[{"publication_status":"published","page":"1509-1527","extern":"1","title":"Kuroda’s formula and arithmetic statistics","abstract":[{"lang":"eng","text":"Kuroda’s formula relates the class number of a multiquadratic number field K to the class numbers of its quadratic subfields ki. A key component in this formula is the unit group index (math formular). We study how Q(K) behaves on average in certain natural families of totally real biquadratic fields K parametrized by prime numbers."}],"author":[{"last_name":"Chan","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","orcid":"0000-0001-8467-4106","first_name":"Yik Tung","full_name":"Chan, Yik Tung"},{"full_name":"Milovic, Djordjo","first_name":"Djordjo","last_name":"Milovic"}],"day":"17","issue":"2","OA_type":"green","article_processing_charge":"No","oa":1,"OA_place":"repository","year":"2021","article_type":"original","external_id":{"arxiv":["1905.09745"]},"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"publication":"Mathematische Zeitschrift","doi":"10.1007/s00209-021-02823-6","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1905.09745"}],"scopus_import":"1","_id":"19492","month":"08","oa_version":"Preprint","quality_controlled":"1","volume":300,"date_created":"2025-04-05T10:51:04Z","date_updated":"2025-07-10T11:51:48Z","type":"journal_article","arxiv":1,"status":"public","intvolume":"       300","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-08-17T00:00:00Z","citation":{"ista":"Chan S, Milovic D. 2021. Kuroda’s formula and arithmetic statistics. Mathematische Zeitschrift. 300(2), 1509–1527.","chicago":"Chan, Stephanie, and Djordjo Milovic. “Kuroda’s Formula and Arithmetic Statistics.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00209-021-02823-6\">https://doi.org/10.1007/s00209-021-02823-6</a>.","short":"S. Chan, D. Milovic, Mathematische Zeitschrift 300 (2021) 1509–1527.","mla":"Chan, Stephanie, and Djordjo Milovic. “Kuroda’s Formula and Arithmetic Statistics.” <i>Mathematische Zeitschrift</i>, vol. 300, no. 2, Springer Nature, 2021, pp. 1509–27, doi:<a href=\"https://doi.org/10.1007/s00209-021-02823-6\">10.1007/s00209-021-02823-6</a>.","ama":"Chan S, Milovic D. Kuroda’s formula and arithmetic statistics. <i>Mathematische Zeitschrift</i>. 2021;300(2):1509-1527. doi:<a href=\"https://doi.org/10.1007/s00209-021-02823-6\">10.1007/s00209-021-02823-6</a>","ieee":"S. Chan and D. Milovic, “Kuroda’s formula and arithmetic statistics,” <i>Mathematische Zeitschrift</i>, vol. 300, no. 2. Springer Nature, pp. 1509–1527, 2021.","apa":"Chan, S., &#38; Milovic, D. (2021). Kuroda’s formula and arithmetic statistics. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-021-02823-6\">https://doi.org/10.1007/s00209-021-02823-6</a>"},"publisher":"Springer Nature"},{"arxiv":1,"status":"public","intvolume":"        17","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"B. Cheng, M. Bethkenhagen, C.J. Pickard, S. Hamel, Nature Physics 17 (2021) 1228–1232.","chicago":"Cheng, Bingqing, Mandy Bethkenhagen, Chris J. Pickard, and Sebastien Hamel. “Phase Behaviours of Superionic Water at Planetary Conditions.” <i>Nature Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1038/s41567-021-01334-9\">https://doi.org/10.1038/s41567-021-01334-9</a>.","mla":"Cheng, Bingqing, et al. “Phase Behaviours of Superionic Water at Planetary Conditions.” <i>Nature Physics</i>, vol. 17, no. 11, Springer Nature, 2021, pp. 1228–32, doi:<a href=\"https://doi.org/10.1038/s41567-021-01334-9\">10.1038/s41567-021-01334-9</a>.","ista":"Cheng B, Bethkenhagen M, Pickard CJ, Hamel S. 2021. Phase behaviours of superionic water at planetary conditions. Nature Physics. 17(11), 1228–1232.","ieee":"B. Cheng, M. Bethkenhagen, C. J. Pickard, and S. Hamel, “Phase behaviours of superionic water at planetary conditions,” <i>Nature Physics</i>, vol. 17, no. 11. Springer Nature, pp. 1228–1232, 2021.","apa":"Cheng, B., Bethkenhagen, M., Pickard, C. J., &#38; Hamel, S. (2021). Phase behaviours of superionic water at planetary conditions. <i>Nature Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41567-021-01334-9\">https://doi.org/10.1038/s41567-021-01334-9</a>","ama":"Cheng B, Bethkenhagen M, Pickard CJ, Hamel S. Phase behaviours of superionic water at planetary conditions. <i>Nature Physics</i>. 2021;17(11):1228-1232. doi:<a href=\"https://doi.org/10.1038/s41567-021-01334-9\">10.1038/s41567-021-01334-9</a>"},"date_published":"2021-11-01T00:00:00Z","publisher":"Springer Nature","doi":"10.1038/s41567-021-01334-9","scopus_import":"1","date_created":"2025-06-26T11:36:36Z","volume":17,"quality_controlled":"1","date_updated":"2025-06-26T11:49:07Z","_id":"19909","oa_version":"Preprint","month":"11","related_material":{"record":[{"id":"9696","relation":"earlier_version","status":"public"}]},"type":"journal_article","article_type":"original","year":"2021","language":[{"iso":"eng"}],"external_id":{"arxiv":["2103.09035"]},"publication_identifier":{"issn":["1745-2473"],"eissn":["1745-2481"]},"publication":"Nature Physics","page":"1228-1232","publication_status":"published","title":"Phase behaviours of superionic water at planetary conditions","extern":"1","abstract":[{"lang":"eng","text":"Most water in the Universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free-energy methods to overcome the limitations of quantum mechanical simulations and characterize hydrogen diffusion, superionic transitions and phase behaviours of water at extreme conditions. We predict that close-packed superionic phases, which have a fraction of mixed stacking for finite systems, are stable over a wide temperature and pressure range, whereas a body-centred cubic superionic phase is only thermodynamically stable in a small window but is kinetically favoured. Our phase boundaries, which are consistent with existing—albeit scarce—experimental observations, help resolve the fractions of insulating ice, different superionic phases and liquid water inside ice giants."}],"day":"01","author":[{"last_name":"Cheng","id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","orcid":"0000-0002-3584-9632","full_name":"Cheng, Bingqing","first_name":"Bingqing"},{"last_name":"Bethkenhagen","full_name":"Bethkenhagen, Mandy","first_name":"Mandy"},{"first_name":"Chris J.","full_name":"Pickard, Chris J.","last_name":"Pickard"},{"first_name":"Sebastien","full_name":"Hamel, Sebastien","last_name":"Hamel"}],"issue":"11","article_processing_charge":"No","OA_type":"green","OA_place":"repository"},{"publication":"Mathematische Annalen","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"external_id":{"arxiv":["1904.04254"]},"language":[{"iso":"eng"}],"year":"2021","article_type":"original","OA_type":"green","article_processing_charge":"No","oa":1,"OA_place":"repository","author":[{"id":"968ad14a-fd86-11ee-a420-ea29715511a3","last_name":"Chen","full_name":"Chen, Xujia","first_name":"Xujia"},{"last_name":"Zinger","full_name":"Zinger, Aleksey","first_name":"Aleksey"}],"day":"25","issue":"3-4","extern":"1","title":"WDVV-type relations for disk Gromov–Witten invariants in dimension 6","abstract":[{"lang":"eng","text":"The first author’s previous work established Solomon’s WDVV-type relations for Welschinger’s invariant curve counts in real symplectic fourfolds by lifting geometric relations over possibly unorientable morphisms. We apply her framework to obtain WDVV-style relations for the disk invariants of real symplectic sixfolds with some symmetry, in particular confirming Alcolado’s prediction for P^3 and extending it to other spaces. These relations reduce the computation of Welschinger’s invariants of many real symplectic sixfolds to invariants in small degrees and provide lower bounds for counts of real rational curves with positive-dimensional insertions in some cases. In the case of P^3, our lower bounds fit perfectly with Kollár’s vanishing results."}],"publication_status":"published","page":"1231-1313","publisher":"Springer Nature","intvolume":"       379","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Chen X, Zinger A. 2021. WDVV-type relations for disk Gromov–Witten invariants in dimension 6. Mathematische Annalen. 379(3–4), 1231–1313.","mla":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten Invariants in Dimension 6.” <i>Mathematische Annalen</i>, vol. 379, no. 3–4, Springer Nature, 2021, pp. 1231–313, doi:<a href=\"https://doi.org/10.1007/s00208-020-02130-1\">10.1007/s00208-020-02130-1</a>.","short":"X. Chen, A. Zinger, Mathematische Annalen 379 (2021) 1231–1313.","chicago":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Disk Gromov–Witten Invariants in Dimension 6.” <i>Mathematische Annalen</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00208-020-02130-1\">https://doi.org/10.1007/s00208-020-02130-1</a>.","ama":"Chen X, Zinger A. WDVV-type relations for disk Gromov–Witten invariants in dimension 6. <i>Mathematische Annalen</i>. 2021;379(3-4):1231-1313. doi:<a href=\"https://doi.org/10.1007/s00208-020-02130-1\">10.1007/s00208-020-02130-1</a>","apa":"Chen, X., &#38; Zinger, A. (2021). WDVV-type relations for disk Gromov–Witten invariants in dimension 6. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-020-02130-1\">https://doi.org/10.1007/s00208-020-02130-1</a>","ieee":"X. Chen and A. Zinger, “WDVV-type relations for disk Gromov–Witten invariants in dimension 6,” <i>Mathematische Annalen</i>, vol. 379, no. 3–4. Springer Nature, pp. 1231–1313, 2021."