[{"year":"2020","citation":{"apa":"Browning, T. D., & Heath Brown, R. (2020). Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/00127094-2020-0031","mla":"Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal, vol. 169, no. 16, Duke University Press, 2020, pp. 3099–165, doi:10.1215/00127094-2020-0031.","ieee":"T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” Duke Mathematical Journal, vol. 169, no. 16. Duke University Press, pp. 3099–3165, 2020.","ama":"Browning TD, Heath Brown R. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 2020;169(16):3099-3165. doi:10.1215/00127094-2020-0031","short":"T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal. Duke University Press, 2020. https://doi.org/10.1215/00127094-2020-0031.","ista":"Browning TD, Heath Brown R. 2020. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165."},"main_file_link":[{"url":"https://arxiv.org/abs/1805.10715","open_access":"1"}],"quality_controlled":"1","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Heath Brown, Roger","last_name":"Heath Brown","first_name":"Roger"}],"publication_status":"published","abstract":[{"lang":"eng","text":"An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed."}],"title":"Density of rational points on a quadric bundle in ℙ3×ℙ3","publication":"Duke Mathematical Journal","oa":1,"_id":"179","article_type":"original","publisher":"Duke University Press","issue":"16","volume":169,"date_created":"2018-12-11T11:45:02Z","month":"09","status":"public","intvolume":" 169","isi":1,"type":"journal_article","date_updated":"2023-10-17T12:51:10Z","oa_version":"Preprint","day":"10","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","language":[{"iso":"eng"}],"doi":"10.1215/00127094-2020-0031","department":[{"_id":"TiBr"}],"date_published":"2020-09-10T00:00:00Z","external_id":{"arxiv":["1805.10715"],"isi":["000582676300002"]},"page":"3099-3165","arxiv":1,"publication_identifier":{"issn":["0012-7094"]}},{"publication_status":"published","abstract":[{"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.","lang":"eng"}],"related_material":{"link":[{"url":"https://github.com/ratschlab/scim","relation":"software"}]},"oa":1,"_id":"14125","title":"SCIM: Universal single-cell matching with unpaired feature sets","publication":"Bioinformatics","pmid":1,"year":"2020","extern":"1","quality_controlled":"1","author":[{"full_name":"Stark, Stefan G","first_name":"Stefan G","last_name":"Stark"},{"last_name":"Ficek","first_name":"Joanna","full_name":"Ficek, Joanna"},{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","first_name":"Francesco","last_name":"Locatello"},{"first_name":"Ximena","last_name":"Bonilla","full_name":"Bonilla, Ximena"},{"first_name":"Stéphane","last_name":"Chevrier","full_name":"Chevrier, Stéphane"},{"full_name":"Singer, Franziska","first_name":"Franziska","last_name":"Singer"},{"first_name":"Rudolf","last_name":"Aebersold","full_name":"Aebersold, Rudolf"},{"first_name":"Faisal S","last_name":"Al-Quaddoomi","full_name":"Al-Quaddoomi, Faisal S"},{"full_name":"Albinus, Jonas","first_name":"Jonas","last_name":"Albinus"},{"last_name":"Alborelli","first_name":"Ilaria","full_name":"Alborelli, Ilaria"},{"full_name":"Andani, Sonali","first_name":"Sonali","last_name":"Andani"},{"full_name":"Attinger, Per-Olof","last_name":"Attinger","first_name":"Per-Olof"},{"full_name":"Bacac, Marina","first_name":"Marina","last_name":"Bacac"},{"full_name":"Baumhoer, Daniel","first_name":"Daniel","last_name":"Baumhoer"},{"full_name":"Beck-Schimmer, Beatrice","first_name":"Beatrice","last_name":"Beck-Schimmer"},{"full_name":"Beerenwinkel, Niko","last_name":"Beerenwinkel","first_name":"Niko"},{"last_name":"Beisel","first_name":"Christian","full_name":"Beisel, Christian"},{"full_name":"Bernasconi, Lara","first_name":"Lara","last_name":"Bernasconi"},{"last_name":"Bertolini","first_name":"Anne","full_name":"Bertolini, Anne"},{"full_name":"Bodenmiller, Bernd","last_name":"Bodenmiller","first_name":"Bernd"},{"full_name":"Bonilla, Ximena","last_name":"Bonilla","first_name":"Ximena"},{"full_name":"Casanova, Ruben","first_name":"Ruben","last_name":"Casanova"},{"full_name":"Chevrier, Stéphane","last_name":"Chevrier","first_name":"Stéphane"},{"last_name":"Chicherova","first_name":"Natalia","full_name":"Chicherova, Natalia"},{"first_name":"Maya","last_name":"D'Costa","full_name":"D'Costa, Maya"},{"first_name":"Esther","last_name":"Danenberg","full_name":"Danenberg, Esther"},{"full_name":"Davidson, Natalie","first_name":"Natalie","last_name":"Davidson"},{"full_name":"gan, Monica-Andreea Dră","last_name":"gan","first_name":"Monica-Andreea Dră"},{"first_name":"Reinhard","last_name":"Dummer","full_name":"Dummer, Reinhard"},{"first_name":"Stefanie","last_name":"Engler","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"},{"first_name":"André","last_name":"Fedier","full_name":"Fedier, André"},{"last_name":"Ferreira","first_name":"Pedro","full_name":"Ferreira, Pedro"},{"full_name":"Ficek, Joanna","last_name":"Ficek","first_name":"Joanna"},{"full_name":"Frei, Anja L","first_name":"Anja L","last_name":"Frei"},{"full_name":"Frey, Bruno","first_name":"Bruno","last_name":"Frey"},{"last_name":"Goetze","first_name":"Sandra","full_name":"Goetze, Sandra"},{"first_name":"Linda","last_name":"Grob","full_name":"Grob, Linda"},{"first_name":"Gabriele","last_name":"Gut","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"},{"full_name":"Heinzelmann-Schwarz, Viola","last_name":"Heinzelmann-Schwarz","first_name":"Viola"},{"full_name":"Herter, Sylvia","last_name":"Herter","first_name":"Sylvia"},{"full_name":"Holtackers, Rene","first_name":"Rene","last_name":"Holtackers"},{"full_name":"Huesser, Tamara","first_name":"Tamara","last_name":"Huesser"},{"full_name":"Irmisch, Anja","last_name":"Irmisch","first_name":"Anja"},{"first_name":"Francis","last_name":"Jacob","full_name":"Jacob, Francis"},{"full_name":"Jacobs, Andrea","last_name":"Jacobs","first_name":"Andrea"},{"last_name":"Jaeger","first_name":"Tim M","full_name":"Jaeger, Tim M"},{"full_name":"Jahn, Katharina","first_name":"Katharina","last_name":"Jahn"},{"last_name":"James","first_name":"Alva R","full_name":"James, Alva R"},{"first_name":"Philip M","last_name":"Jermann","full_name":"Jermann, Philip M"},{"full_name":"Kahles, André","last_name":"Kahles","first_name":"André"},{"first_name":"Abdullah","last_name":"Kahraman","full_name":"Kahraman, Abdullah"},{"first_name":"Viktor H","last_name":"Koelzer","full_name":"Koelzer, Viktor H"},{"first_name":"Werner","last_name":"Kuebler","full_name":"Kuebler, Werner"},{"first_name":"Jack","last_name":"Kuipers","full_name":"Kuipers, Jack"},{"first_name":"Christian P","last_name":"Kunze","full_name":"Kunze, Christian P"},{"first_name":"Christian","last_name":"Kurzeder","full_name":"Kurzeder, Christian"},{"full_name":"Lehmann, Kjong-Van","last_name":"Lehmann","first_name":"Kjong-Van"},{"full_name":"Levesque, Mitchell","first_name":"Mitchell","last_name":"Levesque"},{"full_name":"Lugert, Sebastian","first_name":"Sebastian","last_name":"Lugert"},{"full_name":"Maass, Gerd","last_name":"Maass","first_name":"Gerd"},{"first_name":"Markus","last_name":"Manz","full_name":"Manz, Markus"},{"first_name":"Philipp","last_name":"Markolin","full_name":"Markolin, Philipp"},{"full_name":"Mena, Julien","last_name":"Mena","first_name":"Julien"},{"full_name":"Menzel, Ulrike","last_name":"Menzel","first_name":"Ulrike"},{"first_name":"Julian M","last_name":"Metzler","full_name":"Metzler, Julian M"},{"full_name":"Miglino, Nicola","first_name":"Nicola","last_name":"Miglino"},{"full_name":"Milani, Emanuela S","first_name":"Emanuela S","last_name":"Milani"},{"full_name":"Moch, Holger","last_name":"Moch","first_name":"Holger"},{"full_name":"Muenst, Simone","first_name":"Simone","last_name":"Muenst"},{"last_name":"Murri","first_name":"Riccardo","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","first_name":"Marta","last_name":"Nowak"},{"first_name":"Patrick GA","last_name":"Pedrioli","full_name":"Pedrioli, Patrick GA"},{"last_name":"Pelkmans","first_name":"Lucas","full_name":"Pelkmans, Lucas"},{"first_name":"Salvatore","last_name":"Piscuoglio","full_name":"Piscuoglio, Salvatore"},{"full_name":"Prummer, Michael","first_name":"Michael","last_name":"Prummer"},{"first_name":"Mathilde","last_name":"Ritter","full_name":"Ritter, Mathilde"},{"full_name":"Rommel, Christian","first_name":"Christian","last_name":"Rommel"},{"last_name":"Rosano-González","first_name":"María