--- OA_type: closed access _id: '18266' abstract: - lang: eng text: Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that refine the notion of optimality in the context of polynomially perturbed matrix games. The first concept captures how the value depends on the perturbation parameter, and the second consists of the existence of a fixed strategy that guarantees the value of the unperturbed matrix game for every sufficiently small positive parameter. We provide polynomial-time algorithms to check whether a polynomially perturbed matrix game satisfies these properties. We further provide the functional form for a parameterized optimal strategy and the value function. Finally, we translate our results to linear programming and stochastic games, where value positivity is related to the existence of robust solutions. acknowledgement: This research was supported by Fondation CFM pour la Recherche, the H2020 European Research Council [Grant ERC-CoG-863818 (ForM-SMArt)], the Austrian Science Fund [Grant 10.55776/COE12], ANID Chile [Grant ACT210005], and Agence Nationale de la Recherche [Grant ANR-21-CE40-0020]. article_processing_charge: No article_type: original author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Miquel full_name: Oliu-Barton, Miquel last_name: Oliu-Barton - first_name: Raimundo J full_name: Saona Urmeneta, Raimundo J id: BD1DF4C4-D767-11E9-B658-BC13E6697425 last_name: Saona Urmeneta orcid: 0000-0001-5103-038X citation: ama: Chatterjee K, Oliu-Barton M, Saona Urmeneta RJ. Value-positivity for matrix games. Mathematics of Operations Research. 2024;50(4):2433-3282. doi:10.1287/moor.2022.0332 apa: Chatterjee, K., Oliu-Barton, M., & Saona Urmeneta, R. J. (2024). Value-positivity for matrix games. Mathematics of Operations Research. Institute for Operations Research and the Management Sciences. https://doi.org/10.1287/moor.2022.0332 chicago: Chatterjee, Krishnendu, Miquel Oliu-Barton, and Raimundo J Saona Urmeneta. “Value-Positivity for Matrix Games.” Mathematics of Operations Research. Institute for Operations Research and the Management Sciences, 2024. https://doi.org/10.1287/moor.2022.0332. ieee: K. Chatterjee, M. Oliu-Barton, and R. J. Saona Urmeneta, “Value-positivity for matrix games,” Mathematics of Operations Research, vol. 50, no. 4. Institute for Operations Research and the Management Sciences, pp. 2433–3282, 2024. ista: Chatterjee K, Oliu-Barton M, Saona Urmeneta RJ. 2024. Value-positivity for matrix games. Mathematics of Operations Research. 50(4), 2433–3282. mla: Chatterjee, Krishnendu, et al. “Value-Positivity for Matrix Games.” Mathematics of Operations Research, vol. 50, no. 4, Institute for Operations Research and the Management Sciences, 2024, pp. 2433–3282, doi:10.1287/moor.2022.0332. short: K. Chatterjee, M. Oliu-Barton, R.J. Saona Urmeneta, Mathematics of Operations Research 50 (2024) 2433–3282. corr_author: '1' das_tickbox: '0' date_created: 2024-10-09T07:02:20Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-10-02T11:30:08Z day: '01' department: - _id: GradSch - _id: KrCh doi: 10.1287/moor.2022.0332 ec_funded: 1 external_id: isi: - '001328875900001' fulldoi: https://doi.org/10.1287/moor.2022.0332 intvolume: ' 50' isi: 1 issue: '4' language: - iso: eng month: '10' oa_version: None page: 2433-3282 project: - _id: 0599E47C-7A3F-11EA-A408-12923DDC885E call_identifier: H2020 grant_number: '863818' name: 'Formal Methods for Stochastic Models: Algorithms and Applications' publication: Mathematics of Operations Research publication_identifier: eissn: - 1526-5471 issn: - 0364-765X publication_status: published publisher: Institute for Operations Research and the Management Sciences quality_controlled: '1' related_material: record: - id: '20234' relation: dissertation_contains status: public researchdata_availability: unclear scopus_import: '1' status: public supplementarymaterial: unclear title: Value-positivity for matrix games type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 50 year: '2024' ... --- OA_place: repository OA_type: green _id: '17047' abstract: - lang: eng text: We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random matrix models. article_number: '2450007' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: Jana full_name: Reker, Jana id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9 last_name: Reker citation: ama: 'Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. 2024;13(2). doi:10.1142/s2010326324500072' apa: 'Dubach, G., & Reker, J. (2024). Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326324500072' chicago: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” Random Matrices: Theory and Applications. World Scientific Publishing, 2024. https://doi.org/10.1142/s2010326324500072.' ieee: 'G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation of a unitary matrix,” Random Matrices: Theory and Applications, vol. 13, no. 2. World Scientific Publishing, 2024.' ista: 'Dubach G, Reker J. 2024. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. 13(2), 2450007.' mla: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” Random Matrices: Theory and Applications, vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:10.1142/s2010326324500072.' short: 'G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).' corr_author: '1' das_tickbox: '0' date_created: 2024-05-23T08:31:57Z date_published: 2024-04-01T00:00:00Z date_updated: 2026-10-02T11:31:29Z day: '01' department: - _id: GradSch - _id: LaEr doi: 10.1142/s2010326324500072 ec_funded: 1 external_id: arxiv: - '2212.14638' isi: - '001229295200002' fulldoi: https://doi.org/10.1142/s2010326324500072 intvolume: ' 13' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2212.14638' month: '04' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: 'Random Matrices: Theory and Applications' publication_identifier: eissn: - 2010-3271 issn: - 2010-3263 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' related_material: record: - id: '17164' relation: dissertation_contains status: public researchdata_availability: unclear scopus_import: '1' status: public supplementarymaterial: unclear title: Dynamics of a rank-one multiplicative perturbation of a unitary matrix type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 13 year: '2024' ... --- OA_place: publisher OA_type: gold _id: '18891' abstract: - lang: eng text: "Deep neural networks (DNNs) exhibit a surprising structure in their final layer\r\nknown as neural collapse (NC), and a growing body of works has currently investigated the propagation of neural collapse to earlier layers of DNNs – a phenomenon\r\ncalled deep neural collapse (DNC). However, existing theoretical results are restricted to special cases: linear models, only two layers or binary classification.\r\nIn contrast, we focus on non-linear models of arbitrary depth in multi-class classification and reveal a surprising qualitative shift. As soon as we go beyond two\r\nlayers or two classes, DNC stops being optimal for the deep unconstrained features\r\nmodel (DUFM) – the standard theoretical framework for the analysis of collapse.\r\nThe main culprit is a low-rank bias of multi-layer regularization schemes: this bias\r\nleads to optimal solutions of even lower rank than the neural collapse. We support\r\nour theoretical findings with experiments on both DUFM and real data, which show\r\nthe emergence of the low-rank structure in the solution found by gradient descent." acknowledged_ssus: - _id: ScienComp acknowledgement: Marco Mondelli is partially supported by the 2019 Lopez-Loreta prize. This research was supported by the Scientific Service Units (SSU) of ISTA through resources provided by Scientific Computing (SciComp). alternative_title: - Advances in Neural Information Processing Systems article_processing_charge: No arxiv: 1 author: - first_name: Peter full_name: Súkeník, Peter id: d64d6a8d-eb8e-11eb-b029-96fd216dec3c last_name: Súkeník - first_name: Christoph full_name: Lampert, Christoph id: 40C20FD2-F248-11E8-B48F-1D18A9856A87 last_name: Lampert orcid: 0000-0001-8622-7887 - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 citation: ama: 'Súkeník P, Lampert C, Mondelli M. Neural collapse versus low-rank bias: Is deep neural collapse really optimal? In: 38th Annual Conference on Neural Information Processing Systems. Vol 37. Neural Information Processing Systems Foundation; 2024.' apa: 'Súkeník, P., Lampert, C., & Mondelli, M. (2024). Neural collapse versus low-rank bias: Is deep neural collapse really optimal? In 38th Annual Conference on Neural Information Processing Systems (Vol. 37). Vancouver, Canada: Neural Information Processing Systems Foundation.' chicago: 'Súkeník, Peter, Christoph Lampert, and Marco Mondelli. “Neural Collapse versus Low-Rank Bias: Is Deep Neural Collapse Really Optimal?” In 38th Annual Conference on Neural Information Processing Systems, Vol. 37. Neural Information Processing Systems Foundation, 2024.' ieee: 'P. Súkeník, C. Lampert, and M. Mondelli, “Neural collapse versus low-rank bias: Is deep neural collapse really optimal?,” in 38th Annual Conference on Neural Information Processing Systems, Vancouver, Canada, 2024, vol. 37.' ista: 'Súkeník P, Lampert C, Mondelli M. 2024. Neural collapse versus low-rank bias: Is deep neural collapse really optimal? 