},"date_published":"2021-01-25T00:00:00Z","arxiv":1,"status":"public","type":"journal_article","scopus_import":"1","_id":"20619","month":"01","oa_version":"Preprint","date_updated":"2025-11-10T15:11:29Z","quality_controlled":"1","volume":379,"date_created":"2025-11-10T08:41:40Z","doi":"10.1007/s00208-020-02130-1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1904.04254","open_access":"1"}]},{"oa":1,"OA_place":"repository","article_processing_charge":"No","OA_type":"green","issue":"2","day":"01","author":[{"full_name":"Chen, Xujia","first_name":"Xujia","id":"968ad14a-fd86-11ee-a420-ea29715511a3","last_name":"Chen"},{"full_name":"Zinger, Aleksey","first_name":"Aleksey","last_name":"Zinger"}],"abstract":[{"lang":"eng","text":"We first recall Solomon’s relations for Welschinger invariants counting real curves in real symplectic fourfolds and the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV)-style relations for Welschinger invariants counting real curves in real symplectic sixfolds with some symmetry. We then explicitly demonstrate that, in some important cases (projective spaces with standard conjugations, real blowups of the projective plane, and two- and threefold products of the one-dimensional projective space with two involutions each), these relations provide complete recursions determining all Welschinger invariants from basic input. We include extensive tables of Welschinger invariants in low degrees obtained from these recursions with Mathematica. These invariants provide lower bounds for counts of real rational curves, including with curve insertions in smooth algebraic threefolds."}],"title":"WDVV-type relations for Welschinger's invariants: Applications","extern":"1","page":"339-376","publication_status":"submitted","publication":"Kyoto Journal of Mathematics","publication_identifier":{"eissn":["2154-3321"]},"language":[{"iso":"eng"}],"external_id":{"arxiv":["1809.08938"]},"year":"2021","type":"journal_article","date_updated":"2025-11-10T15:13:58Z","volume":61,"quality_controlled":"1","date_created":"2025-11-10T08:45:12Z","_id":"20622","month":"06","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1809.08938"}],"doi":"10.1215/21562261-2021-0005","publisher":"Duke University Press","date_published":"2021-06-01T00:00:00Z","citation":{"mla":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Welschinger’s Invariants: Applications.” <i>Kyoto Journal of Mathematics</i>, vol. 61, no. 2, Duke University Press, pp. 339–76, doi:<a href=\"https://doi.org/10.1215/21562261-2021-0005\">10.1215/21562261-2021-0005</a>.","short":"X. Chen, A. Zinger, Kyoto Journal of Mathematics 61 (n.d.) 339–376.","chicago":"Chen, Xujia, and Aleksey Zinger. “WDVV-Type Relations for Welschinger’s Invariants: Applications.” <i>Kyoto Journal of Mathematics</i>. Duke University Press, n.d. <a href=\"https://doi.org/10.1215/21562261-2021-0005\">https://doi.org/10.1215/21562261-2021-0005</a>.","ista":"Chen X, Zinger A. WDVV-type relations for Welschinger’s invariants: Applications. Kyoto Journal of Mathematics. 61(2), 339–376.","apa":"Chen, X., &#38; Zinger, A. (n.d.). WDVV-type relations for Welschinger’s invariants: Applications. <i>Kyoto Journal of Mathematics</i>. Duke University Press. <a href=\"https://doi.org/10.1215/21562261-2021-0005\">https://doi.org/10.1215/21562261-2021-0005</a>","ieee":"X. Chen and A. Zinger, “WDVV-type relations for Welschinger’s invariants: Applications,” <i>Kyoto Journal of Mathematics</i>, vol. 61, no. 2. Duke University Press, pp. 339–376.","ama":"Chen X, Zinger A. WDVV-type relations for Welschinger’s invariants: Applications. <i>Kyoto Journal of Mathematics</i>. 61(2):339-376. doi:<a href=\"https://doi.org/10.1215/21562261-2021-0005\">10.1215/21562261-2021-0005</a>"},"intvolume":"        61","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","arxiv":1},{"publication":"Chemical Communications","publication_identifier":{"issn":["1359-7345"],"eissn":["1364-548X"]},"language":[{"iso":"eng"}],"external_id":{"pmid":["33871510"]},"pmid":1,"article_type":"original","year":"2021","OA_place":"publisher","oa":1,"article_processing_charge":"No","OA_type":"hybrid","issue":"32","ddc":["540"],"day":"15","author":[{"last_name":"Willems","full_name":"Willems, Suzanne","first_name":"Suzanne"},{"last_name":"Toupalas","first_name":"Georgios","full_name":"Toupalas, Georgios"},{"last_name":"Reisenbauer","id":"51d862e9-36ee-11f0-86d3-8534c85a5496","full_name":"Reisenbauer, Julia","first_name":"Julia"},{"last_name":"Morandi","full_name":"Morandi, Bill","first_name":"Bill"}],"abstract":[{"lang":"eng","text":"<p>A cascade Suzuki–Miyaura cross-coupling between two non-symmetrical coupling partners gave rise to 9,10-dihydrophenanthrenes with full site-selectivity. The choice of base was critical to facilitate the challenging coupling of the secondary boronate group.</p>"}],"title":"A site-selective and stereospecific cascade Suzuki–Miyaura annulation of alkyl 1,2-bisboronic esters and 2,2′-dihalo 1,1′-biaryls","extern":"1","page":"3909-3912","publication_status":"published","publisher":"Royal Society of Chemistry","citation":{"short":"S. Willems, G. Toupalas, J. Reisenbauer, B. Morandi, Chemical Communications 57 (2021) 3909–3912.","chicago":"Willems, Suzanne, Georgios Toupalas, Julia Reisenbauer, and Bill Morandi. “A Site-Selective and Stereospecific Cascade Suzuki–Miyaura Annulation of Alkyl 1,2-Bisboronic Esters and 2,2′-Dihalo 1,1′-Biaryls.” <i>Chemical Communications</i>. Royal Society of Chemistry, 2021. <a href=\"https://doi.org/10.1039/d1cc00648g\">https://doi.org/10.1039/d1cc00648g</a>.","mla":"Willems, Suzanne, et al. “A Site-Selective and Stereospecific Cascade Suzuki–Miyaura Annulation of Alkyl 1,2-Bisboronic Esters and 2,2′-Dihalo 1,1′-Biaryls.” <i>Chemical Communications</i>, vol. 57, no. 32, Royal Society of Chemistry, 2021, pp. 3909–12, doi:<a href=\"https://doi.org/10.1039/d1cc00648g\">10.1039/d1cc00648g</a>.","ista":"Willems S, Toupalas G, Reisenbauer J, Morandi B. 2021. A site-selective and stereospecific cascade Suzuki–Miyaura annulation of alkyl 1,2-bisboronic esters and 2,2′-dihalo 1,1′-biaryls. Chemical Communications. 57(32), 3909–3912.","ieee":"S. Willems, G. Toupalas, J. Reisenbauer, and B. Morandi, “A site-selective and stereospecific cascade Suzuki–Miyaura annulation of alkyl 1,2-bisboronic esters and 2,2′-dihalo 1,1′-biaryls,” <i>Chemical Communications</i>, vol. 57, no. 32. Royal Society of Chemistry, pp. 3909–3912, 2021.","apa":"Willems, S., Toupalas, G., Reisenbauer, J., &#38; Morandi, B. (2021). A site-selective and stereospecific cascade Suzuki–Miyaura annulation of alkyl 1,2-bisboronic esters and 2,2′-dihalo 1,1′-biaryls. <i>Chemical Communications</i>. Royal Society of Chemistry. <a href=\"https://doi.org/10.1039/d1cc00648g\">https://doi.org/10.1039/d1cc00648g</a>","ama":"Willems S, Toupalas G, Reisenbauer J, Morandi B. A site-selective and stereospecific cascade Suzuki–Miyaura annulation of alkyl 1,2-bisboronic esters and 2,2′-dihalo 1,1′-biaryls. <i>Chemical Communications</i>. 2021;57(32):3909-3912. doi:<a href=\"https://doi.org/10.1039/d1cc00648g\">10.1039/d1cc00648g</a>"},"date_published":"2021-03-15T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        57","status":"public","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","short":"CC BY (3.0)"},"has_accepted_license":"1","type":"journal_article","date_updated":"2025-12-16T12:06:53Z","date_created":"2025-12-09T14:25:17Z","volume":57,"quality_controlled":"1","_id":"20765","month":"03","oa_version":"Published Version","scopus_import":"1","main_file_link":[{"url":"DOI\thttps://doi.org/10.1039/D1CC00648G","open_access":"1"}],"doi":"10.1039/d1cc00648g"},{"department":[{"_id":"SaSi"}],"file_date_updated":"2022-05-13T07:40:15Z","publisher":"Association for Research in Vision and Ophthalmology","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        62","citation":{"ama":"Schmitt HM, Fehrman RL, Maes ME, et al. Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression. <i>Investigative Ophthalmology and Visual Science</i>. 2021;62(10). doi:<a href=\"https://doi.org/10.1167/IOVS.62.10.14\">10.1167/IOVS.62.10.14</a>","apa":"Schmitt, H. M., Fehrman, R. L., Maes, M. E., Yang, H., Guo, L. W., Schlamp, C. L., … Nickells, R. W. (2021). Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression. <i>Investigative Ophthalmology and Visual Science</i>. Association for Research in Vision and Ophthalmology. <a href=\"https://doi.org/10.1167/IOVS.62.10.14\">https://doi.org/10.1167/IOVS.62.10.14</a>","ieee":"H. M. Schmitt <i>et al.</i>, “Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression,” <i>Investigative Ophthalmology and Visual Science</i>, vol. 62, no. 10. Association for Research in Vision and Ophthalmology, 2021.","ista":"Schmitt HM, Fehrman RL, Maes ME, Yang H, Guo LW, Schlamp CL, Pelzel HR, Nickells RW. 2021. Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression. Investigative Ophthalmology and Visual Science. 62(10), 14.","mla":"Schmitt, Heather M., et al. “Increased Susceptibility and Intrinsic Apoptotic Signaling in Neurons by Induced HDAC3 Expression.” <i>Investigative Ophthalmology and Visual Science</i>, vol. 62, no. 10, 14, Association for Research in Vision and Ophthalmology, 2021, doi:<a href=\"https://doi.org/10.1167/IOVS.62.10.14\">10.1167/IOVS.62.10.14</a>.","short":"H.M. Schmitt, R.L. Fehrman, M.E. Maes, H. Yang, L.W. Guo, C.L. Schlamp, H.R. Pelzel, R.W. Nickells, Investigative Ophthalmology and Visual Science 62 (2021).","chicago":"Schmitt, Heather M., Rachel L. Fehrman, Margaret E Maes, Huan Yang, Lian Wang Guo, Cassandra L. Schlamp, Heather R. Pelzel, and Robert W. Nickells. “Increased Susceptibility and Intrinsic Apoptotic Signaling in Neurons by Induced HDAC3 Expression.” <i>Investigative Ophthalmology and Visual Science</i>. Association for Research in Vision and Ophthalmology, 2021. <a href=\"https://doi.org/10.1167/IOVS.62.10.14\">https://doi.org/10.1167/IOVS.62.10.14</a>."},"date_published":"2021-08-16T00:00:00Z","article_number":"14","status":"public","type":"journal_article","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"has_accepted_license":"1","scopus_import":"1","quality_controlled":"1","date_updated":"2023-08-14T06:35:17Z","date_created":"2021-09-12T22:01:23Z","volume":62,"_id":"10000","oa_version":"Published Version","month":"08","doi":"10.1167/IOVS.62.10.14","publication":"Investigative Ophthalmology and Visual Science","isi":1,"file":[{"content_type":"application/pdf","access_level":"open_access","date_updated":"2022-05-13T07:40:15Z","date_created":"2022-05-13T07:40:15Z","file_size":19707796,"creator":"dernst","success":1,"checksum":"c430967746f653aa1ae84ee617f62b73","file_id":"11369","relation":"main_file","file_name":"2021_IOVS_Schmitt.pdf"}],"publication_identifier":{"eissn":["1552-5783"],"issn":["0146-0404"]},"language":[{"iso":"eng"}],"external_id":{"pmid":["34398198"],"isi":["000695230000014"]},"pmid":1,"article_type":"original","year":"2021","article_processing_charge":"Yes","oa":1,"ddc":["570"],"day":"16","author":[{"full_name":"Schmitt, Heather M.","first_name":"Heather M.","last_name":"Schmitt"},{"last_name":"Fehrman","full_name":"Fehrman, Rachel L.","first_name":"Rachel L."