[{"project":[{"grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7"},{"_id":"258AA5B2-B435-11E9-9278-68D0E5697425","grant_number":"682815","call_identifier":"H2020","name":"Teaching Old Crypto New Tricks"}],"quality_controlled":"1","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"page":"51 - 65","date_published":"2018-06-01T00:00:00Z","publisher":"ACM","publication_status":"published","abstract":[{"text":"We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF.","lang":"eng"}],"external_id":{"isi":["000516620100005"]},"_id":"193","doi":"10.1145/3196494.3196534","date_created":"2018-12-11T11:45:07Z","publist_id":"7723","citation":{"apa":"Alwen, J. F., Gazi, P., Kamath Hosdurg, C., Klein, K., Osang, G. F., Pietrzak, K. Z., … Rybar, M. (2018). On the memory hardness of data independent password hashing functions. In <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i> (pp. 51–65). Incheon, Republic of Korea: ACM. <a href=\"https://doi.org/10.1145/3196494.3196534\">https://doi.org/10.1145/3196494.3196534</a>","short":"J.F. Alwen, P. Gazi, C. Kamath Hosdurg, K. Klein, G.F. Osang, K.Z. Pietrzak, L. Reyzin, M. Rolinek, M. Rybar, in:, Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65.","ieee":"J. F. Alwen <i>et al.</i>, “On the memory hardness of data independent password hashing functions,” in <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, Incheon, Republic of Korea, 2018, pp. 51–65.","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>. ACM; 2018:51-65. doi:<a href=\"https://doi.org/10.1145/3196494.3196534\">10.1145/3196494.3196534</a>","ista":"Alwen JF, Gazi P, Kamath Hosdurg C, Klein K, Osang GF, Pietrzak KZ, Reyzin L, Rolinek M, Rybar M. 2018. On the memory hardness of data independent password hashing functions. Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ASIACCS: Asia Conference on Computer and Communications Security , 51–65.","chicago":"Alwen, Joel F, Peter Gazi, Chethan Kamath Hosdurg, Karen Klein, Georg F Osang, Krzysztof Z Pietrzak, Lenoid Reyzin, Michal Rolinek, and Michal Rybar. “On the Memory Hardness of Data Independent Password Hashing Functions.” In <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, 51–65. ACM, 2018. <a href=\"https://doi.org/10.1145/3196494.3196534\">https://doi.org/10.1145/3196494.3196534</a>.","mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” <i>Proceedings of the 2018 on Asia Conference on Computer and Communication Security</i>, ACM, 2018, pp. 51–65, doi:<a href=\"https://doi.org/10.1145/3196494.3196534\">10.1145/3196494.3196534</a>."},"year":"2018","acknowledgement":"Leonid Reyzin was supported in part by IST Austria and by US NSF grants 1012910, 1012798, and 1422965; this research was performed while he was visiting IST Austria.","ec_funded":1,"type":"conference","status":"public","author":[{"id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","last_name":"Alwen","full_name":"Alwen, Joel F","first_name":"Joel F"},{"full_name":"Gazi, Peter","first_name":"Peter","last_name":"Gazi"},{"last_name":"Kamath Hosdurg","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","full_name":"Kamath Hosdurg, Chethan","first_name":"Chethan"},{"first_name":"Karen","full_name":"Klein, Karen","last_name":"Klein","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Osang, Georg F","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang"},{"first_name":"Krzysztof Z","full_name":"Pietrzak, Krzysztof Z","last_name":"Pietrzak","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654"},{"last_name":"Reyzin","first_name":"Lenoid","full_name":"Reyzin, Lenoid"},{"first_name":"Michal","full_name":"Rolinek, Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek"},{"full_name":"Rybar, Michal","first_name":"Michal","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","last_name":"Rybar"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","main_file_link":[{"url":"https://eprint.iacr.org/2016/783","open_access":"1"}],"oa_version":"Submitted Version","month":"06","conference":{"location":"Incheon, Republic of Korea","end_date":"2018-06-08","name":"ASIACCS: Asia Conference on Computer and Communications Security ","start_date":"2018-06-04"},"language":[{"iso":"eng"}],"publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","title":"On the memory hardness of data independent password hashing functions","article_processing_charge":"No","oa":1,"date_updated":"2023-09-13T09:13:12Z","scopus_import":"1","isi":1},{"publication_status":"published","ddc":["514","516"],"abstract":[{"text":"We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications.","lang":"eng"}],"supervisor":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"}],"date_published":"2018-06-11T00:00:00Z","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"page":"171","year":"2018","publist_id":"7712","date_created":"2018-12-11T11:45:10Z","citation":{"mla":"Iglesias Ham, Mabel. <i>Multiple Covers with Balls</i>. Institute of Science and Technology Austria, 2018, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th_1026\">10.15479/AT:ISTA:th_1026</a>.","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. <a href=\"https://doi.org/10.15479/AT:ISTA:th_1026\">https://doi.org/10.15479/AT:ISTA:th_1026</a>.","ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th_1026\">10.15479/AT:ISTA:th_1026</a>","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","apa":"Iglesias Ham, M. (2018). <i>Multiple covers with balls</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:th_1026\">https://doi.org/10.15479/AT:ISTA:th_1026</a>"},"degree_awarded":"PhD","_id":"201","file_date_updated":"2020-07-14T12:45:24Z","doi":"10.15479/AT:ISTA:th_1026","author":[{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel","first_name":"Mabel"}],"publication_identifier":{"issn":["2663-337X"]},"month":"06","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"access_level":"closed","relation":"source_file","content_type":"application/zip","file_size":11827713,"creator":"kschuh","date_created":"2019-02-05T07:43:31Z","date_updated":"2020-07-14T12:45:24Z","checksum":"dd699303623e96d1478a6ae07210dd05","file_id":"5918","file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip"},{"date_created":"2019-02-05T07:43:45Z","date_updated":"2020-07-14T12:45:24Z","checksum":"ba163849a190d2b41d66fef0e4983294","file_id":"5919","file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf","file_size":4783846,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","creator":"kschuh"}],"day":"11","oa_version":"Published Version","status":"public","type":"dissertation","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","oa":1,"date_updated":"2023-09-07T12:25:32Z","pubrep_id":"1026","title":"Multiple covers with balls","has_accepted_license":"1","language":[{"iso":"eng"}]},{"doi":"10.1137/16M110407X","_id":"58","ec_funded":1,"date_created":"2018-12-11T11:44:24Z","publist_id":"7996","citation":{"apa":"Akopyan, A., &#38; Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/16M110407X\">https://doi.org/10.1137/16M110407X</a>","ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:<a href=\"https://doi.org/10.1137/16M110407X\">10.1137/16M110407X</a>.","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics , 2018. <a href=\"https://doi.org/10.1137/16M110407X\">https://doi.org/10.1137/16M110407X</a>.