunner, G. Jablonski, M. Mrozek, Foundations of Computational Mathematics 15 (2015) 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>.","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>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","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"}],"publication_status":"published","title":"The persistent homology of a self-map","oa_version":"Published Version","page":"1213 - 1244","file_date_updated":"2020-07-14T12:45:26Z","quality_controlled":"1"},{"abstract":[{"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.","lang":"eng"}],"oa_version":"None","title":"On the distribution of local extrema in quantum chaos","publication_status":"published","page":"535 - 541","quality_controlled":"1","intvolume":"       379","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. ","volume":379,"_id":"1938","scopus_import":"1","doi":"10.1016/j.physleta.2014.12.010","author":[{"id":"2A77D7A2-F248-11E8-B48F-1D18A9856A87","full_name":"Pausinger, Florian","last_name":"Pausinger","orcid":"0000-0002-8379-3768","first_name":"Florian"},{"first_name":"Stefan","last_name":"Steinerberger","full_name":"Steinerberger, Stefan"}],"date_created":"2018-12-11T11:54:49Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2015-03-06T00:00:00Z","citation":{"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>","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>.","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>.","short":"F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.","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>","ista":"Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.","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."},"language":[{"iso":"eng"}],"date_updated":"2025-09-23T09:44:12Z","status":"public","external_id":{"isi":["000349586000006"]},"publication":"Physics Letters, Section A","isi":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"No","year":"2015","type":"journal_article","corr_author":"1","month":"03","publisher":"Elsevier","publist_id":"5152","day":"06","issue":"6"},{"type":"conference","publication_identifier":{"eisbn":["978-1-4673-6964-0 "]},"year":"2015","date_created":"2018-12-11T11:52:17Z","doi":"10.1109/CVPR.2015.7299106","author":[{"first_name":"Jan","last_name":"Reininghaus","full_name":"Reininghaus, Jan","id":"4505473A-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-8871-5814","last_name":"Huber","first_name":"Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan"},{"full_name":"Bauer, Ulrich","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","first_name":"Ulrich","last_name":"Bauer","orcid":"0000-0002-9683-0724"},{"last_name":"Kwitt","first_name":"Roland","full_name":"Kwitt, Roland"}],"conference":{"location":"Boston, MA, USA","end_date":"2015-06-12","name":"CVPR: Computer Vision and Pattern Recognition","start_date":"2015-06-07"},"publisher":"IEEE","_id":"1483","month":"10","scopus_import":"1","oa":1,"date_published":"2015-10-14T00:00:00Z","citation":{"ieee":"J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, “A stable multi-scale kernel for topological machine learning,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 4741–4748.","ista":"Reininghaus J, Huber S, Bauer U, Kwitt R. 2015. A stable multi-scale kernel for topological machine learning. CVPR: Computer Vision and Pattern Recognition, 4741–4748.","apa":"Reininghaus, J., Huber, S., Bauer, U., &#38; Kwitt, R. (2015). A stable multi-scale kernel for topological machine learning (pp. 4741–4748). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>","chicago":"Reininghaus, Jan, Stefan Huber, Ulrich Bauer, and Roland Kwitt. “A Stable Multi-Scale Kernel for Topological Machine Learning,” 4741–48. IEEE, 2015. <a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">https://doi.org/10.1109/CVPR.2015.7299106</a>.","short":"J. Reininghaus, S. Huber, U. Bauer, R. Kwitt, in:, IEEE, 2015, pp. 4741–4748.","mla":"Reininghaus, Jan, et al. <i>A Stable Multi-Scale Kernel for Topological Machine Learning</i>. IEEE, 2015, pp. 4741–48, doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>.","ama":"Reininghaus J, Huber S, Bauer U, Kwitt R. A stable multi-scale kernel for topological machine learning. In: IEEE; 2015:4741-4748. doi:<a href=\"https://doi.org/10.1109/CVPR.2015.7299106\">10.1109/CVPR.2015.7299106</a>"},"arxiv":1,"day":"14","publist_id":"5709","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes."}],"publication_status":"published","date_updated":"2025-06-11T06:37:43Z","oa_version":"Preprint","title":"A stable multi-scale kernel for topological machine learning","page":"4741 - 4748","external_id":{"arxiv":["1412.6821"]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1412.6821"}],"status":"public","article_processing_charge":"No","department":[{"_id":"HeEd"}]},{"volume":"2015-August","_id":"1495","scopus_import":"1","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel"},{"full_name":"Kurlin, Vitaliy","last_name":"Kurlin","first_name":"Vitaliy"}],"date_created":"2018-12-11T11:52:21Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_published":"2015-08-01T00:00:00Z","arxiv":1,"citation":{"apa":"Edelsbrunner, H., Iglesias Ham, M., &#38; Kurlin, V. (2015). Relaxed disk packing. In <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i> (Vol. 2015–August, pp. 128–135). Ontario, Canada: Queen’s University.","ama":"Edelsbrunner H, Iglesias Ham M, Kurlin V. Relaxed disk packing. In: <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>. Vol 2015-August. Queen’s University; 2015:128-135.","short":"H. Edelsbrunner, M. Iglesias Ham, V. Kurlin, in:, Proceedings of the 27th Canadian Conference on Computational Geometry, Queen’s University, 2015, pp. 128–135.","mla":"Edelsbrunner, Herbert, et al. “Relaxed Disk Packing.” <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, vol. 2015–August, Queen’s University, 2015, pp. 128–35.","chicago":"Edelsbrunner, Herbert, Mabel Iglesias Ham, and Vitaliy Kurlin. “Relaxed Disk Packing.” In <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, 2015–August:128–35. Queen’s University, 2015.","ieee":"H. Edelsbrunner, M. Iglesias Ham, and V. Kurlin, “Relaxed disk packing,” in <i>Proceedings of the 27th Canadian Conference on Computational Geometry</i>, Ontario, Canada, 2015, vol. 2015–August, pp. 128–135.","ista":"Edelsbrunner H, Iglesias Ham M, Kurlin V. 2015. Relaxed disk packing. Proceedings of the 27th Canadian Conference on Computational Geometry. CCCG: Canadian Conference on Computational Geometry vol. 2015–August, 128–135."},"abstract":[{"lang":"eng","text":"Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. "}],"title":"Relaxed disk packing","oa_version":"Submitted Version","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1505.03402","open_access":"1"}],"page":"128-135","quality_controlled":"1","ec_funded":1,"year":"2015","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493","call_identifier":"FP7","name":"Topological Complex Systems"}],"type":"conference","month":"08","conference":{"start_date":"2015-08-10","name":"CCCG: Canadian Conference on Computational Geometry","end_date":"2015-08-12","location":"Ontario, Canada"},"publisher":"Queen's University","day":"01","publist_id":"5684","language":[{"iso":"eng"}],"date_updated":"2025-06-11T06:38:01Z","status":"public","external_id":{"arxiv":["1505.03402"]},"publication":"Proceedings of the 27th Canadian Conference on Computational Geometry","department":[{"_id":"HeEd"}],"article_processing_charge":"No"},{"intvolume":"        34","alternative_title":["LIPIcs"],"volume":34,"doi":"10.4230/LIPIcs.SOCG.2015.842","date_created":"2018-12-11T11:52:26Z","author":[{"last_name":"Franek","orcid":"0000-0001-8878-8397","first_name":"Peter","id":"473294AE-F248-11E8-B48F-1D18A9856A87","full_name":"Franek, Peter"},{"full_name":"Krcál, Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87","first_name":"Marek","last_name":"Krcál"}],"scopus_import":1,"_id":"1510","citation":{"ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>.","mla":"Franek, Peter, and Marek Krcál. <i>On Computability and Triviality of Well Groups</i>. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>.","short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856.","apa":"Franek, P., &#38; Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>","ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856."