},{"full_name":"Maes, Margaret E","first_name":"Margaret E","orcid":"0000-0001-9642-1085","last_name":"Maes","id":"3838F452-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Huan","full_name":"Yang, Huan","last_name":"Yang"},{"last_name":"Guo","full_name":"Guo, Lian Wang","first_name":"Lian Wang"},{"full_name":"Schlamp, Cassandra L.","first_name":"Cassandra L.","last_name":"Schlamp"},{"last_name":"Pelzel","first_name":"Heather R.","full_name":"Pelzel, Heather R."},{"first_name":"Robert W.","full_name":"Nickells, Robert W.","last_name":"Nickells"}],"issue":"10","title":"Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression","abstract":[{"lang":"eng","text":"Inhibition or targeted deletion of histone deacetylase 3 (HDAC3) is neuroprotective in a variety neurodegenerative conditions, including retinal ganglion cells (RGCs) after acute optic nerve damage. Consistent with this, induced HDAC3 expression in cultured cells shows selective toxicity to neurons. Despite an established role for HDAC3 in neuronal pathology, little is known regarding the mechanism of this pathology."}],"acknowledgement":"The authors thank Joel Dietz for maintaining the mice used in this study, Satoshi Kinoshita and the Translational Research Initiative in Pathology Laboratory at the University of Wisconsin-Madison for cutting retinal sections analyzed in this study, and Mark Banghart for statistical review of the data analysis. Supported by National Eye Institute Grants R01 EY012223 (RWN), R01 EY030123 (RWN), R01 EY029809 (LWG), R01 EY029809 (LWG) and a Vision Research CORE grant P30 EY016665, NRSA grant T32 GM081061, by an unrestricted research grant from Research to Prevent Blindness, Inc., and by a University of Wisconsin-Madison Vilas Life Cycle award and the Frederick A. Davis Research Chair (RWN). ","publication_status":"published"},{"oa":1,"article_processing_charge":"No","day":"07","author":[{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"first_name":"Wolfgang","full_name":"Dvorak, Wolfgang","last_name":"Dvorak"},{"full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530"},{"full_name":"Svozil, Alexander","first_name":"Alexander","last_name":"Svozil"}],"abstract":[{"text":"We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with  n  vertices and  m  edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires  O(n2)  symbolic operations and  O(1)  symbolic space. The only other symbolic algorithm for the MEC decomposition requires  O(nm−−√)  symbolic operations and  O(m−−√)  symbolic space. A main open question is whether the worst-case  O(n2)  bound for symbolic operations can be beaten. We present a symbolic algorithm that requires  O˜(n1.5)  symbolic operations and  O˜(n−−√)  symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all  0<ϵ≤1/2  the symbolic algorithm requires  O˜(n2−ϵ)  symbolic operations and  O˜(nϵ)  symbolic space ( O˜  hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of  ω -regular objectives for MDPs. We consider the canonical parity objectives for  ω -regular objectives, and for parity objectives with  d -priorities we present an algorithm that computes the almost-sure winning region with  O˜(n2−ϵ)  symbolic operations and  O˜(nϵ)  symbolic space, for all  0<ϵ≤1/2 .","lang":"eng"}],"title":"Symbolic time and space tradeoffs for probabilistic verification","page":"1-13","publication_status":"published","acknowledgement":"The authors are grateful to the anonymous referees for their valuable comments. A. S. is fully supported by the Vienna Science and Technology Fund (WWTF) through project ICT15–003. K. C. is supported by the Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE) and by the ERC CoG 863818 (ForM-SMArt). For M. H. the research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement no. 340506.","publication":"Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science","publication_identifier":{"issn":["1043-6871"],"isbn":["978-1-6654-4896-3"],"eisbn":["978-1-6654-4895-6"]},"isi":1,"language":[{"iso":"eng"}],"external_id":{"isi":["000947350400089"],"arxiv":["2104.07466"]},"year":"2021","conference":{"start_date":"2021-06-29","location":"Rome, Italy","name":"LICS: Logic in Computer Science","end_date":"2021-07-02"},"type":"conference","keyword":["Computer science","Computational modeling","Markov processes","Probabilistic logic","Formal verification","Game Theory"],"quality_controlled":"1","date_updated":"2025-07-10T11:15:45Z","date_created":"2021-09-12T22:01:24Z","oa_version":"Preprint","_id":"10002","month":"07","project":[{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","call_identifier":"FWF","grant_number":"S11407"},{"grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2104.07466"}],"doi":"10.1109/LICS52264.2021.9470739","department":[{"_id":"KrCh"}],"publisher":"Institute of Electrical and Electronics Engineers","citation":{"ista":"Chatterjee K, Dvorak W, Henzinger M, Svozil A. 2021. Symbolic time and space tradeoffs for probabilistic verification. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 1–13.","chicago":"Chatterjee, Krishnendu, Wolfgang Dvorak, Monika Henzinger, and Alexander Svozil. “Symbolic Time and Space Tradeoffs for Probabilistic Verification.” In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, 1–13. Institute of Electrical and Electronics Engineers, 2021. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470739\">https://doi.org/10.1109/LICS52264.2021.9470739</a>.","short":"K. Chatterjee, W. Dvorak, M. Henzinger, A. Svozil, in:, Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13.","mla":"Chatterjee, Krishnendu, et al. “Symbolic Time and Space Tradeoffs for Probabilistic Verification.” <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13, doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470739\">10.1109/LICS52264.2021.9470739</a>.","ama":"Chatterjee K, Dvorak W, Henzinger M, Svozil A. Symbolic time and space tradeoffs for probabilistic verification. In: <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>. Institute of Electrical and Electronics Engineers; 2021:1-13. doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470739\">10.1109/LICS52264.2021.9470739</a>","ieee":"K. Chatterjee, W. Dvorak, M. Henzinger, and A. Svozil, “Symbolic time and space tradeoffs for probabilistic verification,” in <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Rome, Italy, 2021, pp. 1–13.","apa":"Chatterjee, K., Dvorak, W., Henzinger, M., &#38; Svozil, A. (2021). Symbolic time and space tradeoffs for probabilistic verification. In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i> (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470739\">https://doi.org/10.1109/LICS52264.2021.9470739</a>"},"date_published":"2021-07-07T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"status":"public","arxiv":1},{"doi":"10.1109/LICS52264.2021.9470595","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2104.07278"}],"scopus_import":"1","project":[{"call_identifier":"H2020","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"_id":"10004","month":"07","oa_version":"Preprint","date_created":"2021-09-12T22:01:25Z","date_updated":"2025-09-08T14:54:13Z","quality_controlled":"1","keyword":["Computer science","Heuristic algorithms","Memory management","Automata","Markov processes","Probability distribution","Complexity theory"],"related_material":{"record":[{"relation":"later_version","id":"18630","status":"public"}]},"type":"conference","conference":{"end_date":"2021-07-02","name":"LICS: Logic in Computer Science","location":"Rome, Italy","start_date":"2021-06-29"},"arxiv":1,"status":"public","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Chatterjee K, Doyen L. 2021. Stochastic processes with expected stopping time. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 1–13.","short":"K. Chatterjee, L. Doyen, in:, Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13.","chicago":"Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, 1–13. Institute of Electrical and Electronics Engineers, 2021. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">https://doi.org/10.1109/LICS52264.2021.9470595</a>.","mla":"Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13, doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">10.1109/LICS52264.2021.9470595</a>.","ama":"Chatterjee K, Doyen L. Stochastic processes with expected stopping time. In: <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>. Institute of Electrical and Electronics Engineers; 2021:1-13. doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">10.1109/LICS52264.2021.9470595</a>","ieee":"K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,” in <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Rome, Italy, 2021, pp. 1–13.","apa":"Chatterjee, K., &#38; Doyen, L. (2021). Stochastic processes with expected stopping time. In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i> (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">https://doi.org/10.1109/LICS52264.2021.9470595</a>"},"date_published":"2021-07-07T00:00:00Z","publisher":"Institute of Electrical and Electronics Engineers","department":[{"_id":"KrCh"}],"acknowledgement":"We are grateful to the anonymous reviewers of LICS 2021 and of a previous version of this paper for insightful comments that helped improving the presentation. This research was partially supported by the grant ERC CoG 863818 (ForM-SMArt).","publication_status":"published","page":"1-13","title":"Stochastic processes with expected stopping time","abstract":[{"lang":"eng","text":"Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs."}],"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"last_name":"Doyen","first_name":"Laurent","full_name":"Doyen, Laurent"}],"day":"07","article_processing_charge":"No","oa":1,"year":"2021","external_id":{"isi":["000947350400036"],"arxiv":["2104.07278"]},"language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"eisbn":["978-1-6654-4895-6"],"issn":["1043-6871"],"isbn":["978-1-6654-4896-3"]},"publication":"Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science"},{"quality_controlled":"1","date_updated":"2025-05-14T10:50:14Z","date_created":"2021-09-12T22:01:25Z","volume":31,"_id":"10005","oa_version":"Preprint","month":"08","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2009.06917"}],"doi":"10.1142/S0218202521500457","type":"journal_article","keyword":["Nonlinear parabolic systems","implicit constitutive theory","weak solutions","existence","uniqueness"],"citation":{"ista":"Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09).","chicago":"Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>.","short":"M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021).","mla":"Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>.","ama":"Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(09). doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>","ieee":"M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic type with implicit constitutive equations involving flux,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09. World Scientific Publishing, 2021.","apa":"Bulíček, M., Maringová, E., &#38; Málek, J. (2021). On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>"},"date_published":"2021-08-25T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        31","status":"public","arxiv":1,"department":[{"_id":"JuFi"}],"publisher":"World Scientific Publishing","abstract":[{"text":"We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.","lang":"eng"}],"title":"On nonlinear problems of parabolic type with implicit constitutive equations involving flux","publication_status":"published","acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers of the Nečas Center for Mathematical Modelling.\r\n","oa":1,"article_processing_charge":"No","issue":"09","day":"25","author":[{"last_name":"Bulíček","first_name":"Miroslav","full_name":"Bulíček, Miroslav"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","full_name":"Maringová, Erika","first_name":"Erika"},{"first_name":"Josef","full_name":"Málek, Josef","last_name":"Málek"}],"language":[{"iso":"eng"}],"external_id":{"isi":["000722222900004"],"arxiv":["2009.06917"]},"article_type":"original","year":"2021","publication":"Mathematical Models and Methods in Applied Sciences","publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"isi":1},{"department":[{"_id":"GradSch"},{"_id":"JuFi"}],"file_date_updated":"2021-09-15T14:37:30Z","publisher":"Institute of Science and Technology Austria","date_published":"2021-09-14T00:00:00Z","citation":{"ista":"Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria.","mla":"Hensel, Sebastian. <i>Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10007\">10.15479/at:ista:10007</a>.","chicago":"Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:10007\">https://doi.org/10.15479/at:ista:10007</a>.","short":"S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts, Institute of Science and Technology Austria, 2021.","ama":"Hensel S. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:10007\">10.15479/at:ista:10007</a>","apa":"Hensel, S. (2021). <i>Curvature driven interface evolution: Uniqueness properties of weak solution concepts</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:10007\">https://doi.org/10.15479/at:ista:10007</a>","ieee":"S. Hensel, “Curvature driven interface evolution: Uniqueness properties of weak solution concepts,” Institute of Science and Technology Austria, 2021."},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","ec_funded":1,"status":"public","corr_author":"1","alternative_title":["ISTA Thesis"],"has_accepted_license":"1","type":"dissertation","related_material":{"record":[{"relation":"part_of_dissertation","id":"10012","status":"public"},{"id":"10013","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"7489","status":"public"}]},"date_created":"2021-09-13T11:12:34Z","date_updated":"2026-04-08T07:01:01Z","oa_version":"Published Version","_id":"10007","month":"09","project":[{"call_identifier":"H2020","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program"},{"name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","call_identifier":"H2020"}],"doi":"10.15479/at:ista:10007","publication_identifier":{"issn":["2663-337X"]},"file":[{"creator":"shensel","date_created":"2021-09-13T11:03:24Z","file_size":15022154,"date_updated":"2021-09-15T14:37:30Z","content_type":"application/x-zip-compressed","access_level":"closed","file_name":"thesis_final_Hensel.zip","file_id":"10008","relation":"source_file","checksum":"c8475faaf0b680b4971f638f1db16347"},{"checksum":"1a609937aa5275452822f45f2da17f07","file_name":"thesis_final_Hensel.pdf","file_id":"10014","relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"shensel","date_created":"2021-09-13T14:18:56Z","file_size":6583638,"date_updated":"2021-09-14T09:52:47Z"}],"language":[{"iso":"eng"}],"year":"2021","OA_place":"publisher","oa":1,"degree_awarded":"PhD","article_processing_charge":"No","supervisor":[{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L"}],"day":"14","ddc":["515"],"author":[{"orcid":"0000-0001-7252-8072","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","full_name":"Hensel, Sebastian","first_name":"Sebastian"}],"abstract":[{"text":"The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis.","lang":"eng"}],"title":"Curvature driven interface evolution: Uniqueness properties of weak solution concepts","page":"300","publication_status":"published"},{"oa":1,"article_processing_charge":"No","author":[{"orcid":"0000-0001-7252-8072","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","first_name":"Sebastian","full_name":"Hensel, Sebastian"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"}],"day":"03","abstract":[{"lang":"eng","text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions."}],"title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","publication_status":"draft","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","publication":"arXiv","external_id":{"arxiv":["2108.01733"]},"language":[{"iso":"eng"}],"year":"2021","type":"preprint","related_material":{"record":[{"id":"13043","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"10007"}]},"month":"08","_id":"10013","oa_version":"Preprint","date_updated":"2026-04-08T07:01:01Z","date_created":"2021-09-13T12:17:11Z","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819"}],"main_file_link":[{"url":"https://arxiv.org/abs/2108.01733","open_access":"1"}],"doi":"10.48550/arXiv.2108.01733","department":[{"_id":"JuFi"}],"citation":{"ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2108.01733\">10.48550/arXiv.2108.01733</a>","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” <i>arXiv</i>. .","apa":"Hensel, S., &#38; Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature flow of double bubbles. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2108.01733\">https://doi.org/10.48550/arXiv.2108.01733</a>","ista":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv, 2108.01733.","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2108.01733\">https://doi.org/10.48550/arXiv.2108.01733</a>.","short":"S. Hensel, T. Laux, ArXiv (n.d.).","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” <i>ArXiv</i>, 2108.01733, doi:<a href=\"https://doi.org/10.48550/arXiv.2108.01733\">10.48550/arXiv.2108.01733</a>."},"date_published":"2021-08-03T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","status":"public","ec_funded":1,"article_number":"2108.01733","arxiv":1},{"oa":1,"article_processing_charge":"Yes","author":[{"last_name":"Floreani","first_name":"Simone","full_name":"Floreani, Simone"},{"full_name":"Redig, Frank","first_name":"Frank","last_name":"Redig"},{"full_name":"Sau, Federico","first_name":"Federico","last_name":"Sau","id":"E1836206-9F16-11E9-8814-AEFDE5697425"}],"ddc":["519"],"day":"27","abstract":[{"text":"In this paper, we introduce a random environment for the exclusion process in  obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020).","lang":"eng"}],"title":"Hydrodynamics for the partial exclusion process in random environment","publication_status":"published","page":"124-158","acknowledgement":"The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and  Cristian  Giardina,  Frank  den  Hollander  and  Shubhamoy  Nandan  for  inspiring  discussions.  S.F.  acknowledges  Simona  Villa  for  her  help  in  creating  the  picture.  Furthermore, the  authors  thank  two  anonymous  referees  for  the  careful  reading  of  the  manuscript.  S.F. acknowledges  financial  support  from  NWO,  The  Netherlands  via  the  grant  TOP1.17.019. F.S.  acknowledges  financial  support  from  NWO  via  the  TOP1  grant  613.001.552  as  well  as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","publication":"Stochastic Processes and their Applications","publication_identifier":{"issn":["0304-4149"]},"file":[{"creator":"dernst","success":1,"date_updated":"2022-05-13T07:55:50Z","file_size":2115791,"date_created":"2022-05-13T07:55:50Z","content_type":"application/pdf","access_level":"open_access","file_name":"2021_StochasticProcessesAppl_Floreani.pdf","file_id":"11370","relation":"main_file","checksum":"56768c553d7218ee5714902ffec90ec4"}],"isi":1,"external_id":{"arxiv":["1911.12564"],"isi":["000697748500005"]},"language":[{"iso":"eng"}],"year":"2021","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"oa_version":"Published Version","_id":"10024","month":"08","date_created":"2021-09-19T22:01:25Z","quality_controlled":"1","volume":142,"date_updated":"2025-04-14T07:43:46Z","scopus_import":"1","project":[{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"doi":"10.1016/j.spa.2021.08.006","file_date_updated":"2022-05-13T07:55:50Z","department":[{"_id":"JaMa"}],"publisher":"Elsevier","citation":{"ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and their Applications</i>. 