[{"tmp":{"short":"CC BY-ND (4.0)","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png"},"publication_identifier":{"eissn":["1077-8926"]},"fulldoi":"https://doi.org/10.37236/10794","citation":{"ista":"Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 29(4), P4.13.","chicago":"Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles in Random Hypergraphs.” The Electronic Journal of Combinatorics. Electronic Journal of Combinatorics, 2022. https://doi.org/10.37236/10794.","short":"O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29 (2022).","ama":"Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. 2022;29(4). doi:10.37236/10794","mla":"Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” The Electronic Journal of Combinatorics, vol. 29, no. 4, P4.13, Electronic Journal of Combinatorics, 2022, doi:10.37236/10794.","ieee":"O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,” The Electronic Journal of Combinatorics, vol. 29, no. 4. Electronic Journal of Combinatorics, 2022.","apa":"Cooley, O., Kang, M., & Zalla, J. (2022). Loose cores and cycles in random hypergraphs. The Electronic Journal of Combinatorics. Electronic Journal of Combinatorics. https://doi.org/10.37236/10794"},"scopus_import":"1","oa":1,"article_type":"original","day":"21","file":[{"success":1,"access_level":"open_access","file_name":"2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf","file_size":626953,"file_id":"12462","date_created":"2023-01-30T11:45:13Z","relation":"main_file","date_updated":"2023-01-30T11:45:13Z","content_type":"application/pdf","creator":"dernst","checksum":"00122b2459f09b5ae43073bfba565e94"}],"file_date_updated":"2023-01-30T11:45:13Z","month":"10","oa_version":"Published Version","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.37236/10794","date_updated":"2026-08-04T09:29:03Z","date_created":"2023-01-16T10:03:57Z","department":[{"_id":"MaKw"}],"type":"journal_article","issue":"4","article_number":"P4.13","external_id":{"isi":["000876763300001"]},"keyword":["Computational Theory and Mathematics","Geometry and Topology","Theoretical Computer Science","Applied Mathematics","Discrete Mathematics and Combinatorics"],"quality_controlled":"1","_id":"12286","article_processing_charge":"No","publisher":"Electronic Journal of Combinatorics","volume":29,"publication":"The Electronic Journal of Combinatorics","abstract":[{"text":"Inspired by the study of loose cycles in hypergraphs, we define the loose core in hypergraphs as a structurewhich mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition at a certain critical threshold and determine this order, as well as the number of edges, asymptotically in the subcritical and supercritical regimes.
\r\nOur main tool is an algorithm called CoreConstruct, which enables us to analyse a peeling process for the loose core. By analysing this algorithm we determine the asymptotic degree distribution of vertices in the loose core and in particular how many vertices and edges the loose core contains. As a corollary we obtain an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$.","lang":"eng"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","intvolume":" 29","language":[{"iso":"eng"}],"status":"public","acknowledgement":"Supported by Austrian Science Fund (FWF): I3747, W1230.","publication_status":"published","has_accepted_license":"1","year":"2022","isi":1,"title":"Loose cores and cycles in random hypergraphs","author":[{"full_name":"Cooley, Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","last_name":"Cooley","first_name":"Oliver"},{"last_name":"Kang","first_name":"Mihyun","full_name":"Kang, Mihyun"},{"full_name":"Zalla, Julian","first_name":"Julian","last_name":"Zalla"}],"date_published":"2022-10-21T00:00:00Z"},{"acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer for valuable remarks.","language":[{"iso":"eng"}],"intvolume":" 9","status":"public","abstract":[{"text":"We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.","lang":"eng"}],"publication":"Analysis and Geometry in Metric Spaces","volume":9,"_id":"10856","publisher":"De Gruyter","article_processing_charge":"No","external_id":{"isi":["000734286800001"],"arxiv":["2004.02674"]},"issue":"1","quality_controlled":"1","keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"date_published":"2021-01-29T00:00:00Z","author":[{"first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory"},{"full_name":"Tsiutsiurupa, Igor","last_name":"Tsiutsiurupa","first_name":"Igor"}],"title":"On the volume of sections of the cube","isi":1,"publication_status":"published","year":"2021","has_accepted_license":"1","file":[{"access_level":"open_access","success":1,"checksum":"7e615ac8489f5eae580b6517debfdc53","creator":"dernst","content_type":"application/pdf","date_created":"2022-03-18T09:31:59Z","relation":"main_file","date_updated":"2022-03-18T09:31:59Z","file_id":"10857","file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","file_size":789801}],"file_date_updated":"2022-03-18T09:31:59Z","article_type":"original","day":"29","scopus_import":"1","oa":1,"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:10.1515/agms-2020-0103.","ieee":"G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.","apa":"Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103","ama":"Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103","chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103.","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18."},"fulldoi":"https://doi.org/10.1515/agms-2020-0103","publication_identifier":{"issn":["2299-3274"]},"page":"1-18","department":[{"_id":"UlWa"}],"type":"journal_article","doi":"10.1515/agms-2020-0103","date_updated":"2023-08-17T07:07:58Z","date_created":"2022-03-18T09:25:14Z","month":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"ddc":["510"],"oa_version":"Published Version"},{"isi":1,"publication_status":"published","year":"2021","date_published":"2021-12-18T00:00:00Z","author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","last_name":"Ivanov","first_name":"Grigory"}],"title":"Tight frames and related geometric problems","_id":"10860","publisher":"Canadian Mathematical Society","article_processing_charge":"No","external_id":{"arxiv":["1804.10055"],"isi":["000730165300021"]},"issue":"4","quality_controlled":"1","keyword":["General Mathematics","Tight frame","Grassmannian","zonotope"],"acknowledgement":"The author was supported by the Swiss National Science Foundation grant 200021_179133. The author acknowledges the financial support from the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no. 075-15-2019-1926.","status":"public","language":[{"iso":"eng"}],"intvolume":" 64","abstract":[{"lang":"eng","text":"A tight frame is the orthogonal projection of some orthonormal basis of Rn onto Rk. We show that a set of vectors is a tight frame if and only if the set of all cross products of these vectors is a tight frame. We reformulate a range of problems on the volume of projections (or sections) of regular polytopes in terms of tight frames and write a first-order necessary condition for local extrema of these problems. As applications, we prove new results for the problem of maximization of the volume of zonotopes."}],"publication":"Canadian Mathematical Bulletin","volume":64,"date_created":"2022-03-18T09:55:59Z","doi":"10.4153/s000843952000096x","date_updated":"2024-10-09T21:01:50Z","month":"12","arxiv":1,"corr_author":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","page":"942-963","department":[{"_id":"UlWa"}],"type":"journal_article","scopus_import":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1804.10055","open_access":"1"}],"publication_identifier":{"eissn":["1496-4287"],"issn":["0008-4395"]},"fulldoi":"https://doi.org/10.4153/s000843952000096x","citation":{"ieee":"G. Ivanov, “Tight frames and related geometric problems,” Canadian Mathematical Bulletin, vol. 64, no. 4. Canadian Mathematical Society, pp. 942–963, 2021.","mla":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin, vol. 64, no. 4, Canadian Mathematical Society, 2021, pp. 942–63, doi:10.4153/s000843952000096x.","apa":"Ivanov, G. (2021). Tight frames and related geometric problems. Canadian Mathematical Bulletin. Canadian Mathematical Society. https://doi.org/10.4153/s000843952000096x","ama":"Ivanov G. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 2021;64(4):942-963. doi:10.4153/s000843952000096x","chicago":"Ivanov, Grigory. “Tight Frames and Related Geometric Problems.” Canadian Mathematical Bulletin. Canadian Mathematical Society, 2021. https://doi.org/10.4153/s000843952000096x.","ista":"Ivanov G. 2021. Tight frames and related geometric problems. Canadian Mathematical Bulletin. 64(4), 942–963.","short":"G. Ivanov, Canadian Mathematical Bulletin 64 (2021) 942–963."