L","full_name":"Rosano-González, María L"},{"full_name":"Rätsch, Gunnar","last_name":"Rätsch","first_name":"Gunnar"},{"full_name":"Santacroce, Natascha","first_name":"Natascha","last_name":"Santacroce"},{"last_name":"Castillo","first_name":"Jacobo Sarabia del","full_name":"Castillo, Jacobo Sarabia del"},{"full_name":"Schlenker, Ramona","first_name":"Ramona","last_name":"Schlenker"},{"last_name":"Schwalie","first_name":"Petra C","full_name":"Schwalie, Petra C"},{"first_name":"Severin","last_name":"Schwan","full_name":"Schwan, Severin"},{"last_name":"Schär","first_name":"Tobias","full_name":"Schär, Tobias"},{"full_name":"Senti, Gabriela","first_name":"Gabriela","last_name":"Senti"},{"last_name":"Singer","first_name":"Franziska","full_name":"Singer, Franziska"},{"full_name":"Sivapatham, Sujana","last_name":"Sivapatham","first_name":"Sujana"},{"first_name":"Berend","last_name":"Snijder","full_name":"Snijder, Berend"},{"last_name":"Sobottka","first_name":"Bettina","full_name":"Sobottka, Bettina"},{"full_name":"Sreedharan, Vipin T","last_name":"Sreedharan","first_name":"Vipin T"},{"first_name":"Stefan","last_name":"Stark","full_name":"Stark, Stefan"},{"last_name":"Stekhoven","first_name":"Daniel J","full_name":"Stekhoven, Daniel J"},{"full_name":"Theocharides, Alexandre PA","first_name":"Alexandre PA","last_name":"Theocharides"},{"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","first_name":"Vinko","last_name":"Tosevski"},{"last_name":"Toussaint","first_name":"Nora C","full_name":"Toussaint, Nora C"},{"last_name":"Tuncel","first_name":"Mustafa A","full_name":"Tuncel, Mustafa A"},{"first_name":"Marina","last_name":"Tusup","full_name":"Tusup, Marina"},{"full_name":"Drogen, Audrey Van","last_name":"Drogen","first_name":"Audrey Van"},{"last_name":"Vetter","first_name":"Marcus","full_name":"Vetter, Marcus"},{"full_name":"Vlajnic, Tatjana","first_name":"Tatjana","last_name":"Vlajnic"},{"first_name":"Sandra","last_name":"Weber","full_name":"Weber, Sandra"},{"last_name":"Weber","first_name":"Walter P","full_name":"Weber, Walter P"},{"full_name":"Wegmann, Rebekka","first_name":"Rebekka","last_name":"Wegmann"},{"full_name":"Weller, Michael","first_name":"Michael","last_name":"Weller"},{"first_name":"Fabian","last_name":"Wendt","full_name":"Wendt, Fabian"},{"last_name":"Wey","first_name":"Norbert","full_name":"Wey, Norbert"},{"full_name":"Wicki, Andreas","last_name":"Wicki","first_name":"Andreas"},{"last_name":"Wollscheid","first_name":"Bernd","full_name":"Wollscheid, Bernd"},{"full_name":"Yu, Shuqing","first_name":"Shuqing","last_name":"Yu"},{"full_name":"Ziegler, Johanna","first_name":"Johanna","last_name":"Ziegler"},{"last_name":"Zimmermann","first_name":"Marc","full_name":"Zimmermann, Marc"},{"full_name":"Zoche, Martin","first_name":"Martin","last_name":"Zoche"},{"last_name":"Zuend","first_name":"Gregor","full_name":"Zuend, Gregor"},{"first_name":"Gunnar","last_name":"Rätsch","full_name":"Rätsch, Gunnar"},{"first_name":"Kjong-Van","last_name":"Lehmann","full_name":"Lehmann, Kjong-Van"}],"citation":{"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","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.","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","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.","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."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/bioinformatics/btaa843"}],"status":"public","date_created":"2023-08-21T12:28:20Z","month":"12","intvolume":" 36","article_type":"original","publisher":"Oxford University Press","volume":36,"issue":"Supplement_2","doi":"10.1093/bioinformatics/btaa843","language":[{"iso":"eng"}],"department":[{"_id":"FrLo"}],"day":"01","date_updated":"2023-09-11T10:21:00Z","type":"journal_article","oa_version":"Published Version","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1367-4811"]},"scopus_import":"1","page":"i919-i927","date_published":"2020-12-01T00:00:00Z","external_id":{"pmid":["33381818"]},"keyword":["Computational Mathematics","Computational Theory and Mathematics","Computer Science Applications","Molecular Biology","Biochemistry","Statistics and Probability"]},{"oa_version":"Preprint","date_updated":"2023-09-12T07:44:48Z","type":"conference","day":"28","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","department":[{"_id":"FrLo"}],"doi":"10.1609/aaai.v34i09.7120","language":[{"iso":"eng"}],"external_id":{"arxiv":["2007.14184"]},"date_published":"2020-07-28T00:00:00Z","page":"13681-13684","arxiv":1,"scopus_import":"1","publication_identifier":{"isbn":["9781577358350"],"eissn":["2374-3468"]},"year":"2020","citation":{"apa":"Locatello, F., Bauer, S., Lucic, M., Rätsch, G., Gelly, S., Schölkopf, B., & Bachem, O. (2020). A commentary on the unsupervised learning of disentangled representations. In The 34th AAAI Conference on Artificial Intelligence (Vol. 34, pp. 13681–13684). New York, NY, United States: Association for the Advancement of Artificial Intelligence. https://doi.org/10.1609/aaai.v34i09.7120","mla":"Locatello, Francesco, et al. “A Commentary on the Unsupervised Learning of Disentangled Representations.” The 34th AAAI Conference on Artificial Intelligence, vol. 34, no. 9, Association for the Advancement of Artificial Intelligence, 2020, pp. 13681–84, doi:10.1609/aaai.v34i09.7120.","ama":"Locatello F, Bauer S, Lucic M, et al. A commentary on the unsupervised learning of disentangled representations. In: The 34th AAAI Conference on Artificial Intelligence. Vol 34. Association for the Advancement of Artificial Intelligence; 2020:13681-13684. doi:10.1609/aaai.v34i09.7120","ieee":"F. Locatello et al., “A commentary on the unsupervised learning of disentangled representations,” in The 34th AAAI Conference on Artificial Intelligence, New York, NY, United States, 2020, vol. 34, no. 9, pp. 13681–13684.","short":"F. Locatello, S. Bauer, M. Lucic, G. Rätsch, S. Gelly, B. Schölkopf, O. Bachem, in:, The 34th AAAI Conference on Artificial Intelligence, Association for the Advancement of Artificial Intelligence, 2020, pp. 13681–13684.","chicago":"Locatello, Francesco, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, and Olivier Bachem. “A Commentary on the Unsupervised Learning of Disentangled Representations.” In The 34th AAAI Conference on Artificial Intelligence, 34:13681–84. Association for the Advancement of Artificial Intelligence, 2020. https://doi.org/10.1609/aaai.v34i09.7120.","ista":"Locatello F, Bauer S, Lucic M, Rätsch G, Gelly S, Schölkopf B, Bachem O. 2020. A commentary on the unsupervised learning of disentangled representations. The 34th AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 34, 13681–13684."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2007.14184"}],"quality_controlled":"1","extern":"1","author":[{"id":"26cfd52f-2483-11ee-8040-88983bcc06d4","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","first_name":"Francesco","last_name":"Locatello"},{"full_name":"Bauer, Stefan","first_name":"Stefan","last_name":"Bauer"},{"full_name":"Lucic, Mario","last_name":"Lucic","first_name":"Mario"},{"full_name":"Rätsch, Gunnar","first_name":"Gunnar","last_name":"Rätsch"},{"last_name":"Gelly","first_name":"Sylvain","full_name":"Gelly, Sylvain"},{"full_name":"Schölkopf, Bernhard","first_name":"Bernhard","last_name":"Schölkopf"},{"first_name":"Olivier","last_name":"Bachem","full_name":"Bachem, Olivier"}],"abstract":[{"lang":"eng","text":"The goal of the unsupervised learning of disentangled representations is to\r\nseparate the independent explanatory factors of variation in the data without\r\naccess to supervision. In this paper, we summarize the results of Locatello et\r\nal., 2019, and focus on their implications for practitioners. We discuss the\r\ntheoretical result showing that the unsupervised learning of disentangled\r\nrepresentations is fundamentally impossible without inductive biases and the\r\npractical challenges it entails. Finally, we comment on our experimental\r\nfindings, highlighting the limitations of state-of-the-art approaches and\r\ndirections for future research."