},"oa":1,"date_published":"2015-06-11T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r &gt; 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K &lt; 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. ","lang":"eng"}],"publication_status":"published","oa_version":"Published Version","title":"On computability and triviality of well groups","page":"842 - 856","file_date_updated":"2020-07-14T12:44:59Z","quality_controlled":"1","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"pubrep_id":"503","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"type":"conference","year":"2015","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","conference":{"end_date":"2015-06-25","name":"SoCG: Symposium on Computational Geometry","start_date":"2015-06-22","location":"Eindhoven, Netherlands"},"month":"06","publist_id":"5667","day":"11","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"later_version","id":"1408","status":"public"}]},"date_updated":"2025-09-18T14:30:52Z","file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:44:59Z","file_size":623563,"creator":"system","access_level":"open_access","checksum":"49eb5021caafaabe5356c65b9c5f8c9c","date_created":"2018-12-12T10:13:19Z","file_id":"5001","file_name":"IST-2016-503-v1+1_32.pdf","relation":"main_file"}],"ddc":["510"],"status":"public","has_accepted_license":"1","department":[{"_id":"UlWa"},{"_id":"HeEd"}]},{"abstract":[{"text":"The Heat Kernel Signature (HKS) is a scalar quantity which is derived from the heat kernel of a given shape. Due to its robustness, isometry invariance, and multiscale nature, it has been successfully applied in many geometric applications. From a more general point of view, the HKS can be considered as a descriptor of the metric of a Riemannian manifold. Given a symmetric positive definite tensor field we may interpret it as the metric of some Riemannian manifold and thereby apply the HKS to visualize and analyze the given tensor data. In this paper, we propose a generalization of this approach that enables the treatment of indefinite tensor fields, like the stress tensor, by interpreting them as a generator of a positive definite tensor field. To investigate the usefulness of this approach we consider the stress tensor from the two-point-load model example and from a mechanical work piece.","lang":"eng"}],"publication_status":"published","title":"Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature","oa_version":"None","page":"257 - 267","quality_controlled":"1","intvolume":"        40","volume":40,"publication_identifier":{"isbn":["978-3-319-15089-5"]},"alternative_title":["Mathematics and Visualization"],"date_created":"2018-12-11T11:52:33Z","doi":"10.1007/978-3-319-15090-1_13","author":[{"last_name":"Zobel","first_name":"Valentin","full_name":"Zobel, Valentin"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","full_name":"Reininghaus, Jan","last_name":"Reininghaus","first_name":"Jan"},{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"}],"_id":"1531","scopus_import":"1","date_published":"2015-01-01T00:00:00Z","citation":{"ieee":"V. Zobel, J. Reininghaus, and I. Hotz, “Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature,” in <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, 1st ed., vol. 40, I. Hotz and T. Schultz, Eds. Springer, 2015, pp. 257–267.","ista":"Zobel V, Reininghaus J, Hotz I. 2015.Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization, vol. 40, 257–267.","apa":"Zobel, V., Reininghaus, J., &#38; Hotz, I. (2015). Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In I. Hotz &#38; T. Schultz (Eds.), <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i> (1st ed., Vol. 40, pp. 257–267). Springer. <a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">https://doi.org/10.1007/978-3-319-15090-1_13</a>","mla":"Zobel, Valentin, et al. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz, 1st ed., vol. 40, Springer, 2015, pp. 257–67, doi:<a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">10.1007/978-3-319-15090-1_13</a>.","short":"V. Zobel, J. Reininghaus, I. Hotz, in:, I. Hotz, T. Schultz (Eds.), Visualization and Processing of Higher Order Descriptors for Multi-Valued Data, 1st ed., Springer, 2015, pp. 257–267.","chicago":"Zobel, Valentin, Jan Reininghaus, and Ingrid Hotz. “Visualizing Symmetric Indefinite 2D Tensor Fields Using The Heat Kernel Signature.” In <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>, edited by Ingrid Hotz and Thomas Schultz, 1st ed., 40:257–67. Springer, 2015. <a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">https://doi.org/10.1007/978-3-319-15090-1_13</a>.","ama":"Zobel V, Reininghaus J, Hotz I. Visualizing symmetric indefinite 2D tensor fields using The Heat Kernel Signature. In: Hotz I, Schultz T, eds. <i>Visualization and Processing of Higher Order Descriptors for Multi-Valued Data</i>. Vol 40. 