},"article_type":"original","day":"18"},{"fulldoi":"https://doi.org/10.1007/s00454-021-00299-z","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"citation":{"apa":"Avvakumov, S., & Kudrya, S. (2021). Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00299-z","ieee":"S. Avvakumov and S. Kudrya, “Vanishing of all equivariant obstructions and the mapping degree,” Discrete & Computational Geometry, vol. 66, no. 3. Springer Nature, pp. 1202–1216, 2021.","mla":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” Discrete & Computational Geometry, vol. 66, no. 3, Springer Nature, 2021, pp. 1202–16, doi:10.1007/s00454-021-00299-z.","ama":"Avvakumov S, Kudrya S. Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. 2021;66(3):1202-1216. doi:10.1007/s00454-021-00299-z","chicago":"Avvakumov, Sergey, and Sergey Kudrya. “Vanishing of All Equivariant Obstructions and the Mapping Degree.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-021-00299-z.","ista":"Avvakumov S, Kudrya S. 2021. Vanishing of all equivariant obstructions and the mapping degree. Discrete & Computational Geometry. 66(3), 1202–1216.","short":"S. Avvakumov, S. Kudrya, Discrete & Computational Geometry 66 (2021) 1202–1216."},"scopus_import":"1","day":"01","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","arxiv":1,"oa_version":"Preprint","month":"10","date_updated":"2025-04-14T09:10:06Z","doi":"10.1007/s00454-021-00299-z","date_created":"2022-06-17T08:45:15Z","type":"journal_article","page":"1202-1216","related_material":{"record":[{"id":"8182","relation":"earlier_version","status":"public"}]},"keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Theoretical Computer Science"],"quality_controlled":"1","external_id":{"arxiv":["1910.12628"]},"issue":"3","article_processing_charge":"No","publisher":"Springer Nature","_id":"11446","publication":"Discrete & Computational Geometry","volume":66,"acknowledgement":"S. Avvakumov has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Grant agreement ERC StG 716424–CASe. S. Kudrya was supported by the Austrian Academic Exchange Service (OeAD), ICM-2019-13577.","intvolume":" 66","language":[{"iso":"eng"}],"status":"public","abstract":[{"lang":"eng","text":"Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group Sn, there exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}. Previously, the special cases of this statement for certain X were usually proved using the equivartiant obstruction theory. Such calculations are difficult and may become infeasible past the first (primary) obstruction. We take a different approach which allows us to prove the vanishing of all obstructions simultaneously. The essential step in the proof is classifying the possible degrees of Sn-equivariant maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant maps between spaces is important for many questions arising from discrete mathematics and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate the utility of our result applying it to one such question, a specific instance of envy-free division problem."}],"year":"2021","publication_status":"published","extern":"1","title":"Vanishing of all equivariant obstructions and the mapping degree","author":[{"first_name":"Sergey","orcid":"0000-0002-7840-5062","last_name":"Avvakumov","full_name":"Avvakumov, Sergey","id":"3827DAC8-F248-11E8-B48F-1D18A9856A87"},{"id":"ecf01965-d252-11ea-95a5-8ada5f6c6a67","full_name":"Kudrya, Sergey","first_name":"Sergey","last_name":"Kudrya"}],"date_published":"2021-10-01T00:00:00Z"},{"scopus_import":"1","fulldoi":"https://doi.org/10.1137/20m1366502","citation":{"ama":"Czumaj A, Davies P, Parter M. Simple, deterministic, constant-round coloring in congested clique and MPC. SIAM Journal on Computing. 2021;50(5):1603-1626. doi:10.1137/20m1366502","apa":"Czumaj, A., Davies, P., & Parter, M. (2021). Simple, deterministic, constant-round coloring in congested clique and MPC. SIAM Journal on Computing. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20m1366502","ieee":"A. Czumaj, P. Davies, and M. Parter, “Simple, deterministic, constant-round coloring in congested clique and MPC,” SIAM Journal on Computing, vol. 50, no. 5. Society for Industrial and Applied Mathematics, pp. 1603–1626, 2021.","mla":"Czumaj, Artur, et al. “Simple, Deterministic, Constant-Round Coloring in Congested Clique and MPC.” SIAM Journal on Computing, vol. 50, no. 5, Society for Industrial and Applied Mathematics, 2021, pp. 1603–26, doi:10.1137/20m1366502.","short":"A. Czumaj, P. Davies, M. Parter, SIAM Journal on Computing 50 (2021) 1603–1626.","ista":"Czumaj A, Davies P, Parter M. 2021. Simple, deterministic, constant-round coloring in congested clique and MPC. SIAM Journal on Computing. 50(5), 1603–1626.","chicago":"Czumaj, Artur, Peter Davies, and Merav Parter. “Simple, Deterministic, Constant-Round Coloring in Congested Clique and MPC.” SIAM Journal on Computing. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/20m1366502."},"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"article_type":"original","day":"01","date_created":"2024-04-03T07:53:22Z","date_updated":"2025-09-10T10:14:11Z","doi":"10.1137/20m1366502","month":"01","oa_version":"None","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","page":"1603-1626","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"ec_funded":1,"department":[{"_id":"DaAl"}],"type":"journal_article","_id":"15271","publisher":"Society for Industrial and Applied Mathematics","article_processing_charge":"No","issue":"5","external_id":{"isi":["000713008600004"]},"keyword":["General Mathematics","General Computer Science"],"quality_controlled":"1","abstract":[{"lang":"eng","text":"We settle the complexity of the (∆ + 1)-coloring and (∆ + 1)-list coloring problems intheCONGESTED CLIQUEmodel by presenting a simpledeterministicalgorithm for both problemsrunning in a constant number of rounds. This matches the complexity of the recent breakthroughrandomizedconstant-round (∆ + 1)-list coloring algorithm due to Chang et al. [Proceedings of the38th ACM Symposium on Principles of Distributed Computing, 2019] and significantly improvesupon the state-of-the-artO(log ∆)-round deterministic (∆ + 1)-coloring bound of Parter [Proceed-ings of the 45th Annual International Colloquium on Automata, Languages and Programming]. Aremarkable property of our algorithm is its simplicity. Whereas the state-of-the-artrandomizedal-gorithms for this problem are based on the quite involved local coloring algorithm of Chang, Li, andPettie [Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018],our algorithm can be described in just a few lines. At a high level, it applies a careful derandomiza-tion of a recursive procedure which partitions the nodes and their respective palettes into separatebins. We show that afterO(1) recursion steps, the remaining uncolored subgraph within each bin haslinear size and thus can be solved locally by collecting it to a single node. This algorithm can alsobe implemented in the massively parallel computation (MPC) model provided that each machine haslinear (inn, the number of nodes in the input graph) space. We also show an extension of our algo-rithm to theMPCregime, in which machines havesublinearspace: we present the first deterministic(∆ + 1)-list coloring algorithm designed for sublinear-spaceMPC, which runs inO(log ∆ + log logn)rounds."}],"language":[{"iso":"eng"}],"intvolume":" 50","status":"public","acknowledgement":"The first author was partially supported by the Centre for Discrete Mathematics and its Applications, by the IBM Faculty Award, and by the EPSRC award EP/N011163/1. The second author was partially supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement 754411. The first and third authors were partially supported by a Weizmann-UK Making Connections grant.","volume":50,"publication":"SIAM Journal on Computing","isi":1,"publication_status":"published","year":"2021","date_published":"2021-01-01T00:00:00Z","title":"Simple, deterministic, constant-round coloring in congested clique and MPC","author":[{"full_name":"Czumaj, Artur","last_name":"Czumaj","first_name":"Artur"},{"full_name":"Davies, Peter","id":"11396234-BB50-11E9-B24C-90FCE5697425","orcid":"0000-0002-5646-9524","first_name":"Peter","last_name":"Davies"},{"last_name":"Parter","first_name":"Merav","full_name":"Parter, Merav"}]},{"author":[{"first_name":"Jacob","last_name":"Fox","full_name":"Fox, Jacob"},{"first_name":"János","last_name":"Pach","full_name":"Pach, János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4"},{"full_name":"Suk, Andrew","last_name":"Suk","first_name":"Andrew"}],"title":"Bounded VC-dimension implies the Schur-Erdős conjecture","date_published":"2021-11-20T00:00:00Z","publication_status":"published","year":"2021","volume":41,"publication":"Combinatorica","abstract":[{"lang":"eng","text":"In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension."}],"language":[{"iso":"eng"}],"status":"public","intvolume":" 41","issue":"6","external_id":{"arxiv":["1912.02342"]},"quality_controlled":"1","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics"],"_id":"15275","article_processing_charge":"No","publisher":"Springer Nature","department":[{"_id":"HeEd"}],"type":"journal_article","page":"803-813","month":"11","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"date_created":"2024-04-03T07:59:57Z","date_updated":"2024-04-09T10:40:08Z","doi":"10.1007/s00493-021-4530-9","article_type":"original","day":"20","fulldoi":"https://doi.org/10.1007/s00493-021-4530-9","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"citation":{"ama":"Fox J, Pach J, Suk A. Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. 2021;41(6):803-813. doi:10.1007/s00493-021-4530-9","ieee":"J. Fox, J. Pach, and A. Suk, “Bounded VC-dimension implies the Schur-Erdős conjecture,” Combinatorica, vol. 41, no. 6. Springer Nature, pp. 803–813, 2021.","mla":"Fox, Jacob, et al. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” Combinatorica, vol. 41, no. 6, Springer Nature, 2021, pp. 803–13, doi:10.1007/s00493-021-4530-9.","apa":"Fox, J., Pach, J., & Suk, A. (2021). Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-021-4530-9","short":"J. Fox, J. Pach, A. Suk, Combinatorica 41 (2021) 803–813.","ista":"Fox J, Pach J, Suk A. 2021. Bounded VC-dimension implies the Schur-Erdős conjecture. Combinatorica. 41(6), 803–813.","chicago":"Fox, Jacob, János Pach, and Andrew Suk. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.” Combinatorica. Springer Nature, 2021. https://doi.org/10.1007/s00493-021-4530-9."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.02342","open_access":"1"}],"oa":1},{"author":[{"orcid":"0000-0002-0479-558X","first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Neukamm, Stefan","last_name":"Neukamm","first_name":"Stefan"}],"title":"Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems","date_published":"2021-06-30T00:00:00Z","publication_status":"published","has_accepted_license":"1","year":"2021","isi":1,"volume":242,"publication":"Archive for Rational Mechanics and Analysis","abstract":[{"lang":"eng","text":"We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \\mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \\varepsilon >0, we establish homogenization error estimates of the order \\varepsilon in case d\\geqq 3, and of the order \\varepsilon |\\log \\varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \\varepsilon ^\\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\\alpha } regularity theory is available."}],"language":[{"iso":"eng"}],"intvolume":" 242","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441.","status":"public","issue":"1","external_id":{"isi":["000668431200001"],"arxiv":["1908.02273"]},"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"quality_controlled":"1","_id":"10549","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"type":"journal_article","page":"343-452","month":"06","oa_version":"Published Version","ddc":["530"],"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s00205-021-01686-9","date_updated":"2023-08-17T06:23:21Z","date_created":"2021-12-16T12:12:33Z","article_type":"original","day":"30","file":[{"access_level":"open_access","success":1,"creator":"cchlebak","content_type":"application/pdf","checksum":"cc830b739aed83ca2e32c4e0ce266a4c","file_id":"10558","file_name":"2021_ArchRatMechAnalysis_Fischer.pdf","file_size":1640121,"date_updated":"2021-12-16T14:58:08Z","date_created":"2021-12-16T14:58:08Z","relation":"main_file"}],"file_date_updated":"2021-12-16T14:58:08Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.1007/s00205-021-01686-9","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"citation":{"mla":"Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:10.1007/s00205-021-01686-9.","apa":"Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9","ieee":"J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” Archive for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021.","ama":"Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9","chicago":"Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9.","ista":"Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452.","short":"J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452."},"oa":1,"scopus_import":"1"},{"publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"fulldoi":"https://doi.org/10.1090/proc/15205","citation":{"ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","apa":"Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2021. https://doi.org/10.1090/proc/15205."},"scopus_import":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1910.08286","open_access":"1"}],"article_type":"original","day":"01","month":"01","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","date_created":"2020-11-19T10:17:40Z","doi":"10.1090/proc/15205","date_updated":"2025-04-14T07:43:50Z","department":[{"_id":"HeEd"}],"ec_funded":1,"type":"journal_article","page":"37-52","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"issue":"1","quality_controlled":"1","keyword":["Applied Mathematics","General Mathematics"],"_id":"8773","publisher":"American Mathematical Society","article_processing_charge":"No","publication":"Proceedings of the American Mathematical Society","volume":149,"intvolume":" 149","status":"public","acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell."}],"publication_status":"published","year":"2021","isi":1,"author":[{"last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Romanov, Anna","last_name":"Romanov","first_name":"Anna"}],"title":"Contravariant forms on Whittaker modules","date_published":"2021-01-01T00:00:00Z"},{"has_accepted_license":"1","year":"2021","publication_status":"published","isi":1,"title":"Triangulating submanifolds: An elementary and quantified version of Whitney’s method","author":[{"first_name":"Jean-Daniel","last_name":"Boissonnat","full_name":"Boissonnat, Jean-Daniel"},{"first_name":"Siargey","last_name":"Kachanovich","full_name":"Kachanovich, Siargey"},{"orcid":"0000-0002-7472-2220","first_name":"Mathijs","last_name":"Wintraecken","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","full_name":"Wintraecken, Mathijs"}],"date_published":"2021-07-01T00:00:00Z","quality_controlled":"1","keyword":["Theoretical Computer Science","Computational Theory and Mathematics","Geometry and Topology","Discrete Mathematics and Combinatorics"],"issue":"1","external_id":{"isi":["000597770300001"]},"publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","_id":"8940","volume":66,"publication":"Discrete & Computational Geometry","abstract":[{"lang":"eng","text":"We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric."}],"language":[{"iso":"eng"}],"status":"public","intvolume":" 66","acknowledgement":"This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement Number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). The third author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. Open access funding provided by the Institute of Science and Technology (IST Austria).","ddc":["516"],"oa_version":"Published Version","corr_author":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"07","date_updated":"2025-04-14T07:43:50Z","doi":"10.1007/s00454-020-00250-8","date_created":"2020-12-12T11:07:02Z","type":"journal_article","ec_funded":1,"department":[{"_id":"HeEd"}],"page":"386-434","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"fulldoi":"https://doi.org/10.1007/s00454-020-00250-8","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"citation":{"ama":"Boissonnat J-D, Kachanovich S, Wintraecken M. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 2021;66(1):386-434. doi:10.1007/s00454-020-00250-8","ieee":"J.-D. Boissonnat, S. Kachanovich, and M. Wintraecken, “Triangulating submanifolds: An elementary and quantified version of Whitney’s method,” Discrete & Computational Geometry, vol. 66, no. 1. Springer Nature, pp. 386–434, 2021.","mla":"Boissonnat, Jean-Daniel, et al. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry, vol. 66, no. 1, Springer Nature, 2021, pp. 386–434, doi:10.1007/s00454-020-00250-8.","apa":"Boissonnat, J.-D., Kachanovich, S., & Wintraecken, M. (2021). Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-020-00250-8","short":"J.-D. Boissonnat, S. Kachanovich, M. Wintraecken, Discrete & Computational Geometry 66 (2021) 386–434.","ista":"Boissonnat J-D, Kachanovich S, Wintraecken M. 2021. Triangulating submanifolds: An elementary and quantified version of Whitney’s method. Discrete & Computational Geometry. 66(1), 386–434.","chicago":"Boissonnat, Jean-Daniel, Siargey Kachanovich, and Mathijs Wintraecken. “Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s Method.” Discrete & Computational Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00454-020-00250-8."