}],"publication_status":"published","publication":"The 34th AAAI Conference on Artificial Intelligence","title":"A commentary on the unsupervised learning of disentangled representations","_id":"14186","oa":1,"publisher":"Association for the Advancement of Artificial Intelligence","volume":34,"issue":"9","conference":{"end_date":"2020-02-12","name":"AAAI: Conference on Artificial Intelligence","start_date":"2020-02-07","location":"New York, NY, United States"},"month":"07","date_created":"2023-08-22T14:07:26Z","status":"public","intvolume":" 34"},{"alternative_title":["PMLR"],"arxiv":1,"external_id":{"arxiv":["2002.11860"]},"date_published":"2020-07-27T00:00:00Z","page":"7253-7262","department":[{"_id":"FrLo"}],"language":[{"iso":"eng"}],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","date_updated":"2023-09-12T08:03:40Z","type":"conference","day":"27","intvolume":" 119","conference":{"start_date":"2020-07-13","location":"Virtual","end_date":"2020-07-18","name":"International Conference on Machine Learning"},"month":"07","date_created":"2023-08-22T14:07:52Z","status":"public","volume":119,"title":"Stochastic Frank-Wolfe for constrained finite-sum minimization","publication":"Proceedings of the 37th International Conference on Machine Learning","_id":"14187","oa":1,"abstract":[{"text":"We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient)\r\nalgorithm for constrained smooth finite-sum minimization with a generalized\r\nlinear prediction/structure. This class of problems includes empirical risk\r\nminimization with sparse, low-rank, or other structured constraints. The\r\nproposed method is simple to implement, does not require step-size tuning, and\r\nhas a constant per-iteration cost that is independent of the dataset size.\r\nFurthermore, as a byproduct of the method we obtain a stochastic estimator of\r\nthe Frank-Wolfe gap that can be used as a stopping criterion. Depending on the\r\nsetting, the proposed method matches or improves on the best computational\r\nguarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several\r\ndatasets highlight different regimes in which the proposed method exhibits a\r\nfaster empirical convergence than related methods. Finally, we provide an\r\nimplementation of all considered methods in an open-source package.","lang":"eng"}],"publication_status":"published","citation":{"mla":"Négiar, Geoffrey, et al. “Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization.” Proceedings of the 37th International Conference on Machine Learning, vol. 119, 2020, pp. 7253–62.","apa":"Négiar, G., Dresdner, G., Tsai, A., Ghaoui, L. E., Locatello, F., Freund, R. M., & Pedregosa, F. (2020). Stochastic Frank-Wolfe for constrained finite-sum minimization. In Proceedings of the 37th International Conference on Machine Learning (Vol. 119, pp. 7253–7262). Virtual.","chicago":"Négiar, Geoffrey, Gideon Dresdner, Alicia Tsai, Laurent El Ghaoui, Francesco Locatello, Robert M. Freund, and Fabian Pedregosa. “Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization.” In Proceedings of the 37th International Conference on Machine Learning, 119:7253–62, 2020.","short":"G. Négiar, G. Dresdner, A. Tsai, L.E. Ghaoui, F. Locatello, R.M. Freund, F. Pedregosa, in:, Proceedings of the 37th International Conference on Machine Learning, 2020, pp. 7253–7262.","ista":"Négiar G, Dresdner G, Tsai A, Ghaoui LE, Locatello F, Freund RM, Pedregosa F. 2020. Stochastic Frank-Wolfe for constrained finite-sum minimization. Proceedings of the 37th International Conference on Machine Learning. International Conference on Machine Learning, PMLR, vol. 119, 7253–7262.","ama":"Négiar G, Dresdner G, Tsai A, et al. Stochastic Frank-Wolfe for constrained finite-sum minimization. In: Proceedings of the 37th International Conference on Machine Learning. Vol 119. ; 2020:7253-7262.","ieee":"G. Négiar et al., “Stochastic Frank-Wolfe for constrained finite-sum minimization,” in Proceedings of the 37th International Conference on Machine Learning, Virtual, 2020, vol. 119, pp. 7253–7262."},"main_file_link":[{"url":"https://arxiv.org/abs/2002.11860","open_access":"1"}],"quality_controlled":"1","author":[{"first_name":"Geoffrey","last_name":"Négiar","full_name":"Négiar, Geoffrey"},{"full_name":"Dresdner, Gideon","first_name":"Gideon","last_name":"Dresdner"},{"last_name":"Tsai","first_name":"Alicia","full_name":"Tsai, Alicia"},{"full_name":"Ghaoui, Laurent El","first_name":"Laurent El","last_name":"Ghaoui"},{"first_name":"Francesco","last_name":"Locatello","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","full_name":"Locatello, Francesco","orcid":"0000-0002-4850-0683"},{"first_name":"Robert M.","last_name":"Freund","full_name":"Freund, Robert M."},{"full_name":"Pedregosa, Fabian","last_name":"Pedregosa","first_name":"Fabian"}],"extern":"1","year":"2020"},{"department":[{"_id":"FrLo"}],"language":[{"iso":"eng"}],"day":"07","oa_version":"Preprint","date_updated":"2023-09-12T07:59:29Z","type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","arxiv":1,"scopus_import":"1","alternative_title":["PMLR"],"page":"6348–6359","external_id":{"arxiv":["2002.02886"]},"date_published":"2020-07-07T00:00:00Z","abstract":[{"text":"Intelligent agents should be able to learn useful representations by\r\nobserving changes in their environment. We model such observations as pairs of\r\nnon-i.i.d. images sharing at least one of the underlying factors of variation.\r\nFirst, we theoretically show that only knowing how many factors have changed,\r\nbut not which ones, is sufficient to learn disentangled representations.\r\nSecond, we provide practical algorithms that learn disentangled representations\r\nfrom pairs of images without requiring annotation of groups, individual\r\nfactors, or the number of factors that have changed. Third, we perform a\r\nlarge-scale empirical study and show that such pairs of observations are\r\nsufficient to reliably learn disentangled representations on several benchmark\r\ndata sets. Finally, we evaluate our learned representations and find that they\r\nare simultaneously useful on a diverse suite of tasks, including generalization\r\nunder covariate shifts, fairness, and abstract reasoning. Overall, our results\r\ndemonstrate that weak supervision enables learning of useful disentangled\r\nrepresentations in realistic scenarios.","lang":"eng"}],"publication_status":"published","_id":"14188","oa":1,"title":"Weakly-supervised disentanglement without compromises","publication":"Proceedings of the 37th International Conference on Machine Learning","year":"2020","quality_controlled":"1","extern":"1","author":[{"first_name":"Francesco","last_name":"Locatello","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","id":"26cfd52f-2483-11ee-8040-88983bcc06d4"},{"last_name":"Poole","first_name":"Ben","full_name":"Poole, Ben"},{"full_name":"Rätsch, Gunnar","last_name":"Rätsch","first_name":"Gunnar"},{"first_name":"Bernhard","last_name":"Schölkopf","full_name":"Schölkopf, Bernhard"},{"last_name":"Bachem","first_name":"Olivier","full_name":"Bachem, Olivier"},{"last_name":"Tschannen","first_name":"Michael","full_name":"Tschannen, Michael"}],"citation":{"ista":"Locatello F, Poole B, Rätsch G, Schölkopf B, Bachem O, Tschannen M. 2020. Weakly-supervised disentanglement without compromises. Proceedings of the 37th International Conference on Machine Learning. International Conference on Machine Learning, PMLR, vol. 119, 6348–6359.","short":"F. Locatello, B. Poole, G. Rätsch, B. Schölkopf, O. Bachem, M. Tschannen, in:, Proceedings of the 37th International Conference on Machine Learning, 2020, pp. 6348–6359.","chicago":"Locatello, Francesco, Ben Poole, Gunnar Rätsch, Bernhard Schölkopf, Olivier Bachem, and Michael Tschannen. “Weakly-Supervised Disentanglement without Compromises.” In Proceedings of the 37th International Conference on Machine Learning, 119:6348–6359, 2020.","ieee":"F. Locatello, B. Poole, G. Rätsch, B. Schölkopf, O. Bachem, and M. Tschannen, “Weakly-supervised disentanglement without compromises,” in Proceedings of the 37th International Conference on Machine Learning, Virtual, 2020, vol. 119, pp. 6348–6359.","ama":"Locatello F, Poole B, Rätsch G, Schölkopf B, Bachem O, Tschannen M. Weakly-supervised disentanglement without compromises. In: Proceedings of the 37th International Conference on Machine Learning. Vol 119. ; 2020:6348–6359.","apa":"Locatello, F., Poole, B., Rätsch, G., Schölkopf, B., Bachem, O., & Tschannen, M. (2020). Weakly-supervised disentanglement without compromises. In Proceedings of the 37th International Conference on Machine Learning (Vol. 119, pp. 6348–6359). Virtual.","mla":"Locatello, Francesco, et al. “Weakly-Supervised Disentanglement without Compromises.” Proceedings of the 37th International Conference on Machine Learning, vol. 119, 2020, pp. 6348–6359."