38th Annual Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 37.' mla: 'Súkeník, Peter, et al. “Neural Collapse versus Low-Rank Bias: Is Deep Neural Collapse Really Optimal?” 38th Annual Conference on Neural Information Processing Systems, vol. 37, Neural Information Processing Systems Foundation, 2024.' short: P. Súkeník, C. Lampert, M. Mondelli, in:, 38th Annual Conference on Neural Information Processing Systems, Neural Information Processing Systems Foundation, 2024. conference: end_date: 2024-12-16 location: Vancouver, Canada name: 'NeurIPS: Neural Information Processing Systems' start_date: 2024-12-16 corr_author: '1' das_tickbox: '0' date_created: 2025-01-27T11:15:18Z date_published: 2024-12-01T00:00:00Z date_updated: 2026-10-02T11:34:35Z day: '01' ddc: - '000' department: - _id: GradSch - _id: MaMo - _id: ChLa external_id: arxiv: - '2405.14468' file: - access_level: open_access checksum: b7b79f1ea3ac1e9e11b3d91faaeb0780 content_type: application/pdf creator: dernst date_created: 2025-02-04T08:11:25Z date_updated: 2025-02-04T08:11:25Z file_id: '18989' file_name: 2024_NeurIPS_Sukenik.pdf file_size: 1784118 relation: main_file success: 1 file_date_updated: 2025-02-04T08:11:25Z has_accepted_license: '1' intvolume: ' 37' language: - iso: eng month: '12' oa: 1 oa_version: Published Version project: - _id: 059876FA-7A3F-11EA-A408-12923DDC885E name: Prix Lopez-Loretta 2019 - Marco Mondelli publication: 38th Annual Conference on Neural Information Processing Systems publication_status: published publisher: Neural Information Processing Systems Foundation quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: 'Neural collapse versus low-rank bias: Is deep neural collapse really optimal?' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 37 year: '2024' ... --- OA_place: publisher OA_type: gold _id: '18515' abstract: - lang: eng text: "Understanding the role of evolutionary processes in shaping genetic variation has been a\r\nprimary goal in evolutionary genetics. In this regard, a key question is how genetically\r\ndistinct populations evolve in the face of gene flow, thereby generating genetic and\r\nphenotypic divergence and reproductive isolation (RI). This requires quantifying the role\r\nand relative contributions of prezygotic and postzygotic isolating mechanisms on the\r\nreduction of gene exchange between populations, and identifying regions in the genome\r\nthat mediate RI, which is often polygenic. Further, this needs distinguishing neutral and\r\nselected regions in the genome, and discerning how selection influences patterns of neutral\r\ndivergence.\r\nPopulation structure, defined as any deviation from panmixia, such as geographic distribution, movement and mating patterns of individuals, influences how genetic variation is\r\nstructured in space and shapes the neutral null model. Availability of large scale spatial\r\ngenomic datasets now enables us to detect signatures of population structure in genetic\r\ndata and infer population genetic parameters. Such inferences are crucial and have wide\r\napplications in biodiversity, conservation genetics, population management and medical\r\ngenetics. However, inferences are based on assumptions that do not always match the\r\ncomplex reality, thus leading to erroneous conclusions. Moreover, the role and interaction\r\nof heterogeneous population density and dispersal, which are ubiquitous in nature, has\r\nbeen challenging to study owing to their mathematical complexity. In such scenarios,\r\nfeedback between theory, data and simulations can prove to be useful.\r\nIn this thesis, I examine the effect of population structure on neutral genetic variation\r\nand barriers to gene exchange in hybridising populations, thereby bridging together the\r\nfields of spatial population genetics and speciation.\r\nDespite being a key concept in speciation, reproductive isolation (RI) lacks a quantitative\r\ndefinition and has been used and measured differently across different fields. Chapter 2\r\ngives a quantitative definition of RI, in terms of the effect of genetic differences on gene\r\nflow. We give analytical predictions for RI in a range of scenarios, in terms of effective migration rates for discrete populations and barrier strength for continuous populations.\r\nIn addition to this, we discuss current measures of RI and their limitations, and propose\r\nthe need for new measures that combine organismal and genetic perspectives of RI.\r\nIn chapter 3, I examine the combined effect of assortative mating, sexual selection\r\nand viability selection on RI. For this, we consider a polygenic ‘magic’ trait under a\r\nmainland-island model. We obtain novel theoretical predictions for molecular divergence\r\nin terms of effective migration rates, which bears a simple relationship to measurable\r\nfitness components of migrants and various early generation hybrids. We explore the\r\nconditions under which local adaptation can be maintained despite maladaptive gene flow\r\nand quantify the relative contributions of viability and sexual selection to genome-wide\r\nbarriers to gene flow.\r\nThe next two chapters of the thesis focus on a hybrid zone of Antirrhinum majus that\r\nconsist of two subspecies- the magenta flowered A. m. pseudomajus and the yellow\r\nflowered A.m. striatum. Previous studies have suggested that flower colour is target of\r\npollinator mediated selection and is influenced only by few genes. While these regions\r\nshow high genetic differentiation between the subspecies, the rest of the genome is seen\r\nto be well mixed. Chapter 4 examines the effects of heterogeneous population density\r\nand leptokurtic dispersal on isolation by distance and the distribution of heterozygosity\r\nby focusing on non-flower colour markers.\r\nChapter 5 analyses cline shapes and associations among 6 focal flower colour markers to\r\nunderstand how selection and dispersal maintain this hybrid zone. We see sharp coincident\r\nstepped clines at all loci and positive associations throughout the hybrid zone, contrary to\r\nthe expected patterns from diffusive gene flow. With a novel scheme of inferring dispersal\r\ncombined with multilocus simulations, we show that stepped clines do not reflect genetic\r\nbarriers to gene flow, but are rather a result of long-distance migration. This framework\r\nallows us to get realistic estimates gene flow and selection and shows how traditional cline\r\nanalysis may lead to inaccurate conclusions when assumptions of the theory are not met.\r\nOverall, this thesis investigates how different features of population structure leave\r\ndetectable signatures in genetic variation, namely in patterns of isolation by distance,\r\nlinkage disequilibrium and genetic divergence. It also highlights how effective migration\r\nrates provide useful way of analysing polygenic architectures and shed new light into\r\nhybrid zones. In doing so, I identify scenarios when simple models become insufficient\r\nand suggest possibe directions by combining genetic data with simulations." acknowledged_ssus: - _id: ScienComp acknowledgement: "I also acknowledge the funding agencies Marie Curie COFUND Doctoral Fellowship,\r\nAustrian Science Fund FWF (grant P32166) and ERC (grant PR1000ERC02) for financially\r\nsupporting my research over the years." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Parvathy full_name: Surendranadh, Parvathy id: 455235B8-F248-11E8-B48F-1D18A9856A87 last_name: Surendranadh orcid: 0000-0001-6395-386X citation: ama: Surendranadh P. Effect of population structure on neutral genetic variation and barriers to gene exchange. 2024. doi:10.15479/at:ista:18515 apa: Surendranadh, P. (2024). Effect of population structure on neutral genetic variation and barriers to gene exchange. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18515 chicago: Surendranadh, Parvathy. “Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18515. ieee: P. Surendranadh, “Effect of population structure on neutral genetic variation and barriers to gene exchange,” Institute of Science and Technology Austria, 2024. ista: Surendranadh P. 2024. Effect of population structure on neutral genetic variation and barriers to gene exchange. Institute of Science and Technology Austria. mla: Surendranadh, Parvathy. Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18515. short: P. Surendranadh, Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '1' date_created: 2024-11-06T21:25:37Z date_published: 2024-11-07T00:00:00Z date_updated: 2026-10-02T11:36:48Z day: '07' ddc: - '576' degree_awarded: PhD department: - _id: GradSch - _id: NiBa doi: 10.15479/at:ista:18515 doi_confirm: '1' file: - access_level: open_access checksum: c32cf7bc75748d9c551d8eb70178bbec content_type: application/pdf creator: psurendr date_created: 2024-11-07T10:59:29Z date_updated: 2024-11-07T10:59:29Z file_id: '18519' file_name: PhD_Thesis__Parvathy_071124_PDFA.pdf file_size: 37019760 relation: main_file success: 1 - access_level: closed checksum: 4417e02d54084d89e75734e18caaa96d content_type: application/zip creator: psurendr date_created: 2024-11-07T10:59:42Z date_updated: 2024-11-07T10:59:42Z file_id: '18520' file_name: PhD Thesis- Parvathy_071124.zip file_size: 41198857 relation: source_file file_date_updated: 2024-11-07T10:59:42Z fulldoi: https://doi.org/10.15479/at:ista:18515 has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: '219' project: - _id: 05959E1C-7A3F-11EA-A408-12923DDC885E grant_number: P32166 name: Snapdragon Speciation - _id: bd6958e0-d553-11ed-ba76-86eba6a76c00 grant_number: '101055327' name: Understanding the evolution of continuous genomes publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria researchdata_availability: yes status: public supervisor: - first_name: Nicholas H full_name: Barton, Nicholas H id: 4880FE40-F248-11E8-B48F-1D18A9856A87 last_name: Barton orcid: 0000-0002-8548-5240 supplementarymaterial: no title: Effect of population structure on neutral genetic variation and barriers to gene exchange tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- APC_amount: 3028,31 EUR DOAJ_listed: '1' OA_place: publisher OA_type: gold _id: '18087' abstract: - lang: eng text: We present a theory describing the interaction of structured light, such as light carrying orbital angular momentum, with molecules. The light-matter interaction Hamiltonian we derive is expressed through couplings between spherical gradients of the electric field and the (transition) electric multipole moments of a particle of any nontrivial rotation point group. Our model can therefore accommodate an arbitrary complexity of the molecular and electric field structure, and it can be straightforwardly extended to atoms or nanostructures. Applying this framework to rovibrational spectroscopy of molecules, we uncover the general mechanism of angular momentum exchange between the spin and orbital angular momenta of light, molecular rotation, and its center-of-mass motion. We show that the nonzero vorticity of Laguerre-Gaussian beams can strongly enhance certain rovibrational transitions that are considered forbidden in the case of nonhelical light. We discuss the experimental requirements for the observation of these forbidden transitions in state-of-the-art spatially resolved spectroscopy measurements. acknowledgement: We are grateful to Emilio Pisanty and Philipp Lunt for valuable discussions. This research was funded wholly or in part by the Austrian Science Fund (FWF) [10.55776/F1004]. G.M.K. gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. M.L. acknowledges support by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). O.H.H. acknowledges support by the Austrian Science Fund (FWF) [10.55776/P36040]. Furthermore, the financial support by the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association is gratefully acknowledged. article_number: '033277' article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Mikhail full_name: Maslov, Mikhail id: 2E65BB0E-F248-11E8-B48F-1D18A9856A87 last_name: Maslov orcid: 0000-0003-4074-2570 - first_name: Georgios full_name: Koutentakis, Georgios id: d7b23d3a-9e21-11ec-b482-f76739596b95 last_name: Koutentakis - first_name: Mateja full_name: Hrast, Mateja id: 48dbb294-2a9c-11ef-905d-f56be71f0e5d last_name: Hrast - first_name: Oliver H. full_name: Heckl, Oliver H. last_name: Heckl - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 citation: ama: Maslov M, Koutentakis G, Hrast M, Heckl OH, Lemeshko M. Theory of angular momentum transfer from light to molecules. Physical Review Research. 2024;6(3). doi:10.1103/physrevresearch.6.033277 apa: Maslov, M., Koutentakis, G., Hrast, M., Heckl, O. H., & Lemeshko, M. (2024). Theory of angular momentum transfer from light to molecules. Physical Review Research. American Physical Society. https://doi.org/10.1103/physrevresearch.6.033277 chicago: Maslov, Mikhail, Georgios Koutentakis, Mateja Hrast, Oliver H. Heckl, and Mikhail Lemeshko. “Theory of Angular Momentum Transfer from Light to Molecules.” Physical Review Research. American Physical Society, 2024. https://doi.org/10.1103/physrevresearch.6.033277. ieee: M. Maslov, G. Koutentakis, M. Hrast, O. H. Heckl, and M. Lemeshko, “Theory of angular momentum transfer from light to molecules,” Physical Review Research, vol. 6, no. 3. American Physical Society, 2024. ista: Maslov M, Koutentakis G, Hrast M, Heckl OH, Lemeshko M. 2024. Theory of angular momentum transfer from light to molecules. Physical Review Research. 6(3), 033277. mla: Maslov, Mikhail, et al. “Theory of Angular Momentum Transfer from Light to Molecules.” Physical Review Research, vol. 6, no. 3, 033277, American Physical Society, 2024, doi:10.1103/physrevresearch.6.033277. short: M. Maslov, G. Koutentakis, M. Hrast, O.H. Heckl, M. Lemeshko, Physical Review Research 6 (2024). corr_author: '1' das_tickbox: '0' date_created: 2024-09-18T11:43:16Z date_published: 2024-09-10T00:00:00Z date_updated: 2026-10-02T11:36:24Z day: '10' ddc: - '530' department: - _id: GradSch - _id: MiLe doi: 10.1103/physrevresearch.6.033277 ec_funded: 1 external_id: arxiv: - '2310.00095' file: - access_level: open_access checksum: 8f744d94956a1683b473b1cf9b411a37 content_type: application/pdf creator: dernst date_created: 2024-09-23T09:46:20Z date_updated: 2024-09-23T09:46:20Z file_id: '18125' file_name: 2024_PhysicalReviewResearch_Maslov.pdf file_size: 1563824 relation: main_file success: 1 file_date_updated: 2024-09-23T09:46:20Z fulldoi: https://doi.org/10.1103/physrevresearch.6.033277 has_accepted_license: '1' intvolume: ' 6' issue: '3' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 7c040762-9f16-11ee-852c-dd79eeee4ab3 grant_number: F100403 name: Coherent Optical Metrology Beyond Electric-Dipole-Allowed Transitions - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund publication: Physical Review Research publication_identifier: eissn: - 2643-1564 publication_status: published publisher: American Physical Society quality_controlled: '1' related_material: record: - id: '19048' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: yes title: Theory of angular momentum transfer from light to molecules tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 6 year: '2024' ... --- OA_place: publisher _id: '15020' abstract: - lang: eng text: "This thesis consists of four distinct pieces of work within theoretical biology, with two themes in common: the concept of optimization in biological systems, and the use of information-theoretic tools to quantify biological stochasticity and statistical uncertainty.\r\nChapter 2 develops a statistical framework for studying biological systems which we believe to be optimized for a particular utility function, such as retinal neurons conveying information about visual stimuli. We formalize such beliefs as maximum-entropy Bayesian priors, constrained by the expected utility. We explore how such priors aid inference of system parameters with limited data and enable optimality hypothesis testing: is the utility higher than by chance?\r\nChapter 3 examines the ultimate biological optimization process: evolution by natural selection. As some individuals survive and reproduce more successfully than others, populations evolve towards fitter genotypes and phenotypes. We formalize this as accumulation of genetic information, and use population genetics theory to study how much such information can be accumulated per generation and maintained in the face of random mutation and genetic drift. We identify the population size and fitness variance as the key quantities that control information accumulation and maintenance.\r\nChapter 4 reuses the concept of genetic information from Chapter 3, but from a different perspective: we ask how much genetic information organisms actually need, in particular in the context of gene regulation. For example, how much information is needed to bind transcription factors at correct locations within the genome? Population genetics provides us with a refined answer: with an increasing population size, populations achieve higher fitness by maintaining more genetic information. Moreover, regulatory parameters experience selection pressure to optimize the fitness-information trade-off, i.e. minimize the information needed for a given fitness. This provides an evolutionary derivation of the optimization priors introduced in Chapter 2.