},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"scopus_import":"1","day":"01","article_type":"original","file_date_updated":"2021-08-06T09:52:29Z","file":[{"success":1,"access_level":"open_access","date_created":"2021-08-06T09:52:29Z","relation":"main_file","date_updated":"2021-08-06T09:52:29Z","file_name":"2021_DescreteCompGeopmetry_Boissonnat.pdf","file_size":983307,"file_id":"9795","checksum":"c848986091e56699dc12de85adb1e39c","content_type":"application/pdf","creator":"kschuh"}]},{"publication_status":"published","year":"2021","isi":1,"author":[{"last_name":"Virosztek","orcid":"0000-0003-1109-5511","first_name":"Daniel","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"title":"The metric property of the quantum Jensen-Shannon divergence","date_published":"2021-03-26T00:00:00Z","issue":"3","article_number":"107595","external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"keyword":["General Mathematics"],"quality_controlled":"1","_id":"9036","article_processing_charge":"No","publisher":"Elsevier","volume":380,"publication":"Advances in Mathematics","abstract":[{"text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space.","lang":"eng"}],"status":"public","intvolume":" 380","language":[{"iso":"eng"}],"acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","month":"03","oa_version":"Preprint","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2021-01-22T17:55:17Z","date_updated":"2025-04-14T07:50:40Z","doi":"10.1016/j.aim.2021.107595","ec_funded":1,"department":[{"_id":"LaEr"}],"type":"journal_article","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"}],"fulldoi":"https://doi.org/10.1016/j.aim.2021.107595","citation":{"ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.","short":"D. Virosztek, Advances in Mathematics 380 (2021)."},"publication_identifier":{"issn":["0001-8708"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"scopus_import":"1","oa":1,"article_type":"original","day":"26"},{"abstract":[{"lang":"eng","text":"We report the complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This result suggests that fixation of a deleterious allele that follows a click of the Muller’s ratchet is governed by natural selection, instead of random drift."}],"language":[{"iso":"eng"}],"status":"public","intvolume":" 524","acknowledgement":"This work was supported by the Russian Science Foundation grant N 16-14-10173.","volume":524,"publication":"Journal of Theoretical Biology","_id":"9387","article_processing_charge":"No","publisher":"Elsevier","article_number":"110729","external_id":{"isi":["000659161500002"],"pmid":["33901507"]},"keyword":["General Biochemistry","Genetics and Molecular Biology","Modelling and Simulation","Statistics and Probability","General Immunology and Microbiology","Applied Mathematics","General Agricultural and Biological Sciences","General Medicine"],"quality_controlled":"1","das_tickbox":"1","date_published":"2021-04-24T00:00:00Z","author":[{"id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","full_name":"Khudiakova, Kseniia","first_name":"Kseniia","orcid":"0000-0002-6246-1465","last_name":"Khudiakova"},{"last_name":"Neretina","first_name":"Tatiana Yu.","full_name":"Neretina, Tatiana Yu."},{"full_name":"Kondrashov, Alexey S.","last_name":"Kondrashov","first_name":"Alexey S."}],"title":"Two linked loci under mutation-selection balance and Muller’s ratchet","isi":1,"publication_status":"published","year":"2021","article_type":"original","day":"24","main_file_link":[{"url":"https://www.biorxiv.org/content/10.1101/477489v1","open_access":"1"}],"oa":1,"scopus_import":"1","citation":{"ama":"Khudiakova K, Neretina TY, Kondrashov AS. Two linked loci under mutation-selection balance and Muller’s ratchet. Journal of Theoretical Biology. 2021;524. doi:10.1016/j.jtbi.2021.110729","apa":"Khudiakova, K., Neretina, T. Y., & Kondrashov, A. S. (2021). Two linked loci under mutation-selection balance and Muller’s ratchet. Journal of Theoretical Biology. Elsevier. https://doi.org/10.1016/j.jtbi.2021.110729","mla":"Khudiakova, Kseniia, et al. “Two Linked Loci under Mutation-Selection Balance and Muller’s Ratchet.” Journal of Theoretical Biology, vol. 524, 110729, Elsevier, 2021, doi:10.1016/j.jtbi.2021.110729.","ieee":"K. Khudiakova, T. Y. Neretina, and A. S. Kondrashov, “Two linked loci under mutation-selection balance and Muller’s ratchet,” Journal of Theoretical Biology, vol. 524. Elsevier, 2021.","short":"K. Khudiakova, T.Y. Neretina, A.S. Kondrashov, Journal of Theoretical Biology 524 (2021).","ista":"Khudiakova K, Neretina TY, Kondrashov AS. 2021. Two linked loci under mutation-selection balance and Muller’s ratchet. Journal of Theoretical Biology. 524, 110729.","chicago":"Khudiakova, Kseniia, Tatiana Yu. Neretina, and Alexey S. Kondrashov. “Two Linked Loci under Mutation-Selection Balance and Muller’s Ratchet.” Journal of Theoretical Biology. Elsevier, 2021. https://doi.org/10.1016/j.jtbi.2021.110729."},"fulldoi":"https://doi.org/10.1016/j.jtbi.2021.110729","publication_identifier":{"issn":["0022-5193"]},"pmid":1,"department":[{"_id":"GradSch"}],"type":"journal_article","date_updated":"2026-07-06T12:58:31Z","doi":"10.1016/j.jtbi.2021.110729","date_created":"2021-05-12T05:58:42Z","month":"04","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"department":[{"_id":"BeBi"}],"ec_funded":1,"type":"journal_article","related_material":{"link":[{"relation":"press_release","url":"https://ist.ac.at/en/news/designing-with-elastic-structures/","description":"News on IST Website"}],"record":[{"id":"12897","status":"public","relation":"dissertation_contains"}]},"project":[{"call_identifier":"H2020","_id":"24F9549A-B435-11E9-9278-68D0E5697425","grant_number":"715767","name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling"}],"month":"07","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","conference":{"name":"SIGGRAF: Special Interest Group on Computer Graphics and Interactive Techniques","start_date":"2021-08-09","location":"Virtual","end_date":"2021-08-13"},"oa_version":"Published Version","ddc":["516"],"date_created":"2021-08-08T22:01:26Z","doi":"10.1145/3450626.3459800","date_updated":"2026-09-12T22:30:07Z","article_type":"original","day":"19","file":[{"relation":"main_file","date_created":"2021-10-18T10:42:15Z","date_updated":"2021-10-18T10:42:15Z","file_id":"10150","file_size":17064290,"file_name":"elastic-curves-paper.pdf","checksum":"7e5d08ce46b0451b3102eacd3d00f85f","creator":"chafner","content_type":"application/pdf","success":1,"access_level":"open_access"},{"creator":"chafner","content_type":"application/pdf","checksum":"0088643478be7c01a703b5b10767348f","file_id":"10151","file_name":"elastic-curves-supp.pdf","file_size":547156,"relation":"supplementary_material","date_updated":"2021-10-18T10:42:22Z","date_created":"2021-10-18T10:42:22Z","access_level":"open_access"}],"file_date_updated":"2021-10-18T10:42:22Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"apa":"Hafner, C., & Bickel, B. (2021). The design space of plane elastic curves. ACM Transactions on Graphics. Virtual: Association for Computing Machinery. https://doi.org/10.1145/3450626.3459800","ieee":"C. Hafner and B. Bickel, “The design space of plane elastic curves,” ACM Transactions on Graphics, vol. 40, no. 4. Association for Computing Machinery, 2021.","mla":"Hafner, Christian, and Bernd Bickel. “The Design Space of Plane Elastic Curves.” ACM Transactions on Graphics, vol. 40, no. 4, 126, Association for Computing Machinery, 2021, doi:10.1145/3450626.3459800.","ama":"Hafner C, Bickel B. The design space of plane elastic curves. ACM Transactions on Graphics. 2021;40(4). doi:10.1145/3450626.3459800","short":"C. Hafner, B. Bickel, ACM Transactions on Graphics 40 (2021).","chicago":"Hafner, Christian, and Bernd Bickel. “The Design Space of Plane Elastic Curves.” ACM Transactions on Graphics. Association for Computing Machinery, 2021. https://doi.org/10.1145/3450626.3459800.","ista":"Hafner C, Bickel B. 2021. The design space of plane elastic curves. ACM Transactions on Graphics. 40(4), 126."},"fulldoi":"https://doi.org/10.1145/3450626.3459800","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"scopus_import":"1","oa":1,"title":"The design space of plane elastic curves","author":[{"first_name":"Christian","last_name":"Hafner","id":"400429CC-F248-11E8-B48F-1D18A9856A87","full_name":"Hafner, Christian"},{"id":"49876194-F248-11E8-B48F-1D18A9856A87","full_name":"Bickel, Bernd","last_name":"Bickel","orcid":"0000-0001-6511-9385","first_name":"Bernd"}],"date_published":"2021-07-19T00:00:00Z","publication_status":"published","year":"2021","has_accepted_license":"1","isi":1,"publication":"ACM Transactions on Graphics","volume":40,"intvolume":" 40","status":"public","language":[{"iso":"eng"}],"acknowledgement":"We thank the anonymous reviewers for their generous feedback, and Michal Piovarči for his help in producing the supplemental video. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 715767).\r\n","abstract":[{"text":"Elastic bending of initially flat slender elements allows the realization and economic fabrication of intriguing curved shapes. In this work, we derive an intuitive but rigorous geometric characterization of the design space of plane elastic rods with variable stiffness. It enables designers to determine which shapes are physically viable with active bending by visual inspection alone. Building on these insights, we propose a method for efficiently designing the geometry of a flat elastic rod that realizes a target equilibrium curve, which only requires solving a linear program. We implement this method in an interactive computational design tool that gives feedback about the feasibility of a design, and computes the geometry of the structural elements necessary to realize it within an instant. The tool also offers an iterative optimization routine that improves the fabricability of a model while modifying it as little as possible. In addition, we use our geometric characterization to derive an algorithm for analyzing and recovering the stability of elastic curves that would otherwise snap out of their unstable equilibrium shapes by buckling. We show the efficacy of our approach by designing and manufacturing several physical models that are assembled from flat elements.","lang":"eng"}],"external_id":{"isi":["000674930900091"]},"article_number":"126","issue":"4","quality_controlled":"1","keyword":["Computing methodologies","shape modeling","modeling and simulation","theory of computation","computational geometry","mathematics of computing","mathematical optimization"],"_id":"9817","article_processing_charge":"No","publisher":"Association for Computing Machinery"},{"abstract":[{"text":"In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.","lang":"eng"}],"language":[{"iso":"eng"}],"acknowledgement":" Supported by the Russian Foundation for Basic Research grant 18-01-00036.","intvolume":" 2020","status":"public","volume":2020,"publication":"International Mathematics Research Notices","_id":"10867","publisher":"Oxford University Press","article_processing_charge":"No","issue":"3","external_id":{"arxiv":["1702.07513"],"isi":["000522852700002"]},"keyword":["General Mathematics"],"quality_controlled":"1","date_published":"2020-02-01T00:00:00Z","author":[{"orcid":"0000-0002-2548-617X","first_name":"Arseniy","last_name":"Akopyan","full_name":"Akopyan, Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"}],"title":"Waist of balls in hyperbolic and spherical spaces","isi":1,"publication_status":"published","year":"2020","article_type":"original","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1702.07513","open_access":"1"}],"scopus_import":"1","oa":1,"fulldoi":"https://doi.org/10.1093/imrn/rny037","citation":{"short":"A. Akopyan, R. Karasev, International Mathematics Research Notices 2020 (2020) 669–697.","ista":"Akopyan A, Karasev R. 2020. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020(3), 669–697.","chicago":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny037.","ama":"Akopyan A, Karasev R. Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. 2020;2020(3):669-697. doi:10.1093/imrn/rny037","ieee":"A. Akopyan and R. Karasev, “Waist of balls in hyperbolic and spherical spaces,” International Mathematics Research Notices, vol. 2020, no. 3. Oxford University Press, pp. 669–697, 2020.","apa":"Akopyan, A., & Karasev, R. (2020). Waist of balls in hyperbolic and spherical spaces. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny037","mla":"Akopyan, Arseniy, and Roman Karasev. “Waist of Balls in Hyperbolic and Spherical Spaces.” International Mathematics Research Notices, vol. 2020, no. 3, Oxford University Press, 2020, pp. 669–97, doi:10.1093/imrn/rny037."},"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"page":"669-697","department":[{"_id":"HeEd"}],"type":"journal_article","date_updated":"2023-08-24T14:19:55Z","date_created":"2022-03-18T11:39:30Z","doi":"10.1093/imrn/rny037","month":"02","oa_version":"Preprint","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"date_updated":"2023-09-11T10:21:00Z","date_created":"2023-08-21T12:28:20Z","doi":"10.1093/bioinformatics/btaa843","month":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","related_material":{"link":[{"url":"https://github.com/ratschlab/scim","relation":"software"}]},"pmid":1,"page":"i919-i927","department":[{"_id":"FrLo"}],"type":"journal_article","scopus_import":"1","oa":1,"main_file_link":[{"url":"https://doi.org/10.1093/bioinformatics/btaa843","open_access":"1"}],"fulldoi":"https://doi.org/10.1093/bioinformatics/btaa843","publication_identifier":{"eissn":["1367-4811"]},"citation":{"mla":"Stark, Stefan G., et al. “SCIM: Universal Single-Cell Matching with Unpaired Feature Sets.” Bioinformatics, vol. 36, no. Supplement_2, Oxford University Press, 2020, pp. i919–27, doi:10.1093/bioinformatics/btaa843.","ieee":"S. G. Stark et al., “SCIM: Universal single-cell matching with unpaired feature sets,” Bioinformatics, vol. 36, no. Supplement_2. Oxford University Press, pp. i919–i927, 2020.","apa":"Stark, S. G., Ficek, J., Locatello, F., Bonilla, X., Chevrier, S., Singer, F., … Lehmann, K.-V. (2020). SCIM: Universal single-cell matching with unpaired feature sets. Bioinformatics. Oxford University Press. https://doi.org/10.1093/bioinformatics/btaa843","ama":"Stark SG, Ficek J, Locatello F, et al. SCIM: Universal single-cell matching with unpaired feature sets. Bioinformatics. 2020;36(Supplement_2):i919-i927. doi:10.1093/bioinformatics/btaa843","chicago":"Stark, Stefan G, Joanna Ficek, Francesco Locatello, Ximena Bonilla, Stéphane Chevrier, Franziska Singer, Rudolf Aebersold, et al. “SCIM: Universal Single-Cell Matching with Unpaired Feature Sets.” Bioinformatics. Oxford University Press, 2020. https://doi.org/10.1093/bioinformatics/btaa843.","ista":"Stark SG et al. 2020. SCIM: Universal single-cell matching with unpaired feature sets. Bioinformatics. 36(Supplement_2), i919–i927.","short":"S.G. Stark, J. Ficek, F. Locatello, X. Bonilla, S. Chevrier, F. Singer, R. Aebersold, F.S. Al-Quaddoomi, J. Albinus, I. Alborelli, S. Andani, P.-O. Attinger, M. Bacac, D. Baumhoer, B. Beck-Schimmer, N. Beerenwinkel, C. Beisel, L. Bernasconi, A. Bertolini, B. Bodenmiller, X. Bonilla, R. Casanova, S. Chevrier, N. Chicherova, M. D’Costa, E. Danenberg, N. Davidson, M.-A.D. gan, R. Dummer, S. Engler, M. Erkens, K. Eschbach, C. Esposito, A. Fedier, P. Ferreira, J. Ficek, A.L. Frei, B. Frey, S. Goetze, L. Grob, G. Gut, D. Günther, M. Haberecker, P. Haeuptle, V. Heinzelmann-Schwarz, S. Herter, R. Holtackers, T. Huesser, A. Irmisch, F. Jacob, A. Jacobs, T.M. Jaeger, K. Jahn, A.R. James, P.M. Jermann, A. Kahles, A. Kahraman, V.H. Koelzer, W. Kuebler, J. Kuipers, C.P. Kunze, C. Kurzeder, K.-V. Lehmann, M. Levesque, S. Lugert, G. Maass, M. Manz, P. Markolin, J. Mena, U. Menzel, J.M. Metzler, N. Miglino, E.S. Milani, H. Moch, S. Muenst, R. Murri, C.K. Ng, S. Nicolet, M. Nowak, P.G. Pedrioli, L. Pelkmans, S. Piscuoglio, M. Prummer, M. Ritter, C. Rommel, M.L. Rosano-González, G. Rätsch, N. Santacroce, J.S. del Castillo, R. Schlenker, P.C. Schwalie, S. Schwan, T. Schär, G. Senti, F. Singer, S. Sivapatham, B. Snijder, B. Sobottka, V.T. Sreedharan, S. Stark, D.J. Stekhoven, A.P. Theocharides, T.M. Thomas, M. Tolnay, V. Tosevski, N.C. Toussaint, M.A. Tuncel, M. Tusup, A.V. Drogen, M. Vetter, T. Vlajnic, S. Weber, W.P. Weber, R. Wegmann, M. Weller, F. Wendt, N. Wey, A. Wicki, B. Wollscheid, S. Yu, J. Ziegler, M. Zimmermann, M. Zoche, G. Zuend, G. Rätsch, K.-V. Lehmann, Bioinformatics 36 (2020) i919–i927."