[{"oa_version":"Preprint","date_created":"2020-07-30T10:45:51Z","date_updated":"2023-09-07T13:12:17Z","related_material":{"record":[{"id":"8156","relation":"dissertation_contains","status":"public"}],"link":[{"url":"https://doi.org/10.1112/mtk.12059","relation":"later_version"}]},"author":[{"first_name":"Sergey","last_name":"Avvakumov","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"department":[{"_id":"UlWa"}],"status":"public","title":"Envy-free division using mapping degree","publication_status":"submitted","_id":"8185","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2019","abstract":[{"text":"In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi, Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment\r\npartition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power.","lang":"eng"}],"type":"preprint","article_number":"1907.11183","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.1907.11183","date_published":"2019-07-25T00:00:00Z","project":[{"grant_number":"P31312","_id":"26611F5C-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Algorithms for Embeddings and Homotopy Theory"}],"oa":1,"citation":{"chicago":"Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1907.11183.","mla":"Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183.","short":"S. Avvakumov, R. Karasev, ArXiv (n.d.).","ista":"Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv, 1907.11183.","apa":"Avvakumov, S., & Karasev, R. (n.d.). Envy-free division using mapping degree. arXiv. https://doi.org/10.48550/arXiv.1907.11183","ieee":"S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv. .","ama":"Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv. doi:10.48550/arXiv.1907.11183"},"external_id":{"arxiv":["1907.11183"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1907.11183"}],"publication":"arXiv","article_processing_charge":"No","day":"25","month":"07"},{"scopus_import":1,"month":"10","day":"08","article_processing_charge":"No","page":"61","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"publication":"arXiv:1910.03372","oa":1,"citation":{"apa":"Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372. ArXiv.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” arXiv:1910.03372. ArXiv.","ista":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, .","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:191003372.","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372. ArXiv, n.d.","short":"A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.).","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372, ArXiv."},"main_file_link":[{"url":"https://arxiv.org/abs/1910.03372","open_access":"1"}],"language":[{"iso":"eng"}],"date_published":"2019-10-08T00:00:00Z","type":"preprint","abstract":[{"lang":"eng","text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$ and inverse temperature $\\beta$ differs from the one of the non-interacting system by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ = \\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho \\ll 1$ and if $\\beta \\rho \\gtrsim 1$."}],"ec_funded":1,"status":"public","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","publication_status":"draft","department":[{"_id":"RoSe"}],"publisher":"ArXiv","_id":"7524","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2019","date_created":"2020-02-26T08:46:40Z","date_updated":"2023-09-07T13:12:41Z","oa_version":"Preprint","author":[{"full_name":"Deuchert, Andreas","last_name":"Deuchert","first_name":"Andreas","orcid":"0000-0003-3146-6746","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Mayer","first_name":"Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","full_name":"Mayer, Simon"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert"}],"related_material":{"record":[{"id":"7790","status":"public","relation":"later_version"},{"status":"public","relation":"dissertation_contains","id":"7514"}]}},{"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","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"Elsevier_2019_Edelsbrunner.pdf","creator":"kschuh","content_type":"application/pdf","file_size":2665013,"file_id":"6624","relation":"main_file","checksum":"7c99be505dc7533257d42eb1830cef04","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-08T15:24:26Z"}],"title":"Holes and dependences in an ordered complex","status":"public","ddc":["000"],"intvolume":" 73","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6608","day":"01","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2019-08-01T00:00:00Z","page":"1-15","publication":"Computer Aided Geometric