},"main_file_link":[{"url":"https://arxiv.org/abs/2002.02886","open_access":"1"}],"status":"public","conference":{"location":"Virtual","start_date":"2020-07-13","name":"International Conference on Machine Learning","end_date":"2020-07-18"},"month":"07","date_created":"2023-08-22T14:08:14Z","intvolume":" 119","volume":119},{"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2020","main_file_link":[{"open_access":"1","url":"https://jmlr.csail.mit.edu/papers/v21/19-976.html"}],"citation":{"ista":"Locatello F, Bauer S, Lucic M, Rätsch G, Gelly S, Schölkopf B, Bachem O. 2020. A sober look at the unsupervised learning of disentangled representations and their evaluation. Journal of Machine Learning Research. 21, 209.","short":"F. Locatello, S. Bauer, M. Lucic, G. Rätsch, S. Gelly, B. Schölkopf, O. Bachem, Journal of Machine Learning Research 21 (2020).","chicago":"Locatello, Francesco, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, and Olivier Bachem. “A Sober Look at the Unsupervised Learning of Disentangled Representations and Their Evaluation.” Journal of Machine Learning Research. MIT Press, 2020.","ieee":"F. Locatello et al., “A sober look at the unsupervised learning of disentangled representations and their evaluation,” Journal of Machine Learning Research, vol. 21. MIT Press, 2020.","ama":"Locatello F, Bauer S, Lucic M, et al. A sober look at the unsupervised learning of disentangled representations and their evaluation. Journal of Machine Learning Research. 2020;21.","apa":"Locatello, F., Bauer, S., Lucic, M., Rätsch, G., Gelly, S., Schölkopf, B., & Bachem, O. (2020). A sober look at the unsupervised learning of disentangled representations and their evaluation. Journal of Machine Learning Research. MIT Press.","mla":"Locatello, Francesco, et al. “A Sober Look at the Unsupervised Learning of Disentangled Representations and Their Evaluation.” Journal of Machine Learning Research, vol. 21, 209, MIT Press, 2020."},"quality_controlled":"1","extern":"1","author":[{"first_name":"Francesco","last_name":"Locatello","orcid":"0000-0002-4850-0683","full_name":"Locatello, Francesco","id":"26cfd52f-2483-11ee-8040-88983bcc06d4"},{"first_name":"Stefan","last_name":"Bauer","full_name":"Bauer, Stefan"},{"full_name":"Lucic, Mario","last_name":"Lucic","first_name":"Mario"},{"full_name":"Rätsch, Gunnar","first_name":"Gunnar","last_name":"Rätsch"},{"first_name":"Sylvain","last_name":"Gelly","full_name":"Gelly, Sylvain"},{"last_name":"Schölkopf","first_name":"Bernhard","full_name":"Schölkopf, Bernhard"},{"last_name":"Bachem","first_name":"Olivier","full_name":"Bachem, Olivier"}],"abstract":[{"text":"The idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train over 14000\r\n models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, different evaluation metrics do not always agree on what should be considered “disentangled” and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.","lang":"eng"}],"publication_status":"published","title":"A sober look at the unsupervised learning of disentangled representations and their evaluation","publication":"Journal of Machine Learning Research","_id":"14195","ddc":["000"],"oa":1,"publisher":"MIT Press","article_type":"original","volume":21,"month":"09","date_created":"2023-08-22T14:10:34Z","article_number":"209","status":"public","intvolume":" 21","oa_version":"Published Version","date_updated":"2023-09-12T09:23:56Z","type":"journal_article","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","has_accepted_license":"1","department":[{"_id":"FrLo"}],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2010.14766"]},"date_published":"2020-09-01T00:00:00Z","arxiv":1,"scopus_import":"1"},{"publication":"Advances in Neural Information Processing Systems","title":"Object-centric learning with slot attention","_id":"14326","department":[{"_id":"FrLo"}],"oa":1,"language":[{"iso":"eng"}],"abstract":[{"text":"Learning object-centric representations of complex scenes is a promising step towards enabling efficient abstract reasoning from low-level perceptual features. Yet, most deep learning approaches learn distributed representations that do not capture the compositional properties of natural scenes. In this paper, we present the Slot Attention module, an architectural component that interfaces with perceptual representations such as the output of a convolutional neural network and produces a set of task-dependent abstract representations which we call slots. These slots are exchangeable and can bind to any object in the input by specializing through a competitive procedure over multiple rounds of attention. We empirically demonstrate that Slot Attention can extract object-centric representations that enable generalization to unseen compositions when trained on unsupervised object discovery and supervised property prediction tasks.\r\n\r\n","lang":"eng"}],"publication_status":"published","citation":{"ista":"Locatello F, Weissenborn D, Unterthiner T, Mahendran A, Heigold G, Uszkoreit J, Dosovitskiy A, Kipf T. 2020. Object-centric learning with slot attention. Advances in Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems vol. 33, 11525–11538.","chicago":"Locatello, Francesco, Dirk Weissenborn, Thomas Unterthiner, Aravindh Mahendran, Georg Heigold, Jakob Uszkoreit, Alexey Dosovitskiy, and Thomas Kipf. “Object-Centric Learning with Slot Attention.” In Advances in Neural Information Processing Systems, 33:11525–38. Curran Associates, 2020.","short":"F. Locatello, D. Weissenborn, T. Unterthiner, A. Mahendran, G. Heigold, J. Uszkoreit, A. Dosovitskiy, T. Kipf, in:, Advances in Neural Information Processing Systems, Curran Associates, 2020, pp. 11525–11538.","ama":"Locatello F, Weissenborn D, Unterthiner T, et al. Object-centric learning with slot attention. In: Advances in Neural Information Processing Systems. Vol 33. Curran Associates; 2020:11525-11538.","ieee":"F. Locatello et al., “Object-centric learning with slot attention,” in Advances in Neural Information Processing Systems, Virtual, 2020, vol. 33, pp. 11525–11538.","mla":"Locatello, Francesco, et al. “Object-Centric Learning with Slot Attention.” Advances in Neural Information Processing Systems, vol. 33, Curran Associates, 2020, pp. 11525–38.","apa":"Locatello, F., Weissenborn, D., Unterthiner, T., Mahendran, A., Heigold, G., Uszkoreit, J., … Kipf, T. (2020). Object-centric learning with slot attention. In Advances in Neural Information Processing Systems (Vol. 33, pp. 11525–11538). Virtual: Curran Associates."},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2006.15055","open_access":"1"}],"article_processing_charge":"No","author":[{"first_name":"Francesco","last_name":"Locatello","full_name":"Locatello, Francesco","orcid":"0000-0002-4850-0683","id":"26cfd52f-2483-11ee-8040-88983bcc06d4"},{"full_name":"Weissenborn, Dirk","last_name":"Weissenborn","first_name":"Dirk"},{"full_name":"Unterthiner, Thomas","last_name":"Unterthiner","first_name":"Thomas"},{"full_name":"Mahendran, Aravindh","first_name":"Aravindh","last_name":"Mahendran"},{"last_name":"Heigold","first_name":"Georg","full_name":"Heigold, Georg"},{"full_name":"Uszkoreit, Jakob","first_name":"Jakob","last_name":"Uszkoreit"},{"first_name":"Alexey","last_name":"Dosovitskiy","full_name":"Dosovitskiy, Alexey"},{"full_name":"Kipf, Thomas","last_name":"Kipf","first_name":"Thomas"}],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","oa_version":"Preprint","type":"conference","date_updated":"2023-09-13T12:19:19Z","year":"2020","intvolume":" 33","publication_identifier":{"isbn":["9781713829546"]},"arxiv":1,"conference":{"name":"NeurIPS: Neural Information Processing Systems","end_date":"2020-12-12","start_date":"2020-12-06","location":"Virtual"},"date_created":"2023-09-13T12:03:46Z","status":"public","external_id":{"arxiv":["2006.15055"]},"date_published":"2020-01-01T00:00:00Z","volume":33,"page":"11525-11538","publisher":"Curran Associates"},{"_id":"14592","department":[{"_id":"FlSc"}],"has_accepted_license":"1","ddc":["570"],"related_material":{"record":[{"id":"8586","status":"public","relation":"research_data"}]},"oa":1,"doi":"10.15479/AT:ISTA:14592","title":"STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy","abstract":[{"lang":"eng","text":"Cryo-electron microscopy (cryo-EM) of cellular specimens provides insights into biological processes and structures within a native context. However, a major challenge still lies in the efficient and reproducible preparation of adherent cells for subsequent cryo-EM analysis. This is due to the sensitivity of many cellular specimens to the varying seeding and culturing conditions required for EM experiments, the often limited amount of cellular material and also the fragility of EM grids and their substrate. Here, we present low-cost and reusable 3D printed grid holders, designed to improve specimen preparation when culturing challenging cellular samples directly on grids. The described grid holders increase cell culture reproducibility and throughput, and reduce the resources required for cell culturing. We show that grid holders can be integrated into various cryo-EM workflows, including micro-patterning approaches to control cell seeding on grids, and for generating samples for cryo-focused ion beam milling and cryo-electron tomography experiments. Their adaptable design allows for the generation of specialized grid holders customized to a large variety of applications."