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257.","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. <i>SIAM Journal on Discrete Mathematics</i>. 2018;32(3):2242-2257. doi:<a href=\"https://doi.org/10.1137/16M110407X\">10.1137/16M110407X</a>","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018."},"year":"2018","page":"2242 - 2257","department":[{"_id":"HeEd"}],"volume":32,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","date_published":"2018-09-06T00:00:00Z","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"external_id":{"isi":["000450810500036"],"arxiv":["1604.00960"]},"abstract":[{"text":"Inside a two-dimensional region (``cake&quot;&quot;), there are m nonoverlapping tiles of a certain kind (``toppings&quot;&quot;). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,&quot;&quot; such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks.","lang":"eng"}],"publication_status":"published","publication":"SIAM Journal on Discrete Mathematics","language":[{"iso":"eng"}],"intvolume":"        32","scopus_import":"1","isi":1,"title":"Counting blanks in polygonal arrangements","oa":1,"date_updated":"2023-09-11T12:48:39Z","issue":"3","article_processing_charge":"No","status":"public","type":"journal_article","oa_version":"Preprint","day":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"09","author":[{"orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"first_name":"Erel","full_name":"Segal Halevi, Erel","last_name":"Segal Halevi"}],"arxiv":1},{"publisher":"Cambridge University Press","date_published":"2018-05-31T00:00:00Z","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"quality_controlled":"1","volume":6,"project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"abstract":[{"text":"We  prove  that  any  cyclic  quadrilateral  can  be  inscribed  in  any  closed  convex C1-curve.  The smoothness condition is not required if the quadrilateral is a rectangle.","lang":"eng"}],"publication_status":"published","doi":"10.1017/fms.2018.7","file_date_updated":"2020-07-14T12:47:28Z","_id":"6355","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"8156","status":"public"}]},"article_number":"e7","year":"2018","citation":{"apa":"Akopyan, A., &#38; Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>","mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>, vol. 6, e7, Cambridge University Press, 2018, doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2018. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>.","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” <i>Forum of Mathematics, Sigma</i>, vol. 6. Cambridge University Press, 2018.","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. 2018;6. doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018)."},"date_created":"2019-04-30T06:09:57Z","type":"journal_article","status":"public","month":"05","publication_identifier":{"issn":["2050-5094"]},"day":"31","oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"creator":"dernst","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_size":249246,"file_name":"2018_ForumMahtematics_Akopyan.pdf","file_id":"6356","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","date_updated":"2020-07-14T12:47:28Z","date_created":"2019-04-30T06:14:58Z"}],"author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X"},{"first_name":"Sergey","full_name":"Avvakumov, Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1,"publication":"Forum of Mathematics, Sigma","language":[{"iso":"eng"}],"isi":1,"has_accepted_license":"1","intvolume":"         6","oa":1,"date_updated":"2023-09-19T14:50:12Z","article_processing_charge":"No","title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve"},{"doi":"10.1007/s00283-018-9795-5","_id":"106","year":"2018","date_created":"2018-12-11T11:44:40Z","citation":{"chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” <i>Mathematical Intelligencer</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00283-018-9795-5\">https://doi.org/10.1007/s00283-018-9795-5</a>.","mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” <i>Mathematical Intelligencer</i>, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:<a href=\"https://doi.org/10.1007/s00283-018-9795-5\">10.1007/s00283-018-9795-5</a>.","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31.","short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. <i>Mathematical Intelligencer</i>. 2018;40(3):26-31. doi:<a href=\"https://doi.org/10.1007/s00283-018-9795-5\">10.1007/s00283-018-9795-5</a>","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” <i>Mathematical Intelligencer</i>, vol. 40, no. 3. Springer, pp. 26–31, 2018.","apa":"Akopyan, A., &#38; Petrunin, A. (2018). Long geodesics on convex surfaces. <i>Mathematical Intelligencer</i>. Springer. <a href=\"https://doi.org/10.1007/s00283-018-9795-5\">https://doi.org/10.1007/s00283-018-9795-5</a>"},"publist_id":"7948","date_published":"2018-09-01T00:00:00Z","publisher":"Springer","volume":40,"quality_controlled":"1","page":"26 - 31","department":[{"_id":"HeEd"}],"abstract":[{"lang":"eng","text":"The goal of this article is to introduce the reader to the theory of intrinsic geometry of convex surfaces. We illustrate the power of the tools by proving a theorem on convex surfaces containing an arbitrarily long closed simple geodesic. Let us remind ourselves that a curve in a surface is called geodesic if every sufficiently short arc of the curve is length minimizing; if, in addition, it has no self-intersections, we call it simple geodesic. A tetrahedron with equal opposite edges is called isosceles. The axiomatic method of Alexandrov geometry allows us to work with the metrics of convex surfaces directly, without approximating it first by a smooth or polyhedral metric. Such approximations destroy the closed geodesics on the surface; therefore it is difficult (if at all possible) to apply approximations in the proof of our theorem. On the other hand, a proof in the smooth or polyhedral case usually admits a translation into Alexandrov’s language; such translation makes the result more general. In fact, our proof resembles a translation of the proof given by Protasov. Note that the main theorem implies in particular that a smooth convex surface does not have arbitrarily long simple closed geodesics. However we do not know a proof of this corollary that is essentially simpler than the one presented below."