[{"author":[{"full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy"},{"full_name":"Fedorov, Roman","last_name":"Fedorov","first_name":"Roman"}],"volume":147,"date_created":"2019-02-24T22:59:19Z","date_updated":"2023-08-24T14:48:59Z","year":"2019","publisher":"AMS","department":[{"_id":"HeEd"}],"publication_status":"published","month":"01","doi":"10.1090/proc/14240","language":[{"iso":"eng"}],"external_id":{"arxiv":["1709.02562"],"isi":["000450363900008"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1709.02562"}],"isi":1,"quality_controlled":"1","abstract":[{"lang":"eng","text":"We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely many families of pairs of circles for which such construction is possible. "}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6050","intvolume":" 147","status":"public","title":"Two circles and only a straightedge","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2019-01-01T00:00:00Z","citation":{"ama":"Akopyan A, Fedorov R. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 2019;147:91-102. doi:10.1090/proc/14240","ista":"Akopyan A, Fedorov R. 2019. Two circles and only a straightedge. Proceedings of the American Mathematical Society. 147, 91–102.","ieee":"A. Akopyan and R. Fedorov, “Two circles and only a straightedge,” Proceedings of the American Mathematical Society, vol. 147. AMS, pp. 91–102, 2019.","apa":"Akopyan, A., & Fedorov, R. (2019). Two circles and only a straightedge. Proceedings of the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14240","mla":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society, vol. 147, AMS, 2019, pp. 91–102, doi:10.1090/proc/14240.","short":"A. Akopyan, R. Fedorov, Proceedings of the American Mathematical Society 147 (2019) 91–102.","chicago":"Akopyan, Arseniy, and Roman Fedorov. “Two Circles and Only a Straightedge.” Proceedings of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14240."},"publication":"Proceedings of the American Mathematical Society","page":"91-102"},{"author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"},{"full_name":"Hubard, Alfredo","first_name":"Alfredo","last_name":"Hubard"},{"first_name":"Roman","last_name":"Karasev","full_name":"Karasev, Roman"}],"volume":53,"date_updated":"2023-08-29T06:32:48Z","date_created":"2019-07-14T21:59:19Z","year":"2019","publisher":"Akademicka Platforma Czasopism","department":[{"_id":"HeEd"}],"publication_status":"published","ec_funded":1,"doi":"10.12775/TMNA.2019.008","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1612.06926","open_access":"1"}],"external_id":{"arxiv":["1612.06926"],"isi":["000472541600004"]},"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"isi":1,"quality_controlled":"1","month":"06","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6634","intvolume":" 53","status":"public","title":"Lower and upper bounds for the waists of different spaces","issue":"2","abstract":[{"text":"In this paper we prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk-Ulam-Crofton technique, consider waists of real and complex projective spaces, flat tori, convex bodies in Euclidean space; and establish waist-type results in terms of the Hausdorff measure.","lang":"eng"}],"type":"journal_article","date_published":"2019-06-01T00:00:00Z","citation":{"mla":"Akopyan, Arseniy, et al. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis, vol. 53, no. 2, Akademicka Platforma Czasopism, 2019, pp. 457–90, doi:10.12775/TMNA.2019.008.","short":"A. Akopyan, A. Hubard, R. Karasev, Topological Methods in Nonlinear Analysis 53 (2019) 457–490.","chicago":"Akopyan, Arseniy, Alfredo Hubard, and Roman Karasev. “Lower and Upper Bounds for the Waists of Different Spaces.” Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism, 2019. https://doi.org/10.12775/TMNA.2019.008.","ama":"Akopyan A, Hubard A, Karasev R. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 2019;53(2):457-490. doi:10.12775/TMNA.2019.008","ista":"Akopyan A, Hubard A, Karasev R. 2019. Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. 53(2), 457–490.","ieee":"A. Akopyan, A. Hubard, and R. Karasev, “Lower and upper bounds for the waists of different spaces,” Topological Methods in Nonlinear Analysis, vol. 53, no. 2. Akademicka Platforma Czasopism, pp. 457–490, 2019.","apa":"Akopyan, A., Hubard, A., & Karasev, R. (2019). Lower and upper bounds for the waists of different spaces. Topological Methods in Nonlinear Analysis. Akademicka Platforma Czasopism. https://doi.org/10.12775/TMNA.2019.008"},"publication":"Topological Methods in Nonlinear Analysis","page":"457-490","article_processing_charge":"No","day":"01","scopus_import":"1"},{"abstract":[{"lang":"eng","text":"We study the topology generated by the temperature fluctuations of the cosmic microwave background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the ΛCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over 𝕊2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of “masks” is of importance, we introduce the concept of relative homology. The parametric χ2-test shows differences between observations and simulations, yielding p-values at percent to less than permil levels roughly between 2 and 7°, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b0 and b1 is approximately between 3σ and 4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66° in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and first Betti numbers, respectively. Further, since these topological descriptors show consistent anomalous behaviour over independent measurements of Planck and WMAP, instrumental and systematic errors may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations based on power-spectrum matching the characteristics of the observed dipped power spectrum are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB, whether cosmological in nature or arising due to late-time effects, is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate the study of primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology, including topological defect models."