}],"project":[{"grant_number":"P33367","name":"Structure and isoform diversity of the Arp2/3 complex","_id":"9B954C5C-BA93-11EA-9121-9846C619BF3A"}],"author":[{"last_name":"Schur","first_name":"Florian KM","id":"48AD8942-F248-11E8-B48F-1D18A9856A87","full_name":"Schur, Florian KM","orcid":"0000-0003-4790-8078"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","citation":{"chicago":"Schur, Florian KM. “STL-Files for 3D-Printed Grid Holders Described in Fäßler F, Zens B, et Al.; 3D Printed Cell Culture Grid Holders for Improved Cellular Specimen Preparation in Cryo-Electron Microscopy.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:14592.","short":"F.K. Schur, (2020).","ista":"Schur FK. 2020. STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy, Institute of Science and Technology Austria, 10.15479/AT:ISTA:14592.","ama":"Schur FK. STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy. 2020. doi:10.15479/AT:ISTA:14592","ieee":"F. K. Schur, “STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy.” Institute of Science and Technology Austria, 2020.","apa":"Schur, F. K. (2020). STL-files for 3D-printed grid holders described in Fäßler F, Zens B, et al.; 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:14592","mla":"Schur, Florian KM. STL-Files for 3D-Printed Grid Holders Described in Fäßler F, Zens B, et Al.; 3D Printed Cell Culture Grid Holders for Improved Cellular Specimen Preparation in Cryo-Electron Microscopy. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:14592."},"year":"2020","day":"01","contributor":[{"contributor_type":"researcher","last_name":"Fäßler","first_name":"Florian","id":"404F5528-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7149-769X"},{"id":"45FD126C-F248-11E8-B48F-1D18A9856A87","contributor_type":"researcher","last_name":"Zens","first_name":"Bettina"},{"id":"4E01D6B4-F248-11E8-B48F-1D18A9856A87","contributor_type":"researcher","last_name":"Hauschild","first_name":"Robert"},{"first_name":"Florian KM","last_name":"Schur","contributor_type":"researcher","orcid":"0000-0003-4790-8078","id":"48AD8942-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png"},"date_updated":"2024-02-21T12:44:48Z","type":"research_data","status":"public","month":"12","date_created":"2023-11-22T15:00:57Z","file":[{"success":1,"date_updated":"2023-11-22T14:58:44Z","file_id":"14593","file_name":"3Dprint-files_download_v2.zip","checksum":"0108616e2a59e51879ea51299a29b091","access_level":"open_access","relation":"main_file","date_created":"2023-11-22T14:58:44Z","creator":"fschur","content_type":"application/zip","file_size":49297},{"file_id":"14637","date_updated":"2023-12-01T10:39:59Z","success":1,"access_level":"open_access","file_name":"readme.txt","checksum":"4c66ddedee4d01c1c4a7978208350cfc","date_created":"2023-12-01T10:39:59Z","relation":"main_file","file_size":641,"content_type":"text/plain","creator":"cchlebak"}],"date_published":"2020-12-01T00:00:00Z","publisher":"Institute of Science and Technology Austria","file_date_updated":"2023-12-01T10:39:59Z"},{"volume":25,"file_date_updated":"2023-12-18T10:42:32Z","article_type":"original","publisher":"EMS Press","intvolume":" 25","date_created":"2023-12-18T10:37:43Z","month":"09","status":"public","citation":{"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.","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","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.","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.","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.","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.","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"},"quality_controlled":"1","author":[{"first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2020","publication":"Documenta Mathematica","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","ddc":["510"],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"6183"}]},"oa":1,"_id":"14694","publication_status":"published","abstract":[{"lang":"eng","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."}],"date_published":"2020-09-01T00:00:00Z","external_id":{"arxiv":["1804.07752"]},"file":[{"file_name":"2020_DocumentaMathematica_Alt.pdf","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","access_level":"open_access","success":1,"date_updated":"2023-12-18T10:42:32Z","file_id":"14695","file_size":1374708,"content_type":"application/pdf","creator":"dernst","relation":"main_file","date_created":"2023-12-18T10:42:32Z"}],"keyword":["General Mathematics"],"page":"1421-1539","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"arxiv":1,"article_processing_charge":"Yes","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","date_updated":"2023-12-18T10:46:09Z","oa_version":"Published Version","day":"01","language":[{"iso":"eng"}],"doi":"10.4171/dm/780","has_accepted_license":"1","department":[{"_id":"LaEr"}]},{"publication_identifier":{"issn":["10772626"],"eissn":["19410506"]},"scopus_import":"1","date_published":"2020-06-01T00:00:00Z","external_id":{"pmid":["30507534"],"isi":["000532295600014"]},"file":[{"creator":"wojtan","content_type":"application/pdf","file_size":21910098,"relation":"main_file","date_created":"2020-10-08T08:34:53Z","checksum":"8d4c55443a0ee335bb5bb652de503042","file_name":"preprint.pdf","access_level":"open_access","success":1,"file_id":"8626","date_updated":"2020-10-08T08:34:53Z"}],"page":"2288-2302","acknowledged_ssus":[{"_id":"ScienComp"}],"doi":"10.1109/TVCG.2018.2883628","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"ChWo"}],"acknowledgement":"This work was partially supported by JSPS Grant-in-Aid forYoung Scientists (Start-up) 16H07410, the ERC StartingGrantsrealFlow(StG-2015-637014) andBigSplash(StG-2014-638176). This research was supported by the Scientific Ser-vice Units (SSU) of IST Austria through resources providedby Scientific Computing. We would like to express my grati-tude to Nobuyuki Umetani and Tomas Skrivan for insight-ful discussion.","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","article_processing_charge":"No","type":"journal_article","date_updated":"2023-09-18T09:30:01Z","oa_version":"Submitted Version","day":"01","intvolume":" 26","isi":1,"date_created":"2018-12-16T22:59:21Z","month":"06","status":"public","issue":"6","volume":26,"file_date_updated":"2020-10-08T08:34:53Z","article_type":"original","publisher":"IEEE","publication":"IEEE Transactions on Visualization and Computer Graphics","title":"Simulating liquids on dynamically warping grids","pmid":1,"oa":1,"ddc":["006"],"_id":"5681","publication_status":"published","abstract":[{"text":"We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms.","lang":"eng"}],"citation":{"ieee":"I. Hikaru, C. Wojtan, N. Thuerey, T. Igarashi, and R. Ando, “Simulating liquids on dynamically warping grids,” IEEE Transactions on Visualization and Computer Graphics, vol. 26, no. 6. IEEE, pp. 2288–2302, 2020.","ama":"Hikaru I, Wojtan C, Thuerey N, Igarashi T, Ando R. Simulating liquids on dynamically warping grids. IEEE Transactions on Visualization and Computer Graphics. 2020;26(6):2288-2302. doi:10.1109/TVCG.2018.2883628","ista":"Hikaru I, Wojtan C, Thuerey N, Igarashi T, Ando R. 2020. Simulating liquids on dynamically warping grids. IEEE Transactions on Visualization and Computer Graphics. 