2021;142:124-158. doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>","ieee":"S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” <i>Stochastic Processes and their Applications</i>, vol. 142. Elsevier, pp. 124–158, 2021.","apa":"Floreani, S., Redig, F., &#38; Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>","ista":"Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158.","short":"S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158.","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>.","mla":"Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>, vol. 142, Elsevier, 2021, pp. 124–58, doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>."},"date_published":"2021-08-27T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       142","status":"public","ec_funded":1,"arxiv":1},{"publication":"Nature","isi":1,"publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"language":[{"iso":"eng"}],"external_id":{"isi":["000706977400002"],"arxiv":["2104.00653"]},"article_type":"original","year":"2021","article_processing_charge":"No","oa":1,"day":"01","author":[{"full_name":"Zhou, Haoxin","first_name":"Haoxin","last_name":"Zhou"},{"last_name":"Xie","full_name":"Xie, Tian","first_name":"Tian"},{"id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87","last_name":"Ghazaryan","orcid":"0000-0001-9666-3543","full_name":"Ghazaryan, Areg","first_name":"Areg"},{"first_name":"Tobias","full_name":"Holder, Tobias","last_name":"Holder"},{"full_name":"Ehrets, James R.","first_name":"James R.","last_name":"Ehrets"},{"first_name":"Eric M.","full_name":"Spanton, Eric M.","last_name":"Spanton"},{"first_name":"Takashi","full_name":"Taniguchi, Takashi","last_name":"Taniguchi"},{"full_name":"Watanabe, Kenji","first_name":"Kenji","last_name":"Watanabe"},{"last_name":"Berg","full_name":"Berg, Erez","first_name":"Erez"},{"last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827","full_name":"Serbyn, Maksym","first_name":"Maksym"},{"first_name":"Andrea F.","full_name":"Young, Andrea F.","last_name":"Young"}],"title":"Half and quarter metals in rhombohedral trilayer graphene","abstract":[{"text":"Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized `half-metal', and spin and valley polarized `quarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moiré superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moiré materials to be fundamentally itinerant in nature.","lang":"eng"}],"acknowledgement":"The authors acknowledge discussions with A. Macdonald, L. Fu, F. Wang and M. Zaletel. AFY acknowledges support of the National Science Foundation under DMR1654186, and the Gordon and Betty Moore Foundation under award GBMF9471. The authors acknowledge the use of the research facilities within the California NanoSystems Institute, supported by the University of California, Santa Barbara and the University of California, Office of the President.\r\nK.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001 and JSPS KAKENHI, Grant Number JP20H00354. EB and TH were supported by the European Research Council (ERC) under grant HQMAT (Grant Agreement No. 817799). A.G. acknowledges support by the European Unions Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement\r\nNo. 754411.\r\n","publication_status":"published","department":[{"_id":"MaSe"},{"_id":"MiLe"}],"publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Zhou H, Xie T, Ghazaryan A, Holder T, Ehrets JR, Spanton EM, Taniguchi T, Watanabe K, Berg E, Serbyn M, Young AF. 2021. Half and quarter metals in rhombohedral trilayer graphene. Nature.","mla":"Zhou, Haoxin, et al. “Half and Quarter Metals in Rhombohedral Trilayer Graphene.” <i>Nature</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1038/s41586-021-03938-w\">10.1038/s41586-021-03938-w</a>.","chicago":"Zhou, Haoxin, Tian Xie, Areg Ghazaryan, Tobias Holder, James R. Ehrets, Eric M. Spanton, Takashi Taniguchi, et al. “Half and Quarter Metals in Rhombohedral Trilayer Graphene.” <i>Nature</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1038/s41586-021-03938-w\">https://doi.org/10.1038/s41586-021-03938-w</a>.","short":"H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J.R. Ehrets, E.M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, A.F. Young, Nature (2021).","ama":"Zhou H, Xie T, Ghazaryan A, et al. Half and quarter metals in rhombohedral trilayer graphene. <i>Nature</i>. 2021. doi:<a href=\"https://doi.org/10.1038/s41586-021-03938-w\">10.1038/s41586-021-03938-w</a>","apa":"Zhou, H., Xie, T., Ghazaryan, A., Holder, T., Ehrets, J. R., Spanton, E. M., … Young, A. F. (2021). Half and quarter metals in rhombohedral trilayer graphene. <i>Nature</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41586-021-03938-w\">https://doi.org/10.1038/s41586-021-03938-w</a>","ieee":"H. Zhou <i>et al.</i>, “Half and quarter metals in rhombohedral trilayer graphene,” <i>Nature</i>. Springer Nature, 2021."},"date_published":"2021-09-01T00:00:00Z","arxiv":1,"ec_funded":1,"status":"public","type":"journal_article","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1038/s41586-021-04181-z"}]},"keyword":["condensed matter - mesoscale and nanoscale physics","condensed matter - strongly correlated electrons","multidisciplinary"],"project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"scopus_import":"1","quality_controlled":"1","date_created":"2021-09-19T22:01:25Z","date_updated":"2025-04-14T07:43:46Z","oa_version":"Preprint","_id":"10025","month":"09","doi":"10.1038/s41586-021-03938-w","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2104.00653"}]},{"type":"preprint","related_material":{"record":[{"status":"public","relation":"research_data","id":"9636"},{"id":"10851","relation":"later_version","status":"public"}]},"project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020"}],"oa_version":"Preprint","_id":"10029","month":"07","date_created":"2021-09-21T08:41:02Z","date_updated":"2025-04-15T06:54:43Z","doi":"10.48550/arXiv.2107.03695","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2107.03695"}],"department":[{"_id":"MaSe"},{"_id":"AnHi"},{"_id":"MiLe"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Phan DT, Senior JL, Ghazaryan A, Hatefipour M, Strickland WM, Shabani J, Serbyn M, Higginbotham AP. Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid. arXiv, 2107.03695.","mla":"Phan, Duc T., et al. “Breakdown of Induced P±ip Pairing in a Superconductor-Semiconductor Hybrid.” <i>ArXiv</i>, 2107.03695, doi:<a href=\"https://doi.org/10.48550/arXiv.2107.03695\">10.48550/arXiv.2107.03695</a>.","chicago":"Phan, Duc T, Jorden L Senior, Areg Ghazaryan, M. Hatefipour, W. M. Strickland, J. Shabani, Maksym Serbyn, and Andrew P Higginbotham. “Breakdown of Induced P±ip Pairing in a Superconductor-Semiconductor Hybrid.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2107.03695\">https://doi.org/10.48550/arXiv.2107.03695</a>.","short":"D.T. Phan, J.L. Senior, A. Ghazaryan, M. Hatefipour, W.M. Strickland, J. Shabani, M. Serbyn, A.P. Higginbotham, ArXiv (n.d.).","ama":"Phan DT, Senior JL, Ghazaryan A, et al. Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2107.03695\">10.48550/arXiv.2107.03695</a>","apa":"Phan, D. T., Senior, J. L., Ghazaryan, A., Hatefipour, M., Strickland, W. M., Shabani, J., … Higginbotham, A. P. (n.d.). Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2107.03695\">https://doi.org/10.48550/arXiv.2107.03695</a>","ieee":"D. T. Phan <i>et al.</i>, “Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid,” <i>arXiv</i>. ."},"date_published":"2021-07-08T00:00:00Z","arxiv":1,"article_number":"2107.03695","status":"public","ec_funded":1,"article_processing_charge":"No","oa":1,"author":[{"id":"29C8C0B4-F248-11E8-B48F-1D18A9856A87","last_name":"Phan","first_name":"Duc T","full_name":"Phan, Duc T"},{"full_name":"Senior, Jorden L","first_name":"Jorden L","last_name":"Senior","id":"5479D234-2D30-11EA-89CC-40953DDC885E","orcid":"0000-0002-0672-9295"},{"orcid":"0000-0001-9666-3543","last_name":"Ghazaryan","id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87","full_name":"Ghazaryan, Areg","first_name":"Areg"},{"last_name":"Hatefipour","full_name":"Hatefipour, M.","first_name":"M."},{"last_name":"Strickland","full_name":"Strickland, W. M.","first_name":"W. M."},{"first_name":"J.","full_name":"Shabani, J.","last_name":"Shabani"},{"full_name":"Serbyn, Maksym","first_name":"Maksym","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827"},{"orcid":"0000-0003-2607-2363","last_name":"Higginbotham","id":"4AD6785A-F248-11E8-B48F-1D18A9856A87","first_name":"Andrew P","full_name":"Higginbotham, Andrew P"}],"day":"08","title":"Breakdown of induced p±ip pairing in a superconductor-semiconductor hybrid","abstract":[{"lang":"eng","text":"Superconductor-semiconductor hybrids are platforms for realizing effective p-wave superconductivity. Spin-orbit coupling, combined with the proximity effect, causes the two-dimensional semiconductor to inherit p±ip intraband pairing, and application of magnetic field can then result in transitions to the normal state, partial Bogoliubov Fermi surfaces, or topological phases with Majorana modes. Experimentally probing the hybrid superconductor-semiconductor interface is challenging due to the shunting effect of the conventional superconductor. Consequently, the nature of induced pairing remains an open question. Here, we use the circuit quantum electrodynamics architecture to probe induced superconductivity in a two dimensional Al-InAs hybrid system. We observe a strong suppression of superfluid density and enhanced dissipation driven by magnetic field, which cannot be accounted for by the depairing theory of an s-wave superconductor. These observations are explained by a picture of independent intraband p±ip superconductors giving way to partial Bogoliubov Fermi surfaces, and allow for the first characterization of key properties of the hybrid superconducting system."