}],"type":"journal_article","oa_version":"Published Version","file":[{"file_name":"2019_AstronomyAstrophysics_Pranav.pdf","access_level":"open_access","file_size":14420451,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"6766","date_updated":"2020-07-14T12:47:39Z","date_created":"2019-08-05T08:08:59Z","checksum":"83b9209ed9eefbdcefd89019c5a97805"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6756","ddc":["520","530"],"status":"public","title":"Unexpected topology of the temperature fluctuations in the cosmic microwave background","intvolume":" 627","day":"17","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_published":"2019-07-17T00:00:00Z","publication":"Astronomy and Astrophysics","citation":{"ista":"Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.","apa":"Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman, A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. EDP Sciences. https://doi.org/10.1051/0004-6361/201834916","ieee":"P. Pranav et al., “Unexpected topology of the temperature fluctuations in the cosmic microwave background,” Astronomy and Astrophysics, vol. 627. EDP Sciences, 2019.","ama":"Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature fluctuations in the cosmic microwave background. Astronomy and Astrophysics. 2019;627. doi:10.1051/0004-6361/201834916","chicago":"Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner, Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics. EDP Sciences, 2019. https://doi.org/10.1051/0004-6361/201834916.","mla":"Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.” Astronomy and Astrophysics, vol. 627, A163, EDP Sciences, 2019, doi:10.1051/0004-6361/201834916.","short":"P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman, H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019)."},"article_type":"original","file_date_updated":"2020-07-14T12:47:39Z","article_number":"A163","author":[{"full_name":"Pranav, Pratyush","first_name":"Pratyush","last_name":"Pranav"},{"last_name":"Adler","first_name":"Robert J.","full_name":"Adler, Robert J."},{"last_name":"Buchert","first_name":"Thomas","full_name":"Buchert, Thomas"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Jones, Bernard J.T.","first_name":"Bernard J.T.","last_name":"Jones"},{"last_name":"Schwartzman","first_name":"Armin","full_name":"Schwartzman, Armin"},{"full_name":"Wagner, Hubert","last_name":"Wagner","first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Van De Weygaert, Rien","last_name":"Van De Weygaert","first_name":"Rien"}],"date_updated":"2023-08-29T07:01:48Z","date_created":"2019-08-04T21:59:18Z","volume":627,"year":"2019","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"EDP Sciences","month":"07","publication_identifier":{"issn":["00046361"],"eissn":["14320746"]},"doi":"10.1051/0004-6361/201834916","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000475839300003"],"arxiv":["1812.07678"]},"quality_controlled":"1","isi":1,"project":[{"_id":"265683E4-B435-11E9-9278-68D0E5697425","grant_number":"M62909-18-1-2038","name":"Toward Computational Information Topology"},{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}]},{"ec_funded":1,"year":"2019","department":[{"_id":"HeEd"}],"publisher":"London Mathematical Society","publication_status":"published","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"first_name":"Ivan","last_name":"Izmestiev","full_name":"Izmestiev, Ivan"}],"volume":51,"date_created":"2019-08-11T21:59:23Z","date_updated":"2023-08-29T07:08:34Z","publication_identifier":{"issn":["00246093"],"eissn":["14692120"]},"month":"10","external_id":{"arxiv":["1903.04929"],"isi":["000478560200001"]},"main_file_link":[{"url":"https://arxiv.org/abs/1903.04929","open_access":"1"}],"oa":1,"project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"}],"isi":1,"quality_controlled":"1","doi":"10.1112/blms.12276","language":[{"iso":"eng"}],"type":"journal_article","issue":"5","abstract":[{"text":"The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here, we give a simple geometric proof of Regge symmetries in Euclidean, spherical, and hyperbolic geometry.","lang":"eng"}],"_id":"6793","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 51","title":"The Regge symmetry, confocal conics, and the Schläfli formula","status":"public","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"ama":"Akopyan A, Izmestiev I. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 2019;51(5):765-775. doi:10.1112/blms.12276","apa":"Akopyan, A., & Izmestiev, I. (2019). The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12276","ieee":"A. Akopyan and I. Izmestiev, “The Regge symmetry, confocal conics, and the Schläfli formula,” Bulletin of the London Mathematical Society, vol. 51, no. 5. London Mathematical Society, pp. 765–775, 2019.","ista":"Akopyan A, Izmestiev I. 2019. The Regge symmetry, confocal conics, and the Schläfli formula. Bulletin of the London Mathematical Society. 51(5), 765–775.","short":"A. Akopyan, I. Izmestiev, Bulletin of the London Mathematical Society 51 (2019) 765–775.","mla":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society, vol. 51, no. 5, London Mathematical Society, 2019, pp. 765–75, doi:10.1112/blms.12276.","chicago":"Akopyan, Arseniy, and Ivan Izmestiev. “The Regge Symmetry, Confocal Conics, and the Schläfli Formula.” Bulletin of the London Mathematical Society. London Mathematical Society, 2019. https://doi.org/10.1112/blms.12276."