26(6), 2288–2302.","chicago":"Hikaru, Ibayashi, Chris Wojtan, Nils Thuerey, Takeo Igarashi, and Ryoichi Ando. “Simulating Liquids on Dynamically Warping Grids.” IEEE Transactions on Visualization and Computer Graphics. IEEE, 2020. https://doi.org/10.1109/TVCG.2018.2883628.","short":"I. Hikaru, C. Wojtan, N. Thuerey, T. Igarashi, R. Ando, IEEE Transactions on Visualization and Computer Graphics 26 (2020) 2288–2302.","mla":"Hikaru, Ibayashi, et al. “Simulating Liquids on Dynamically Warping Grids.” IEEE Transactions on Visualization and Computer Graphics, vol. 26, no. 6, IEEE, 2020, pp. 2288–302, doi:10.1109/TVCG.2018.2883628.","apa":"Hikaru, I., Wojtan, C., Thuerey, N., Igarashi, T., & Ando, R. (2020). Simulating liquids on dynamically warping grids. IEEE Transactions on Visualization and Computer Graphics. IEEE. https://doi.org/10.1109/TVCG.2018.2883628"},"author":[{"full_name":"Hikaru, Ibayashi","first_name":"Ibayashi","last_name":"Hikaru"},{"first_name":"Christopher J","last_name":"Wojtan","id":"3C61F1D2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6646-5546","full_name":"Wojtan, Christopher J"},{"full_name":"Thuerey, Nils","last_name":"Thuerey","first_name":"Nils"},{"full_name":"Igarashi, Takeo","first_name":"Takeo","last_name":"Igarashi"},{"full_name":"Ando, Ryoichi","first_name":"Ryoichi","last_name":"Ando"}],"quality_controlled":"1","year":"2020"},{"publication_identifier":{"issn":["0091-1798"]},"scopus_import":"1","arxiv":1,"date_published":"2020-03-01T00:00:00Z","external_id":{"isi":["000528269100013"],"arxiv":["1804.07744"]},"page":"963-1001","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1214/19-AOP1379","department":[{"_id":"LaEr"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_updated":"2024-02-22T14:34:33Z","type":"journal_article","oa_version":"Preprint","day":"01","intvolume":" 48","isi":1,"date_created":"2019-03-28T09:20:08Z","month":"03","status":"public","issue":"2","volume":48,"article_type":"original","publisher":"Institute of Mathematical Statistics","title":"Correlated random matrices: Band rigidity and edge universality","publication":"Annals of Probability","oa":1,"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"},{"id":"6179","status":"public","relation":"dissertation_contains"}]},"_id":"6184","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publication_status":"published","abstract":[{"lang":"eng","text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models."}],"main_file_link":[{"url":"https://arxiv.org/abs/1804.07744","open_access":"1"}],"citation":{"mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379","ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379"},"quality_controlled":"1","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes"},{"last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"year":"2020"},{"date_created":"2019-03-28T10:21:15Z","month":"09","status":"public","intvolume":" 378","isi":1,"file_date_updated":"2020-11-18T11:14:37Z","article_type":"original","publisher":"Springer Nature","volume":378,"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication_status":"published","abstract":[{"lang":"eng","text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969)."}],"publication":"Communications in Mathematical Physics","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","ddc":["530","510"],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"oa":1,"_id":"6185","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2020","citation":{"short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 2020;378:1203-1278. doi:10.1007/s00220-019-03657-4","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4."},"quality_controlled":"1","author":[{"last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Torben H","last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"}],"arxiv":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"scopus_import":"1","date_published":"2020-09-01T00:00:00Z","file":[{"creator":"dernst","content_type":"application/pdf","file_size":2904574,"relation":"main_file","date_created":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","checksum":"c3a683e2afdcea27afa6880b01e53dc2","access_level":"open_access","success":1,"date_updated":"2020-11-18T11:14:37Z","file_id":"8771"}],"external_id":{"isi":["000529483000001"],"arxiv":["1809.03971"]},"page":"1203-1278","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","ec_funded":1,"doi":"10.1007/s00220-019-03657-4","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"has_accepted_license":"1","date_updated":"2023-09-07T12:54:12Z","type":"journal_article","oa_version":"Published Version","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)"},{"volume":178,"issue":"2","file_date_updated":"2020-07-14T12:47:28Z","publisher":"Springer Nature","article_type":"original","intvolume":" 178","isi":1,"date_created":"2019-04-30T07:34:18Z","month":"01","status":"public","citation":{"ista":"Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378.","chicago":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w.","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.","ama":"Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w","ieee":"E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems,” Journal of Statistical Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.","mla":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w.","apa":"Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w"},"author":[{"full_name":"Carlen, Eric A.","last_name":"Carlen","first_name":"Eric A."},{"last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2020","publication":"Journal of Statistical Physics","title":"Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems","oa":1,"related_material":{"link":[{"url":"https://doi.org/10.1007/s10955-020-02671-4","relation":"erratum"}]},"ddc":["500"],"_id":"6358","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"},{"call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":" F06504","name":"Taming Complexity in Partial Di erential Systems"}],"publication_status":"published","abstract":[{"lang":"eng","text":"We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates."}],"date_published":"2020-01-01T00:00:00Z","external_id":{"isi":["000498933300001"],"arxiv":["1811.04572"]},"file":[{"date_created":"2019-12-23T12:03:09Z","relation":"main_file","file_size":905538,"content_type":"application/pdf","creator":"dernst","date_updated":"2020-07-14T12:47:28Z","file_id":"7209","access_level":"open_access","checksum":"7b04befbdc0d4982c0ee945d25d19872","file_name":"2019_JourStatistPhysics_Carlen.pdf"}],"page":"319-378","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"scopus_import":"1","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","date_updated":"2023-08-17T13:49:40Z","type":"journal_article","oa_version":"Published Version","day":"01","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/s10955-019-02434-w","department":[{"_id":"JaMa"}],"has_accepted_license":"1"},{"file_date_updated":"2020-09-21T13:15:02Z","article_type":"original","publisher":"Institute of Mathematical Statistics","volume":25,"month":"07","date_created":"2019-04-30T07:40:17Z","article_number":"82","status":"public","intvolume":" 25","isi":1,"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2020","citation":{"apa":"Dareiotis, K., & Gerencser, M. (2020). On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-EJP479","mla":"Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability, vol. 25, 82, Institute of Mathematical Statistics, 2020, doi:10.1214/20-EJP479.","ama":"Dareiotis K, Gerencser M. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 2020;25. doi:10.1214/20-EJP479","ieee":"K. Dareiotis and M. Gerencser, “On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift,” Electronic Journal of Probability, vol. 25. Institute of Mathematical Statistics, 2020.","chicago":"Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the Noise for the Euler-Maruyama Scheme with Irregular Drift.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-EJP479.","short":"K. Dareiotis, M. Gerencser, Electronic Journal of Probability 25 (2020).","ista":"Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability. 25, 82."