Design","citation":{"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.","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.","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","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"},"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","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":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"full_name":"Ölsböck, Katharina","first_name":"Katharina","last_name":"Ölsböck","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4672-8297"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","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","quality_controlled":"1","isi":1,"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Persistence and stability of geometric complexes"}],"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"]},"oa":1},{"date_created":"2019-07-24T09:20:53Z","date_updated":"2023-09-07T13:15:55Z","author":[{"full_name":"Choudhuri, Arka Rai","first_name":"Arka Rai","last_name":"Choudhuri"},{"last_name":"Hubáček","first_name":"Pavel","full_name":"Hubáček, Pavel"},{"id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","first_name":"Chethan","last_name":"Kamath Hosdurg","full_name":"Kamath Hosdurg, Chethan"},{"full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","last_name":"Pietrzak"},{"full_name":"Rosen, Alon","last_name":"Rosen","first_name":"Alon"},{"last_name":"Rothblum","first_name":"Guy N.","full_name":"Rothblum, Guy N."}],"related_material":{"record":[{"id":"7896","status":"public","relation":"dissertation_contains"}]},"publication_status":"published","department":[{"_id":"KrPi"}],"publisher":"ACM Press","year":"2019","ec_funded":1,"language":[{"iso":"eng"}],"conference":{"location":"Phoenix, AZ, United States","start_date":"2019-06-23","end_date":"2019-06-26","name":"STOC: Symposium on Theory of Computing"},"doi":"10.1145/3313276.3316400","isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Teaching Old Crypto New Tricks","grant_number":"682815","_id":"258AA5B2-B435-11E9-9278-68D0E5697425"}],"external_id":{"isi":["000523199100100"]},"main_file_link":[{"url":"https://eprint.iacr.org/2019/549","open_access":"1"}],"oa":1,"month":"06","publication_identifier":{"isbn":["9781450367059"]},"oa_version":"Preprint","status":"public","title":"Finding a Nash equilibrium is no easier than breaking Fiat-Shamir","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6677","abstract":[{"text":"The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography.\r\n\r\nWe show that solving the END−OF−METERED−LINE problem is no easier than breaking the soundness of the Fiat-Shamir transformation when applied to the sumcheck protocol. In particular, if the transformed protocol is sound, then any hard problem in #P gives rise to a hard distribution in the class CLS, which is contained in PPAD. Our result opens up the possibility of sampling moderately-sized games for which it is hard to find a Nash equilibrium, by reducing the inversion of appropriately chosen one-way functions to #SAT.\r\n\r\nOur main technical contribution is a stateful incrementally verifiable procedure that, given a SAT instance over n variables, counts the number of satisfying assignments. This is accomplished via an exponential sequence of small steps, each computable in time poly(n). Incremental verifiability means that each intermediate state includes a sumcheck-based proof of its correctness, and the proof can be updated and verified in time poly(n).","lang":"eng"}],"type":"conference","date_published":"2019-06-01T00:00:00Z","page":"1103-1114","publication":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019","citation":{"apa":"Choudhuri, A. R., Hubáček, P., Kamath Hosdurg, C., Pietrzak, K. Z., Rosen, A., & Rothblum, G. N. (2019). Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019 (pp. 1103–1114). Phoenix, AZ, United States: ACM Press. https://doi.org/10.1145/3313276.3316400","ieee":"A. R. Choudhuri, P. Hubáček, C. Kamath Hosdurg, K. Z. Pietrzak, A. Rosen, and G. N. Rothblum, “Finding a Nash equilibrium is no easier than breaking Fiat-Shamir,” in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019, Phoenix, AZ, United States, 2019, pp. 1103–1114.","ista":"Choudhuri AR, Hubáček P, Kamath Hosdurg C, Pietrzak KZ, Rosen A, Rothblum GN. 2019. Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019. STOC: Symposium on Theory of Computing, 1103–1114.","ama":"Choudhuri AR, Hubáček P, Kamath Hosdurg C, Pietrzak KZ, Rosen A, Rothblum GN. Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019. ACM Press; 2019:1103-1114. doi:10.1145/3313276.3316400","chicago":"Choudhuri, Arka Rai, Pavel Hubáček, Chethan Kamath Hosdurg, Krzysztof Z Pietrzak, Alon Rosen, and Guy N. Rothblum. “Finding a Nash Equilibrium Is No Easier than Breaking Fiat-Shamir.” In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019, 1103–14. ACM Press, 2019. https://doi.org/10.1145/3313276.3316400.","short":"A.R. Choudhuri, P. Hubáček, C. Kamath Hosdurg, K.Z. Pietrzak, A. Rosen, G.N. Rothblum, in:, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019, ACM Press, 2019, pp. 1103–1114.","mla":"Choudhuri, Arka Rai, et al. “Finding a Nash Equilibrium Is No Easier than Breaking Fiat-Shamir.” Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019, ACM Press, 2019, pp. 1103–14, doi:10.1145/3313276.3316400."},"day":"01","article_processing_charge":"No","scopus_import":"1"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5986","title":"A proof of the orbit conjecture for flipping edge-labelled triangulations","ddc":["000"],"status":"public","intvolume":" 61","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"5988","date_created":"2019-02-14T11:57:22Z","date_updated":"2020-07-14T12:47:14Z","checksum":"e1bff88f1d77001b53b78c485ce048d7","file_name":"2018_DiscreteGeometry_Lubiw.pdf","access_level":"open_access","file_size":556276,"content_type":"application/pdf","creator":"dernst"}],"type":"journal_article","abstract":[{"text":"Given a triangulation of a point set in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral, and replaces e by the opposite diagonal of the quadrilateral. It is well known that any triangulation of a point set can be reconfigured to any other triangulation by some sequence of flips. We explore this question in the setting where each edge of a triangulation has a label, and a flip transfers the label of the removed edge to the new edge. It is not true that every labelled triangulation of a point set can be reconfigured to every other labelled triangulation via a sequence of flips, but we characterize when this is possible. There is an obvious necessary condition: for each label l, if edge e has label l in the first triangulation and edge f has label l in the second triangulation, then there must be some sequence of flips that moves label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot formulated the Orbit Conjecture, which states that this necessary condition is also sufficient, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination. We prove this conjecture. Furthermore, we give a polynomial-time algorithm (with 𝑂(𝑛8) being a crude bound on the run-time) to find a sequence of flips to reconfigure one labelled triangulation to another, if such a sequence exists, and we prove an upper bound of 𝑂(𝑛7) on the length of the flip sequence. Our proof uses the topological result that the sets of pairwise non-crossing edges on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional ball (this follows from a result of Orden and Santos; we give a different proof based on a shelling argument). The dual cell complex of this simplicial ball, called the flip complex, has the usual flip graph as its 1-skeleton. We use properties of the 2-skeleton of the flip complex to prove the Orbit Conjecture.","lang":"eng"}],"issue":"4","publication":"Discrete & Computational Geometry","citation":{"ama":"Lubiw A, Masárová Z, Wagner U. A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. 2019;61(4):880-898. doi:10.1007/s00454-018-0035-8","ista":"Lubiw A, Masárová Z, Wagner U. 2019. A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. 61(4), 880–898.","ieee":"A. Lubiw, Z. Masárová, and U. Wagner, “A proof of the orbit conjecture for flipping edge-labelled triangulations,” Discrete & Computational Geometry, vol. 61, no. 4. Springer Nature, pp. 880–898, 2019.","apa":"Lubiw, A., Masárová, Z., & Wagner, U. (2019). A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-018-0035-8","mla":"Lubiw, Anna, et al. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry, vol. 61, no. 4, Springer Nature, 2019, pp. 880–98, doi:10.1007/s00454-018-0035-8.","short":"A. Lubiw, Z. Masárová, U. Wagner, Discrete & Computational Geometry 61 (2019) 880–898.","chicago":"Lubiw, Anna, Zuzana Masárová, and Uli Wagner. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry. Springer Nature, 2019. https://doi.org/10.1007/s00454-018-0035-8."},"article_type":"original","page":"880-898","date_published":"2019-06-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","year":"2019","publication_status":"published","department":[{"_id":"UlWa"}],"publisher":"Springer Nature","author":[{"first_name":"Anna","last_name":"Lubiw","full_name":"Lubiw, Anna"},{"full_name":"Masárová, Zuzana","last_name":"Masárová","first_name":"Zuzana","orcid":"0000-0002-6660-1322","id":"45CFE238-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Wagner, Uli"}],"related_material":{"record":[{"id":"683","relation":"earlier_version","status":"public"},{"id":"7944","relation":"dissertation_contains","status":"public"}]},"date_created":"2019-02-14T11:54:08Z","date_updated":"2023-09-07T13:17:36Z","volume":61,"file_date_updated":"2020-07-14T12:47:14Z","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":{"isi":["000466130000009"],"arxiv":["1710.02741"]},"quality_controlled":"1","isi":1,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"doi":"10.1007/s00454-018-0035-8","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]}}]