},"publication":"Bulletin of the London Mathematical Society","page":"765-775","article_type":"original","date_published":"2019-10-01T00:00:00Z"},{"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1805.04676","open_access":"1"}],"external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"quality_controlled":"1","isi":1,"doi":"10.1016/j.jalgebra.2019.07.027","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"issn":["0021-8693"]},"year":"2019","publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"author":[{"full_name":"Brown, Adam","last_name":"Brown","first_name":"Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"}],"date_created":"2019-08-22T07:54:13Z","date_updated":"2023-08-29T07:11:47Z","volume":538,"publication":"Journal of Algebra","citation":{"ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 2019;538:261-289. doi:10.1016/j.jalgebra.2019.07.027","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. Elsevier. https://doi.org/10.1016/j.jalgebra.2019.07.027","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” Journal of Algebra, vol. 538. Elsevier, pp. 261–289, 2019.","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289.","short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra, vol. 538, Elsevier, 2019, pp. 261–89, doi:10.1016/j.jalgebra.2019.07.027.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” Journal of Algebra. Elsevier, 2019. https://doi.org/10.1016/j.jalgebra.2019.07.027."},"article_type":"original","page":"261-289","date_published":"2019-11-15T00:00:00Z","day":"15","article_processing_charge":"No","_id":"6828","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"Arakawa-Suzuki functors for Whittaker modules","intvolume":" 538","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group ."}]},{"quality_controlled":"1","isi":1,"publication":"2019 IEEE Intelligent Transportation Systems Conference","external_id":{"isi":["000521238102050"]},"citation":{"short":"G.F. Osang, J. Cook, A. Fabrikant, M. Gruteser, in:, 2019 IEEE Intelligent Transportation Systems Conference, IEEE, 2019.","mla":"Osang, Georg F., et al. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” 2019 IEEE Intelligent Transportation Systems Conference, 8917514, IEEE, 2019, doi:10.1109/ITSC.2019.8917514.","chicago":"Osang, Georg F, James Cook, Alex Fabrikant, and Marco Gruteser. “LiveTraVeL: Real-Time Matching of Transit Vehicle Trajectories to Transit Routes at Scale.” In 2019 IEEE Intelligent Transportation Systems Conference. IEEE, 2019. https://doi.org/10.1109/ITSC.2019.8917514.","ama":"Osang GF, Cook J, Fabrikant A, Gruteser M. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In: 2019 IEEE Intelligent Transportation Systems Conference. IEEE; 2019. doi:10.1109/ITSC.2019.8917514","ieee":"G. F. Osang, J. Cook, A. Fabrikant, and M. Gruteser, “LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale,” in 2019 IEEE Intelligent Transportation Systems Conference, Auckland, New Zealand, 2019.","apa":"Osang, G. F., Cook, J., Fabrikant, A., & Gruteser, M. (2019). LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. In 2019 IEEE Intelligent Transportation Systems Conference. Auckland, New Zealand: IEEE. https://doi.org/10.1109/ITSC.2019.8917514","ista":"Osang GF, Cook J, Fabrikant A, Gruteser M. 2019. LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale. 2019 IEEE Intelligent Transportation Systems Conference. ITSC: Intelligent Transportation Systems Conference, 8917514."},"language":[{"iso":"eng"}],"conference":{"location":"Auckland, New Zealand","start_date":"2019-10-27","end_date":"2019-10-30","name":"ITSC: Intelligent Transportation Systems Conference"},"date_published":"2019-11-28T00:00:00Z","doi":"10.1109/ITSC.2019.8917514","scopus_import":"1","month":"11","day":"28","article_processing_charge":"No","publication_identifier":{"isbn":["9781538670248"]},"title":"LiveTraVeL: Real-time matching of transit vehicle trajectories to transit routes at scale","status":"public","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"IEEE","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"7216","year":"2019","date_updated":"2023-09-06T14:50:28Z","date_created":"2019-12-29T23:00:47Z","oa_version":"None","author":[{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","first_name":"Georg F"},{"first_name":"James","last_name":"Cook","full_name":"Cook, James"},{"first_name":"Alex","last_name":"Fabrikant","full_name":"Fabrikant, Alex"},{"full_name":"Gruteser, Marco","last_name":"Gruteser","first_name":"Marco"}],"article_number":"8917514","type":"conference","abstract":[{"lang":"eng","text":"We present LiveTraVeL (Live Transit Vehicle Labeling), a real-time system to label a stream of noisy observations of transit vehicle trajectories with the transit routes they are serving (e.g., northbound bus #5). In order to scale efficiently to large transit networks, our system first retrieves a small set of candidate routes from a geometrically indexed data structure, then applies a fine-grained scoring step to choose the best match. Given that real-time data remains unavailable for the majority of the world’s transit agencies, these inferences can help feed a real-time map of a transit system’s trips, infer transit trip delays in real time, or measure and correct noisy transit tracking data. This system can run on vehicle observations from a variety of sources that don’t attach route information to vehicle observations, such as public imagery streams or user-contributed transit vehicle sightings.We abstract away the specifics of the sensing system and demonstrate the effectiveness of our system on a \"semisynthetic\" dataset of all New York City buses, where we simulate sensed trajectories by starting with fully labeled vehicle trajectories reported via the GTFS-Realtime protocol, removing the transit route IDs, and perturbing locations with synthetic noise. Using just the geometric shapes of the trajectories, we demonstrate that our system converges on the correct route ID within a few minutes, even after a vehicle switches from serving one trip to the next."}]},{"_id":"5678","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 62","status":"public","title":"Poisson–Delaunay Mosaics of Order k","ddc":["516"],"file":[{"access_level":"open_access","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","file_size":599339,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"5932","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","date_created":"2019-02-06T10:10:46Z","date_updated":"2020-07-14T12:47:10Z"}],"oa_version":"Published Version","type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold."}],"citation":{"apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2."