}],"acknowledgement":"This research was supported by the Scientific Service Units of IST Austria through resources provided by the MIBA Machine Shop and the nanofabrication facility. JS and AG were supported by funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No.754411.","publication_status":"draft","publication":"arXiv","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"external_id":{"arxiv":["2107.03695"]},"language":[{"iso":"eng"}],"year":"2021"},{"file":[{"checksum":"8cd60dcb8762e8f21867e21e8001e183","file_id":"10032","relation":"source_file","file_name":"tex_and_pictures.zip","content_type":"application/x-zip-compressed","access_level":"closed","file_size":3876668,"date_updated":"2022-03-10T12:14:42Z","date_created":"2021-09-21T09:17:34Z","creator":"cchlebak"},{"checksum":"9789e9d967c853c1503ec7f307170279","file_id":"10047","relation":"main_file","file_name":"thesis_portinale_Final (1).pdf","content_type":"application/pdf","access_level":"open_access","file_size":2532673,"date_updated":"2021-09-27T11:14:31Z","date_created":"2021-09-27T11:14:31Z","creator":"cchlebak"}],"acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"year":"2021","article_processing_charge":"No","degree_awarded":"PhD","oa":1,"OA_place":"publisher","author":[{"first_name":"Lorenzo","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale"}],"day":"22","ddc":["515"],"supervisor":[{"full_name":"Maas, Jan","first_name":"Jan","last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338"}],"title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","abstract":[{"text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces.","lang":"eng"}],"acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","publication_status":"published","file_date_updated":"2022-03-10T12:14:42Z","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"publisher":"Institute of Science and Technology Austria","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","citation":{"ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021.","apa":"Portinale, L. (2021). <i>Discrete-to-continuum limits of transport problems and gradient flows in the space of measures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>","ama":"Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>.","mla":"Portinale, Lorenzo. <i>Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>.","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria."},"date_published":"2021-09-22T00:00:00Z","alternative_title":["ISTA Thesis"],"status":"public","corr_author":"1","type":"dissertation","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","related_material":{"record":[{"id":"9792","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"10022","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"7573"}]},"project":[{"grant_number":"W1245","call_identifier":"FWF","name":"Dissipation and dispersion in nonlinear partial differential equations","_id":"260788DE-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"_id":"10030","month":"09","oa_version":"Published Version","date_created":"2021-09-21T09:14:15Z","date_updated":"2026-04-08T07:00:04Z","doi":"10.15479/at:ista:10030"},{"author":[{"last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6889-1418","first_name":"Quoc P","full_name":"Ho, Quoc P"}],"day":"21","ddc":["514"],"article_processing_charge":"Yes (via OA deal)","oa":1,"acknowledgement":"The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.","publication_status":"published","title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","abstract":[{"lang":"eng","text":"The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5]."}],"file":[{"access_level":"open_access","content_type":"application/pdf","creator":"qho","date_updated":"2021-09-21T15:58:52Z","date_created":"2021-09-21T15:58:52Z","file_size":840635,"checksum":"f3c0086d41af11db31c00014efb38072","file_name":"1-s2.0-S000187082100431X-main.pdf","relation":"main_file","file_id":"10034"}],"isi":1,"publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"publication":"Advances in Mathematics","year":"2021","article_type":"original","external_id":{"arxiv":["1610.00212"],"isi":["000707040300031"]},"language":[{"iso":"eng"}],"keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"type":"journal_article","has_accepted_license":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.1016/j.aim.2021.107992","scopus_import":"1","project":[{"call_identifier":"FWF","grant_number":"M02751","_id":"26B96266-B435-11E9-9278-68D0E5697425","name":"Algebro-Geometric Applications of Factorization Homology"}],"_id":"10033","month":"09","oa_version":"Published Version","volume":392,"date_updated":"2025-04-14T09:09:35Z","date_created":"2021-09-21T15:58:59Z","quality_controlled":"1","publisher":"Elsevier","file_date_updated":"2021-09-21T15:58:52Z","department":[{"_id":"TaHa"}],"article_number":"107992","arxiv":1,"status":"public","corr_author":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       392","date_published":"2021-09-21T00:00:00Z","citation":{"ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>.","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>.","short":"Q.P. Ho, Advances in Mathematics 392 (2021).","ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. 2021;392. doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>","apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>","ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021."}},{"corr_author":"1","status":"public","ec_funded":1,"citation":{"ista":"Klein K, Pascual Perez G, Walter M, Kamath Hosdurg C, Capretto M, Cueto Noval M, Markov I, Yeo MX, Alwen JF, Pietrzak KZ. 2021. Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement. 2021 IEEE Symposium on Security and Privacy . SP: Symposium on Security and Privacy, 268–284.","short":"K. Klein, G. Pascual Perez, M. Walter, C. Kamath Hosdurg, M. Capretto, M. Cueto Noval, I. Markov, M.X. Yeo, J.F. Alwen, K.Z. Pietrzak, in:, 2021 IEEE Symposium on Security and Privacy , IEEE, 2021, pp. 268–284.","chicago":"Klein, Karen, Guillermo Pascual Perez, Michael Walter, Chethan Kamath Hosdurg, Margarita Capretto, Miguel Cueto Noval, Ilia Markov, Michelle X Yeo, Joel F Alwen, and Krzysztof Z Pietrzak. “Keep the Dirt: Tainted TreeKEM, Adaptively and Actively Secure Continuous Group Key Agreement.” In <i>2021 IEEE Symposium on Security and Privacy </i>, 268–84. IEEE, 2021. <a href=\"https://doi.org/10.1109/sp40001.2021.00035\">https://doi.org/10.1109/sp40001.2021.00035</a>.","mla":"Klein, Karen, et al. “Keep the Dirt: Tainted TreeKEM, Adaptively and Actively Secure Continuous Group Key Agreement.” <i>2021 IEEE Symposium on Security and Privacy </i>, IEEE, 2021, pp. 268–84, doi:<a href=\"https://doi.org/10.1109/sp40001.2021.00035\">10.1109/sp40001.2021.00035</a>.","ama":"Klein K, Pascual Perez G, Walter M, et al. Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement. In: <i>2021 IEEE Symposium on Security and Privacy </i>. IEEE; 2021:268-284. doi:<a href=\"https://doi.org/10.1109/sp40001.2021.00035\">10.1109/sp40001.2021.00035</a>","ieee":"K. Klein <i>et al.</i>, “Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement,” in <i>2021 IEEE Symposium on Security and Privacy </i>, San Francisco, CA, United States, 2021, pp. 268–284.","apa":"Klein, K., Pascual Perez, G., Walter, M., Kamath Hosdurg, C., Capretto, M., Cueto Noval, M., … Pietrzak, K. Z. (2021). Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement. In <i>2021 IEEE Symposium on Security and Privacy </i> (pp. 268–284). San Francisco, CA, United States: IEEE. <a href=\"https://doi.org/10.1109/sp40001.2021.00035\">https://doi.org/10.1109/sp40001.2021.00035</a>"},"date_published":"2021-08-26T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"IEEE","department":[{"_id":"KrPi"},{"_id":"DaAl"}],"main_file_link":[{"url":"https://eprint.iacr.org/2019/1489","open_access":"1"}],"doi":"10.1109/sp40001.2021.00035","month":"08","_id":"10049","oa_version":"Preprint","quality_controlled":"1","date_updated":"2026-04-08T07:01:44Z","date_created":"2021-09-27T13:46:27Z","scopus_import":"1","project":[{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020"},{"_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","call_identifier":"H2020","grant_number":"682815"}],"related_material":{"record":[{"id":"18088","relation":"dissertation_contains","status":"public"},{"status":"public","relation":"dissertation_contains","id":"10035"}]},"conference":{"start_date":"2021-05-24","location":"San Francisco, CA, United States","name":"SP: Symposium on Security and Privacy","end_date":"2021-05-27"},"type":"conference","year":"2021","external_id":{"isi":["001316065000016"]},"language":[{"iso":"eng"}],"isi":1,"publication":"2021 IEEE Symposium on Security and Privacy ","publication_status":"published","page":"268-284","acknowledgement":"The first three authors contributed equally to this work. Funded by the European Research Council (ERC) under the European Union’s Horizon2020 research and innovation programme (682815-TOCNeT). Funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No.665385.","abstract":[{"text":"While messaging systems with strong security guarantees are widely used in practice, designing a protocol that scales efficiently to large groups and enjoys similar security guarantees remains largely open. The two existing proposals to date are ART (Cohn-Gordon et al., CCS18) and TreeKEM (IETF, The Messaging Layer Security Protocol, draft). TreeKEM is the currently considered candidate by the IETF MLS working group, but dynamic group operations (i.e. adding and removing users) can cause efficiency issues. In this paper we formalize and analyze a variant of TreeKEM which we term Tainted TreeKEM (TTKEM for short). The basic idea underlying TTKEM was suggested by Millican (MLS mailing list, February 2018). This version is more efficient than TreeKEM for some natural distributions of group operations, we quantify this through simulations.Our second contribution is two security proofs for TTKEM which establish post compromise and forward secrecy even against adaptive attackers. The security loss (to the underlying PKE) in the Random Oracle Model is a polynomial factor, and a quasipolynomial one in the Standard Model. Our proofs can be adapted to TreeKEM as well. Before our work no security proof for any TreeKEM-like protocol establishing tight security against an adversary who can adaptively choose the sequence of operations was known. We also are the first to prove (or even formalize) active security where the server can arbitrarily deviate from the protocol specification. Proving fully active security – where also the users can arbitrarily deviate – remains open.","lang":"eng"}],"title":"Keep the dirt: tainted TreeKEM, adaptively