},"article_type":"original","day":"01","extern":"1","publication_status":"published","year":"2020","date_published":"2020-12-01T00:00:00Z","author":[{"last_name":"Stark","first_name":"Stefan G","full_name":"Stark, Stefan G"},{"full_name":"Ficek, Joanna","last_name":"Ficek","first_name":"Joanna"},{"last_name":"Locatello","orcid":"0000-0002-4850-0683","first_name":"Francesco","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","full_name":"Locatello, Francesco"},{"last_name":"Bonilla","first_name":"Ximena","full_name":"Bonilla, Ximena"},{"first_name":"Stéphane","last_name":"Chevrier","full_name":"Chevrier, Stéphane"},{"full_name":"Singer, Franziska","first_name":"Franziska","last_name":"Singer"},{"full_name":"Aebersold, Rudolf","first_name":"Rudolf","last_name":"Aebersold"},{"full_name":"Al-Quaddoomi, Faisal S","last_name":"Al-Quaddoomi","first_name":"Faisal S"},{"full_name":"Albinus, Jonas","last_name":"Albinus","first_name":"Jonas"},{"full_name":"Alborelli, Ilaria","first_name":"Ilaria","last_name":"Alborelli"},{"full_name":"Andani, Sonali","first_name":"Sonali","last_name":"Andani"},{"first_name":"Per-Olof","last_name":"Attinger","full_name":"Attinger, Per-Olof"},{"full_name":"Bacac, Marina","last_name":"Bacac","first_name":"Marina"},{"first_name":"Daniel","last_name":"Baumhoer","full_name":"Baumhoer, Daniel"},{"full_name":"Beck-Schimmer, Beatrice","first_name":"Beatrice","last_name":"Beck-Schimmer"},{"full_name":"Beerenwinkel, Niko","first_name":"Niko","last_name":"Beerenwinkel"},{"full_name":"Beisel, Christian","last_name":"Beisel","first_name":"Christian"},{"full_name":"Bernasconi, Lara","last_name":"Bernasconi","first_name":"Lara"},{"first_name":"Anne","last_name":"Bertolini","full_name":"Bertolini, Anne"},{"full_name":"Bodenmiller, Bernd","last_name":"Bodenmiller","first_name":"Bernd"},{"first_name":"Ximena","last_name":"Bonilla","full_name":"Bonilla, Ximena"},{"first_name":"Ruben","last_name":"Casanova","full_name":"Casanova, Ruben"},{"last_name":"Chevrier","first_name":"Stéphane","full_name":"Chevrier, Stéphane"},{"full_name":"Chicherova, Natalia","last_name":"Chicherova","first_name":"Natalia"},{"last_name":"D'Costa","first_name":"Maya","full_name":"D'Costa, Maya"},{"last_name":"Danenberg","first_name":"Esther","full_name":"Danenberg, Esther"},{"full_name":"Davidson, Natalie","last_name":"Davidson","first_name":"Natalie"},{"full_name":"gan, Monica-Andreea Dră","first_name":"Monica-Andreea Dră","last_name":"gan"},{"last_name":"Dummer","first_name":"Reinhard","full_name":"Dummer, Reinhard"},{"last_name":"Engler","first_name":"Stefanie","full_name":"Engler, Stefanie"},{"full_name":"Erkens, Martin","last_name":"Erkens","first_name":"Martin"},{"last_name":"Eschbach","first_name":"Katja","full_name":"Eschbach, Katja"},{"full_name":"Esposito, Cinzia","last_name":"Esposito","first_name":"Cinzia"},{"last_name":"Fedier","first_name":"André","full_name":"Fedier, André"},{"full_name":"Ferreira, Pedro","last_name":"Ferreira","first_name":"Pedro"},{"last_name":"Ficek","first_name":"Joanna","full_name":"Ficek, Joanna"},{"full_name":"Frei, Anja L","last_name":"Frei","first_name":"Anja L"},{"full_name":"Frey, Bruno","first_name":"Bruno","last_name":"Frey"},{"first_name":"Sandra","last_name":"Goetze","full_name":"Goetze, Sandra"},{"first_name":"Linda","last_name":"Grob","full_name":"Grob, Linda"},{"last_name":"Gut","first_name":"Gabriele","full_name":"Gut, Gabriele"},{"full_name":"Günther, Detlef","first_name":"Detlef","last_name":"Günther"},{"first_name":"Martina","last_name":"Haberecker","full_name":"Haberecker, Martina"},{"full_name":"Haeuptle, Pirmin","last_name":"Haeuptle","first_name":"Pirmin"},{"first_name":"Viola","last_name":"Heinzelmann-Schwarz","full_name":"Heinzelmann-Schwarz, Viola"},{"full_name":"Herter, Sylvia","first_name":"Sylvia","last_name":"Herter"},{"first_name":"Rene","last_name":"Holtackers","full_name":"Holtackers, Rene"},{"last_name":"Huesser","first_name":"Tamara","full_name":"Huesser, Tamara"},{"full_name":"Irmisch, Anja","last_name":"Irmisch","first_name":"Anja"},{"full_name":"Jacob, Francis","first_name":"Francis","last_name":"Jacob"},{"last_name":"Jacobs","first_name":"Andrea","full_name":"Jacobs, Andrea"},{"last_name":"Jaeger","first_name":"Tim M","full_name":"Jaeger, Tim M"},{"last_name":"Jahn","first_name":"Katharina","full_name":"Jahn, Katharina"},{"last_name":"James","first_name":"Alva R","full_name":"James, Alva R"},{"full_name":"Jermann, Philip M","first_name":"Philip M","last_name":"Jermann"},{"full_name":"Kahles, André","last_name":"Kahles","first_name":"André"},{"first_name":"Abdullah","last_name":"Kahraman","full_name":"Kahraman, Abdullah"},{"last_name":"Koelzer","first_name":"Viktor H","full_name":"Koelzer, Viktor H"},{"first_name":"Werner","last_name":"Kuebler","full_name":"Kuebler, Werner"},{"last_name":"Kuipers","first_name":"Jack","full_name":"Kuipers, Jack"},{"full_name":"Kunze, Christian P","first_name":"Christian P","last_name":"Kunze"},{"last_name":"Kurzeder","first_name":"Christian","full_name":"Kurzeder, Christian"},{"full_name":"Lehmann, Kjong-Van","first_name":"Kjong-Van","last_name":"Lehmann"},{"full_name":"Levesque, Mitchell","last_name":"Levesque","first_name":"Mitchell"},{"first_name":"Sebastian","last_name":"Lugert","full_name":"Lugert, Sebastian"},{"full_name":"Maass, Gerd","last_name":"Maass","first_name":"Gerd"},{"last_name":"Manz","first_name":"Markus","full_name":"Manz, Markus"},{"full_name":"Markolin, Philipp","first_name":"Philipp","last_name":"Markolin"},{"full_name":"Mena, Julien","last_name":"Mena","first_name":"Julien"},{"last_name":"Menzel","first_name":"Ulrike","full_name":"Menzel, Ulrike"},{"last_name":"Metzler","first_name":"Julian M","full_name":"Metzler, Julian M"},{"full_name":"Miglino, Nicola","first_name":"Nicola","last_name":"Miglino"},{"full_name":"Milani, Emanuela S","last_name":"Milani","first_name":"Emanuela S"},{"full_name":"Moch, Holger","first_name":"Holger","last_name":"Moch"},{"full_name":"Muenst, Simone","first_name":"Simone","last_name":"Muenst"},{"first_name":"Riccardo","last_name":"Murri","full_name":"Murri, Riccardo"},{"first_name":"Charlotte KY","last_name":"Ng","full_name":"Ng, Charlotte KY"},{"last_name":"Nicolet","first_name":"Stefan","full_name":"Nicolet, Stefan"},{"full_name":"Nowak, Marta","last_name":"Nowak","first_name":"Marta"},{"last_name":"Pedrioli","first_name":"Patrick GA","full_name":"Pedrioli, Patrick GA"},{"first_name":"Lucas","last_name":"Pelkmans","full_name":"Pelkmans, Lucas"},{"first_name":"Salvatore","last_name":"Piscuoglio","full_name":"Piscuoglio, Salvatore"},{"first_name":"Michael","last_name":"Prummer","full_name":"Prummer, Michael"},{"first_name":"Mathilde","last_name":"Ritter","full_name":"Ritter, Mathilde"},{"first_name":"Christian","last_name":"Rommel","full_name":"Rommel, Christian"},{"full_name":"Rosano-González, María L","last_name":"Rosano-González","first_name":"María L"},{"last_name":"Rätsch","first_name":"Gunnar","full_name":"Rätsch, Gunnar"},{"full_name":"Santacroce, Natascha","first_name":"Natascha","last_name":"Santacroce"},{"full_name":"Castillo, Jacobo Sarabia del","first_name":"Jacobo Sarabia del","last_name":"Castillo"},{"first_name":"Ramona","last_name":"Schlenker","full_name":"Schlenker, Ramona"},{"full_name":"Schwalie, Petra C","last_name":"Schwalie","first_name":"Petra C"},{"first_name":"Severin","last_name":"Schwan","full_name":"Schwan, Severin"},{"full_name":"Schär, Tobias","first_name":"Tobias","last_name":"Schär"},{"full_name":"Senti, Gabriela","last_name":"Senti","first_name":"Gabriela"},{"last_name":"Singer","first_name":"Franziska","full_name":"Singer, Franziska"},{"last_name":"Sivapatham","first_name":"Sujana","full_name":"Sivapatham, Sujana"},{"full_name":"Snijder, Berend","last_name":"Snijder","first_name":"Berend"},{"full_name":"Sobottka, Bettina","first_name":"Bettina","last_name":"Sobottka"},{"full_name":"Sreedharan, Vipin T","first_name":"Vipin T","last_name":"Sreedharan"},{"full_name":"Stark, Stefan","first_name":"Stefan","last_name":"Stark"},{"full_name":"Stekhoven, Daniel J","first_name":"Daniel J","last_name":"Stekhoven"},{"full_name":"Theocharides, Alexandre PA","last_name":"Theocharides","first_name":"Alexandre PA"},{"last_name":"Thomas","first_name":"Tinu M","full_name":"Thomas, Tinu M"},{"full_name":"Tolnay, Markus","first_name":"Markus","last_name":"Tolnay"},{"full_name":"Tosevski, Vinko","last_name":"Tosevski","first_name":"Vinko"},{"full_name":"Toussaint, Nora C","last_name":"Toussaint","first_name":"Nora C"},{"last_name":"Tuncel","first_name":"Mustafa A","full_name":"Tuncel, Mustafa A"},{"full_name":"Tusup, Marina","first_name":"Marina","last_name":"Tusup"},{"full_name":"Drogen, Audrey Van","last_name":"Drogen","first_name":"Audrey Van"},{"first_name":"Marcus","last_name":"Vetter","full_name":"Vetter, Marcus"},{"first_name":"Tatjana","last_name":"Vlajnic","full_name":"Vlajnic, Tatjana"},{"full_name":"Weber, Sandra","last_name":"Weber","first_name":"Sandra"},{"first_name":"Walter P","last_name":"Weber","full_name":"Weber, Walter P"},{"first_name":"Rebekka","last_name":"Wegmann","full_name":"Wegmann, Rebekka"},{"full_name":"Weller, Michael","last_name":"Weller","first_name":"Michael"},{"first_name":"Fabian","last_name":"Wendt","full_name":"Wendt, Fabian"},{"full_name":"Wey, Norbert","last_name":"Wey","first_name":"Norbert"},{"last_name":"Wicki","first_name":"Andreas","full_name":"Wicki, Andreas"},{"full_name":"Wollscheid, Bernd","first_name":"Bernd","last_name":"Wollscheid"},{"full_name":"Yu, Shuqing","last_name":"Yu","first_name":"Shuqing"},{"full_name":"Ziegler, Johanna","first_name":"Johanna","last_name":"Ziegler"},{"full_name":"Zimmermann, Marc","first_name":"Marc","last_name":"Zimmermann"},{"first_name":"Martin","last_name":"Zoche","full_name":"Zoche, Martin"},{"last_name":"Zuend","first_name":"Gregor","full_name":"Zuend, Gregor"},{"first_name":"Gunnar","last_name":"Rätsch","full_name":"Rätsch, Gunnar"},{"last_name":"Lehmann","first_name":"Kjong-Van","full_name":"Lehmann, Kjong-Van"}],"title":"SCIM: Universal single-cell matching with unpaired feature sets","_id":"14125","article_processing_charge":"No","publisher":"Oxford University Press","external_id":{"pmid":["33381818"]},"issue":"Supplement_2","quality_controlled":"1","keyword":["Computational Mathematics","Computational Theory and Mathematics","Computer Science Applications","Molecular Biology","Biochemistry","Statistics and Probability"],"status":"public","language":[{"iso":"eng"}],"intvolume":" 36","abstract":[{"lang":"eng","text":"Motivation: Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed.\r\nResults: We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively."}],"publication":"Bioinformatics","volume":36},{"publication_status":"published","has_accepted_license":"1","year":"2020","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","first_name":"Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"}],"title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","date_published":"2020-09-01T00:00:00Z","external_id":{"arxiv":["1804.07752"]},"keyword":["General Mathematics"],"quality_controlled":"1","_id":"14694","article_processing_charge":"Yes","publisher":"EMS Press","volume":25,"publication":"Documenta Mathematica","abstract":[{"text":"We study the unique solution m of the Dyson equation \\( -m(z)^{-1} = z\\1 - a + S[m(z)] \\) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases.","lang":"eng"}],"status":"public","intvolume":" 25","language":[{"iso":"eng"}],"month":"09","ddc":["510"],"oa_version":"Published Version","corr_author":"1","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-12-18T10:37:43Z","doi":"10.4171/dm/780","date_updated":"2025-04-15T08:05:00Z","department":[{"_id":"LaEr"}],"type":"journal_article","related_material":{"record":[{"id":"6183","relation":"earlier_version","status":"public"}]},"page":"1421-1539","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"fulldoi":"https://doi.org/10.4171/dm/780","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"citation":{"ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press, pp. 1421–1539, 2020.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/780","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020, pp. 1421–539, doi:10.4171/dm/780.","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica. EMS Press, 2020. https://doi.org/10.4171/dm/780.","ista":"Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539."},"oa":1,"article_type":"original","day":"01","file":[{"access_level":"open_access","success":1,"checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","content_type":"application/pdf","creator":"dernst","relation":"main_file","date_created":"2023-12-18T10:42:32Z","date_updated":"2023-12-18T10:42:32Z","file_size":1374708,"file_name":"2020_DocumentaMathematica_Alt.pdf","file_id":"14695"}],"file_date_updated":"2023-12-18T10:42:32Z"},{"file":[{"date_updated":"2020-11-18T07:26:10Z","date_created":"2020-11-18T07:26:10Z","relation":"main_file","file_name":"2020_PlosCompBio_Kaveh.pdf","file_size":2498594,"file_id":"8768","checksum":"555456dd0e47bcf9e0994bcb95577e88","content_type":"application/pdf","creator":"dernst","success":1,"access_level":"open_access"}],"file_date_updated":"2020-11-18T07:26:10Z","article_type":"original","day":"05","oa":1,"scopus_import":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"short":"K. Kaveh, A. McAvoy, K. Chatterjee, M.A. Nowak, PLOS Computational Biology 16 (2020).","ista":"Kaveh K, McAvoy A, Chatterjee K, Nowak MA. 2020. The Moran process on 2-chromatic graphs. PLOS Computational Biology. 16(11), e1008402.","chicago":"Kaveh, Kamran, Alex McAvoy, Krishnendu Chatterjee, and Martin A. Nowak. “The Moran Process on 2-Chromatic Graphs.” PLOS Computational Biology. Public Library of Science, 2020. https://doi.org/10.1371/journal.pcbi.1008402.","ama":"Kaveh K, McAvoy A, Chatterjee K, Nowak MA. The Moran process on 2-chromatic graphs. PLOS Computational Biology. 2020;16(11). doi:10.1371/journal.pcbi.1008402","ieee":"K. Kaveh, A. McAvoy, K. Chatterjee, and M. A. Nowak, “The Moran process on 2-chromatic graphs,” PLOS Computational Biology, vol. 16, no. 11. Public Library of Science, 2020.","apa":"Kaveh, K., McAvoy, A., Chatterjee, K., & Nowak, M. A. (2020). The Moran process on 2-chromatic graphs. PLOS Computational Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1008402","mla":"Kaveh, Kamran, et al. “The Moran Process on 2-Chromatic Graphs.” PLOS Computational Biology, vol. 16, no. 11, e1008402, Public Library of Science, 2020, doi:10.1371/journal.pcbi.1008402."},"fulldoi":"https://doi.org/10.1371/journal.pcbi.1008402","publication_identifier":{"issn":["1553-734X"],"eissn":["1553-7358"]},"pmid":1,"department":[{"_id":"KrCh"}],"type":"journal_article","date_updated":"2025-06-12T07:02:01Z","doi":"10.1371/journal.pcbi.1008402","date_created":"2020-11-18T07:20:23Z","month":"11","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"oa_version":"Published Version","acknowledgement":"We thank Igor Erovenko for many helpful comments on an earlier version of this paper. : Army Research Laboratory (grant W911NF-18-2-0265) (M.A.N.); the Bill & Melinda Gates Foundation (grant OPP1148627) (M.A.N.); the NVIDIA Corporation (A.M.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.","language":[{"iso":"eng"}],"intvolume":" 16","status":"public","abstract":[{"text":"Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.","lang":"eng"}],"publication":"PLOS Computational Biology","volume":16,"_id":"8767","publisher":"Public Library of Science","article_processing_charge":"No","external_id":{"isi":["000591317200004"],"pmid":["33151935"]},"issue":"11","article_number":"e1008402","keyword":["Ecology","Modelling and Simulation","Computational Theory and Mathematics","Genetics","Ecology","Evolution","Behavior and Systematics","Molecular Biology","Cellular and Molecular Neuroscience"],"quality_controlled":"1","date_published":"2020-11-05T00:00:00Z","author":[{"full_name":"Kaveh, Kamran","last_name":"Kaveh","first_name":"Kamran"},{"first_name":"Alex","last_name":"McAvoy","full_name":"McAvoy, Alex"},{"full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","orcid":"0000-0002-4561-241X"},{"last_name":"Nowak","first_name":"Martin A.","full_name":"Nowak, Martin A."}],"title":"The Moran process on 2-chromatic graphs","isi":1,"publication_status":"published","year":"2020","has_accepted_license":"1"},{"author":[{"first_name":"Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian"},{"first_name":"Tommaso","last_name":"Rosati","full_name":"Rosati, Tommaso"}],"title":"Modelled distributions of Triebel–Lizorkin type","date_published":"2020-03-01T00:00:00Z","publication_status":"published","year":"2020","isi":1,"volume":252,"publication":"Studia Mathematica","abstract":[{"lang":"eng","text":"In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its derivatives up to the required order at the point x itself. In other words, one could say that a regular function is locally modelled by the set of polynomials. The theory of regularity structures due to Hairer generalizes this observation and provides an abstract setup, which in the application to singular SPDE extends the set of polynomials by functionals constructed from, e.g., white noise. In this context, the notion of Taylor polynomials is lifted to the notion of so-called modelled distributions. The celebrated reconstruction theorem, which in turn was inspired by Gubinelli’s \\textit {sewing lemma}, is of paramount importance for the theory. It enables one to reconstruct a modelled distribution as a true distribution on Rd which is locally approximated by this extended set of models or “monomials”. In the original work of Hairer, the error is measured by means of Hölder norms. This was then generalized to the whole scale of Besov spaces by Hairer and Labbé. It is the aim of this work to adapt the analytic part of the theory of regularity structures to the scale of Triebel–Lizorkin spaces."}],"language":[{"iso":"eng"}],"intvolume":" 252","status":"public","issue":"3","external_id":{"isi":["000558100500002"],"arxiv":["1709.05202"]},"keyword":["General Mathematics"],"quality_controlled":"1","_id":"9196","article_processing_charge":"No","publisher":"Instytut Matematyczny","department":[{"_id":"JuFi"},{"_id":"GradSch"}],"type":"journal_article","page":"251-297","month":"03","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"date_updated":"2025-06-24T12:07:06Z","doi":"10.4064/sm180411-11-2","date_created":"2021-02-25T08:55:03Z","article_type":"original","day":"01","publication_identifier":{"eissn":["1730-6337"],"issn":["0039-3223"]},"fulldoi":"https://doi.org/10.4064/sm180411-11-2","citation":{"ama":"Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2","apa":"Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. Instytut Matematyczny. https://doi.org/10.4064/sm180411-11-2","ieee":"S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” Studia Mathematica, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297, 2020.","mla":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica, vol. 252, no. 3, Instytut Matematyczny, 2020, pp. 251–97, doi:10.4064/sm180411-11-2.","short":"S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.","ista":"Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297.","chicago":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica. Instytut Matematyczny, 2020. https://doi.org/10.4064/sm180411-11-2."