},"publication":"Discrete and Computational Geometry","page":"865–878","article_type":"original","date_published":"2019-12-01T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","year":"2019","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"full_name":"Nikitenko, Anton","first_name":"Anton","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"}],"volume":62,"date_created":"2018-12-16T22:59:20Z","date_updated":"2023-09-07T12:07:12Z","ec_funded":1,"file_date_updated":"2020-07-14T12:47:10Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"project":[{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00454-018-0049-2","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"month":"12"},{"abstract":[{"lang":"eng","text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram."}],"type":"journal_article","file":[{"checksum":"7c99be505dc7533257d42eb1830cef04","date_created":"2019-07-08T15:24:26Z","date_updated":"2020-07-14T12:47:34Z","relation":"main_file","file_id":"6624","content_type":"application/pdf","file_size":2665013,"creator":"kschuh","access_level":"open_access","file_name":"Elsevier_2019_Edelsbrunner.pdf"}],"oa_version":"Published Version","title":"Holes and dependences in an ordered complex","status":"public","ddc":["000"],"intvolume":" 73","_id":"6608","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_published":"2019-08-01T00:00:00Z","page":"1-15","publication":"Computer Aided Geometric Design","citation":{"chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design. Elsevier, 2019. https://doi.org/10.1016/j.cagd.2019.06.003.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” Computer Aided Geometric Design, vol. 73, Elsevier, 2019, pp. 1–15, doi:10.1016/j.cagd.2019.06.003.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” Computer Aided Geometric Design, vol. 73. Elsevier, pp. 1–15, 2019.","apa":"Edelsbrunner, H., & Ölsböck, K. (2019). Holes and dependences in an ordered complex. Computer Aided Geometric Design. Elsevier. https://doi.org/10.1016/j.cagd.2019.06.003","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 2019;73:1-15. doi:10.1016/j.cagd.2019.06.003"},"file_date_updated":"2020-07-14T12:47:34Z","ec_funded":1,"date_created":"2019-07-07T21:59:20Z","date_updated":"2023-09-07T13:15:29Z","volume":73,"author":[{"last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297","full_name":"Ölsböck, Katharina"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7460"}]},"publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"year":"2019","month":"08","language":[{"iso":"eng"}],"doi":"10.1016/j.cagd.2019.06.003","isi":1,"quality_controlled":"1","project":[{"name":"Alpha Shape Theory Extended","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"external_id":{"isi":["000485207800001"]}},{"related_material":{"record":[{"id":"7944","relation":"dissertation_contains","status":"public"},{"status":"public","relation":"later_version","id":"12833"}]},"author":[{"first_name":"Ahmad","last_name":"Biniaz","full_name":"Biniaz, Ahmad"},{"full_name":"Jain, Kshitij","first_name":"Kshitij","last_name":"Jain"},{"full_name":"Lubiw, Anna","last_name":"Lubiw","first_name":"Anna"},{"first_name":"Zuzana","last_name":"Masárová","id":"45CFE238-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6660-1322","full_name":"Masárová, Zuzana"},{"full_name":"Miltzow, Tillmann","first_name":"Tillmann","last_name":"Miltzow"},{"first_name":"Debajyoti","last_name":"Mondal","full_name":"Mondal, Debajyoti"},{"full_name":"Naredla, Anurag Murty","first_name":"Anurag Murty","last_name":"Naredla"},{"last_name":"Tkadlec","first_name":"Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","full_name":"Tkadlec, Josef"},{"first_name":"Alexi","last_name":"Turcotte","full_name":"Turcotte, Alexi"}],"oa_version":"Preprint","date_updated":"2024-01-04T12:42:08Z","date_created":"2020-06-08T12:25:25Z","_id":"7950","year":"2019","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"},{"_id":"UlWa"},{"_id":"KrCh"}],"status":"public","publication_status":"submitted","title":"Token swapping on trees","abstract":[{"text":"The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.","lang":"eng"}],"type":"preprint","article_number":"1903.06981","date_published":"2019-03-16T00:00:00Z","language":[{"iso":"eng"}],"citation":{"ista":"Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981.","ieee":"A. Biniaz et al., “Token swapping on trees,” arXiv. .","apa":"Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv.","ama":"Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv.","chicago":"Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d.","mla":"Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981.","short":"A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.)."},"main_file_link":[{"url":"https://arxiv.org/abs/1903.06981","open_access":"1"}],"external_id":{"arxiv":["1903.06981"]},"oa":1,"publication":"arXiv","article_processing_charge":"No","day":"16","month":"03"},{"oa_version":"Published Version","file":[{"creator":"dernst","content_type":"application/pdf","file_size":489080,"file_name":"2018_LIPIcs_Edelsbrunner.pdf","access_level":"open_access","date_created":"2018-12-17T16:31:31Z","date_updated":"2020-07-14T12:45:20Z","checksum":"7509403803b3ac1aee94bbc2ad293d21","file_id":"5724","relation":"main_file"}],"_id":"188","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 99","title":"Smallest enclosing spheres and Chernoff points in Bregman geometry","status":"public","ddc":["000"],"abstract":[{"text":"Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.","lang":"eng"}],"type":"conference","alternative_title":["Leibniz International Proceedings in Information, LIPIcs"],"date_published":"2018-06-11T00:00:00Z","citation":{"ama":"Edelsbrunner H, Virk Z, Wagner H. Smallest enclosing spheres and Chernoff points in Bregman geometry. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:35:1-35:13. doi:10.4230/LIPIcs.SoCG.2018.35","ieee":"H. Edelsbrunner, Z. Virk, and H. Wagner, “Smallest enclosing spheres and Chernoff points in Bregman geometry,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 35:1-35:13.","apa":"Edelsbrunner, H., Virk, Z., & Wagner, H. (2018). Smallest enclosing spheres and Chernoff points in Bregman geometry (Vol. 99, p. 35:1-35:13). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.35","ista":"Edelsbrunner H, Virk Z, Wagner H. 2018. Smallest enclosing spheres and Chernoff points in Bregman geometry. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 35:1-35:13.","short":"H. Edelsbrunner, Z. Virk, H. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13.","mla":"Edelsbrunner, Herbert, et al. Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 35:1-35:13, doi:10.4230/LIPIcs.SoCG.2018.35.","chicago":"Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Smallest Enclosing Spheres and Chernoff Points in Bregman Geometry,” 99:35:1-35:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.35."},"page":"35:1 - 35:13","has_accepted_license":"1","day":"11","scopus_import":1,"author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Virk, Ziga","last_name":"Virk","first_name":"Ziga"},{"full_name":"Wagner, Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Hubert"}],"volume":99,"date_updated":"2021-01-12T06:53:48Z","date_created":"2018-12-11T11:45:05Z","acknowledgement":"This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund","year":"2018","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"publication_status":"published","publist_id":"7733","file_date_updated":"2020-07-14T12:45:20Z","doi":"10.4230/LIPIcs.SoCG.2018.35","conference":{"end_date":"2018-06-14","start_date":"2018-06-11","location":"Budapest, Hungary","name":"SoCG: Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","month":"06"},{"abstract":[{"lang":"eng","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."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"pubrep_id":"1026","oa_version":"Published Version","file":[{"file_name":"IST-2018-1025-v2+5_ist-thesis-iglesias-11June2018(1).zip","access_level":"closed","file_size":11827713,"content_type":"application/zip","creator":"kschuh","relation":"source_file","file_id":"5918","date_created":"2019-02-05T07:43:31Z","date_updated":"2020-07-14T12:45:24Z","checksum":"dd699303623e96d1478a6ae07210dd05"},{"creator":"kschuh","file_size":4783846,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2018-1025-v2+4_ThesisIglesiasFinal11June2018.pdf","checksum":"ba163849a190d2b41d66fef0e4983294","date_created":"2019-02-05T07:43:45Z","date_updated":"2020-07-14T12:45:24Z","file_id":"5919","relation":"main_file"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"201","title":"Multiple covers with balls","ddc":["514","516"],"status":"public","article_processing_charge":"No","has_accepted_license":"1","day":"11","date_published":"2018-06-11T00:00:00Z","citation":{"mla":"Iglesias Ham, Mabel. Multiple Covers with Balls. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1026.","short":"M. Iglesias Ham, Multiple Covers with Balls, Institute of Science and Technology Austria, 2018.","chicago":"Iglesias Ham, Mabel. “Multiple Covers with Balls.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1026.","ama":"Iglesias Ham M. Multiple covers with balls. 2018. doi:10.15479/AT:ISTA:th_1026","ista":"Iglesias Ham M. 2018. Multiple covers with balls. Institute of Science and Technology Austria.","apa":"Iglesias Ham, M. (2018). Multiple covers with balls. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1026","ieee":"M. Iglesias Ham, “Multiple covers with balls,” Institute of Science and Technology Austria, 2018."},"page":"171","publist_id":"7712","file_date_updated":"2020-07-14T12:45:24Z","author":[{"full_name":"Iglesias Ham, Mabel","first_name":"Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:45:10Z","date_updated":"2023-09-07T12:25:32Z","year":"2018","publisher":"Institute of Science and Technology Austria","department":[{"_id":"HeEd"}],"publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"month":"06","doi":"10.15479/AT:ISTA:th_1026","language":[{"iso":"eng"}],"supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"degree_awarded":"PhD","oa":1},{"day":"11","has_accepted_license":"1","scopus_import":1,"date_published":"2018-06-11T00:00:00Z","citation":{"ama":"Edelsbrunner H, Osang GF. The multi-cover persistence of Euclidean balls. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.34","ista":"Edelsbrunner H, Osang GF. 2018. The multi-cover persistence of Euclidean balls. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 34.","apa":"Edelsbrunner, H., & Osang, G. F. (2018). The multi-cover persistence of Euclidean balls (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.34","ieee":"H. Edelsbrunner and G. F. Osang, “The multi-cover persistence of Euclidean balls,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. The Multi-Cover Persistence of Euclidean Balls. Vol. 99, 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.34.","short":"H. Edelsbrunner, G.F. Osang, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “The Multi-Cover Persistence of Euclidean Balls,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.34."},"abstract":[{"text":"Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers. ","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"file":[{"date_created":"2018-12-18T09:27:22Z","date_updated":"2020-07-14T12:45:19Z","checksum":"d8c0533ad0018eb4ed1077475eb8fc18","relation":"main_file","file_id":"5738","file_size":528018,"content_type":"application/pdf","creator":"dernst","file_name":"2018_LIPIcs_Edelsbrunner_Osang.pdf","access_level":"open_access"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"187","status":"public","ddc":["516"],"title":"The multi-cover persistence of Euclidean balls","intvolume":" 99","month":"06","conference":{"end_date":"2018-06-14","start_date":"2018-06-11","location":"Budapest, Hungary","name":"SoCG: Symposium on Computational Geometry"},"doi":"10.4230/LIPIcs.SoCG.2018.34","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","project":[{"name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"file_date_updated":"2020-07-14T12:45:19Z","publist_id":"7732","article_number":"34","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8882-5116"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"9317"},{"id":"9056","relation":"dissertation_contains","status":"public"}]},"date_created":"2018-12-11T11:45:05Z","date_updated":"2023-09-07T13:29:00Z","volume":99,"acknowledgement":"This work is partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF).","year":"2018","publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}]},{"date_published":"2018-06-01T00:00:00Z","page":"55 - 64","article_type":"original","citation":{"short":"A. Akopyan, Geometriae Dedicata 194 (2018) 55–64.","mla":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata, vol. 194, no. 1, Springer, 2018, pp. 55–64, doi:10.1007/s10711-017-0265-6.","chicago":"Akopyan, Arseniy. “3-Webs Generated by Confocal Conics and Circles.