}],"external_id":{"isi":["000444141200005"],"arxiv":["1702.05172"]},"publication_status":"published","publication":"Mathematical Intelligencer","language":[{"iso":"eng"}],"isi":1,"intvolume":"        40","scopus_import":"1","issue":"3","article_processing_charge":"No","date_updated":"2023-09-13T08:49:16Z","oa":1,"title":"Long geodesics on convex surfaces","type":"journal_article","status":"public","month":"09","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1702.05172","open_access":"1"}],"arxiv":1,"author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"first_name":"Anton","full_name":"Petrunin, Anton","last_name":"Petrunin"}]},{"year":"2018","citation":{"apa":"Akopyan, A., Balitskiy, A., &#38; Grigorev, M. (2018). On the circle covering theorem by A.W. Goodman and R.E. Goodman. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-017-9883-x\">https://doi.org/10.1007/s00454-017-9883-x</a>","mla":"Akopyan, Arseniy, et al. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” <i>Discrete &#38; Computational Geometry</i>, vol. 59, no. 4, Springer, 2018, pp. 1001–09, doi:<a href=\"https://doi.org/10.1007/s00454-017-9883-x\">10.1007/s00454-017-9883-x</a>.","chicago":"Akopyan, Arseniy, Alexey Balitskiy, and Mikhail Grigorev. “On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00454-017-9883-x\">https://doi.org/10.1007/s00454-017-9883-x</a>.","ista":"Akopyan A, Balitskiy A, Grigorev M. 2018. On the circle covering theorem by A.W. Goodman and R.E. Goodman. Discrete &#38; Computational Geometry. 59(4), 1001–1009.","ieee":"A. Akopyan, A. Balitskiy, and M. Grigorev, “On the circle covering theorem by A.W. Goodman and R.E. Goodman,” <i>Discrete &#38; Computational Geometry</i>, vol. 59, no. 4. Springer, pp. 1001–1009, 2018.","ama":"Akopyan A, Balitskiy A, Grigorev M. On the circle covering theorem by A.W. Goodman and R.E. Goodman. <i>Discrete &#38; Computational Geometry</i>. 2018;59(4):1001-1009. doi:<a href=\"https://doi.org/10.1007/s00454-017-9883-x\">10.1007/s00454-017-9883-x</a>","short":"A. Akopyan, A. Balitskiy, M. Grigorev, Discrete &#38; Computational Geometry 59 (2018) 1001–1009."},"date_created":"2018-12-11T11:49:57Z","publist_id":"6324","ec_funded":1,"article_type":"original","_id":"1064","file_date_updated":"2019-01-18T09:27:36Z","doi":"10.1007/s00454-017-9883-x","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["516","000"],"abstract":[{"lang":"eng","text":"In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, … , rn in the plane, it is always possible to cover them by a disk of radius R= ∑ ri, provided they cannot be separated into two subfamilies by a straight line disjoint from the disks. In this note we show that essentially the same idea may work for different analogues and generalizations of their result. In particular, we prove the following: Given a family of positive homothetic copies of a fixed convex body K⊂ Rd with homothety coefficients τ1, … , τn> 0 , it is always possible to cover them by a translate of d+12(∑τi)K, provided they cannot be separated into two subfamilies by a hyperplane disjoint from the homothets."}],"external_id":{"isi":["000432205500011"]},"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"date_published":"2018-06-01T00:00:00Z","publisher":"Springer","quality_controlled":"1","volume":59,"department":[{"_id":"HeEd"}],"page":"1001-1009","article_processing_charge":"Yes (via OA deal)","issue":"4","oa":1,"date_updated":"2023-09-20T12:08:51Z","title":"On the circle covering theorem by A.W. Goodman and R.E. Goodman","isi":1,"scopus_import":"1","intvolume":"        59","has_accepted_license":"1","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Balitskiy, Alexey","first_name":"Alexey","last_name":"Balitskiy"},{"first_name":"Mikhail","full_name":"Grigorev, Mikhail","last_name":"Grigorev"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"month":"06","file":[{"file_size":482518,"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_created":"2019-01-18T09:27:36Z","date_updated":"2019-01-18T09:27:36Z","success":1,"file_name":"2018_DiscreteComp_Akopyan.pdf","file_id":"5844"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","oa_version":"Published Version","status":"public","type":"journal_article"},{"publication":"SIAM J Discrete Math","language":[{"iso":"eng"}],"isi":1,"intvolume":"        32","scopus_import":"1","oa":1,"date_updated":"2023-09-13T09:34:38Z","article_processing_charge":"No","issue":"1","title":"On the optimality of the FCC lattice for soft sphere packing","type":"journal_article","status":"public","month":"03","publication_identifier":{"issn":["08954801"]},"oa_version":"Submitted Version","main_file_link":[{"url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf","open_access":"1"}],"day":"29","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}],"doi":"10.1137/16M1097201","article_type":"original","_id":"312","acknowledgement":"This work was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” through grant I02979-N35 of the Austrian Science Fund (FWF).","year":"2018","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” <i>SIAM J Discrete Math</i>, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:<a href=\"https://doi.org/10.1137/16M1097201\">10.1137/16M1097201</a>.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 32(1), 750–782.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” <i>SIAM J Discrete Math</i>. Society for Industrial and Applied Mathematics , 2018. <a href=\"https://doi.org/10.1137/16M1097201\">https://doi.org/10.1137/16M1097201</a>.","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. <i>SIAM J Discrete Math</i>. 2018;32(1):750-782. doi:<a href=\"https://doi.org/10.1137/16M1097201\">10.1137/16M1097201</a>","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” <i>SIAM J Discrete Math</i>, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018.","short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. <i>SIAM J Discrete Math</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/16M1097201\">https://doi.org/10.1137/16M1097201</a>"},"publist_id":"7553","date_created":"2018-12-11T11:45:46Z","publisher":"Society for Industrial and Applied Mathematics ","date_published":"2018-03-29T00:00:00Z","page":"750 - 782","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":32,"project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"external_id":{"isi":["000428958900038"]},"abstract":[{"text":"Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice.","lang":"eng"}],"publication_status":"published"},{"language":[{"iso":"eng"}],"publication":"Comptes Rendus Mathematique","title":"On the number of non-hexagons in a planar tiling","date_updated":"2023-09-13T09:34:12Z","oa":1,"article_processing_charge":"No","issue":"4","scopus_import":"1","intvolume":"       356","isi":1,"type":"journal_article","status":"public","author":[{"first_name":"Arseniy","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1,"day":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.01652"}],"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"issn":["1631073X"]},"month":"04","article_type":"original","_id":"409","doi":"10.1016/j.crma.2018.03.005","date_created":"2018-12-11T11:46:19Z","citation":{"mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” <i>Comptes Rendus Mathematique</i>, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:<a href=\"https://doi.org/10.1016/j.crma.2018.03.005\">10.1016/j.crma.2018.03.005</a>.","ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414.","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” <i>Comptes Rendus Mathematique</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.crma.2018.03.005\">https://doi.org/10.1016/j.crma.2018.03.005</a>.","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” <i>Comptes Rendus Mathematique</i>, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","ama":"Akopyan A. On the number of non-hexagons in a planar tiling. <i>Comptes Rendus Mathematique</i>. 