\r\nChapter 5 proves an upper bound on mutual information between a signal and a communication channel output (such as neural activity). Mutual information is an important utility measure for biological systems, but its practical use can be difficult due to the large dimensionality of many biological channels. Sometimes, a lower bound on mutual information is computed by replacing the high-dimensional channel outputs with decodes (signal estimates). Our result provides a corresponding upper bound, provided that the decodes are the maximum posterior estimates of the signal." acknowledged_ssus: - _id: ScienComp alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Michal full_name: Hledik, Michal id: 4171253A-F248-11E8-B48F-1D18A9856A87 last_name: Hledik citation: ama: Hledik M. Genetic information and biological optimization. 2024. doi:10.15479/at:ista:15020 apa: Hledik, M. (2024). Genetic information and biological optimization. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15020 chicago: Hledik, Michal. “Genetic Information and Biological Optimization.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15020. ieee: M. Hledik, “Genetic information and biological optimization,” Institute of Science and Technology Austria, 2024. ista: Hledik M. 2024. Genetic information and biological optimization. Institute of Science and Technology Austria. mla: Hledik, Michal. Genetic Information and Biological Optimization. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15020. short: M. Hledik, Genetic Information and Biological Optimization, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-02-23T14:02:04Z date_published: 2024-02-23T00:00:00Z date_updated: 2026-10-02T11:40:30Z day: '23' ddc: - '576' - '519' degree_awarded: PhD department: - _id: GradSch - _id: NiBa - _id: GaTk doi: 10.15479/at:ista:15020 doi_confirm: '1' ec_funded: 1 file: - access_level: open_access checksum: b2d3da47c98d481577a4baf68944fe41 content_type: application/pdf creator: mhledik date_created: 2024-02-23T13:50:53Z date_updated: 2024-02-23T13:50:53Z file_id: '15021' file_name: hledik thesis pdfa 2b.pdf file_size: 7102089 relation: main_file success: 1 - access_level: closed checksum: eda9b9430da2610fee7ce1c1419a479a content_type: application/zip creator: mhledik date_created: 2024-02-23T13:50:54Z date_updated: 2024-02-23T14:20:16Z file_id: '15022' file_name: hledik thesis source.zip file_size: 14014790 relation: source_file file_date_updated: 2024-02-23T14:20:16Z fulldoi: https://doi.org/10.15479/at:ista:15020 has_accepted_license: '1' keyword: - Theoretical biology - Optimality - Evolution - Information language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: '158' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program - _id: 2665AAFE-B435-11E9-9278-68D0E5697425 grant_number: RGP0034/2018 name: Can evolution minimize spurious signaling crosstalk to reach optimal performance? - _id: bd6958e0-d553-11ed-ba76-86eba6a76c00 grant_number: '101055327' name: Understanding the evolution of continuous genomes publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '7606' relation: part_of_dissertation status: public - id: '12081' relation: part_of_dissertation status: public - id: '7553' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Nicholas H full_name: Barton, Nicholas H id: 4880FE40-F248-11E8-B48F-1D18A9856A87 last_name: Barton orcid: 0000-0002-8548-5240 - first_name: Gašper full_name: Tkačik, Gašper id: 3D494DCA-F248-11E8-B48F-1D18A9856A87 last_name: Tkačik orcid: 0000-0002-6699-1455 supplementarymaterial: no title: Genetic information and biological optimization type: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- OA_place: publisher _id: '17225' abstract: - lang: eng text: "This thesis describes the development of an atom interferometer designed to exploit the\r\nadvantages of utilizing quantum entanglement for enhanced precision measurements beyond\r\nthe standard quantum limit. While the project remains ongoing, significant progress has been\r\nmade.\r\nA key contribution of this work is the development of Quantrol, an experimental control\r\nsystem leveraging the ARTIQ framework. This software enables precise timing and control\r\nwithout requiring prior knowledge of ARTIQ’s implementation details or coding experience.\r\nThe interface offers user friendly visual comprehension of the experimental sequence and\r\nextended capabilities, allowing researchers to scan variables with a simple click of a mouse.\r\nThe main proposed project is to implement atom interferometric sequence with squeezed input\r\nstates inside of a dipole trap generated by a high finesse cavity. The presence of the dipole\r\ntrap allows one dimensional atomic cloud split while maintaining relatively strong confinement\r\nin other directions.\r\nWe are currently able to trap and cool 87Rb atoms to few micro kelvin temperatures, load\r\nthem into the dipole trap and state prepare them to be used for squeezing and interferometric\r\nsequence." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Vyacheslav full_name: Li, Vyacheslav id: 3A4FAA92-F248-11E8-B48F-1D18A9856A87 last_name: Li citation: ama: Li V. Towards a quantum entanglement enhanced atom interferomter. 2024. doi:10.15479/at:ista:17225 apa: Li, V. (2024). Towards a quantum entanglement enhanced atom interferomter. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17225 chicago: Li, Vyacheslav. “Towards a Quantum Entanglement Enhanced Atom Interferomter.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17225. ieee: V. Li, “Towards a quantum entanglement enhanced atom interferomter,” Institute of Science and Technology Austria, 2024. ista: Li V. 2024. Towards a quantum entanglement enhanced atom interferomter. Institute of Science and Technology Austria. mla: Li, Vyacheslav. Towards a Quantum Entanglement Enhanced Atom Interferomter. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17225. short: V. Li, Towards a Quantum Entanglement Enhanced Atom Interferomter, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-07-11T09:46:48Z date_published: 2024-07-11T00:00:00Z date_updated: 2026-10-02T11:41:41Z day: '11' ddc: - '530' degree_awarded: PhD department: - _id: GradSch - _id: OnHo doi: 10.15479/at:ista:17225 doi_confirm: '1' file: - access_level: open_access checksum: 15b2dbe8d2c9ed7ca5dd413827928077 content_type: application/pdf creator: vli date_created: 2024-07-11T10:26:22Z date_updated: 2024-07-11T10:26:22Z file_id: '17228' file_name: PhD_Thesis_Vyacheslav_Li_no_signatures_PDFA.pdf file_size: 6729761 relation: main_file success: 1 - access_level: closed checksum: 16e904a11d8d0ebb167cb654ddfc7fe5 content_type: application/x-zip-compressed creator: vli date_created: 2024-07-11T10:26:22Z date_updated: 2024-07-11T10:26:22Z file_id: '17229' file_name: PhD Thesis Vyacheslav Li.zip file_size: 9542859 relation: source_file file_date_updated: 2024-07-11T10:26:22Z fulldoi: https://doi.org/10.15479/at:ista:17225 has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '79' project: - _id: bdb2a702-d553-11ed-ba76-f12e3e5a3bc6 grant_number: '101087907' name: 'A quantum hybrid of atoms and milligram-scale pendulums: towards gravitational quantum mechanics' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '11438' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Onur full_name: Hosten, Onur id: 4C02D85E-F248-11E8-B48F-1D18A9856A87 last_name: Hosten orcid: 0000-0002-2031-204X supplementarymaterial: no title: Towards a quantum entanglement enhanced atom interferomter tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- OA_place: publisher _id: '18135' abstract: - lang: eng text: "This thesis consists of two separate parts. In the first part we consider a dilute Fermi gas interacting through a repulsive interaction in dimensions $d=1,2,3$. Our focus is mostly on the physically most relevant dimension $d=3$ \r\nand the setting of a spin-polarized (equivalently spinless) gas, where the Pauli exclusion principle plays a key role. We show that, at zero temperature, the ground state energy density of the interacting spin-polarized gas differs (to leading order) from that of the free (i.e. non-interacting) gas by a term of order $a_p^d\\rho^{2+2/d}$ \ with $a_p$ the $p$-wave scattering length of the repulsive interaction and $\\rho$ the density. Further, we extend this to positive temperature and show that the pressure of an interacting spin-polarized gas differs from that of the free gas by a now temperature dependent term, again of order $a_p^d\\rho^{2+2/d}$. Lastly, we consider the setting of a spin-$\\frac{1}{2}$ Fermi gas in $d=3$ dimensions and show that here, as an upper bound, the ground state energy density differs from that of the free system by a term of order $a_s \\rho^2$ with an error smaller than $a_s \\rho^2 (a_s\\rho^{1/3})^{1-\\eps}$ for any $\\eps > 0$, where $a_s$ is the $s$-wave scattering length of the repulsive interaction. \r\n\r\nThese asymptotic formulas complement the similar formulas in the literature for the dilute Bose and spin-$\\frac{1}{2}$ Fermi gas, where the ground state energies or pressures differ from that of the corresponding free systems by a term of order $a_s \\rho^2$ in dimension $d=3$. In the spin-polarized setting, the corrections, of order $a_p^3\\rho^{8/3}$ in dimension $d=3$, are thus much smaller and requires a more delicate analysis.