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0265-6.","ama":"Akopyan A. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 2018;194(1):55-64. doi:10.1007/s10711-017-0265-6","apa":"Akopyan, A. (2018). 3-Webs generated by confocal conics and circles. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0265-6","ieee":"A. Akopyan, “3-Webs generated by confocal conics and circles,” Geometriae Dedicata, vol. 194, no. 1. Springer, pp. 55–64, 2018.","ista":"Akopyan A. 2018. 3-Webs generated by confocal conics and circles. Geometriae Dedicata. 194(1), 55–64."},"publication":"Geometriae Dedicata","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","scopus_import":"1","file":[{"creator":"kschuh","content_type":"application/pdf","file_size":1140860,"access_level":"open_access","file_name":"2018_Springer_Akopyan.pdf","checksum":"1febcfc1266486053a069e3425ea3713","date_created":"2020-01-03T11:35:08Z","date_updated":"2020-07-14T12:47:44Z","file_id":"7222","relation":"main_file"}],"oa_version":"Published Version","intvolume":" 194","ddc":["510"],"title":"3-Webs generated by confocal conics and circles","status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"692","issue":"1","abstract":[{"lang":"eng","text":"We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas describing them."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s10711-017-0265-6","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000431418800004"]},"month":"06","volume":194,"date_updated":"2023-09-08T11:40:29Z","date_created":"2018-12-11T11:47:57Z","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"}],"publisher":"Springer","department":[{"_id":"HeEd"}],"publication_status":"published","year":"2018","publist_id":"7014","ec_funded":1,"file_date_updated":"2020-07-14T12:47:44Z"},{"ec_funded":1,"publist_id":"7996","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"full_name":"Segal Halevi, Erel","first_name":"Erel","last_name":"Segal Halevi"}],"date_updated":"2023-09-11T12:48:39Z","date_created":"2018-12-11T11:44:24Z","volume":32,"year":"2018","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"month":"09","doi":"10.1137/16M110407X","language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000450810500036"],"arxiv":["1604.00960"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1604.00960"}],"quality_controlled":"1","isi":1,"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"abstract":[{"lang":"eng","text":"Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" 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."}],"issue":"3","type":"journal_article","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"58","title":"Counting blanks in polygonal arrangements","status":"public","intvolume":" 32","day":"06","article_processing_charge":"No","scopus_import":"1","date_published":"2018-09-06T00:00:00Z","publication":"SIAM Journal on Discrete Mathematics","citation":{"ista":"Akopyan A, Segal Halevi E. 2018. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 32(3), 2242–2257.","apa":"Akopyan, A., & Segal Halevi, E. (2018). Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M110407X","ieee":"A. Akopyan and E. Segal Halevi, “Counting blanks in polygonal arrangements,” SIAM Journal on Discrete Mathematics, vol. 32, no. 3. Society for Industrial and Applied Mathematics , pp. 2242–2257, 2018.","ama":"Akopyan A, Segal Halevi E. Counting blanks in polygonal arrangements. SIAM Journal on Discrete Mathematics. 2018;32(3):2242-2257. doi:10.1137/16M110407X","chicago":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M110407X.","mla":"Akopyan, Arseniy, and Erel Segal Halevi. “Counting Blanks in Polygonal Arrangements.” SIAM Journal on Discrete Mathematics, vol. 32, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 2242–57, doi:10.1137/16M110407X.","short":"A. Akopyan, E. Segal Halevi, SIAM Journal on Discrete Mathematics 32 (2018) 2242–2257."},"page":"2242 - 2257"},{"oa_version":"Preprint","_id":"458","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Incircular nets and confocal conics","intvolume":" 370","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"}],"issue":"4","type":"journal_article","date_published":"2018-04-01T00:00:00Z","publication":"Transactions of the American Mathematical Society","citation":{"ieee":"A. Akopyan and A. Bobenko, “Incircular nets and confocal conics,” Transactions of the American Mathematical Society, vol. 370, no. 4. American Mathematical Society, pp. 2825–2854, 2018.","apa":"Akopyan, A., & Bobenko, A. (2018). Incircular nets and confocal conics. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7292","ista":"Akopyan A, Bobenko A. 2018. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 370(4), 2825–2854.","ama":"Akopyan A, Bobenko A. Incircular nets and confocal conics. Transactions of the American Mathematical Society. 2018;370(4):2825-2854. doi:10.1090/tran/7292","chicago":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society. American Mathematical Society, 2018. https://doi.org/10.1090/tran/7292.","short":"A. Akopyan, A. Bobenko, Transactions of the American Mathematical Society 370 (2018) 2825–2854.","mla":"Akopyan, Arseniy, and Alexander Bobenko. “Incircular Nets and Confocal Conics.” Transactions of the American Mathematical Society, vol. 370, no. 4, American Mathematical Society, 2018, pp. 2825–54, doi:10.1090/tran/7292."