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1709.05202"}],"scopus_import":"1","oa":1},{"publication_status":"published","has_accepted_license":"1","year":"2020","isi":1,"title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball","author":[{"full_name":"Feliciangeli, Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"date_published":"2020-02-12T00:00:00Z","issue":"1","external_id":{"isi":["000546967700022"],"arxiv":["1904.08647 "]},"quality_controlled":"1","keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"das_tickbox":"1","_id":"9781","article_processing_charge":"No","publisher":"Society for Industrial and Applied Mathematics","volume":52,"publication":"SIAM Journal on Mathematical Analysis","abstract":[{"text":"We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum.","lang":"eng"}],"acknowledgement":"We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227.","status":"public","language":[{"iso":"eng"}],"intvolume":" 52","month":"02","ddc":["510"],"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"corr_author":"1","date_updated":"2026-07-06T14:02:25Z","date_created":"2021-08-06T07:34:16Z","doi":"10.1137/19m126284x","ec_funded":1,"department":[{"_id":"RoSe"}],"type":"journal_article","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"9733"}]},"project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}],"page":"605-622","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"fulldoi":"https://doi.org/10.1137/19m126284x","citation":{"short":"D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622.","ista":"Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622.","chicago":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/19m126284x.","ama":"Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 2020;52(1):605-622. doi:10.1137/19m126284x","mla":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical Analysis, vol. 52, no. 1, Society for Industrial and Applied Mathematics, 2020, pp. 605–22, doi:10.1137/19m126284x.","apa":"Feliciangeli, D., & Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19m126284x","ieee":"D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” SIAM Journal on Mathematical Analysis, vol. 52, no. 1. Society for Industrial and Applied Mathematics, pp. 605–622, 2020."},"publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.08647"}],"oa":1,"scopus_import":"1","article_type":"original","day":"12"},{"abstract":[{"text":"For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0.","lang":"eng"}],"language":[{"iso":"eng"}],"status":"public","intvolume":" 233","volume":233,"publication":"Archive for Rational Mechanics and Analysis","_id":"8418","article_processing_charge":"No","publisher":"Springer Nature","issue":"2","keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"quality_controlled":"1","date_published":"2019-03-12T00:00:00Z","title":"Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem","author":[{"full_name":"Guardia, Marcel","first_name":"Marcel","last_name":"Guardia"},{"full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"full_name":"Zhang, Jianlu","last_name":"Zhang","first_name":"Jianlu"}],"extern":"1","publication_status":"published","year":"2019","article_type":"original","day":"12","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00205-019-01368-7"}],"oa":1,"citation":{"short":"M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis 233 (2019) 799–836.","chicago":"Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” Archive for Rational Mechanics and Analysis. Springer Nature, 2019. https://doi.org/10.1007/s00205-019-01368-7.","ista":"Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 233(2), 799–836.","mla":"Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” Archive for Rational Mechanics and Analysis, vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:10.1007/s00205-019-01368-7.","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem,” Archive for Rational Mechanics and Analysis, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019.","apa":"Guardia, M., Kaloshin, V., & Zhang, J. (2019). Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01368-7","ama":"Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 2019;233(2):799-836. doi:10.1007/s00205-019-01368-7"},"fulldoi":"https://doi.org/10.1007/s00205-019-01368-7","publication_identifier":{"issn":["0003-9527","1432-0673"]},"page":"799-836","type":"journal_article","date_updated":"2021-01-12T08:19:09Z","doi":"10.1007/s00205-019-01368-7","date_created":"2020-09-17T10:41:51Z","month":"03","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"isi":1,"year":"2019","publication_status":"published","date_published":"2019-06-01T00:00:00Z","title":"A mean-field model with discontinuous coefficients for neurons with spatial interaction","author":[{"last_name":"Flandoli","first_name":"Franco","full_name":"Flandoli, Franco"},{"first_name":"Enrico","last_name":"Priola","full_name":"Priola, Enrico"},{"full_name":"Zanco, Giovanni A","id":"47491882-F248-11E8-B48F-1D18A9856A87","last_name":"Zanco","first_name":"Giovanni A","orcid":"0000-0002-4680-9740"}],"publisher":"AIMS","article_processing_charge":"No","_id":"10878","keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics","Analysis"],"quality_controlled":"1","external_id":{"arxiv":["1708.04156"],"isi":["000459954800003"]},"issue":"6","language":[{"iso":"eng"}],"intvolume":" 39","acknowledgement":"The second author has been partially supported by INdAM through the GNAMPA Research\r\nProject (2017) “Sistemi stocastici singolari: buona posizione e problemi di controllo”. The third\r\nauthor was partly funded by the Austrian Science Fund (FWF) project F 65.","status":"public","abstract":[{"text":"Starting from a microscopic model for a system of neurons evolving in time which individually follow a stochastic integrate-and-fire type model, we study a mean-field limit of the system. Our model is described by a system of SDEs with discontinuous coefficients for the action potential of each neuron and takes into account the (random) spatial configuration of neurons allowing the interaction to depend on it. In the limit as the number of particles tends to infinity, we obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only with respect to one variable and discontinuous coefficients. We also study strong well-posedness of the system of SDEs and prove the existence and uniqueness of a weak measure-valued solution to the PDE, obtained as the limit of the laws of the empirical measures for the system of particles.","lang":"eng"}],"publication":"Discrete and Continuous Dynamical Systems","volume":39,"date_updated":"2026-08-12T06:18:59Z","doi":"10.3934/dcds.2019126","date_created":"2022-03-18T12:33:34Z","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","oa_version":"Preprint","month":"06","page":"3037-3067","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"type":"journal_article","department":[{"_id":"JaMa"}],"scopus_import":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.04156"}],"fulldoi":"https://doi.org/10.3934/dcds.2019126","publication_identifier":{"issn":["1553-5231"]},"citation":{"short":"F. Flandoli, E. Priola, G.A. Zanco, Discrete and Continuous Dynamical Systems 39 (2019) 3037–3067.","chicago":"Flandoli, Franco, Enrico Priola, and Giovanni A Zanco. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems. AIMS, 2019. https://doi.org/10.3934/dcds.2019126.","ista":"Flandoli F, Priola E, Zanco GA. 2019. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 39(6), 3037–3067.","ieee":"F. Flandoli, E. Priola, and G. A. Zanco, “A mean-field model with discontinuous coefficients for neurons with spatial interaction,” Discrete and Continuous Dynamical Systems, vol. 39, no. 6. AIMS, pp. 3037–3067, 2019.","mla":"Flandoli, Franco, et al. “A Mean-Field Model with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems, vol. 39, no. 6, AIMS, 2019, pp. 3037–67, doi:10.3934/dcds.2019126.","apa":"Flandoli, F., Priola, E., & Zanco, G. A. (2019). A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. AIMS. https://doi.org/10.3934/dcds.2019126","ama":"Flandoli F, Priola E, Zanco GA. A mean-field model with discontinuous coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical Systems. 2019;39(6):3037-3067. doi:10.3934/dcds.2019126"},"day":"01","article_type":"original"}]