\r\n\r\nIn the second part of the thesis we consider the Bardeen--Cooper--Schrieffer (BCS) theory of superconductivity and in particular its associated critical temperature and energy gap. We prove that the ratio of the zero-temperature energy gap and critical temperature $\\Xi(T=0)/T_c$ approaches a universal constant $\\pi e^{-\\gamma}\\approx 1.76$ in both the limit of high density in dimension $d=3$ and in the limit of weak coupling in dimensions $d=1,2$. This complements the proofs in the literature of this universal behaviour in the limit of weak coupling or low density in dimension $d=3$. Secondly, we prove that the ratio of the energy gap at positive temperature and critical temperature $\\Xi(T)/T_c$ approaches a universal function of the relative temperature $T/T_c$ in the limit of weak coupling in dimensions $d=1,2,3$." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Lauritsen AB. Energies of dilute Fermi gases and universalities in BCS theory. 2024. doi:10.15479/at:ista:18135 apa: Lauritsen, A. B. (2024). Energies of dilute Fermi gases and universalities in BCS theory. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18135 chicago: Lauritsen, Asbjørn Bækgaard. “Energies of Dilute Fermi Gases and Universalities in BCS Theory.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18135. ieee: A. B. Lauritsen, “Energies of dilute Fermi gases and universalities in BCS theory,” Institute of Science and Technology Austria, 2024. ista: Lauritsen AB. 2024. Energies of dilute Fermi gases and universalities in BCS theory. Institute of Science and Technology Austria. mla: Lauritsen, Asbjørn Bækgaard. Energies of Dilute Fermi Gases and Universalities in BCS Theory. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18135. short: A.B. Lauritsen, Energies of Dilute Fermi Gases and Universalities in BCS Theory, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-09-24T10:56:25Z date_published: 2024-09-23T00:00:00Z date_updated: 2026-10-02T11:43:01Z day: '23' ddc: - '515' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:18135 doi_confirm: '1' ec_funded: 1 file: - access_level: open_access checksum: c7bc3b31e430d57c65393051ca439575 content_type: application/pdf creator: alaurits date_created: 2024-09-26T13:11:24Z date_updated: 2024-09-26T13:11:24Z file_id: '18147' file_name: Lauritsen-thesis-final.pdf file_size: 3648831 relation: main_file success: 1 - access_level: closed checksum: 39f6b1b7f83e25a3bf9f933f1ea0bc06 content_type: application/x-zip-compressed creator: alaurits date_created: 2024-09-26T13:12:55Z date_updated: 2024-09-26T13:12:55Z file_id: '18148' file_name: Lauritsen-thesis-source.zip file_size: 1625888 relation: source_file file_date_updated: 2024-09-26T13:12:55Z fulldoi: https://doi.org/10.15479/at:ista:18135 has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '353' project: - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_identifier: isbn: - 978-3-99078-042-8 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '11732' relation: part_of_dissertation status: public - id: '17240' relation: part_of_dissertation status: public - id: '14931' relation: part_of_dissertation status: public - id: '14542' relation: part_of_dissertation status: public - id: '18107' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 supplementarymaterial: no title: Energies of dilute Fermi gases and universalities in BCS theory tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '14542' abstract: - lang: eng text: "It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit." acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427. article_number: '2360005 ' article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 citation: ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2024;36(9). doi:10.1142/s0129055x2360005x apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2024). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2024. https://doi.org/10.1142/s0129055x2360005x. ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics, vol. 36, no. 9. World Scientific Publishing, 2024. ista: Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005. mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:10.1142/s0129055x2360005x. short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024). corr_author: '1' das_tickbox: '0' date_created: 2023-11-15T23:48:14Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-10-02T11:43:00Z day: '01' ddc: - '510' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1142/s0129055x2360005x ec_funded: 1 external_id: arxiv: - '2301.05621' isi: - '001099640300002' file: - access_level: open_access checksum: 2b053a4223b4db14b90520999ec56054 content_type: application/pdf creator: dernst date_created: 2025-01-09T07:56:28Z date_updated: 2025-01-09T07:56:28Z file_id: '18786' file_name: 2024_ReviewsmathPhysics_Henheik.pdf file_size: 503910 relation: main_file success: 1 file_date_updated: 2025-01-09T07:56:28Z fulldoi: https://doi.org/10.1142/s0129055x2360005x has_accepted_license: '1' intvolume: ' 36' isi: 1 issue: '9' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' related_material: record: - id: '19540' relation: dissertation_contains status: public - id: '18135' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Universality in low-dimensional BCS theory tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 36 year: '2024' ... --- _id: '14931' abstract: - lang: eng text: We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15]. acknowledgement: A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged. article_number: '110320' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 2024;286(7). doi:10.1016/j.jfa.2024.110320' apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110320' chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110320.' ieee: 'A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” Journal of Functional Analysis, vol. 286, no. 7. Elsevier, 2024.' ista: 'Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320.' mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal of Functional Analysis, vol. 286, no. 7, 110320, Elsevier, 2024, doi:10.1016/j.jfa.2024.110320.' short: A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024). corr_author: '1' das_tickbox: '1' dataavailabilitystatement: No data was used for the research described in the article. date_created: 2024-02-04T23:00:53Z date_published: 2024-04-01T00:00:00Z date_updated: 2026-10-02T11:43:00Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1016/j.jfa.2024.110320 ec_funded: 1 external_id: arxiv: - '2301.04894' isi: - '001170294000001' file: - access_level: open_access checksum: ee203cf2dc4420ad90d3c9970d246a78 content_type: application/pdf creator: dernst date_created: 2024-07-22T11:11:56Z date_updated: 2024-07-22T11:11:56Z file_id: '17305' file_name: 2024_JourFunctAnalysis_Lauritsen.pdf file_size: 1381063 relation: main_file success: 1 file_date_updated: 2024-07-22T11:11:56Z fulldoi: https://doi.org/10.1016/j.jfa.2024.110320 has_accepted_license: '1' intvolume: ' 286' isi: 1 issue: '7' language: - iso: eng month: '04' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '18135' relation: dissertation_contains status: public researchdata_availability: not applicable scopus_import: '1' status: public supplementarymaterial: no title: 'Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 286 year: '2024' ... --- _id: '18107' abstract: - lang: eng text: We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and ρ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260). acknowledgement: 'Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged.' article_number: e78 article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 2024;12. doi:10.1017/fms.2024.56' apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2024.56' chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” Forum of Mathematics, Sigma. Cambridge University Press, 2024. https://doi.org/10.1017/fms.2024.56.' ieee: 'A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” Forum of Mathematics, Sigma, vol. 12. Cambridge University Press, 2024.' ista: 'Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78.' mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” Forum of Mathematics, Sigma, vol. 12, e78, Cambridge University Press, 2024, doi:10.1017/fms.2024.56.' short: A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024). corr_author: '1' das_tickbox: '0' date_created: 2024-09-20T12:25:25Z date_published: 2024-09-09T00:00:00Z date_updated: 2026-10-02T11:43:00Z day: '09' ddc: - '510' department: - _id: GradSch - _id: RoSe doi: 10.1017/fms.2024.56 external_id: arxiv: - '2407.05990' isi: - '001307817400001' file: - access_level: open_access checksum: 330b881240013213a8e08538fec13d29 content_type: application/pdf creator: dernst date_created: 2024-09-23T09:56:17Z date_updated: 2024-09-23T09:56:17Z file_id: '18126' file_name: 2024_ForumMath_Lauritsen.pdf file_size: 599886 relation: main_file success: 1 file_date_updated: 2024-09-23T09:56:17Z fulldoi: https://doi.org/10.1017/fms.2024.56 has_accepted_license: '1' intvolume: ' 12' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '18135' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'Pressure of a dilute spin-polarized Fermi gas: Lower bound' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 12 year: '2024' ... --- OA_place: publisher OA_type: free access _id: '18443' abstract: - lang: eng text: "In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they\r\nconjecture an equivalence between categories of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler structures and the\r\ncorresponding branes on affine torus bundles. We use the techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles and connections. This T-duality in the appropriate context specializes to\r\nT-duality between BBB and BAA-branes.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Maria A full_name: Sisak, Maria A id: 44A03D04-AEA4-11E9-B225-EA2DE6697425 last_name: Sisak citation: ama: Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:10.15479/at:ista:18443 apa: Sisak, M. A. (2024). T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18443 chicago: Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18443. ieee: M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024. ista: Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. mla: Sisak, Maria A. T-Dual Branes on Hyperkähler Manifolds. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18443. short: M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-10-19T12:00:37Z date_published: 2024-10-24T00:00:00Z date_updated: 2026-10-02T11:43:57Z day: '24' ddc: - '516' degree_awarded: PhD department: - _id: GradSch - _id: TaHa doi: 10.15479/at:ista:18443 doi_confirm: '1' file: - access_level: open_access checksum: 8c4893e726aaa4b3efb82758da9b6851 content_type: application/pdf creator: msisak date_created: 2024-10-23T14:42:45Z date_updated: 2024-10-23T14:42:45Z file_id: '18467' file_name: MASisak_dissertation.pdf file_size: 1672547 relation: main_file success: 1 - access_level: closed checksum: 1831b072e861a1e5481024ca9d02b036 content_type: application/x-zip-compressed creator: msisak date_created: 2024-10-23T14:43:56Z date_updated: 2024-10-24T08:09:13Z file_id: '18468' file_name: MASisak_source.zip file_size: 617913 relation: source_file file_date_updated: 2024-10-24T08:09:13Z fulldoi: https://doi.org/10.15479/at:ista:18443 has_accepted_license: '1' keyword: - hyperkaehler geometry - branes - mirror symmetry - T-duality language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '178' project: - _id: 6286e8c4-2b32-11ec-9570-f5297902f67f grant_number: '26069' name: Branes on hyperkähler manifolds publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria researchdata_availability: no status: public supervisor: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel orcid: 0000-0002-9582-2634 supplementarymaterial: no title: T-dual branes on hyperkähler manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- APC_amount: 2748 EUR OA_place: publisher OA_type: hybrid _id: '17634' abstract: - lang: eng text: System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach, mapping each execution to a real number by incorporating weighted transitions and value functions generalizing acceptance conditions. In this paper, we introduce QuAK, the first tool designed to automate the analysis of quantitative automata. QuAK currently supports a variety of quantitative automaton types, including Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg automata, and implements decision procedures for problems such as emptiness, universality, inclusion, equivalence, as well as for checking whether an automaton is safe, live, or constant. Additionally, QuAK is able to compute extremal values when possible, construct safety-liveness decompositions, and monitor system behaviors. We demonstrate the effectiveness of QuAK through experiments focusing on the inclusion, constant-function check, and monitoring problems. acknowledgement: This work was supported in part by the ERC-2020-AdG 101020093. N. Mazzocchi was affiliated with ISTA when his collaboration started. alternative_title: - LNCS article_processing_charge: Yes (in subscription journal) arxiv: 1 author: - first_name: Marek full_name: Chalupa, Marek id: 87e34708-d6c6-11ec-9f5b-9391e7be2463 last_name: Chalupa - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000-0002-2985-7724 - first_name: Nicolas Adrien full_name: Mazzocchi, Nicolas Adrien id: b26baa86-3308-11ec-87b0-8990f34baa85 last_name: Mazzocchi - first_name: Naci E full_name: Sarac, Naci E id: 8C6B42F8-C8E6-11E9-A03A-F2DCE5697425 last_name: Sarac citation: ama: 'Chalupa M, Henzinger TA, Mazzocchi NA, Sarac NE. QuAK: Quantitative Automata Kit. In: 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation. Vol 15222. Springer Nature; 2024:3-20. doi:10.1007/978-3-031-75387-9_1' apa: 'Chalupa, M., Henzinger, T. A., Mazzocchi, N. A., & Sarac, N. E. (2024). QuAK: Quantitative Automata Kit. In 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation (Vol. 15222, pp. 3–20). Crete, Greece: Springer Nature. https://doi.org/10.1007/978-3-031-75387-9_1' chicago: 'Chalupa, Marek, Thomas A Henzinger, Nicolas Adrien Mazzocchi, and Naci E Sarac. “QuAK: Quantitative Automata Kit.” In 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, 15222:3–20. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-75387-9_1.' ieee: 'M. Chalupa, T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “QuAK: Quantitative Automata Kit,” in 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, Crete, Greece, 2024, vol. 15222, pp. 3–20.' ista: 'Chalupa M, Henzinger TA, Mazzocchi NA, Sarac NE. 2024. QuAK: Quantitative Automata Kit. 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation. ISoLA: International Symposium on Leveraging Applications, LNCS, vol. 15222, 3–20.' mla: 'Chalupa, Marek, et al. “QuAK: Quantitative Automata Kit.” 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, vol. 15222, Springer Nature, 2024, pp. 3–20, doi:10.1007/978-3-031-75387-9_1.' short: M. Chalupa, T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, Springer Nature, 2024, pp. 3–20. conference: end_date: 2024-10-31 location: Crete, Greece name: 'ISoLA: International Symposium on Leveraging Applications' start_date: 2024-10-27 corr_author: '1' das_tickbox: '0' date_created: 2024-09-05T14:27:08Z date_published: 2024-10-26T00:00:00Z date_updated: 2026-10-02T11:44:52Z day: '26' ddc: - '000' department: - _id: GradSch - _id: ToHe doi: 10.1007/978-3-031-75387-9_1 ec_funded: 1 external_id: arxiv: - '2409.03569' isi: - '001419008700001' file: - access_level: open_access checksum: 43e432f82be376434b358f3dd7a94b71 content_type: application/pdf creator: esarac date_created: 2024-09-05T14:26:02Z date_updated: 2024-09-05T14:26:02Z file_id: '17635' file_name: isola24.pdf file_size: 847422 relation: main_file success: 1 - access_level: open_access checksum: 6bc04f07bb5612c0e7ea00ac121a69b6 content_type: application/pdf creator: dernst date_created: 2025-01-21T14:39:49Z date_updated: 2025-01-21T14:39:49Z file_id: '18865' file_name: 2024_LNCS_Chalupa.pdf file_size: 1358706 relation: main_file success: 1 file_date_updated: 2025-01-21T14:39:49Z fulldoi: https://doi.org/10.1007/978-3-031-75387-9_1 has_accepted_license: '1' intvolume: ' 15222' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 3-20 project: - _id: 62781420-2b32-11ec-9570-8d9b63373d4d call_identifier: H2020 grant_number: '101020093' name: Vigilant Algorithmic Monitoring of Software publication: 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation publication_identifier: eissn: - 1611-3349 isbn: - '9783031753862' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '20147' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'QuAK: Quantitative Automata Kit' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 15222 year: '2024' ... --- _id: '14345' abstract: - lang: eng text: For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970)). acknowledgement: Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Alexey full_name: Garber, Alexey last_name: Garber - first_name: Mohadese full_name: Ghafari, Mohadese last_name: Ghafari - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 2024;72:29-48. doi:10.1007/s00454-023-00566-1 