},"author":[{"last_name":"Dareiotis","first_name":"Konstantinos","full_name":"Dareiotis, Konstantinos"},{"last_name":"Gerencser","first_name":"Mate","full_name":"Gerencser, Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","abstract":[{"text":"The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.","lang":"eng"}],"publication_status":"published","publication":"Electronic Journal of Probability","title":"On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift","_id":"6359","ddc":["510"],"oa":1,"external_id":{"isi":["000550150700001"],"arxiv":["1812.04583"]},"file":[{"checksum":"8e7c42e72596f6889d786e8e8b89994f","file_name":"2020_EJournProbab_Dareiotis.pdf","access_level":"open_access","success":1,"date_updated":"2020-09-21T13:15:02Z","file_id":"8549","file_size":273042,"creator":"dernst","content_type":"application/pdf","relation":"main_file","date_created":"2020-09-21T13:15:02Z"}],"date_published":"2020-07-16T00:00:00Z","arxiv":1,"scopus_import":"1","publication_identifier":{"eissn":["1083-6489"]},"oa_version":"Published Version","type":"journal_article","date_updated":"2023-10-16T09:22:50Z","day":"16","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"JaMa"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"doi":"10.1214/20-EJP479"},{"volume":9,"issue":"3","article_type":"original","publisher":"World Scientific Publishing","isi":1,"intvolume":" 9","article_number":"2050006","status":"public","month":"07","date_created":"2019-05-26T21:59:14Z","quality_controlled":"1","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"citation":{"apa":"Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:10.1142/S2010326320500069.","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:10.1142/S2010326320500069","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.08751"}],"year":"2020","_id":"6488","oa":1,"publication":"Random Matrices: Theory and Application","title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","abstract":[{"lang":"eng","text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish."}],"publication_status":"published","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"external_id":{"isi":["000547464400001"],"arxiv":["1806.08751"]},"date_published":"2020-07-01T00:00:00Z","scopus_import":"1","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","day":"01","oa_version":"Preprint","date_updated":"2023-08-28T08:38:48Z","type":"journal_article","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"doi":"10.1142/S2010326320500069","ec_funded":1},{"page":"311-330","date_published":"2020-04-01T00:00:00Z","external_id":{"arxiv":["1312.2337"],"isi":["000522437400004"]},"publication_identifier":{"issn":["16153375"],"eissn":["16153383"]},"scopus_import":"1","arxiv":1,"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","date_updated":"2023-08-17T13:50:44Z","type":"journal_article","oa_version":"Preprint","doi":"10.1007/s10208-019-09419-x","language":[{"iso":"eng"}],"department":[{"_id":"UlWa"}],"volume":20,"publisher":"Springer Nature","article_type":"original","isi":1,"intvolume":" 20","status":"public","date_created":"2019-06-16T21:59:14Z","month":"04","author":[{"last_name":"Filakovský","first_name":"Marek","id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","full_name":"Filakovský, Marek"},{"last_name":"Vokřínek","first_name":"Lukas","full_name":"Vokřínek, Lukas"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1312.2337"}],"citation":{"ieee":"M. Filakovský and L. Vokřínek, “Are two given maps homotopic? An algorithmic viewpoint,” Foundations of Computational Mathematics, vol. 20. Springer Nature, pp. 311–330, 2020.","ama":"Filakovský M, Vokřínek L. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 2020;20:311-330. doi:10.1007/s10208-019-09419-x","chicago":"Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic Viewpoint.” Foundations of Computational Mathematics. Springer Nature, 2020. https://doi.org/10.1007/s10208-019-09419-x.","short":"M. Filakovský, L. Vokřínek, Foundations of Computational Mathematics 20 (2020) 311–330.","ista":"Filakovský M, Vokřínek L. 2020. Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. 20, 311–330.","mla":"Filakovský, Marek, and Lukas Vokřínek. “Are Two given Maps Homotopic? An Algorithmic Viewpoint.” Foundations of Computational Mathematics, vol. 20, Springer Nature, 2020, pp. 311–30, doi:10.1007/s10208-019-09419-x.","apa":"Filakovský, M., & Vokřínek, L. (2020). Are two given maps homotopic? An algorithmic viewpoint. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-019-09419-x"},"year":"2020","oa":1,"_id":"6563","title":"Are two given maps homotopic? An algorithmic viewpoint","publication":"Foundations of Computational Mathematics","publication_status":"published","abstract":[{"text":"This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.","lang":"eng"}],"project":[{"grant_number":"P31312","name":"Algorithms for Embeddings and Homotopy Theory","_id":"26611F5C-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}]},{"publication_identifier":{"issn":["1017-1398"],"eissn":["1572-9265"]},"scopus_import":"1","date_published":"2020-05-01T00:00:00Z","file":[{"date_updated":"2020-07-14T12:47:34Z","file_id":"6927","access_level":"open_access","file_name":"ExtragradientMethodPaper.pdf","checksum":"bb1a1eb3ebb2df380863d0db594673ba","date_created":"2019-10-01T13:14:10Z","relation":"main_file","file_size":359654,"creator":"kschuh","content_type":"application/pdf"}],"external_id":{"isi":["000528979000015"]},"page":"365-388","acknowledgement":"The research of this author is supported by the ERC grant at the IST.","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/s11075-019-00758-y","has_accepted_license":"1","department":[{"_id":"VlKo"}],"type":"journal_article","date_updated":"2023-08-17T13:51:18Z","oa_version":"Submitted Version","day":"01","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2019-06-27T20:09:33Z","month":"05","status":"public","intvolume":" 84","isi":1,"file_date_updated":"2020-07-14T12:47:34Z","publisher":"Springer Nature","article_type":"original","volume":84,"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"publication_status":"published","abstract":[{"lang":"eng","text":"We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising."}],"publication":"Numerical Algorithms","title":"An efficient projection-type method for monotone variational inequalities in Hilbert spaces","oa":1,"ddc":["000"],"_id":"6593","year":"2020","citation":{"mla":"Shehu, Yekini, et al. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms, vol. 84, Springer Nature, 2020, pp. 365–88, doi:10.1007/s11075-019-00758-y.","apa":"Shehu, Y., Li, X.-H., & Dong, Q.-L. (2020). An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. Springer Nature. https://doi.org/10.1007/s11075-019-00758-y","ista":"Shehu Y, Li X-H, Dong Q-L. 2020. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 84, 365–388.","short":"Y. Shehu, X.-H. Li, Q.-L. Dong, Numerical Algorithms 84 (2020) 365–388.","chicago":"Shehu, Yekini, Xiao-Huan Li, and Qiao-Li Dong. “An Efficient Projection-Type Method for Monotone Variational Inequalities in Hilbert Spaces.” Numerical Algorithms. Springer Nature, 2020. https://doi.org/10.1007/s11075-019-00758-y.","ama":"Shehu Y, Li X-H, Dong Q-L. An efficient projection-type method for monotone variational inequalities in Hilbert spaces. Numerical Algorithms. 2020;84:365-388. doi:10.1007/s11075-019-00758-y","ieee":"Y. Shehu, X.-H. Li, and Q.-L. Dong, “An efficient projection-type method for monotone variational inequalities in Hilbert spaces,” Numerical Algorithms, vol. 84. Springer Nature, pp. 365–388, 2020."},"author":[{"id":"3FC7CB58-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-9224-7139","full_name":"Shehu, Yekini","first_name":"Yekini","last_name":"Shehu"},{"last_name":"Li","first_name":"Xiao-Huan","full_name":"Li, Xiao-Huan"},{"full_name":"Dong, Qiao-Li","last_name":"Dong","first_name":"Qiao-Li"}],"quality_controlled":"1"},{"date_published":"2020-03-01T00:00:00Z","external_id":{"isi":["000527910700019"],"arxiv":["1809.01902"]},"file":[{"file_id":"6668","date_updated":"2020-07-14T12:47:35Z","access_level":"open_access","checksum":"f9dd6dd615a698f1d3636c4a092fed23","file_name":"2019_CommMathPhysics_Benedikter.pdf","date_created":"2019-07-24T07:19:10Z","relation":"main_file","file_size":853289,"content_type":"application/pdf","creator":"dernst"}],"page":"2097–2150","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"scopus_import":"1","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","date_updated":"2023-08-17T13:51:50Z","type":"journal_article","oa_version":"Published Version","day":"01","ec_funded":1,"doi":"10.1007/s00220-019-03505-5","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"has_accepted_license":"1","volume":374,"file_date_updated":"2020-07-14T12:47:35Z","publisher":"Springer Nature","article_type":"original","intvolume":" 374","isi":1,"date_created":"2019-07-18T13:30:04Z","month":"03","status":"public","citation":{"ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03505-5.