1st ed. Springer; 2015:257-267. doi:<a href=\"https://doi.org/10.1007/978-3-319-15090-1_13\">10.1007/978-3-319-15090-1_13</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"date_updated":"2022-06-10T09:50:14Z","editor":[{"first_name":"Ingrid","last_name":"Hotz","full_name":"Hotz, Ingrid"},{"first_name":"Thomas","last_name":"Schultz","full_name":"Schultz, Thomas"}],"status":"public","article_processing_charge":"No","publication":"Visualization and Processing of Higher Order Descriptors for Multi-Valued Data","department":[{"_id":"HeEd"}],"edition":"1","type":"book_chapter","year":"2015","publisher":"Springer","month":"01","day":"01","publist_id":"5640"},{"month":"01","publisher":"Society for Industrial and Applied Mathematics ","day":"01","publist_id":"5616","issue":"2","ec_funded":1,"year":"2015","project":[{"grant_number":"622033","name":"Persistent Homology - Images, Data and Maps","call_identifier":"FP7","_id":"255F06BE-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","status":"public","external_id":{"isi":["000357310400015"]},"publication":"SIAM Journal on Applied Dynamical Systems","isi":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"No","language":[{"iso":"eng"}],"date_updated":"2025-09-23T10:37:17Z","ddc":["510"],"_id":"1555","scopus_import":"1","author":[{"full_name":"Knipl, Diána","first_name":"Diána","last_name":"Knipl"},{"first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Gergely","last_name":"Röst","full_name":"Röst, Gergely"}],"doi":"10.1137/140993934","date_created":"2018-12-11T11:52:42Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"date_published":"2015-01-01T00:00:00Z","citation":{"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.","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.","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>","short":"D. Knipl, P. Pilarczyk, G. Röst, SIAM Journal on Applied Dynamical Systems 14 (2015) 980–1017.","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>.","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>.","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>"},"intvolume":"        14","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.","volume":14,"publication_identifier":{"eissn":["1536-0040"]},"article_type":"original","main_file_link":[{"open_access":"1","url":"http://discovery.ucl.ac.uk/1473750/1/99393.pdf"}],"page":"980 - 1017","quality_controlled":"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."}],"oa_version":"Published Version","title":"Rich bifurcation structure in a two patch vaccination model","publication_status":"published"},{"issue":"1","day":"01","publist_id":"5608","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2015-03-01T00:00:00Z","citation":{"apa":"Graff, G., &#38; Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies. <a href=\"https://doi.org/10.12775/TMNA.2015.014\">https://doi.org/10.12775/TMNA.2015.014</a>","mla":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:<a href=\"https://doi.org/10.12775/TMNA.2015.014\">10.12775/TMNA.2015.014</a>.","chicago":"Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies, 2015. <a href=\"https://doi.org/10.12775/TMNA.2015.014\">https://doi.org/10.12775/TMNA.2015.014</a>.","short":"G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286.","ama":"Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. 2015;45(1):273-286. doi:<a href=\"https://doi.org/10.12775/TMNA.2015.014\">10.12775/TMNA.2015.014</a>","ieee":"G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015.","ista":"Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286."},"_id":"1563","month":"03","scopus_import":1,"date_created":"2018-12-11T11:52:44Z","author":[{"first_name":"Grzegorz","last_name":"Graff","full_name":"Graff, Grzegorz"},{"first_name":"Pawel","last_name":"Pilarczyk","full_name":"Pilarczyk, Pawel","id":"3768D56A-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.12775/TMNA.2015.014","publisher":"Juliusz Schauder Center for Nonlinear Studies","volume":45,"year":"2015","type":"journal_article","intvolume":"        45","publication":"Topological Methods in Nonlinear Analysis","quality_controlled":"1","department":[{"_id":"HeEd"}],"status":"public","page":"273 - 286","title":"An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds","oa_version":"None","publication_status":"published","date_updated":"2021-01-12T06:51:37Z","abstract":[{"lang":"eng","text":"For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\\tt http://www.pawelpilarczyk.com/combtop/}."