apa: Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., & Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00566-1 chicago: Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry. Springer Nature, 2024. https://doi.org/10.1007/s00454-023-00566-1. ieee: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” Discrete and Computational Geometry, vol. 72. Springer Nature, pp. 29–48, 2024. ista: Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48. mla: Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” Discrete and Computational Geometry, vol. 72, Springer Nature, 2024, pp. 29–48, doi:10.1007/s00454-023-00566-1. short: H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48. corr_author: '1' das_tickbox: '0' date_created: 2023-09-17T22:01:10Z date_published: 2024-07-01T00:00:00Z date_updated: 2026-10-02T11:45:50Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00454-023-00566-1 ec_funded: 1 external_id: arxiv: - '2204.01076' isi: - '001060727600004' pmid: - '39610762' file: - access_level: open_access checksum: b207b4e00f904e8ea8a30e24f0251f79 content_type: application/pdf creator: dernst date_created: 2024-07-22T09:43:19Z date_updated: 2024-07-22T09:43:19Z file_id: '17301' file_name: 2024_DiscreteComputGeom_Edelsbrunner.pdf file_size: 892019 relation: main_file success: 1 file_date_updated: 2024-07-22T09:43:19Z fulldoi: https://doi.org/10.1007/s00454-023-00566-1 has_accepted_license: '1' intvolume: ' 72' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 29-48 pmid: 1 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Discrete and Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: yes title: On angles in higher order Brillouin tessellations and related tilings in the plane tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 72 year: '2024' ... --- OA_place: publisher _id: '18132' abstract: - lang: eng text: "In this thesis, we are dealing with both arithmetic and geometric problems coming from the\r\nstudy of rational points with a particular focus on function fields over finite fields:\r\n(1) Using the circle method we produce upper bounds for the number of rational points of\r\nbounded height on diagonal cubic surfaces and fourfolds over Fq(t). This is based on\r\njoint work with Leonhard Hochfilzer.\r\n(2) We study rational points on smooth complete intersections X defined by cubic and\r\nquadratic hypersurfaces over Fq(t). We refine the Farey dissection of the “unit square”\r\ndeveloped by Vishe [202] and use the circle method with a Kloosterman refinement to\r\nestablish an asymptotic formula for the number of rational points of bounded height on\r\nX when dim(X) ≥ 23. Under the same hypotheses, we also verify weak approximation.\r\n(3) In joint work with Hochfilzer, we obtain upper bounds for the number of rational points of\r\nbounded height on del Pezzo surfaces of low degree over any global field. Our approach\r\nis to take hyperplane sections, which reduces the problem to uniform estimates for the\r\nnumber of rational points on curves.\r\n(4) We develop a version of the circle method capable of counting Fq-points on jet schemes\r\nof moduli spaces of rational curves on hypersurfaces. Combining this with a spreading\r\nout argument and a result of Mustaţă [150], this allows us to show that these moduli\r\nspaces only have canonical singularities under suitable assumptions on the degree and the\r\ndimension.\r\nIn addition, we give an overview of guiding questions and conjectures in the field of rational\r\npoints and explain the basic mechanism underlying the circle method.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Counting rational points over function fields. 2024. doi:10.15479/at:ista:18132 apa: Glas, J. (2024). Counting rational points over function fields. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18132 chicago: Glas, Jakob. “Counting Rational Points over Function Fields.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18132. ieee: J. Glas, “Counting rational points over function fields,” Institute of Science and Technology Austria, 2024. ista: Glas J. 2024. Counting rational points over function fields. Institute of Science and Technology Austria. mla: Glas, Jakob. Counting Rational Points over Function Fields. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18132. short: J. Glas, Counting Rational Points over Function Fields, Institute of Science and Technology Austria, 2024. corr_author: '1' das_tickbox: '0' date_created: 2024-09-23T18:58:08Z date_published: 2024-09-23T00:00:00Z date_updated: 2026-10-02T11:44:29Z day: '23' ddc: - '512' degree_awarded: PhD department: - _id: GradSch - _id: TiBr doi: 10.15479/at:ista:18132 doi_confirm: '1' file: - access_level: closed checksum: 2f8cf5cefdab108b1979caa8146cae9a content_type: application/x-zip-compressed creator: jglas date_created: 2024-09-23T18:49:22Z date_updated: 2024-09-23T18:49:22Z file_id: '18133' file_name: PhDthesis (3).zip file_size: 5382106 relation: source_file - access_level: open_access checksum: 08bb6f14c42b47ff25882a2ce3ea0d8a content_type: application/pdf creator: jglas date_created: 2024-09-25T14:08:57Z date_updated: 2024-09-25T14:08:57Z file_id: '18140' file_name: example-phd.pdf file_size: 2380127 relation: main_file success: 1 file_date_updated: 2024-09-25T14:08:57Z fulldoi: https://doi.org/10.15479/at:ista:18132 has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '195' project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '18173' relation: part_of_dissertation status: public - id: '18295' relation: part_of_dissertation status: public - id: '18294' relation: part_of_dissertation status: public - id: '18293' relation: part_of_dissertation status: public researchdata_availability: no status: public supervisor: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 supplementarymaterial: no title: Counting rational points over function fields tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: dissertation user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- _id: '18173' abstract: - lang: eng text: Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation. acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and Pankaj Vishe for useful comments. Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise in exponential sums and geometry. While working on this paper, the author was supported by FWF grant (DOI 10.55776/P36278). article_number: e12991 article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 2024;110(4). doi:10.1112/jlms.12991 apa: Glas, J. (2024). Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.12991 chicago: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.12991. ieee: J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t),” Journal of the London Mathematical Society, vol. 110, no. 4. London Mathematical Society, 2024. ista: Glas J. 2024. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4), e12991. mla: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society, vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:10.1112/jlms.12991. short: J. Glas, Journal of the London Mathematical Society 110 (2024). corr_author: '1' das_tickbox: '0' date_created: 2024-10-06T22:01:11Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-10-02T11:44:29Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1112/jlms.12991 external_id: arxiv: - '2306.02718' file: - access_level: open_access checksum: 11ebf690363151026ce81f91f2220855 content_type: application/pdf creator: dernst date_created: 2024-10-07T08:51:01Z date_updated: 2024-10-07T08:51:01Z file_id: '18181' file_name: 2024_JLondonMathSoc_Glas.pdf file_size: 579601 relation: main_file success: 1 file_date_updated: 2024-10-07T08:51:01Z fulldoi: https://doi.org/10.1112/jlms.12991 has_accepted_license: '1' intvolume: ' 110' issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: London Mathematical Society quality_controlled: '1' related_material: record: - id: '18132' relation: dissertation_contains status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t) tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 110 year: '2024' ... --- OA_place: repository _id: '18295' abstract: - lang: eng text: By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d. article_processing_charge: No arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv. doi:10.48550/arXiv.2405.16648 apa: Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv. https://doi.org/10.48550/arXiv.2405.16648 chicago: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2405.16648. ieee: J. Glas, “Canonical singularities on moduli spaces of rational curves via the  circle method,” arXiv. . ista: Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv, 10.48550/arXiv.2405.16648. mla: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” ArXiv, doi:10.48550/arXiv.2405.16648. short: J. Glas, ArXiv (n.d.). corr_author: '1' das_tickbox: '0' date_created: 2024-10-10T13:15:43Z date_published: 2024-05-26T00:00:00Z date_updated: 2026-10-02T11:44:29Z day: '26' department: - _id: TiBr doi: 10.48550/arXiv.2405.16648 external_id: arxiv: - '2405.16648' fulldoi: https://doi.org/10.48550/arXiv.2405.16648 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.16648 month: '05' oa: 1 oa_version: Preprint project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: arXiv publication_status: submitted related_material: record: - id: '19013' relation: later_version status: public - id: '18132' relation: dissertation_contains status: public researchdata_availability: no status: public supplementarymaterial: no title: Canonical singularities on moduli spaces of rational curves via the circle method tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2024' ... --- _id: '17144' abstract: - lang: eng text: "We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let \U0001D4AE ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set \U0001D4AE. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(\U0001D4AE), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms." acknowledgement: "This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I 02979-N35.\r\nSupported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411, the Austrian science fund (FWF) grant No. M-3073, and the welcome package from IDEX of the Université Cô d'Azur.\r\nWe are greatly indebted to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher Fillmore, and Elizabeth Stephenson for early discussions and all members of the Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape team (Inria) for the atmosphere in which this research was conducted." alternative_title: - LIPIcs article_number: '69' article_processing_charge: No arxiv: 1 author: - first_name: Hana full_name: Kourimska, Hana id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E last_name: Kourimska orcid: 0000-0001-7841-0091 - first_name: André full_name: Lieutier, André last_name: Lieutier - first_name: Mathijs full_name: Wintraecken, Mathijs id: 307CFBC8-F248-11E8-B48F-1D18A9856A87 last_name: Wintraecken orcid: 0000-0002-7472-2220 citation: ama: 'Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.69' apa: 'Kourimska, H., Lieutier, A., & Wintraecken, M. (2024). The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.69' chicago: Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.69. ieee: H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms,” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293. ista: 'Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 69.' mla: Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” 40th International Symposium on Computational Geometry, vol. 293, 69, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.69. short: H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' das_tickbox: '0' date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-10-02T11:46:39Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.69 ec_funded: 1 external_id: arxiv: - '2212.01118' file: - access_level: open_access checksum: b40ff456c19294adb5d9613fcfd751c6 content_type: application/pdf creator: dernst date_created: 2024-06-17T08:33:40Z date_updated: 2024-06-17T08:33:40Z file_id: '17150' file_name: 2024_LIPICS_Kourimska.pdf file_size: 1612558 relation: main_file success: 1 file_date_updated: 2024-06-17T08:33:40Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.69 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc390959-9c52-11eb-aca3-afa58bd282b2 grant_number: M03073 name: Learning and triangulating manifolds via collapses publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ... --- _id: '17146' abstract: - lang: eng text: The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². In particular, there is an arrangement of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers a long-standing open question in computational geometry. acknowledgement: "The first author is supported by the European Research Council (ERC), grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. {I 02979-N35.} The second author is supported by the European Research Council (ERC), grant \"GeoScape\" and by the Hungarian Science Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.\r\nThe authors thank Matt Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart for early discussions on the linked circles construction in three dimensions, and Gábor Tardos for helpful remarks and suggestions." alternative_title: - LIPIcs article_number: '53' article_processing_charge: No arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach citation: ama: 'Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.53' apa: 'Edelsbrunner, H., & Pach, J. (2024). Maximum Betti numbers of Čech complexes. In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.53' chicago: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.53. ieee: H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293. ista: 'Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 53.' mla: Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” 40th International Symposium on Computational Geometry, vol. 293, 53, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.53. short: H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' start_date: 2024-06-11 das_tickbox: '0' date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-10-02T11:48:01Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.53 ec_funded: 1 external_id: arxiv: - '2310.14801' file: - access_level: open_access checksum: 5442d44fb89d77477a87668d6e61aac9 content_type: application/pdf creator: dernst date_created: 2024-06-17T08:46:33Z date_updated: 2024-06-17T08:46:33Z file_id: '17152' file_name: 2024_LIPICS_Edelsbrunner.pdf file_size: 766562 relation: main_file success: 1 file_date_updated: 2024-06-17T08:46:33Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.53 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '20657' relation: later_version status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Maximum Betti numbers of Čech complexes tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ... --- _id: '17145' abstract: - lang: eng text: Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes. acknowledgement: Part of this work was done while G.R. enjoyed the hospitality of the Institute of Science and Technology Austria (ISTA) as a visiting professor during his sabbatical in the winter semester 2022/23. alternative_title: - LIPIcs article_number: '76' article_processing_charge: No arxiv: 1 author: - first_name: Günter full_name: Rote, Günter last_name: Rote - first_name: Moritz full_name: Rüber, Moritz last_name: Rüber - first_name: Morteza full_name: Saghafian, Morteza id: f86f7148-b140-11ec-9577-95435b8df824 last_name: Saghafian citation: ama: 'Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: 40th International Symposium on Computational Geometry. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:10.4230/LIPIcs.SoCG.2024.76' apa: 'Rote, G., Rüber, M., & Saghafian, M. (2024). Grid peeling of parabolas. In 40th International Symposium on Computational Geometry (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2024.76' chicago: Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.” In 40th International Symposium on Computational Geometry, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.SoCG.2024.76. ieee: G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in 40th International Symposium on Computational Geometry, Athens, Greece, 2024, vol. 293. ista: 'Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 76.' mla: Rote, Günter, et al. “Grid Peeling of Parabolas.” 40th International Symposium on Computational Geometry, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:10.4230/LIPIcs.SoCG.2024.76. short: G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. conference: end_date: 2024-06-14 location: Athens, Greece name: 'SoCG: Symposium on Computational Geometry' start_date: 2024-06-11 das_tickbox: '0' date_created: 2024-06-16T22:01:06Z date_published: 2024-06-01T00:00:00Z date_updated: 2026-10-02T11:47:18Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.4230/LIPIcs.SoCG.2024.76 external_id: arxiv: - '2402.15787' file: - access_level: open_access checksum: fbad1de06383a6b7e8a1cb3e8c7205ce content_type: application/pdf creator: dernst date_created: 2024-06-17T08:40:04Z date_updated: 2024-06-17T08:40:04Z file_id: '17151' file_name: 2024_LIPICS_Rote.pdf file_size: 1430896 relation: main_file success: 1 file_date_updated: 2024-06-17T08:40:04Z fulldoi: https://doi.org/10.4230/LIPIcs.SoCG.2024.76 has_accepted_license: '1' intvolume: ' 293' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 40th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959773164' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Grid peeling of parabolas tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 293 year: '2024' ...