},"page":"2825 - 2854","day":"01","article_processing_charge":"No","scopus_import":"1","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"full_name":"Bobenko, Alexander","last_name":"Bobenko","first_name":"Alexander"}],"date_updated":"2023-09-11T14:19:12Z","date_created":"2018-12-11T11:46:35Z","volume":370,"year":"2018","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]","publication_status":"published","department":[{"_id":"HeEd"}],"publisher":"American Mathematical Society","ec_funded":1,"publist_id":"7363","doi":"10.1090/tran/7292","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1602.04637","open_access":"1"}],"external_id":{"isi":["000423197800019"]},"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"month":"04"},{"publist_id":"7948","author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Petrunin","first_name":"Anton","full_name":"Petrunin, Anton"}],"volume":40,"date_created":"2018-12-11T11:44:40Z","date_updated":"2023-09-13T08:49:16Z","year":"2018","department":[{"_id":"HeEd"}],"publisher":"Springer","publication_status":"published","month":"09","doi":"10.1007/s00283-018-9795-5","language":[{"iso":"eng"}],"external_id":{"arxiv":["1702.05172"],"isi":["000444141200005"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1702.05172"}],"isi":1,"quality_controlled":"1","issue":"3","abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"106","intvolume":" 40","title":"Long geodesics on convex surfaces","status":"public","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2018-09-01T00:00:00Z","citation":{"chicago":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer. Springer, 2018. https://doi.org/10.1007/s00283-018-9795-5.","mla":"Akopyan, Arseniy, and Anton Petrunin. “Long Geodesics on Convex Surfaces.” Mathematical Intelligencer, vol. 40, no. 3, Springer, 2018, pp. 26–31, doi:10.1007/s00283-018-9795-5.","short":"A. Akopyan, A. Petrunin, Mathematical Intelligencer 40 (2018) 26–31.","ista":"Akopyan A, Petrunin A. 2018. Long geodesics on convex surfaces. Mathematical Intelligencer. 40(3), 26–31.","ieee":"A. Akopyan and A. Petrunin, “Long geodesics on convex surfaces,” Mathematical Intelligencer, vol. 40, no. 3. Springer, pp. 26–31, 2018.","apa":"Akopyan, A., & Petrunin, A. (2018). Long geodesics on convex surfaces. Mathematical Intelligencer. Springer. https://doi.org/10.1007/s00283-018-9795-5","ama":"Akopyan A, Petrunin A. Long geodesics on convex surfaces. Mathematical Intelligencer. 2018;40(3):26-31. doi:10.1007/s00283-018-9795-5"},"publication":"Mathematical Intelligencer","page":"26 - 31"},{"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}],"volume":68,"date_updated":"2023-09-13T08:59:00Z","date_created":"2018-12-11T11:46:59Z","year":"2018","department":[{"_id":"HeEd"}],"publisher":"Elsevier","publication_status":"published","publist_id":"7289","ec_funded":1,"file_date_updated":"2020-07-14T12:46:38Z","doi":"10.1016/j.comgeo.2017.06.014","language":[{"iso":"eng"}],"external_id":{"isi":["000415778300010"]},"oa":1,"project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"month":"03","file":[{"checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","date_created":"2019-02-12T06:47:52Z","date_updated":"2020-07-14T12:46:38Z","relation":"main_file","file_id":"5953","content_type":"application/pdf","file_size":708357,"creator":"dernst","access_level":"open_access","file_name":"2018_Edelsbrunner.pdf"}],"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"530","intvolume":" 68","ddc":["000"],"title":"Multiple covers with balls I: Inclusion–exclusion","status":"public","abstract":[{"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.","lang":"eng"}],"type":"journal_article","date_published":"2018-03-01T00:00:00Z","citation":{"chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014"},"publication":"Computational Geometry: Theory and Applications","page":"119 - 133","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":"1"},{"month":"06","doi":"10.1145/3196494.3196534","conference":{"name":"ASIACCS: Asia Conference on Computer and Communications Security ","end_date":"2018-06-08","location":"Incheon, Republic of Korea","start_date":"2018-06-04"},"language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000516620100005"]},"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/783"}],"project":[{"_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","call_identifier":"FP7","name":"Discrete Optimization in Computer Vision: Theory and Practice"},{"grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","call_identifier":"H2020"}],"quality_controlled":"1","isi":1,"ec_funded":1,"publist_id":"7723","author":[{"full_name":"Alwen, Joel F","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","last_name":"Alwen","first_name":"Joel F"},{"full_name":"Gazi, Peter","last_name":"Gazi","first_name":"Peter"},{"full_name":"Kamath Hosdurg, Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","last_name":"Kamath Hosdurg","first_name":"Chethan"},{"full_name":"Klein, Karen","first_name":"Karen","last_name":"Klein","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Osang","first_name":"Georg F","orcid":"0000-0002-8882-5116","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F"},{"full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","last_name":"Pietrzak"},{"first_name":"Lenoid","last_name":"Reyzin","full_name":"Reyzin, Lenoid"},{"full_name":"Rolinek, Michal","first_name":"Michal","last_name":"Rolinek","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Rybar, Michal","id":"2B3E3DE8-F248-11E8-B48F-1D18A9856A87","last_name":"Rybar","first_name":"Michal"}],"date_created":"2018-12-11T11:45:07Z","date_updated":"2023-09-13T09:13:12Z","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.","year":"2018","department":[{"_id":"KrPi"},{"_id":"HeEd"},{"_id":"VlKo"}],"publisher":"ACM","publication_status":"published","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2018-06-01T00:00:00Z","citation":{"mla":"Alwen, Joel