}],"language":[{"iso":"eng"}]},{"publication_status":"published","date_updated":"2022-01-28T08:25:00Z","title":"Shape, homology, persistence, and stability","oa_version":"None","language":[{"iso":"eng"}],"abstract":[{"text":"My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the three-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations.","lang":"eng"}],"article_processing_charge":"No","publication":"23rd International Symposium","department":[{"_id":"HeEd"}],"quality_controlled":"1","status":"public","type":"conference","volume":9411,"alternative_title":["LNCS"],"year":"2015","intvolume":"      9411","date_published":"2015-01-01T00:00:00Z","citation":{"ieee":"H. Edelsbrunner, “Shape, homology, persistence, and stability,” in <i>23rd International Symposium</i>, Los Angeles, CA, United States, 2015, vol. 9411.","ista":"Edelsbrunner H. 2015. Shape, homology, persistence, and stability. 23rd International Symposium. GD: Graph Drawing and Network Visualization, LNCS, vol. 9411.","apa":"Edelsbrunner, H. (2015). Shape, homology, persistence, and stability. In <i>23rd International Symposium</i> (Vol. 9411). Los Angeles, CA, United States: Springer Nature.","short":"H. Edelsbrunner, in:, 23rd International Symposium, Springer Nature, 2015.","chicago":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” In <i>23rd International Symposium</i>, Vol. 9411. Springer Nature, 2015.","mla":"Edelsbrunner, Herbert. “Shape, Homology, Persistence, and Stability.” <i>23rd International Symposium</i>, vol. 9411, Springer Nature, 2015.","ama":"Edelsbrunner H. Shape, homology, persistence, and stability. In: <i>23rd International Symposium</i>. Vol 9411. 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The classification of endoscopy images with persistent homology. Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. SYNASC: Symbolic and Numeric Algorithms for Scientific Computing, 7034731.","ieee":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, and D. Malkova, “The classification of endoscopy images with persistent homology,” in <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, Timisoara, Romania, 2015, p. 7034731.","ama":"Dunaeva O, Edelsbrunner H, Lukyanov A, Machin M, Malkova D. The classification of endoscopy images with persistent homology. In: <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>. IEEE; 2015:7034731. doi:<a href=\"https://doi.org/10.1109/SYNASC.2014.81\">10.1109/SYNASC.2014.81</a>","mla":"Dunaeva, Olga, et al. “The Classification of Endoscopy Images with Persistent Homology.” <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, IEEE, 2015, p. 7034731, doi:<a href=\"https://doi.org/10.1109/SYNASC.2014.81\">10.1109/SYNASC.2014.81</a>.","short":"O. Dunaeva, H. Edelsbrunner, A. Lukyanov, M. Machin, D. Malkova, in:, Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE, 2015, p. 7034731.","chicago":"Dunaeva, Olga, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, and Daria Malkova. “The Classification of Endoscopy Images with Persistent Homology.” In <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i>, 7034731. IEEE, 2015. <a href=\"https://doi.org/10.1109/SYNASC.2014.81\">https://doi.org/10.1109/SYNASC.2014.81</a>.","apa":"Dunaeva, O., Edelsbrunner, H., Lukyanov, A., Machin, M., &#38; Malkova, D. (2015). The classification of endoscopy images with persistent homology. In <i>Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing</i> (p. 7034731). Timisoara, Romania: IEEE. <a href=\"https://doi.org/10.1109/SYNASC.2014.81\">https://doi.org/10.1109/SYNASC.2014.81</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","acknowledgement":"This research is supported by the project No. 477 of P.G. Demidov Yaroslavl State University within State Assignment for Research.","page":"7034731","quality_controlled":"1","abstract":[{"text":"Aiming at the automatic diagnosis of tumors from narrow band imaging (NBI) magnifying endoscopy (ME) images of the stomach, we combine methods from image processing, computational topology, and machine learning to classify patterns into normal, tubular, vessel. Training the algorithm on a small number of images of each type, we achieve a high rate of correct classifications. 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Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. 2015;48(7):507-519. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>","apa":"Cao, T., Edelsbrunner, H., &#38; Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","abstract":[{"text":"We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations.","lang":"eng"}],"publication_status":"published","title":"Triangulations from topologically correct digital Voronoi diagrams","oa_version":"None","page":"507 - 519","quality_controlled":"1","type":"journal_article","year":"2015","publisher":"Elsevier","month":"08","publist_id":"5593","issue":"7","day":"01","language":[{"iso":"eng"}],"date_updated":"2025-09-29T10:58:50Z","external_id":{"isi":["000355887700001"]},"status":"public","article_processing_charge":"No","publication":"Computational Geometry","isi":1,"department":[{"_id":"HeEd"}]},{"abstract":[{"text":"We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.","lang":"eng"}],"publication_status":"published","title":"Weighted straight skeletons in the plane","oa_version":"Published Version","page":"120 - 133","quality_controlled":"1","file_date_updated":"2020-07-14T12:45:02Z","intvolume":"        48","volume":48,"doi":"10.1016/j.comgeo.2014.08.006","author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"full_name":"Held, Martin","last_name":"Held","first_name":"Martin"},{"first_name":"Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kaaser, Dominik","first_name":"Dominik","last_name":"Kaaser"},{"full_name":"Palfrader, Peter","last_name":"Palfrader","first_name":"Peter"}],"date_created":"2018-12-11T11:52:51Z","_id":"1582","scopus_import":"1","oa":1,"date_published":"2015-02-01T00:00:00Z","citation":{"ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 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A simple algorithm for computing positively weighted straight skeletons of monotone polygons. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">https://doi.org/10.1016/j.ipl.2014.09.021</a>","ama":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. <i>Information Processing Letters</i>. 2015;115(2):243-247. doi:<a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">10.1016/j.ipl.2014.09.021</a>","chicago":"Biedl, Therese, Martin Held, Stefan Huber, Dominik Kaaser, and Peter Palfrader. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” <i>Information Processing Letters</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">https://doi.org/10.1016/j.ipl.2014.09.021</a>.","mla":"Biedl, Therese, et al. “A Simple Algorithm for Computing Positively Weighted Straight Skeletons of Monotone Polygons.” <i>Information Processing Letters</i>, vol. 115, no. 2, Elsevier, 2015, pp. 243–47, doi:<a href=\"https://doi.org/10.1016/j.ipl.2014.09.021\">10.1016/j.ipl.2014.09.021</a>.","short":"T. Biedl, M. Held, S. Huber, D. Kaaser, P. Palfrader, Information Processing Letters 115 (2015) 243–247.","ieee":"T. Biedl, M. Held, S. Huber, D. Kaaser, and P. Palfrader, “A simple algorithm for computing positively weighted straight skeletons of monotone polygons,” <i>Information Processing Letters</i>, vol. 115, no. 2. Elsevier, pp. 243–247, 2015.","ista":"Biedl T, Held M, Huber S, Kaaser D, Palfrader P. 2015. A simple algorithm for computing positively weighted straight skeletons of monotone polygons. 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We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show that the weighted straight skeleton of even a simple polygon may be non-planar and may contain cycles, and we discuss under which restrictions on the weights and/or the input polygon the weighted straight skeleton still behaves similar to its unweighted counterpart. In particular, we obtain a non-procedural description and a linear-time construction algorithm for the straight skeleton of strictly convex polygons with arbitrary weights.","lang":"eng"}],"citation":{"apa":"Biedl, T., Held, M., Huber, S., Kaaser, D., &#38; Palfrader, P. (2015). Reprint of: Weighted straight skeletons in the plane. <i>Computational Geometry: Theory and Applications</i>. 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Reprint of: Weighted straight skeletons in the plane. Computational Geometry: Theory and Applications. 48(5), 429–442."