2018;356(4):412-414. doi:<a href=\"https://doi.org/10.1016/j.crma.2018.03.005\">10.1016/j.crma.2018.03.005</a>","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. <i>Comptes Rendus Mathematique</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.crma.2018.03.005\">https://doi.org/10.1016/j.crma.2018.03.005</a>"},"publist_id":"7420","year":"2018","department":[{"_id":"HeEd"}],"page":"412-414","quality_controlled":"1","volume":356,"publisher":"Elsevier","date_published":"2018-04-01T00:00:00Z","publication_status":"published","external_id":{"isi":["000430402700009"],"arxiv":["1805.01652"]},"abstract":[{"text":"We give a simple proof of T. Stehling's result [4], whereby in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except a finite number are hexagons.","lang":"eng"}]},{"language":[{"iso":"eng"}],"publication":"Transactions of the American Mathematical Society","date_updated":"2023-09-11T14:19:12Z","oa":1,"article_processing_charge":"No","issue":"4","title":"Incircular nets and confocal conics","isi":1,"scopus_import":"1","intvolume":"       370","type":"journal_article","status":"public","author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"last_name":"Bobenko","full_name":"Bobenko, Alexander","first_name":"Alexander"}],"month":"04","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1602.04637","open_access":"1"}],"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"458","doi":"10.1090/tran/7292","acknowledgement":"DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”; People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA grant agreement n◦[291734]","year":"2018","citation":{"short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. <i>Transactions of the American Mathematical Society</i>. 2018;370(4):2825-2854. doi:<a href=\"https://doi.org/10.1090/tran/7292\">10.1090/tran/7292</a>","ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” <i>Transactions of the American Mathematical Society</i>, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2018. <a href=\"https://doi.org/10.1090/tran/7292\">https://doi.org/10.1090/tran/7292</a>.","mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” <i>Transactions of the American Mathematical Society</i>, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:<a href=\"https://doi.org/10.1090/tran/7292\">10.1090/tran/7292</a>.","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","apa":"Akopyan, A., &#38; Bobenko, A. (2018). Incircular nets and confocal conics. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7292\">https://doi.org/10.1090/tran/7292</a>"},"publist_id":"7363","date_created":"2018-12-11T11:46:35Z","ec_funded":1,"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"publisher":"American Mathematical Society","date_published":"2018-04-01T00:00:00Z","page":"2825 - 2854","department":[{"_id":"HeEd"}],"volume":370,"quality_controlled":"1","publication_status":"published","external_id":{"isi":["000423197800019"]},"abstract":[{"text":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems. Most of our results are valid in hyperbolic and spherical geometries as well. We present also generalizations in spaces of higher dimension, called checkerboard IS-nets. The construction of these nets is based on a new 9 inspheres incidence theorem.","lang":"eng"}]},{"title":"Multiple covers with balls I: Inclusion–exclusion","article_processing_charge":"No","oa":1,"date_updated":"2023-09-13T08:59:00Z","intvolume":"        68","has_accepted_license":"1","scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Computational Geometry: Theory and Applications","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel","first_name":"Mabel"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"date_updated":"2020-07-14T12:46:38Z","date_created":"2019-02-12T06:47:52Z","file_id":"5953","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_name":"2018_Edelsbrunner.pdf","file_size":708357,"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"dernst"}],"oa_version":"Preprint","day":"01","month":"03","type":"journal_article","status":"public","citation":{"apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” <i>Computational Geometry: Theory and Applications</i>, vol. 68, Elsevier, 2018, pp. 119–33, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">10.1016/j.comgeo.2017.06.014</a>.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” <i>Computational Geometry: Theory and Applications</i>, vol. 68. Elsevier, pp. 119–133, 2018.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>. 2018;68:119-133. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">10.1016/j.comgeo.2017.06.014</a>"},"publist_id":"7289","date_created":"2018-12-11T11:46:59Z","year":"2018","ec_funded":1,"_id":"530","file_date_updated":"2020-07-14T12:46:38Z","doi":"10.1016/j.comgeo.2017.06.014","publication_status":"published","abstract":[{"lang":"eng","text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software."}],"external_id":{"isi":["000415778300010"]},"ddc":["000"],"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"volume":68,"quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"119 - 133","date_published":"2018-03-01T00:00:00Z","publisher":"Elsevier"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Submitted Version","day":"28","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.02045"}],"month":"07","publication_identifier":{"issn":["03029743"]},"conference":{"end_date":"2017-08-24","location":"Ystad, Sweden","start_date":"2017-08-22","name":"CAIP: Computer Analysis of Images and Patterns"},"author":[{"first_name":"Teresa","full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","orcid":"0000-0002-1780-2689"},{"first_name":"Hubert","full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner"}],"status":"public","type":"conference","alternative_title":["LNCS"],"scopus_import":"1","intvolume":"     10424","editor":[{"full_name":"Felsberg, Michael","first_name":"Michael","last_name":"Felsberg"},{"last_name":"Heyden","full_name":"Heyden, Anders","first_name":"Anders"},{"full_name":"Krüger, Norbert","first_name":"Norbert","last_name":"Krüger"}],"isi":1,"title":"Streaming algorithm for Euler characteristic curves of multidimensional images","article_processing_charge":"No","oa":1,"date_updated":"2023-09-26T16:10:03Z","language":[{"iso":"eng"}],"abstract":[{"text":"We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams.","lang":"eng"}],"external_id":{"isi":["000432085900032"]},"publication_status":"published","quality_controlled":"1","volume":10424,"department":[{"_id":"HeEd"}],"page":"397 - 409","date_published":"2017-07-28T00:00:00Z","publisher":"Springer","publist_id":"6815","citation":{"mla":"Heiss, Teresa, and Hubert Wagner. <i>Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images</i>. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:<a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">10.1007/978-3-319-64689-3_32</a>.","ista":"Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.","chicago":"Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">https://doi.org/10.1007/978-3-319-64689-3_32</a>.","short":"T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409.","ama":"Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:<a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">10.1007/978-3-319-64689-3_32</a>","ieee":"T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.","apa":"Heiss, T., &#38; Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, &#38; N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. <a href=\"https://doi.org/10.1007/978-3-319-64689-3_32\">https://doi.org/10.1007/978-3-319-64689-3_32</a>"},"date_created":"2018-12-11T11:48:45Z","year":"2017","doi":"10.1007/978-3-319-64689-3_32","_id":"833"},{"author":[{"last_name":"Ethier","first_name":"Marc","full_name":"Ethier, Marc"},{"last_name":"Jablonski","id":"4483EF78-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3536-9866","full_name":"Jablonski, Grzegorz","first_name":"Grzegorz"},{"full_name":"Mrozek, Marian","first_name":"Marian","last_name":"Mrozek"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"None","day":"27","publication_identifier":{"isbn":["978-331956930-7"]},"month":"07","conference":{"start_date":"2015-07-20","name":"ACA: Applications of Computer Algebra","end_date":"2015-07-23","location":"Kalamata, Greece"},"type":"conference","status":"public","alternative_title":["PROMS"],"title":"Finding eigenvalues of self-maps with the Kronecker canonical form","article_processing_charge":"No","date_updated":"2023-09-26T15:50:52Z","intvolume":"       198","scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Special Sessions in Applications of Computer Algebra","publication_status":"published","abstract":[{"text":"Recent research has examined how to study the topological features of a continuous self-map by means of the persistence of the eigenspaces, for given eigenvalues, of the endomorphism induced in homology over a field. This raised the question of how to select dynamically significant eigenvalues. The present paper aims to answer this question, giving an algorithm that computes the persistence of eigenspaces for every eigenvalue simultaneously, also expressing said eigenspaces as direct sums of “finite” and “singular” subspaces.","lang":"eng"}],"external_id":{"isi":["000434088200008"]},"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","volume":198,"department":[{"_id":"HeEd"}],"page":"119 - 136","date_published":"2017-07-27T00:00:00Z","publisher":"Springer","citation":{"apa":"Ethier, M., Jablonski, G., &#38; Mrozek, M. (2017). Finding eigenvalues of self-maps with the Kronecker canonical form. In <i>Special Sessions in Applications of Computer Algebra</i> (Vol. 198, pp. 119–136). Kalamata, Greece: Springer. <a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">https://doi.org/10.1007/978-3-319-56932-1_8</a>","ama":"Ethier M, Jablonski G, Mrozek M. Finding eigenvalues of self-maps with the Kronecker canonical form. In: <i>Special Sessions in Applications of Computer Algebra</i>. Vol 198. Springer; 2017:119-136. doi:<a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">10.1007/978-3-319-56932-1_8</a>","ieee":"M. Ethier, G. Jablonski, and M. Mrozek, “Finding eigenvalues of self-maps with the Kronecker canonical form,” in <i>Special Sessions in Applications of Computer Algebra</i>, Kalamata, Greece, 2017, vol. 198, pp. 119–136.","short":"M. Ethier, G. Jablonski, M. Mrozek, in:, Special Sessions in Applications of Computer Algebra, Springer, 2017, pp. 119–136.","ista":"Ethier M, Jablonski G, Mrozek M. 2017. Finding eigenvalues of self-maps with the Kronecker canonical form. Special Sessions in Applications of Computer Algebra. ACA: Applications of Computer Algebra, PROMS, vol. 198, 119–136.","mla":"Ethier, Marc, et al. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” <i>Special Sessions in Applications of Computer Algebra</i>, vol. 198, Springer, 2017, pp. 119–36, doi:<a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">10.1007/978-3-319-56932-1_8</a>.","chicago":"Ethier, Marc, Grzegorz Jablonski, and Marian Mrozek. “Finding Eigenvalues of Self-Maps with the Kronecker Canonical Form.” In <i>Special Sessions in Applications of Computer Algebra</i>, 198:119–36. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-56932-1_8\">https://doi.org/10.1007/978-3-319-56932-1_8</a>."},"publist_id":"6812","date_created":"2018-12-11T11:48:46Z","year":"2017","ec_funded":1,"_id":"836","doi":"10.1007/978-3-319-56932-1_8"},{"article_processing_charge":"No","year":"2017","date_updated":"2023-10-16T11:15:22Z","citation":{"mla":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” <i>Handbook of Discrete and Computational Geometry, Third Edition</i>, edited by Csaba Toth et al., Taylor &#38; Francis, 2017, pp. 1709–35, doi:<a href=\"https://doi.org/10.1201/9781315119601\">10.1201/9781315119601</a>.","chicago":"Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In <i>Handbook of Discrete and Computational Geometry, Third Edition</i>, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor &#38; Francis, 2017. <a href=\"https://doi.org/10.1201/9781315119601\">https://doi.org/10.1201/9781315119601</a>.","ista":"Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735.","ieee":"H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in <i>Handbook of Discrete and Computational Geometry, Third Edition</i>, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor &#38; Francis, 2017, pp. 1709–1735.","ama":"Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. <i>Handbook of Discrete and Computational Geometry, Third Edition</i>. Handbook of Discrete and Computational Geometry. Taylor &#38; Francis; 2017:1709-1735. doi:<a href=\"https://doi.org/10.1201/9781315119601\">10.1201/9781315119601</a>","short":"H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor &#38; Francis, 2017, pp. 