F., et al. “On the Memory Hardness of Data Independent Password Hashing Functions.” Proceedings of the 2018 on Asia Conference on Computer and Communication Security, ACM, 2018, pp. 51–65, doi:10.1145/3196494.3196534.","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.","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 Proceedings of the 2018 on Asia Conference on Computer and Communication Security, 51–65. ACM, 2018. https://doi.org/10.1145/3196494.3196534.","ama":"Alwen JF, Gazi P, Kamath Hosdurg C, et al. On the memory hardness of data independent password hashing functions. In: Proceedings of the 2018 on Asia Conference on Computer and Communication Security. ACM; 2018:51-65. doi:10.1145/3196494.3196534","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.","ieee":"J. F. Alwen et al., “On the memory hardness of data independent password hashing functions,” in Proceedings of the 2018 on Asia Conference on Computer and Communication Security, Incheon, Republic of Korea, 2018, pp. 51–65.","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 Proceedings of the 2018 on Asia Conference on Computer and Communication Security (pp. 51–65). Incheon, Republic of Korea: ACM. https://doi.org/10.1145/3196494.3196534"},"publication":"Proceedings of the 2018 on Asia Conference on Computer and Communication Security","page":"51 - 65","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"}],"type":"conference","oa_version":"Submitted Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"193","title":"On the memory hardness of data independent password hashing functions","status":"public"},{"date_published":"2018-03-29T00:00:00Z","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math, vol. 32, no. 1, Society for Industrial and Applied Mathematics , 2018, pp. 750–82, doi:10.1137/16M1097201.","short":"H. Edelsbrunner, M. Iglesias Ham, SIAM J Discrete Math 32 (2018) 750–782.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “On the Optimality of the FCC Lattice for Soft Sphere Packing.” SIAM J Discrete Math. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/16M1097201.","ama":"Edelsbrunner H, Iglesias Ham M. On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. 2018;32(1):750-782. doi:10.1137/16M1097201","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.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). On the optimality of the FCC lattice for soft sphere packing. SIAM J Discrete Math. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/16M1097201","ieee":"H. Edelsbrunner and M. Iglesias Ham, “On the optimality of the FCC lattice for soft sphere packing,” SIAM J Discrete Math, vol. 32, no. 1. Society for Industrial and Applied Mathematics , pp. 750–782, 2018."},"publication":"SIAM J Discrete Math","page":"750 - 782","article_type":"original","article_processing_charge":"No","day":"29","scopus_import":"1","oa_version":"Submitted Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"312","intvolume":" 32","status":"public","title":"On the optimality of the FCC lattice for soft sphere packing","issue":"1","abstract":[{"lang":"eng","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."}],"type":"journal_article","doi":"10.1137/16M1097201","language":[{"iso":"eng"}],"external_id":{"isi":["000428958900038"]},"main_file_link":[{"open_access":"1","url":"http://pdfs.semanticscholar.org/d2d5/6da00fbc674e6a8b1bb9d857167e54200dc6.pdf"}],"oa":1,"project":[{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"quality_controlled":"1","isi":1,"publication_identifier":{"issn":["08954801"]},"month":"03","author":[{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","first_name":"Mabel","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87"}],"volume":32,"date_updated":"2023-09-13T09:34:38Z","date_created":"2018-12-11T11:45:46Z","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","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"HeEd"}],"publication_status":"published","publist_id":"7553"},{"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"409","title":"On the number of non-hexagons in a planar tiling","status":"public","intvolume":" 356","abstract":[{"lang":"eng","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."}],"issue":"4","type":"journal_article","date_published":"2018-04-01T00:00:00Z","publication":"Comptes Rendus Mathematique","citation":{"mla":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique, vol. 356, no. 4, Elsevier, 2018, pp. 412–14, doi:10.1016/j.crma.2018.03.005.","short":"A. Akopyan, Comptes Rendus Mathematique 356 (2018) 412–414.","chicago":"Akopyan, Arseniy. “On the Number of Non-Hexagons in a Planar Tiling.” Comptes Rendus Mathematique. Elsevier, 2018. https://doi.org/10.1016/j.crma.2018.03.005.","ama":"Akopyan A. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 2018;356(4):412-414. doi:10.1016/j.crma.2018.03.005","ista":"Akopyan A. 2018. On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. 356(4), 412–414.","ieee":"A. Akopyan, “On the number of non-hexagons in a planar tiling,” Comptes Rendus Mathematique, vol. 356, no. 4. Elsevier, pp. 412–414, 2018.","apa":"Akopyan, A. (2018). On the number of non-hexagons in a planar tiling. Comptes Rendus Mathematique. Elsevier. https://doi.org/10.1016/j.crma.2018.03.005"},"article_type":"original","page":"412-414","day":"01","article_processing_charge":"No","scopus_import":"1","author":[{"full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan"}],"date_updated":"2023-09-13T09:34:12Z","date_created":"2018-12-11T11:46:19Z","volume":356,"year":"2018","publication_status":"published","publisher":"Elsevier","department":[{"_id":"HeEd"}],"publist_id":"7420","doi":"10.1016/j.crma.2018.03.005","language":[{"iso":"eng"}],"external_id":{"arxiv":["1805.01652"],"isi":["000430402700009"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1805.01652","open_access":"1"}],"quality_controlled":"1","isi":1,"month":"04","publication_identifier":{"issn":["1631073X"]}}]