--- _id: '14934' abstract: - lang: eng text: "We study random perturbations of a Riemannian manifold (M, g) by means of so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion, spectral bound, or spectral gap change under the influence of the noise. And if so, is\r\nit possible to quantify these dependencies in terms of key parameters of the noise? Another\r\ngoal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent interest." acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for valuable discussions on this project. They are also grateful to Nathanaël Berestycki, and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24], and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous version of the proof of Proposition 3.10. The authors feel very much indebted to an anonymous reviewer for his/her careful reading and the many valuable suggestions that have significantly contributed to the improvement of the paper. L.D.S. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC 1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65 at Institute of Science and Technology Austria. This research was funded in whole or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen Access funding enabled and organized by Projekt DEAL." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Eva full_name: Kopfer, Eva last_name: Kopfer - first_name: Karl Theodor full_name: Sturm, Karl Theodor last_name: Sturm citation: ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0 apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0 chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature, 2024. https://doi.org/10.1007/s11118-023-10118-0. ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” Potential Analysis. Springer Nature, 2024. ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis. mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0. short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024). date_created: 2024-02-04T23:00:54Z date_published: 2024-01-26T00:00:00Z date_updated: 2024-02-05T13:04:23Z day: '26' department: - _id: JaMa doi: 10.1007/s11118-023-10118-0 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s11118-023-10118-0 month: '01' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Potential Analysis publication_identifier: eissn: - 1572-929X issn: - 0926-2601 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A discovery tour in random Riemannian geometry type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '12104' abstract: - lang: eng text: We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces. acknowledgement: Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156). article_number: '9' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7 apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00859-7 chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations. Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7. ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” Journal of Evolution Equations, vol. 23, no. 1. Springer Nature, 2023. ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9. mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23, no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7. short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023). date_created: 2023-01-08T23:00:53Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-06-28T11:54:35Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00028-022-00859-7 ec_funded: 1 external_id: isi: - '000906214600004' file: - access_level: open_access checksum: 1f34f3e2cb521033de6154f274ea3a4e content_type: application/pdf creator: dernst date_created: 2023-01-20T10:45:06Z date_updated: 2023-01-20T10:45:06Z file_id: '12325' file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf file_size: 422612 relation: main_file success: 1 file_date_updated: 2023-01-20T10:45:06Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '01' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c grant_number: E208 name: Configuration Spaces over Non-Smooth Spaces - _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833 grant_number: ESP156_N name: Gradient flow techniques for quantum Markov semigroups publication: Journal of Evolution Equations publication_identifier: eissn: - 1424-3202 issn: - 1424-3199 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Ergodic decompositions of Dirichlet forms under order isomorphisms 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 23 year: '2023' ... --- _id: '12087' abstract: - lang: eng text: Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups. acknowledgement: H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x apa: Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x chicago: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x. ieee: M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 717–750, 2023. ista: Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750. mla: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 717–50, doi:10.1007/s00023-022-01220-x. short: M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750. date_created: 2022-09-11T22:01:57Z date_published: 2023-03-01T00:00:00Z date_updated: 2023-08-14T11:39:28Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00023-022-01220-x ec_funded: 1 external_id: arxiv: - '2105.08303' isi: - '000837499800002' file: - access_level: open_access checksum: 8c7b185eba5ccd92ef55c120f654222c content_type: application/pdf creator: dernst date_created: 2023-08-14T11:38:28Z date_updated: 2023-08-14T11:38:28Z file_id: '14051' file_name: 2023_AnnalesHenriPoincare_Wirth.pdf file_size: 554871 relation: main_file success: 1 file_date_updated: 2023-08-14T11:38:28Z has_accepted_license: '1' intvolume: ' 24' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 717-750 