1709–1735.","apa":"Edelsbrunner, H., &#38; Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, &#38; J. Goodman (Eds.), <i>Handbook of Discrete and Computational Geometry, Third Edition</i> (pp. 1709–1735). Taylor &#38; Francis. <a href=\"https://doi.org/10.1201/9781315119601\">https://doi.org/10.1201/9781315119601</a>"},"publist_id":"7970","title":"Computational topology for structural molecular biology","date_created":"2018-12-11T11:44:32Z","editor":[{"last_name":"Toth","first_name":"Csaba","full_name":"Toth, Csaba"},{"first_name":"Joseph","full_name":"O'Rourke, Joseph","last_name":"O'Rourke"},{"last_name":"Goodman","full_name":"Goodman, Jacob","first_name":"Jacob"}],"scopus_import":"1","language":[{"iso":"eng"}],"_id":"84","publication":"Handbook of Discrete and Computational Geometry, Third Edition","doi":"10.1201/9781315119601","publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Koehl","full_name":"Koehl, Patrice","first_name":"Patrice"}],"publication_identifier":{"eisbn":["9781498711425"]},"month":"11","series_title":"Handbook of Discrete and Computational Geometry","abstract":[{"lang":"eng","text":"The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","day":"09","date_published":"2017-11-09T00:00:00Z","status":"public","type":"book_chapter","publisher":"Taylor & Francis","quality_controlled":"1","department":[{"_id":"HeEd"}],"page":"1709 - 1735"},{"type":"journal_article","status":"public","arxiv":1,"author":[{"last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"last_name":"Vysotsky","full_name":"Vysotsky, Vladislav","first_name":"Vladislav"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.07997"}],"day":"01","publication_identifier":{"issn":["00029890"]},"month":"01","language":[{"iso":"eng"}],"publication":"The American Mathematical Monthly","title":"On the lengths of curves passing through boundary points of a planar convex shape","issue":"7","article_processing_charge":"No","date_updated":"2023-10-17T11:24:57Z","oa":1,"scopus_import":"1","intvolume":"       124","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"volume":124,"quality_controlled":"1","page":"588 - 596","department":[{"_id":"HeEd"}],"date_published":"2017-01-01T00:00:00Z","publisher":"Mathematical Association of America","publication_status":"published","abstract":[{"text":"We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor &amp;#xbd; cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape.","lang":"eng"}],"external_id":{"isi":["000413947300002"],"arxiv":["1605.07997"]},"_id":"909","article_type":"original","doi":"10.4169/amer.math.monthly.124.7.588","publist_id":"6534","citation":{"apa":"Akopyan, A., &#38; Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. Mathematical Association of America. <a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">https://doi.org/10.4169/amer.math.monthly.124.7.588</a>","short":"A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596.","ieee":"A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” <i>The American Mathematical Monthly</i>, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017.","ama":"Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. <i>The American Mathematical Monthly</i>. 2017;124(7):588-596. doi:<a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">10.4169/amer.math.monthly.124.7.588</a>","chicago":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” <i>The American Mathematical Monthly</i>. Mathematical Association of America, 2017. <a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">https://doi.org/10.4169/amer.math.monthly.124.7.588</a>.","ista":"Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596.","mla":"Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” <i>The American Mathematical Monthly</i>, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:<a href=\"https://doi.org/10.4169/amer.math.monthly.124.7.588\">10.4169/amer.math.monthly.124.7.588</a>."},"date_created":"2018-12-11T11:49:09Z","year":"2017","ec_funded":1},{"month":"08","publication_identifier":{"issn":["00246093"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.06279"}],"oa_version":"Preprint","day":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"orcid":"0000-0002-2548-617X","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","first_name":"Arseniy"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"type":"journal_article","status":"public","scopus_import":1,"intvolume":"        49","date_updated":"2021-01-12T08:11:41Z","oa":1,"issue":"4","title":"A tight estimate for the waist of the ball ","publication":"Bulletin of the London Mathematical Society","language":[{"iso":"eng"}],"abstract":[{"text":"We answer a question of M. Gromov on the waist of the unit ball.","lang":"eng"}],"publication_status":"published","publisher":"Wiley-Blackwell","date_published":"2017-08-01T00:00:00Z","page":"690 - 693","department":[{"_id":"HeEd"}],"volume":49,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"ec_funded":1,"year":"2017","date_created":"2018-12-11T11:48:02Z","publist_id":"6982","citation":{"apa":"Akopyan, A., &#38; Karasev, R. (2017). A tight estimate for the waist of the ball . <i>Bulletin of the London Mathematical Society</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1112/blms.12062\">https://doi.org/10.1112/blms.12062</a>","ieee":"A. Akopyan and R. Karasev, “A tight estimate for the waist of the ball ,” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4. Wiley-Blackwell, pp. 690–693, 2017.","ama":"Akopyan A, Karasev R. A tight estimate for the waist of the ball . <i>Bulletin of the London Mathematical Society</i>. 2017;49(4):690-693. doi:<a href=\"https://doi.org/10.1112/blms.12062\">10.1112/blms.12062</a>","short":"A. Akopyan, R. Karasev, Bulletin of the London Mathematical Society 49 (2017) 690–693.","mla":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” <i>Bulletin of the London Mathematical Society</i>, vol. 49, no. 4, Wiley-Blackwell, 2017, pp. 690–93, doi:<a href=\"https://doi.org/10.1112/blms.12062\">10.1112/blms.12062</a>.","chicago":"Akopyan, Arseniy, and Roman Karasev. “A Tight Estimate for the Waist of the Ball .” <i>Bulletin of the London Mathematical Society</i>. Wiley-Blackwell, 2017. <a href=\"https://doi.org/10.1112/blms.12062\">https://doi.org/10.1112/blms.12062</a>.","ista":"Akopyan A, Karasev R. 2017. A tight estimate for the waist of the ball . Bulletin of the London Mathematical Society. 49(4), 690–693."},"doi":"10.1112/blms.12062","_id":"707"},{"publisher":"Cambridge University Press","date_published":"2017-09-01T00:00:00Z","page":"745 - 767","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":49,"project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"external_id":{"arxiv":["1607.05915"]},"abstract":[{"lang":"eng","text":"Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the points from a Poisson point process in ℝ n , we study the expected number of simplices in the Delaunay mosaic as well as the expected number of critical simplices and nonsingular intervals in the corresponding generalized discrete gradient. Observing connections with other probabilistic models, we obtain precise expressions for the expected numbers in low dimensions. In particular, we obtain the expected numbers of simplices in the Poisson–Delaunay mosaic in dimensions n ≤ 4."