},"date_published":"2015-07-01T00:00:00Z","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"first_name":"Therese","last_name":"Biedl","full_name":"Biedl, Therese"},{"last_name":"Held","first_name":"Martin","full_name":"Held, Martin"},{"id":"4700A070-F248-11E8-B48F-1D18A9856A87","full_name":"Huber, Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber","first_name":"Stefan"},{"full_name":"Kaaser, Dominik","last_name":"Kaaser","first_name":"Dominik"},{"last_name":"Palfrader","first_name":"Peter","full_name":"Palfrader, Peter"}],"date_created":"2018-12-11T11:52:51Z","doi":"10.1016/j.comgeo.2015.01.004","scopus_import":"1","_id":"1584","volume":48,"intvolume":"        48"},{"year":"2015","type":"book_chapter","month":"11","conference":{"location":"Los Angeles, CA, United States","end_date":"2015-09-26","start_date":"2015-09-24","name":"GD: Graph Drawing and Network Visualization"},"publisher":"Springer Nature","publist_id":"5581","day":"27","language":[{"iso":"eng"}],"date_updated":"2025-09-23T10:35:07Z","status":"public","external_id":{"isi":["000373628600028"],"arxiv":["1508.01076"]},"publication":"Graph Drawing and Network Visualization","isi":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"No","intvolume":"      9411","publication_identifier":{"eisbn":["978-3-319-27261-0"],"isbn":["978-3-319-27260-3"]},"volume":9411,"alternative_title":["LNCS"],"_id":"1590","scopus_import":"1","author":[{"first_name":"Oswin","last_name":"Aichholzer","full_name":"Aichholzer, Oswin"},{"full_name":"Biedl, Therese","first_name":"Therese","last_name":"Biedl"},{"last_name":"Hackl","first_name":"Thomas","full_name":"Hackl, Thomas"},{"first_name":"Martin","last_name":"Held","full_name":"Held, Martin"},{"full_name":"Huber, Stefan","id":"4700A070-F248-11E8-B48F-1D18A9856A87","first_name":"Stefan","orcid":"0000-0002-8871-5814","last_name":"Huber"},{"first_name":"Peter","last_name":"Palfrader","full_name":"Palfrader, Peter"},{"first_name":"Birgit","last_name":"Vogtenhuber","full_name":"Vogtenhuber, Birgit"}],"date_created":"2018-12-11T11:52:54Z","doi":"10.1007/978-3-319-27261-0_28","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"date_published":"2015-11-27T00:00:00Z","arxiv":1,"citation":{"ista":"Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and Network Visualization. LNCS, vol. 9411, 335–347.","ieee":"O. Aichholzer <i>et al.</i>, “Representing directed trees as straight skeletons,” in <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–347.","ama":"Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight skeletons. In: <i>Graph Drawing and Network Visualization</i>. Vol 9411. Springer Nature; 2015:335-347. doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>","chicago":"Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber, Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight Skeletons.” In <i>Graph Drawing and Network Visualization</i>, 9411:335–47. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>.","mla":"Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.” <i>Graph Drawing and Network Visualization</i>, vol. 9411, Springer Nature, 2015, pp. 335–47, doi:<a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">10.1007/978-3-319-27261-0_28</a>.","short":"O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber, in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.","apa":"Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P., &#38; Vogtenhuber, B. (2015). Representing directed trees as straight skeletons. In <i>Graph Drawing and Network Visualization</i> (Vol. 9411, pp. 335–347). Los Angeles, CA, United States: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-27261-0_28\">https://doi.org/10.1007/978-3-319-27261-0_28</a>"},"abstract":[{"lang":"eng","text":"The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be the straight skeleton of a polygon? And if so, can we find a suitable simple polygon? We answer these questions for all directed trees where the order of edges around each node is fixed."}],"title":"Representing directed trees as straight skeletons","oa_version":"Preprint","publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.01076"}],"page":"335 - 347","quality_controlled":"1"},{"doi":"10.1145/2751524","author":[{"first_name":"Peter","last_name":"Franek","full_name":"Franek, Peter"},{"id":"33E21118-F248-11E8-B48F-1D18A9856A87","full_name":"Krcál, Marek","last_name":"Krcál","first_name":"Marek"}],"date_created":"2018-12-11T11:53:27Z","scopus_import":"1","_id":"1682","citation":{"chicago":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” <i>Journal of the ACM</i>. ACM, 2015. <a href=\"https://doi.org/10.1145/2751524\">https://doi.org/10.1145/2751524</a>.","mla":"Franek, Peter, and Marek Krcál. “Robust Satisfiability of Systems of Equations.” <i>Journal of the ACM</i>, vol. 62, no. 4, 26, ACM, 2015, doi:<a href=\"https://doi.org/10.1145/2751524\">10.1145/2751524</a>.","short":"P. Franek, M. Krcál, Journal of the ACM 62 (2015).","ama":"Franek P, Krcál M. Robust satisfiability of systems of equations. <i>Journal of the ACM</i>. 