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 2020;374:2097–2150. doi:10.1007/s00220-019-03505-5","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” Communications in Mathematical Physics, vol. 374. Springer Nature, pp. 2097–2150, 2020.","mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:10.1007/s00220-019-03505-5.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03505-5"},"quality_controlled":"1","author":[{"last_name":"Benedikter","first_name":"Niels P","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nam, Phan Thành","first_name":"Phan Thành","last_name":"Nam"},{"last_name":"Porta","first_name":"Marcello","full_name":"Porta, Marcello"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2020","title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","publication":"Communications in Mathematical Physics","oa":1,"ddc":["530"],"_id":"6649","project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","call_identifier":"FWF","name":"FWF Open Access Fund"},{"grant_number":"P27533_N27","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"publication_status":"published","abstract":[{"lang":"eng","text":"While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.\r\n"}]},{"day":"11","date_updated":"2024-03-06T08:28:50Z","type":"journal_article","oa_version":"Preprint","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1214/20-AOS1945","language":[{"iso":"eng"}],"department":[{"_id":"MaMo"}],"page":"3619-3642","date_published":"2020-12-11T00:00:00Z","external_id":{"arxiv":["1901.01375"],"isi":["000598369200021"]},"arxiv":1,"publication_identifier":{"issn":["1932-6157"],"eissn":["1941-7330"]},"year":"2020","quality_controlled":"1","author":[{"full_name":"Javanmard, Adel","last_name":"Javanmard","first_name":"Adel"},{"last_name":"Mondelli","first_name":"Marco","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"full_name":"Montanari, Andrea","last_name":"Montanari","first_name":"Andrea"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1901.01375"}],"citation":{"ieee":"A. Javanmard, M. Mondelli, and A. Montanari, “Analysis of a two-layer neural network via displacement convexity,” Annals of Statistics, vol. 48, no. 6. Institute of Mathematical Statistics, pp. 3619–3642, 2020.","ama":"Javanmard A, Mondelli M, Montanari A. Analysis of a two-layer neural network via displacement convexity. Annals of Statistics. 2020;48(6):3619-3642. doi:10.1214/20-AOS1945","ista":"Javanmard A, Mondelli M, Montanari A. 2020. Analysis of a two-layer neural network via displacement convexity. Annals of Statistics. 48(6), 3619–3642.","short":"A. Javanmard, M. Mondelli, A. Montanari, Annals of Statistics 48 (2020) 3619–3642.","chicago":"Javanmard, Adel, Marco Mondelli, and Andrea Montanari. “Analysis of a Two-Layer Neural Network via Displacement Convexity.” Annals of Statistics. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/20-AOS1945.","apa":"Javanmard, A., Mondelli, M., & Montanari, A. (2020). Analysis of a two-layer neural network via displacement convexity. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/20-AOS1945","mla":"Javanmard, Adel, et al. “Analysis of a Two-Layer Neural Network via Displacement Convexity.” Annals of Statistics, vol. 48, no. 6, Institute of Mathematical Statistics, 2020, pp. 3619–42, doi:10.1214/20-AOS1945."},"publication_status":"published","abstract":[{"text":"Fitting a function by using linear combinations of a large number N of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is non-convex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches.\r\nHere we consider the problem of learning a concave function f on a compact convex domain Ω⊆ℝd, using linear combinations of `bump-like' components (neurons). The parameters to be fitted are the centers of N bumps, and the resulting empirical risk minimization problem is highly non-convex. We prove that, in the limit in which the number of neurons diverges, the evolution of gradient descent converges to a Wasserstein gradient flow in the space of probability distributions over Ω. Further, when the bump width δ tends to 0, this gradient flow has a limit which is a viscous porous medium equation. Remarkably, the cost function optimized by this gradient flow exhibits a special property known as displacement convexity, which implies exponential convergence rates for N→∞, δ→0. Surprisingly, this asymptotic theory appears to capture well the behavior for moderate values of δ,N. Explaining this phenomenon, and understanding the dependence on δ,N in a quantitative manner remains an outstanding challenge.","lang":"eng"}],"oa":1,"_id":"6748","publication":"Annals of Statistics","title":"Analysis of a two-layer neural network via displacement convexity","article_type":"original","publisher":"Institute of Mathematical Statistics","volume":48,"issue":"6","status":"public","date_created":"2019-07-31T09:39:42Z","month":"12","isi":1,"intvolume":" 48"},{"isi":1,"intvolume":" 807","status":"public","date_created":"2019-08-04T21:59:20Z","month":"02","volume":807,"article_type":"original","publisher":"Elsevier","file_date_updated":"2020-10-09T06:31:22Z","ddc":["000"],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"1341"}]},"oa":1,"_id":"6761","publication":"Theoretical Computer Science","title":"Dynamic resource allocation games","publication_status":"published","abstract":[{"lang":"eng","text":"In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability."}],"project":[{"_id":"25F2ACDE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering","grant_number":"S11402-N23"},{"grant_number":"Z211","name":"The Wittgenstein Prize","_id":"25F42A32-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Formal Methods meets Algorithmic Game Theory","grant_number":"M02369","_id":"264B3912-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"quality_controlled":"1","author":[{"full_name":"Avni, Guy","orcid":"0000-0001-5588-8287","id":"463C8BC2-F248-11E8-B48F-1D18A9856A87","first_name":"Guy","last_name":"Avni"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Henzinger, Thomas A","orcid":"0000−0002−2985−7724","last_name":"Henzinger","first_name":"Thomas A"},{"full_name":"Kupferman, Orna","first_name":"Orna","last_name":"Kupferman"}],"citation":{"apa":"Avni, G., Henzinger, T. A., & Kupferman, O. (2020). Dynamic resource allocation games. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2019.06.031","mla":"Avni, Guy, et al. “Dynamic Resource Allocation Games.” Theoretical Computer Science, vol. 807, Elsevier, 2020, pp. 42–55, doi:10.1016/j.tcs.2019.06.031.","ista":"Avni G, Henzinger TA, Kupferman O. 2020. Dynamic resource allocation games. Theoretical Computer Science. 807, 42–55.","chicago":"Avni, Guy, Thomas A Henzinger, and Orna Kupferman. “Dynamic Resource Allocation Games.” Theoretical Computer Science. Elsevier, 2020. https://doi.org/10.1016/j.tcs.2019.06.031.","short":"G. Avni, T.A. Henzinger, O. Kupferman, Theoretical Computer Science 807 (2020) 42–55.","ieee":"G. Avni, T. A. Henzinger, and O. Kupferman, “Dynamic resource allocation games,” Theoretical Computer Science, vol. 807. Elsevier, pp. 42–55, 2020.","ama":"Avni G, Henzinger TA, Kupferman O. Dynamic resource allocation games. Theoretical Computer Science. 2020;807:42-55. doi:10.1016/j.tcs.2019.06.031"},"year":"2020","publication_identifier":{"issn":["03043975"]},"scopus_import":"1","page":"42-55","date_published":"2020-02-06T00:00:00Z","external_id":{"isi":["000512219400004"]},"file":[{"file_size":1413001,"creator":"dernst","content_type":"application/pdf","date_created":"2020-10-09T06:31:22Z","relation":"main_file","access_level":"open_access","file_name":"2020_TheoreticalCS_Avni.pdf","checksum":"e86635417f45eb2cd75778f91382f737","file_id":"8639","date_updated":"2020-10-09T06:31:22Z","success":1}],"doi":"10.1016/j.tcs.2019.06.031","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"ToHe"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","day":"06","date_updated":"2023-08-17T13:52:49Z","type":"journal_article","oa_version":"Submitted Version"}]