}],"publication_status":"published","doi":"10.1017/apr.2017.20","_id":"718","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"6287","status":"public"}]},"year":"2017","publist_id":"6962","citation":{"apa":"Edelsbrunner, H., Nikitenko, A., &#38; Reitzner, M. (2017). Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. <i>Advances in Applied Probability</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/apr.2017.20\">https://doi.org/10.1017/apr.2017.20</a>","short":"H. Edelsbrunner, A. Nikitenko, M. Reitzner, Advances in Applied Probability 49 (2017) 745–767.","ieee":"H. Edelsbrunner, A. Nikitenko, and M. Reitzner, “Expected sizes of poisson Delaunay mosaics and their discrete Morse functions,” <i>Advances in Applied Probability</i>, vol. 49, no. 3. Cambridge University Press, pp. 745–767, 2017.","ama":"Edelsbrunner H, Nikitenko A, Reitzner M. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. <i>Advances in Applied Probability</i>. 2017;49(3):745-767. doi:<a href=\"https://doi.org/10.1017/apr.2017.20\">10.1017/apr.2017.20</a>","ista":"Edelsbrunner H, Nikitenko A, Reitzner M. 2017. Expected sizes of poisson Delaunay mosaics and their discrete Morse functions. Advances in Applied Probability. 49(3), 745–767.","chicago":"Edelsbrunner, Herbert, Anton Nikitenko, and Matthias Reitzner. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” <i>Advances in Applied Probability</i>. Cambridge University Press, 2017. <a href=\"https://doi.org/10.1017/apr.2017.20\">https://doi.org/10.1017/apr.2017.20</a>.","mla":"Edelsbrunner, Herbert, et al. “Expected Sizes of Poisson Delaunay Mosaics and Their Discrete Morse Functions.” <i>Advances in Applied Probability</i>, vol. 49, no. 3, Cambridge University Press, 2017, pp. 745–67, doi:<a href=\"https://doi.org/10.1017/apr.2017.20\">10.1017/apr.2017.20</a>."},"date_created":"2018-12-11T11:48:07Z","status":"public","type":"journal_article","publication_identifier":{"issn":["00018678"]},"month":"09","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1607.05915","open_access":"1"}],"day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","first_name":"Anton","full_name":"Nikitenko, Anton"},{"first_name":"Matthias","full_name":"Reitzner, Matthias","last_name":"Reitzner"}],"arxiv":1,"publication":"Advances in Applied Probability","language":[{"iso":"eng"}],"intvolume":"        49","scopus_import":1,"date_updated":"2023-09-07T12:07:12Z","oa":1,"issue":"3","title":"Expected sizes of poisson Delaunay mosaics and their discrete Morse functions"},{"doi":"10.1016/j.topol.2017.09.015","_id":"737","year":"2017","publist_id":"6930","date_created":"2018-12-11T11:48:14Z","citation":{"apa":"Virk, Z., &#38; Zastrow, A. (2017). A new topology on the universal path space. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">https://doi.org/10.1016/j.topol.2017.09.015</a>","ama":"Virk Z, Zastrow A. A new topology on the universal path space. <i>Topology and its Applications</i>. 2017;231:186-196. doi:<a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">10.1016/j.topol.2017.09.015</a>","ieee":"Z. Virk and A. Zastrow, “A new topology on the universal path space,” <i>Topology and its Applications</i>, vol. 231. Elsevier, pp. 186–196, 2017.","short":"Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.","ista":"Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.","chicago":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” <i>Topology and Its Applications</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">https://doi.org/10.1016/j.topol.2017.09.015</a>.","mla":"Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” <i>Topology and Its Applications</i>, vol. 231, Elsevier, 2017, pp. 186–96, doi:<a href=\"https://doi.org/10.1016/j.topol.2017.09.015\">10.1016/j.topol.2017.09.015</a>."},"date_published":"2017-11-01T00:00:00Z","publisher":"Elsevier","quality_controlled":"1","volume":231,"department":[{"_id":"HeEd"}],"page":"186 - 196","abstract":[{"lang":"eng","text":"We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action."}],"external_id":{"isi":["000413889100012"]},"publication_status":"published","publication":"Topology and its Applications","language":[{"iso":"eng"}],"isi":1,"intvolume":"       231","scopus_import":"1","article_processing_charge":"No","date_updated":"2023-09-27T12:53:01Z","title":"A new topology on the universal path space","type":"journal_article","status":"public","publication_identifier":{"issn":["01668641"]},"month":"11","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"01","oa_version":"None","author":[{"first_name":"Ziga","full_name":"Virk, Ziga","last_name":"Virk","id":"2E36B656-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Andreas","full_name":"Zastrow, Andreas","last_name":"Zastrow"}]},{"intvolume":"        78","scopus_import":"1","isi":1,"title":"Phat - Persistent homology algorithms toolbox","date_updated":"2023-09-20T09:42:40Z","oa":1,"article_processing_charge":"No","publication":"Journal of Symbolic Computation","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1016/j.jsc.2016.03.008","open_access":"1"}],"day":"01","oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"01","publication_identifier":{"issn":[" 07477171"]},"author":[{"full_name":"Bauer, Ulrich","first_name":"Ulrich","last_name":"Bauer"},{"last_name":"Kerber","full_name":"Kerber, Michael","first_name":"Michael"},{"full_name":"Reininghaus, Jan","first_name":"Jan","last_name":"Reininghaus"},{"first_name":"Hubert","full_name":"Wagner, Hubert","last_name":"Wagner","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","status":"public","ec_funded":1,"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10894"}]},"date_created":"2018-12-11T11:51:59Z","publist_id":"5765","citation":{"apa":"Bauer, U., Kerber, M., Reininghaus, J., &#38; Wagner, H. (2017). Phat - Persistent homology algorithms toolbox. <i>Journal of Symbolic Computation</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.jsc.2016.03.008\">https://doi.org/10.1016/j.jsc.2016.03.008</a>","short":"U. Bauer, M. Kerber, J. Reininghaus, H. Wagner, Journal of Symbolic Computation 78 (2017) 76–90.","ama":"Bauer U, Kerber M, Reininghaus J, Wagner H. Phat - Persistent homology algorithms toolbox. <i>Journal of Symbolic Computation</i>. 2017;78:76-90. doi:<a href=\"https://doi.org/10.1016/j.jsc.2016.03.008\">10.1016/j.jsc.2016.03.008</a>","ieee":"U. Bauer, M. Kerber, J. Reininghaus, and H. Wagner, “Phat - Persistent homology algorithms toolbox,” <i>Journal of Symbolic Computation</i>, vol. 78. Academic Press, pp. 76–90, 2017.","ista":"Bauer U, Kerber M, Reininghaus J, Wagner H. 2017. Phat - Persistent homology algorithms toolbox. Journal of Symbolic Computation. 