2015;62(4). doi:<a href=\"https://doi.org/10.1145/2751524\">10.1145/2751524</a>","apa":"Franek, P., &#38; Krcál, M. (2015). Robust satisfiability of systems of equations. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2751524\">https://doi.org/10.1145/2751524</a>","ista":"Franek P, Krcál M. 2015. Robust satisfiability of systems of equations. Journal of the ACM. 62(4), 26.","ieee":"P. Franek and M. Krcál, “Robust satisfiability of systems of equations,” <i>Journal of the ACM</i>, vol. 62, no. 4. ACM, 2015."},"arxiv":1,"oa":1,"date_published":"2015-08-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"        62","volume":62,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1402.0858"}],"quality_controlled":"1","abstract":[{"text":"We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α &gt; 0, it holds that each function g: K → ℝn such that ||g - f || ∞ &lt; α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K &gt; 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.","lang":"eng"}],"publication_status":"published","title":"Robust satisfiability of systems of equations","oa_version":"Preprint","publisher":"ACM","month":"08","corr_author":"1","day":"01","issue":"4","publist_id":"5466","type":"journal_article","year":"2015","article_number":"26","external_id":{"arxiv":["1402.0858"],"isi":["000361200500001"]},"status":"public","article_processing_charge":"No","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"isi":1,"publication":"Journal of the ACM","language":[{"iso":"eng"}],"date_updated":"2025-09-23T10:38:46Z"},{"date_updated":"2025-09-23T09:35:36Z","language":[{"iso":"eng"}],"article_processing_charge":"No","department":[{"_id":"HeEd"}],"isi":1,"publication":"Society for Industrial and Applied Mathematics","external_id":{"isi":["000360691500009"],"arxiv":["1410.3736"]},"status":"public","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"type":"journal_article","year":"2015","ec_funded":1,"issue":"4","day":"14","publist_id":"5423","publisher":"SIAM","month":"07","publication_status":"published","oa_version":"Preprint","title":"Minimal resistance of curves under the single impact assumption","abstract":[{"lang":"eng","text":"We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) &lt; 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) &lt; 0 for 0 ≤ ξ &lt; 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞."}],"quality_controlled":"1","page":"2754 - 2769","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1410.3736"}],"volume":47,"intvolume":"        47","citation":{"ieee":"A. Akopyan and A. Plakhov, “Minimal resistance of curves under the single impact assumption,” <i>Society for Industrial and Applied Mathematics</i>, vol. 47, no. 4. SIAM, pp. 2754–2769, 2015.","ista":"Akopyan A, Plakhov A. 2015. Minimal resistance of curves under the single impact assumption. Society for Industrial and Applied Mathematics. 47(4), 2754–2769.","apa":"Akopyan, A., &#38; Plakhov, A. (2015). Minimal resistance of curves under the single impact assumption. <i>Society for Industrial and Applied Mathematics</i>. SIAM. <a href=\"https://doi.org/10.1137/140993843\">https://doi.org/10.1137/140993843</a>","ama":"Akopyan A, Plakhov A. Minimal resistance of curves under the single impact assumption. <i>Society for Industrial and Applied Mathematics</i>. 2015;47(4):2754-2769. doi:<a href=\"https://doi.org/10.1137/140993843\">10.1137/140993843</a>","chicago":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” <i>Society for Industrial and Applied Mathematics</i>. SIAM, 2015. <a href=\"https://doi.org/10.1137/140993843\">https://doi.org/10.1137/140993843</a>.","mla":"Akopyan, Arseniy, and Alexander Plakhov. “Minimal Resistance of Curves under the Single Impact Assumption.” <i>Society for Industrial and Applied Mathematics</i>, vol. 47, no. 4, SIAM, 2015, pp. 2754–69, doi:<a href=\"https://doi.org/10.1137/140993843\">10.1137/140993843</a>.","short":"A. Akopyan, A. Plakhov, Society for Industrial and Applied Mathematics 47 (2015) 2754–2769."},"arxiv":1,"oa":1,"date_published":"2015-07-14T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2018-12-11T11:53:36Z","doi":"10.1137/140993843","author":[{"first_name":"Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Alexander","last_name":"Plakhov","full_name":"Plakhov, Alexander"}],"scopus_import":"1","_id":"1710"}]