and actively secure continuous group key agreement","author":[{"first_name":"Karen","full_name":"Klein, Karen","id":"3E83A2F8-F248-11E8-B48F-1D18A9856A87","last_name":"Klein"},{"orcid":"0000-0001-8630-415X","last_name":"Pascual Perez","id":"2D7ABD02-F248-11E8-B48F-1D18A9856A87","full_name":"Pascual Perez, Guillermo","first_name":"Guillermo"},{"orcid":"0000-0003-3186-2482","last_name":"Walter","id":"488F98B0-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Walter, Michael"},{"full_name":"Kamath Hosdurg, Chethan","first_name":"Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","last_name":"Kamath Hosdurg","orcid":"0009-0006-6812-7317"},{"first_name":"Margarita","full_name":"Capretto, Margarita","last_name":"Capretto"},{"full_name":"Cueto Noval, Miguel","first_name":"Miguel","orcid":"0000-0002-2505-4246","id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc","last_name":"Cueto Noval"},{"last_name":"Markov","id":"D0CF4148-C985-11E9-8066-0BDEE5697425","first_name":"Ilia","full_name":"Markov, Ilia"},{"last_name":"Yeo","id":"2D82B818-F248-11E8-B48F-1D18A9856A87","orcid":"0009-0001-3676-4809","first_name":"Michelle X","full_name":"Yeo, Michelle X"},{"first_name":"Joel F","full_name":"Alwen, Joel F","last_name":"Alwen","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pietrzak, Krzysztof Z","first_name":"Krzysztof Z","last_name":"Pietrzak","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654"}],"day":"26","oa":1,"article_processing_charge":"No"},{"external_id":{"isi":["000752287700005"],"pmid":["34353898"]},"pmid":1,"language":[{"iso":"eng"}],"year":"2021","article_type":"original","publication":"Journal of Neuroscience","file":[{"access_level":"open_access","content_type":"application/pdf","creator":"dernst","success":1,"file_size":11571961,"date_updated":"2022-05-31T09:10:15Z","date_created":"2022-05-31T09:10:15Z","checksum":"769ab627c7355a50ccfd445e43a5f351","file_name":"2021_JourNeuroscience_Butola.pdf","relation":"main_file","file_id":"11423"}],"isi":1,"publication_identifier":{"eissn":["1529-2401"],"issn":["0270-6474"]},"title":"RIM-binding protein 2 organizes Ca<sup>21</sup> channel topography and regulates release probability and vesicle replenishment at a fast central synapse","abstract":[{"text":"Rab-interacting molecule (RIM)-binding protein 2 (BP2) is a multidomain protein of the presynaptic active zone (AZ). By binding to RIM, bassoon (Bsn), and voltage-gated Ca2+ channels (CaV), it is considered to be a central organizer of the topography of CaV and release sites of synaptic vesicles (SVs) at the AZ. Here, we used RIM-BP2 knock-out (KO) mice and their wild-type (WT) littermates of either sex to investigate the role of RIM-BP2 at the endbulb of Held synapse of auditory nerve fibers (ANFs) with bushy cells (BCs) of the cochlear nucleus, a fast relay of the auditory pathway with high release probability. Disruption of RIM-BP2 lowered release probability altering short-term plasticity and reduced evoked EPSCs. Analysis of SV pool dynamics during high-frequency train stimulation indicated a reduction of SVs with high release probability but an overall normal size of the readily releasable SV pool (RRP). The Ca2+-dependent fast component of SV replenishment after RRP depletion was slowed. Ultrastructural analysis by superresolution light and electron microscopy revealed an impaired topography of presynaptic CaV and a reduction of docked and membrane-proximal SVs at the AZ. We conclude that RIM-BP2 organizes the topography of CaV, and promotes SV tethering and docking. This way RIM-BP2 is critical for establishing a high initial release probability as required to reliably signal sound onset information that we found to be degraded in BCs of RIM-BP2-deficient mice in vivo. SIGNIFICANCE STATEMENT: Rab-interacting molecule (RIM)-binding proteins (BPs) are key organizers of the active zone (AZ). Using a multidisciplinary approach to the calyceal endbulb of Held synapse that transmits auditory information at rates of up to hundreds of Hertz with submillisecond precision we demonstrate a requirement for RIM-BP2 for normal auditory signaling. Endbulb synapses lacking RIM-BP2 show a reduced release probability despite normal whole-terminal Ca2+ influx and abundance of the key priming protein Munc13-1, a reduced rate of SV replenishment, as well as an altered topography of voltage-gated (CaV)2.1 Ca2+ channels, and fewer docked and membrane proximal synaptic vesicles (SVs). This hampers transmission of sound onset information likely affecting downstream neural computations such as of sound localization.","lang":"eng"}],"acknowledgement":"This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Sensory Research Center 1286 [to C.W. (A4) and T.M. (B5)] and under Germany’s Excellence Strategy Grant EXC 2067/1-390729940. We thank S. Gerke, A.J. Goldak, and C. Senger-Freitag for expert technical assistance; G. Hoch for developing image analysis routines; and S. Chepurwar and N. Strenzke for technical support and discussion regarding in vivo experiments. We also thank Dr. Christian Rosenmund, Dr. Katharina Grauel, and Dr. Stephan Sigrist for providing RIM-BP2 KO mice and Dr. Masahiko Watanabe for providing the anti-neurexin-antibody, and Dr. Toshihisa Ohtsuka for the anti-ELKS-antibody. J. Neef for help with the STED imaging and image analysis; E. Neher and S. Rizzoli for discussion and comments on the manuscript; K. Eguchi for help with the statistical analysis; and C. H. Huang and J. Neef for constant support and scientific discussion.","publication_status":"published","page":"7742-7767","article_processing_charge":"No","oa":1,"author":[{"first_name":"Tanvi","full_name":"Butola, Tanvi","last_name":"Butola"},{"last_name":"Alvanos","full_name":"Alvanos, Theocharis","first_name":"Theocharis"},{"first_name":"Anika","full_name":"Hintze, Anika","last_name":"Hintze"},{"last_name":"Koppensteiner","id":"3B8B25A8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3509-1948","first_name":"Peter","full_name":"Koppensteiner, Peter"},{"first_name":"David","full_name":"Kleindienst, David","id":"42E121A4-F248-11E8-B48F-1D18A9856A87","last_name":"Kleindienst"},{"orcid":"0000-0001-8761-9444","id":"499F3ABC-F248-11E8-B48F-1D18A9856A87","last_name":"Shigemoto","full_name":"Shigemoto, Ryuichi","first_name":"Ryuichi"},{"full_name":"Wichmann, Carolin","first_name":"Carolin","last_name":"Wichmann"},{"last_name":"Moser","full_name":"Moser, Tobias","first_name":"Tobias"}],"ddc":["570"],"day":"15","issue":"37","intvolume":"        41","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ama":"Butola T, Alvanos T, Hintze A, et al. RIM-binding protein 2 organizes Ca<sup>21</sup> channel topography and regulates release probability and vesicle replenishment at a fast central synapse. <i>Journal of Neuroscience</i>. 2021;41(37):7742-7767. doi:<a href=\"https://doi.org/10.1523/JNEUROSCI.0586-21.2021\">10.1523/JNEUROSCI.0586-21.2021</a>","apa":"Butola, T., Alvanos, T., Hintze, A., Koppensteiner, P., Kleindienst, D., Shigemoto, R., … Moser, T. (2021). RIM-binding protein 2 organizes Ca<sup>21</sup> channel topography and regulates release probability and vesicle replenishment at a fast central synapse. <i>Journal of Neuroscience</i>. Society for Neuroscience. <a href=\"https://doi.org/10.1523/JNEUROSCI.0586-21.2021\">https://doi.org/10.1523/JNEUROSCI.0586-21.2021</a>","ieee":"T. Butola <i>et al.</i>, “RIM-binding protein 2 organizes Ca<sup>21</sup> channel topography and regulates release probability and vesicle replenishment at a fast central synapse,” <i>Journal of Neuroscience</i>, vol. 41, no. 37. Society for Neuroscience, pp. 7742–7767, 2021.","ista":"Butola T, Alvanos T, Hintze A, Koppensteiner P, Kleindienst D, Shigemoto R, Wichmann C, Moser T. 2021. RIM-binding protein 2 organizes Ca<sup>21</sup> channel topography and regulates release probability and vesicle replenishment at a fast central synapse. Journal of Neuroscience. 41(37), 7742–7767.","mla":"Butola, Tanvi, et al. “RIM-Binding Protein 2 Organizes Ca<sup>21</sup> Channel Topography and Regulates Release Probability and Vesicle Replenishment at a Fast Central Synapse.” <i>Journal of Neuroscience</i>, vol. 41, no. 37, Society for Neuroscience, 2021, pp. 7742–67, doi:<a href=\"https://doi.org/10.1523/JNEUROSCI.0586-21.2021\">10.1523/JNEUROSCI.0586-21.2021</a>.","short":"T. Butola, T. Alvanos, A. Hintze, P. Koppensteiner, D. Kleindienst, R. Shigemoto, C. Wichmann, T. Moser, Journal of Neuroscience 41 (2021) 7742–7767.","chicago":"Butola, Tanvi, Theocharis Alvanos, Anika Hintze, Peter Koppensteiner, David Kleindienst, Ryuichi Shigemoto, Carolin Wichmann, and Tobias Moser. “RIM-Binding Protein 2 Organizes Ca<sup>21</sup> Channel Topography and Regulates Release Probability and Vesicle Replenishment at a Fast Central Synapse.” <i>Journal of Neuroscience</i>. Society for Neuroscience, 2021. <a href=\"https://doi.org/10.1523/JNEUROSCI.0586-21.2021\">https://doi.org/10.1523/JNEUROSCI.0586-21.2021</a>."},"date_published":"2021-09-15T00:00:00Z","status":"public","file_date_updated":"2022-05-31T09:10:15Z","department":[{"_id":"RySh"}],"publisher":"Society for Neuroscience","scopus_import":"1","_id":"10051","month":"09","oa_version":"Published Version","volume":41,"quality_controlled":"1","date_created":"2021-09-27T14:33:13Z","date_updated":"2023-08-14T06:56:30Z","doi":"10.1523/JNEUROSCI.0586-21.2021","type":"journal_article","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1"},{"ec_funded":1,"status":"public","alternative_title":["LIPIcs"],"arxiv":1,"article_number":"18","date_published":"2021-08-13T00:00:00Z","citation":{"mla":"Jecker, Ismael R., et al. “Decomposing Permutation Automata.” <i>32nd International Conference on Concurrency Theory</i>, vol. 203, 18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">10.4230/LIPIcs.CONCUR.2021.18</a>.","short":"I.R. Jecker, N. Mazzocchi, P. Wolf, in:, 32nd International Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","chicago":"Jecker, Ismael R, Nicolas Mazzocchi, and Petra Wolf. “Decomposing Permutation Automata.” In <i>32nd International Conference on Concurrency Theory</i>, Vol. 203. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">https://doi.org/10.4230/LIPIcs.CONCUR.2021.18</a>.","ista":"Jecker IR, Mazzocchi N, Wolf P. 2021. Decomposing permutation automata. 32nd International Conference on Concurrency Theory. CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 203, 18.","apa":"Jecker, I. R., Mazzocchi, N., &#38; Wolf, P. (2021). Decomposing permutation automata. In <i>32nd International Conference on Concurrency Theory</i> (Vol. 203). Paris, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">https://doi.org/10.4230/LIPIcs.CONCUR.2021.18</a>","ieee":"I. R. Jecker, N. Mazzocchi, and P. Wolf, “Decomposing permutation automata,” in <i>32nd International Conference on Concurrency Theory</i>, Paris, France, 2021, vol. 203.","ama":"Jecker IR, Mazzocchi N, Wolf P. Decomposing permutation automata. In: <i>32nd International Conference on Concurrency Theory</i>. Vol 203. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2021.18\">10.4230/LIPIcs.CONCUR.2021.18</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       203","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"KrCh"}],"file_date_updated":"2021-10-01T11:10:53Z","doi":"10.4230/LIPIcs.CONCUR.2021.18","volume":203,"date_created":"2021-09-27T14:33:14Z","quality_controlled":"1","date_updated":"2025-05-14T10:55:28Z","oa_version":"Published Version","_id":"10052","month":"08","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"scopus_import":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","conference":{"start_date":"2021-08-23","location":"Paris, France","name":"CONCUR: Conference on Concurrency Theory","end_date":"2021-08-27"},"type":"conference","year":"2021","language":[{"iso":"eng"}],"external_id":{"arxiv":["2107.04683"]},"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-9597-7203-7"]},"file":[{"checksum":"4722c81be82265cf45e78adf9db91250","file_id":"10064","relation":"main_file","file_name":"2021_CONCUR_Jecker.pdf","content_type":"application/pdf","access_level":"open_access","file_size":1003552,"date_updated":"2021-10-01T11:10:53Z","date_created":"2021-10-01T11:10:53Z","success":1,"creator":"cchlebak"}],"publication":"32nd International Conference on Concurrency Theory","publication_status":"published","acknowledgement":"Ismaël Jecker: Marie Skłodowska-Curie Grant Agreement No. 754411. Nicolas Mazzocchi: BOSCO project PGC2018-102210-B-I00 (MCIU/AEI/FEDER, UE), BLOQUESCM project S2018/TCS-4339, and MINECO grant RYC-2016-20281.\r\nPetra Wolf : DFG project FE 560/9-1.\r\n","abstract":[{"lang":"eng","text":"A deterministic finite automaton (DFA) 𝒜 is composite if its language L(𝒜) can be decomposed into an intersection ⋂_{i = 1}^k L(𝒜_i) of languages of smaller DFAs. Otherwise, 𝒜 is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those for which the transition monoid is a group. We provide an NP algorithm to decide whether a permutation DFA is composite, and show that the difficulty of this problem comes from the number of non-accepting states of the instance: we give a fixed-parameter tractable algorithm with the number of rejecting states as the parameter. Moreover, we investigate the class of commutative permutation DFAs. Their structural properties allow us to decide compositionality in NL, and even in LOGSPACE if the alphabet size is fixed. Despite this low complexity, we show that complex behaviors still arise in this class: we provide a family of composite DFAs each requiring polynomially many factors with respect to its size. We also consider the variant of the problem that asks whether a DFA is k-factor composite, that is, decomposable into k smaller DFAs, for some given integer k ∈ ℕ. We show that, for commutative permutation DFAs, restricting the number of factors makes the decision computationally harder, and yields a problem with tight bounds: it is NP-complete. Finally, we show that in general, this problem is in PSPACE, and it is in LOGSPACE for DFAs with a singleton alphabet."}],"title":"Decomposing permutation automata","day":"13","ddc":["000"],"author":[{"full_name":"Jecker, Ismael R","first_name":"Ismael R","last_name":"Jecker","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425"},{"last_name":"Mazzocchi","first_name":"Nicolas","full_name":"Mazzocchi, Nicolas"},{"last_name":"Wolf","first_name":"Petra","full_name":"Wolf, Petra"}],"oa":1,"article_processing_charge":"No"},{"status":"public","arxiv":1,"citation":{"ieee":"S. A. Hashemi, M. Mondelli, A. Fazeli, A. Vardy, J. Cioffi, and A. Goldsmith, “Parallelism versus latency in simplified successive-cancellation decoding of polar codes,” in <i>2021 IEEE International Symposium on Information Theory</i>, Melbourne, Australia, 2021, pp. 2369–2374.","apa":"Hashemi, S. A., Mondelli, M., Fazeli, A., Vardy, A., Cioffi, J., &#38; Goldsmith, A. (2021). Parallelism versus latency in simplified successive-cancellation decoding of polar codes. In <i>2021 IEEE International Symposium on Information Theory</i> (pp. 2369–2374). Melbourne, Australia: Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/ISIT45174.2021.9518153\">https://doi.org/10.1109/ISIT45174.2021.9518153</a>","ama":"Hashemi SA, Mondelli M, Fazeli A, Vardy A, Cioffi J, Goldsmith A. Parallelism versus latency in simplified successive-cancellation decoding of polar codes. In: <i>2021 IEEE International Symposium on Information Theory</i>. Institute of Electrical and Electronics Engineers; 2021:2369-2374. doi:<a href=\"https://doi.org/10.1109/ISIT45174.2021.9518153\">10.1109/ISIT45174.2021.9518153</a>","chicago":"Hashemi, Seyyed Ali, Marco Mondelli, Arman Fazeli, Alexander Vardy, John Cioffi, and Andrea Goldsmith. “Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes.” In <i>2021 IEEE International Symposium on Information Theory</i>, 2369–74. Institute of Electrical and Electronics Engineers, 2021. <a href=\"https://doi.org/10.1109/ISIT45174.2021.9518153\">https://doi.org/10.1109/ISIT45174.2021.9518153</a>.","short":"S.A. Hashemi, M. Mondelli, A. Fazeli, A. Vardy, J. Cioffi, A. Goldsmith, in:, 2021 IEEE International Symposium on Information Theory, Institute of Electrical and Electronics Engineers, 2021, pp. 2369–2374.","mla":"Hashemi, Seyyed Ali, et al. “Parallelism versus Latency in Simplified Successive-Cancellation Decoding of Polar Codes.” <i>2021 IEEE International Symposium on Information Theory</i>, Institute of Electrical and Electronics Engineers, 2021, pp. 2369–74, doi:<a href=\"https://doi.org/10.1109/ISIT45174.2021.9518153\">10.1109/ISIT45174.2021.9518153</a>.","ista":"Hashemi SA, Mondelli M, Fazeli A, Vardy A, Cioffi J, Goldsmith A. 2021. Parallelism versus latency in simplified successive-cancellation decoding of polar codes. 2021 IEEE International Symposium on Information Theory. ISIT: International Symposium on Information Theory, 2369–2374."},"date_published":"2021-09-01T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Electrical and Electronics Engineers","department":[{"_id":"MaMo"}],"main_file_link":[{"url":"https://arxiv.org/abs/2012.13378","open_access":"1"}],"doi":"10.1109/ISIT45174.2021.9518153","_id":"10053","month":"09","oa_version":"Preprint","quality_controlled":"1","date_updated":"2025-04-15T07:50:11Z","date_created":"2021-09-27T14:33:14Z","scopus_import":"1","project":[{"name":"Prix Lopez-Loretta 2019 - Marco Mondelli","_id":"059876FA-7A3F-11EA-A408-12923DDC885E"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"10364"}]},"conference":{"end_date":"2021-07-20","location":"Melbourne, Australia","name":"ISIT: International Symposium on Information Theory","start_date":"2021-07-12"},"type":"conference","year":"2021","external_id":{"isi":["000701502202078"],"arxiv":["2012.13378"]},"language":[{"iso":"eng"}],"publication_identifier":{"eisbn":["978-1-5386-8209-8"],"isbn":["978-1-5386-8210-4"],"issn":["2157-8095"]},"isi":1,"publication":"2021 IEEE International Symposium on Information Theory","publication_status":"published","page":"2369-2374","acknowledgement":"S. A. Hashemi is supported by a Postdoctoral Fellowship from the Natural Sciences and Engineering Research Council\r\nof Canada (NSERC) and by Huawei. M. Mondelli is partially supported by the 2019 Lopez-Loreta Prize. A. Fazeli and A. Vardy were supported in part by the National Science Foundation under Grant CCF-1764104.","abstract":[{"text":"This paper characterizes the latency of the simplified successive-cancellation (SSC) decoding scheme for polar codes under hardware resource constraints. In particular, when the number of processing elements P that can perform SSC decoding operations in parallel is limited, as is the case in practice, the latency of SSC decoding is O(N1−1 μ+NPlog2log2NP), where N is the block length of the code and μ is the scaling exponent of polar codes for the channel. Three direct consequences of this bound are presented. First, in a fully-parallel implementation where P=N2 , the latency of SSC decoding is O(N1−1/μ) , which is sublinear in the block length. This recovers a result from an earlier work. Second, in a fully-serial implementation where P=1 , the latency of SSC decoding scales as O(Nlog2log2N) . The multiplicative constant is also calculated: we show that the latency of SSC decoding when P=1 is given by (2+o(1))Nlog2log2N . Third, in a semi-parallel implementation, the smallest P that gives the same latency as that of the fully-parallel implementation is P=N1/μ . The tightness of our bound on SSC decoding latency and the applicability of the foregoing results is validated through extensive simulations.","lang":"eng"}],"title":"Parallelism versus latency in simplified successive-cancellation decoding of polar codes","author":[{"last_name":"Hashemi","full_name":"Hashemi, Seyyed Ali","first_name":"Seyyed Ali"},{"last_name":"Mondelli","id":"27EB676C-8706-11E9-9510-7717E6697425","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco","first_name":"Marco"},{"last_name":"Fazeli","full_name":"Fazeli, Arman","first_name":"Arman"},{"last_name":"Vardy","full_name":"Vardy, Alexander","first_name":"Alexander"},{"first_name":"John","full_name":"Cioffi, John","last_name":"Cioffi"},{"last_name":"Goldsmith","first_name":"Andrea","full_name":"Goldsmith, Andrea"}],"day":"01","oa":1,"article_processing_charge":"No"}]