78, 76–90.","mla":"Bauer, Ulrich, et al. “Phat - Persistent Homology Algorithms Toolbox.” <i>Journal of Symbolic Computation</i>, vol. 78, Academic Press, 2017, pp. 76–90, doi:<a href=\"https://doi.org/10.1016/j.jsc.2016.03.008\">10.1016/j.jsc.2016.03.008</a>.","chicago":"Bauer, Ulrich, Michael Kerber, Jan Reininghaus, and Hubert Wagner. “Phat - Persistent Homology Algorithms Toolbox.” <i>Journal of Symbolic Computation</i>. Academic Press, 2017. <a href=\"https://doi.org/10.1016/j.jsc.2016.03.008\">https://doi.org/10.1016/j.jsc.2016.03.008</a>."},"year":"2017","doi":"10.1016/j.jsc.2016.03.008","article_type":"original","_id":"1433","external_id":{"isi":["000384396000005"]},"abstract":[{"text":"Phat is an open-source C. ++ library for the computation of persistent homology by matrix reduction, targeted towards developers of software for topological data analysis. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. We provide numerous different reduction strategies as well as data types to store and manipulate the boundary matrix. We compare the different combinations through extensive experimental evaluation and identify optimization techniques that work well in practical situations. We also compare our software with various other publicly available libraries for persistent homology.","lang":"eng"}],"publication_status":"published","page":"76 - 90","department":[{"_id":"HeEd"}],"quality_controlled":"1","volume":78,"publisher":"Academic Press","date_published":"2017-01-01T00:00:00Z","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}]},{"publication_status":"published","abstract":[{"lang":"eng","text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z&lt; r(f) := (g-1(0): ||g - f|| &lt; r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z&lt; r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r &gt; 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C)."}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"},{"name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425","grant_number":"701309"}],"quality_controlled":"1","volume":19,"page":"313 - 342","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"date_published":"2017-01-01T00:00:00Z","publisher":"International Press","publist_id":"7246","citation":{"short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” <i>Homology, Homotopy and Applications</i>, vol. 19, no. 2. International Press, pp. 313–342, 2017.","ama":"Franek P, Krcál M. Persistence of zero sets. <i>Homology, Homotopy and Applications</i>. 2017;19(2):313-342. doi:<a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">10.4310/HHA.2017.v19.n2.a16</a>","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” <i>Homology, Homotopy and Applications</i>, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:<a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">10.4310/HHA.2017.v19.n2.a16</a>.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” <i>Homology, Homotopy and Applications</i>. International Press, 2017. <a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">https://doi.org/10.4310/HHA.2017.v19.n2.a16</a>.","apa":"Franek, P., &#38; Krcál, M. (2017). Persistence of zero sets. <i>Homology, Homotopy and Applications</i>. International Press. <a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">https://doi.org/10.4310/HHA.2017.v19.n2.a16</a>"},"date_created":"2018-12-11T11:47:14Z","year":"2017","ec_funded":1,"_id":"568","doi":"10.4310/HHA.2017.v19.n2.a16","author":[{"first_name":"Peter","full_name":"Franek, Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"day":"01","oa_version":"Submitted Version","publication_identifier":{"issn":["15320073"]},"month":"01","status":"public","type":"journal_article","title":"Persistence of zero sets","issue":"2","oa":1,"date_updated":"2021-01-12T08:03:12Z","intvolume":"        19","scopus_import":1,"language":[{"iso":"eng"}],"publication":"Homology, Homotopy and Applications"},{"abstract":[{"text":"Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.","lang":"eng"}],"publication_status":"published","place":"Cham","department":[{"_id":"HeEd"}],"page":"93-104","extern":"1","volume":10256,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2017-05-17T00:00:00Z","date_created":"2019-01-08T20:42:56Z","citation":{"ama":"Biswas R, Bhowmick P. Construction of persistent Voronoi diagram on 3D digital plane. In: <i>Combinatorial Image Analysis</i>. Vol 10256. Cham: Springer Nature; 2017:93-104. doi:<a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">10.1007/978-3-319-59108-7_8</a>","ieee":"R. Biswas and P. Bhowmick, “Construction of persistent Voronoi diagram on 3D digital plane,” in <i>Combinatorial image analysis</i>, vol. 10256, Cham: Springer Nature, 2017, pp. 93–104.","short":"R. Biswas, P. Bhowmick, in:, Combinatorial Image Analysis, Springer Nature, Cham, 2017, pp. 93–104.","chicago":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” In <i>Combinatorial Image Analysis</i>, 10256:93–104. Cham: Springer Nature, 2017. <a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">https://doi.org/10.1007/978-3-319-59108-7_8</a>.","ista":"Biswas R, Bhowmick P. 2017.Construction of persistent Voronoi diagram on 3D digital plane. In: Combinatorial image analysis. LNCS, vol. 10256, 93–104.","mla":"Biswas, Ranita, and Partha Bhowmick. “Construction of Persistent Voronoi Diagram on 3D Digital Plane.” <i>Combinatorial Image Analysis</i>, vol. 10256, Springer Nature, 2017, pp. 93–104, doi:<a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">10.1007/978-3-319-59108-7_8</a>.","apa":"Biswas, R., &#38; Bhowmick, P. (2017). Construction of persistent Voronoi diagram on 3D digital plane. In <i>Combinatorial image analysis</i> (Vol. 10256, pp. 93–104). Cham: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-319-59108-7_8\">https://doi.org/10.1007/978-3-319-59108-7_8</a>"},"year":"2017","doi":"10.1007/978-3-319-59108-7_8","_id":"5803","day":"17","oa_version":"None","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","conference":{"start_date":"2017-06-19","name":"IWCIA: International Workshop on Combinatorial Image Analysis","end_date":"2017-06-21","location":"Plovdiv, Bulgaria"},"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["978-3-319-59107-0","978-3-319-59108-7"]},"month":"05","author":[{"first_name":"Ranita","full_name":"Biswas, Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","orcid":"0000-0002-5372-7890"},{"full_name":"Bhowmick, Partha","first_name":"Partha","last_name":"Bhowmick"}],"alternative_title":["LNCS"],"status":"public","type":"book_chapter","intvolume":"     10256","title":"Construction of persistent Voronoi diagram on 3D digital plane","date_updated":"2022-01-28T07:48:24Z","article_processing_charge":"No","publication":"Combinatorial image analysis","language":[{"iso":"eng"}]}]