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Curvature-dimension conditions for symmetric quantum Markov semigroups 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '10145' abstract: - lang: eng text: We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique. acknowledgement: The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 citation: ama: Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y apa: Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y chicago: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis. Springer Nature, 2023. https://doi.org/10.1007/s11118-021-09951-y. ieee: L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615, 2023. ista: Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615. mla: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature, 2023, pp. 573–615, doi:10.1007/s11118-021-09951-y. short: L. Dello Schiavo, Potential Analysis 58 (2023) 573–615. date_created: 2021-10-17T22:01:17Z date_published: 2023-03-01T00:00:00Z date_updated: 2023-10-04T09:19:12Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s11118-021-09951-y ec_funded: 1 external_id: arxiv: - '2003.01366' isi: - '000704213400001' file: - access_level: open_access checksum: 625526482be300ca7281c91c30d41725 content_type: application/pdf creator: dernst date_created: 2023-10-04T09:18:59Z date_updated: 2023-10-04T09:18:59Z file_id: '14387' file_name: 2023_PotentialAnalysis_DelloSchiavo.pdf file_size: 806391 relation: main_file success: 1 file_date_updated: 2023-10-04T09:18:59Z has_accepted_license: '1' intvolume: ' 58' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 573-615 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Potential Analysis publication_identifier: eissn: - 1572-929X issn: - 0926-2601 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Ergodic decomposition of Dirichlet forms via direct integrals and applications 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 year: '2023' ... --- _id: '12959' abstract: - lang: eng text: "This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs." acknowledgement: J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF). article_number: '143' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Peter full_name: Gladbach, Peter last_name: Gladbach - first_name: Eva full_name: Kopfer, Eva last_name: Kopfer - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 2023;62(5). doi:10.1007/s00526-023-02472-z apa: Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-023-02472-z chicago: Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2023. https://doi.org/10.1007/s00526-023-02472-z. ieee: P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5. Springer Nature, 2023. ista: Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143. mla: Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” Calculus of Variations and Partial Differential Equations, vol. 62, no. 5, 143, Springer Nature, 2023, doi:10.1007/s00526-023-02472-z. short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023). date_created: 2023-05-14T22:01:00Z date_published: 2023-04-28T00:00:00Z date_updated: 2023-10-04T11:34:49Z day: '28' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00526-023-02472-z ec_funded: 1 external_id: arxiv: - '2110.15321' isi: - '000980588900001' file: - access_level: open_access checksum: 359bee38d94b7e0aa73925063cb8884d content_type: application/pdf creator: dernst date_created: 2023-10-04T11:34:10Z date_updated: 2023-10-04T11:34:10Z file_id: '14393' file_name: 2023_CalculusEquations_Gladbach.pdf file_size: 1240995 relation: main_file success: 1 file_date_updated: 2023-10-04T11:34:10Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '5' language: - iso: eng month: '04' oa: 1 oa_version: Published Version project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations publication: Calculus of Variations and Partial Differential Equations publication_identifier: eissn: - 1432-0835 issn: - 0944-2669 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Homogenisation of dynamical optimal transport on periodic graphs 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 62 year: '2023' ... --- _id: '12911' abstract: - lang: eng text: 'This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.' acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813." article_number: '109963' article_processing_charge: No article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963 apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963 chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023. ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963. mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963. short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023). date_created: 2023-05-07T22:01:02Z date_published: 2023-08-15T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '15' department: - _id: RoSe - _id: JaMa doi: 10.1016/j.jfa.2023.109963 ec_funded: 1 external_id: arxiv: - '2106.11217' isi: - '000990804300001' intvolume: ' 285' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '08' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems 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: '9792' relation: earlier_version status: public scopus_import: '1' status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '13177' abstract: - lang: eng text: In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established. acknowledgement: The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. article_processing_charge: No article_type: original author: - first_name: Bobo full_name: Hua, Bobo last_name: Hua - first_name: Matthias full_name: Keller, Matthias last_name: Keller - first_name: Michael full_name: Schwarz, Michael last_name: Schwarz - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361 apa: Hua, B., Keller, M., Schwarz, M., & Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/14361 chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/14361. ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” Proceedings of the American Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023. ista: Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414. mla: Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings of the American Mathematical Society, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361. short: B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414. date_created: 2023-07-02T22:00:43Z date_published: 2023-08-01T00:00:00Z date_updated: 2023-11-14T13:07:09Z day: '01' department: - _id: JaMa doi: 10.1090/proc/14361 external_id: arxiv: - '1804.08353' isi: - '000988204400001' intvolume: ' 151' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.1804.08353' month: '08' oa: 1 oa_version: Preprint page: 3401-3414 publication: Proceedings of the American Mathematical Society publication_identifier: eissn: - 1088-6826 issn: - 0002-9939 publication_status: published publisher: American Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Sobolev-type inequalities and eigenvalue growth on graphs with finite measure type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 151 year: '2023' ... --- _id: '13145' abstract: - lang: eng text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes. acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208. article_processing_charge: No article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Eugene full_name: Lytvynov, Eugene last_name: Lytvynov citation: ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528 apa: Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528 chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528. ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023. ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12. mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528. short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12. date_created: 2023-06-18T22:00:48Z date_published: 2023-05-05T00:00:00Z date_updated: 2023-12-13T11:24:57Z day: '05' ddc: - '510' department: - _id: JaMa doi: 10.1214/23-ECP528 external_id: isi: - '001042025400001' file: - access_level: open_access checksum: 4a543fe4b3f9e747cc52167c17bfb524 content_type: application/pdf creator: dernst date_created: 2023-06-19T09:37:40Z date_updated: 2023-06-19T09:37:40Z file_id: '13152' file_name: 2023_ElectronCommProbability_Schiavo.pdf file_size: 271434 relation: main_file success: 1 file_date_updated: 2023-06-19T09:37:40Z has_accepted_license: '1' intvolume: ' 28' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 1-12 project: - _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c grant_number: E208 name: Configuration Spaces over Non-Smooth Spaces publication: Electronic Communications in Probability publication_identifier: eissn: - 1083-589X publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: A Mecke-type characterization of the Dirichlet–Ferguson measure 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2023' ... --- _id: '13318' abstract: - lang: eng text: Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes. acknowledgement: The research of A.V. is supported by NSF DMS-1900286, DMS-2154402 and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284 while both authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity program. article_processing_charge: No article_type: original author: - first_name: Alexander full_name: Volberg, Alexander last_name: Volberg - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. 2023. doi:10.1007/s00208-023-02680-0 apa: Volberg, A., & Zhang, H. (2023). Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-023-02680-0 chicago: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” Mathematische Annalen. Springer Nature, 2023. https://doi.org/10.1007/s00208-023-02680-0. ieee: A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” Mathematische Annalen. Springer Nature, 2023. ista: Volberg A, Zhang H. 2023. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen. mla: Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” Mathematische Annalen, Springer Nature, 2023, doi:10.1007/s00208-023-02680-0. short: A. Volberg, H. Zhang, Mathematische Annalen (2023). date_created: 2023-07-30T22:01:03Z date_published: 2023-07-24T00:00:00Z date_updated: 2023-12-13T11:36:20Z day: '24' department: - _id: JaMa doi: 10.1007/s00208-023-02680-0 external_id: arxiv: - '2210.14468' isi: - '001035665500001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00208-023-02680-0 month: '07' oa: 1 oa_version: Published Version project: - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Noncommutative Bohnenblust–Hille inequalities type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '13271' abstract: - lang: eng text: "In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems." acknowledgement: I am grateful to Boguslaw Zegarliński for asking me the questions in [3] and for helpful communication. I also want to thank Paata Ivanisvili for drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous referee for the valuable comments and for pointing out some errors in an earlier version of the paper. This work is partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. article_processing_charge: No article_type: original author: - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Zhang H. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. 2023. doi:10.1007/s00023-023-01345-7 apa: Zhang, H. (2023). Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-023-01345-7 chicago: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-023-01345-7. ieee: H. Zhang, “Some convexity and monotonicity results of trace functionals,” Annales Henri Poincare. Springer Nature, 2023. ista: Zhang H. 2023. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare. mla: Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” Annales Henri Poincare, Springer Nature, 2023, doi:10.1007/s00023-023-01345-7. short: H. Zhang, Annales Henri Poincare (2023). date_created: 2023-07-23T22:01:15Z date_published: 2023-07-08T00:00:00Z date_updated: 2023-12-13T11:33:46Z day: '08' department: - _id: JaMa doi: 10.1007/s00023-023-01345-7 ec_funded: 1 external_id: arxiv: - '2108.05785' isi: - '001025709100001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2108.05785 month: '07' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Some convexity and monotonicity results of trace functionals type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14732' abstract: - lang: eng text: 'Fragmented landscapes pose a significant threat to the persistence of species as they are highly susceptible to heightened risk of extinction due to the combined effects of genetic and demographic factors such as genetic drift and demographic stochasticity. This paper explores the intricate interplay between genetic load and extinction risk within metapopulations with a focus on understanding the impact of eco-evolutionary feedback mechanisms. We distinguish between two models of selection: soft selection, characterised by subpopulations maintaining carrying capacity despite load, and hard selection, where load can significantly affect population size. Within the soft selection framework, we investigate the impact of gene flow on genetic load at a single locus, while also considering the effect of selection strength and dominance coefficient. We subsequently build on this to examine how gene flow influences both population size and load under hard selection as well as identify critical thresholds for metapopulation persistence. Our analysis employs the diffusion, semi-deterministic and effective migration approximations. Our findings reveal that under soft selection, even modest levels of migration can significantly alleviate the burden of load. In sharp contrast, with hard selection, a much higher degree of gene flow is required to mitigate load and prevent the collapse of the metapopulation. Overall, this study sheds light into the crucial role migration plays in shaping the dynamics of genetic load and extinction risk in fragmented landscapes, offering valuable insights for conservation strategies and the preservation of diversity in a changing world.' article_processing_charge: No author: - first_name: Oluwafunmilola O full_name: Olusanya, Oluwafunmilola O id: 41AD96DC-F248-11E8-B48F-1D18A9856A87 last_name: Olusanya orcid: 0000-0003-1971-8314 - first_name: Kseniia full_name: Khudiakova, Kseniia id: 4E6DC800-AE37-11E9-AC72-31CAE5697425 last_name: Khudiakova orcid: 0000-0002-6246-1465 - first_name: Himani full_name: Sachdeva, Himani id: 42377A0A-F248-11E8-B48F-1D18A9856A87 last_name: Sachdeva citation: ama: Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv. doi:10.1101/2023.12.02.569702 apa: Olusanya, O. O., Khudiakova, K., & Sachdeva, H. (n.d.). Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv. https://doi.org/10.1101/2023.12.02.569702 chicago: Olusanya, Oluwafunmilola O, Kseniia Khudiakova, and Himani Sachdeva. “Genetic Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” BioRxiv, n.d. https://doi.org/10.1101/2023.12.02.569702. ieee: O. O. Olusanya, K. Khudiakova, and H. Sachdeva, “Genetic load, eco-evolutionary feedback and extinction in a metapopulation,” bioRxiv. . ista: Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv, 10.1101/2023.12.02.569702. mla: Olusanya, Oluwafunmilola O., et al. “Genetic Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” BioRxiv, doi:10.1101/2023.12.02.569702. short: O.O. Olusanya, K. Khudiakova, H. Sachdeva, BioRxiv (n.d.). date_created: 2024-01-04T09:35:54Z date_published: 2023-12-04T00:00:00Z date_updated: 2024-01-26T12:00:53Z day: '04' department: - _id: NiBa - _id: JaMa doi: 10.1101/2023.12.02.569702 language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ main_file_link: - open_access: '1' url: https://www.biorxiv.org/content/10.1101/2023.12.02.569702v1 month: '12' oa: 1 oa_version: Preprint project: - _id: c08d3278-5a5b-11eb-8a69-fdb09b55f4b8 grant_number: P32896 name: Causes and consequences of population fragmentation - _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8 grant_number: '26293' name: The impact of deleterious mutations on small populations - _id: 34c872fe-11ca-11ed-8bc3-8534b82131e6 grant_number: '26380' name: Polygenic Adaptation in a Metapopulation publication: bioRxiv publication_status: submitted related_material: record: - id: '14711' relation: dissertation_contains status: public status: public title: Genetic load, eco-evolutionary feedback and extinction in a metapopulation tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ... --- _id: '13319' abstract: - lang: eng text: We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule. acknowledgement: The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Matthijs full_name: Vernooij, Matthijs last_name: Vernooij - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 2023;403:381-416. doi:10.1007/s00220-023-04795-6 apa: Vernooij, M., & Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04795-6 chicago: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04795-6. ieee: M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” Communications in Mathematical Physics, vol. 403. Springer Nature, pp. 381–416, 2023. ista: Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416. mla: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” Communications in Mathematical Physics, vol. 403, Springer Nature, 2023, pp. 381–416, doi:10.1007/s00220-023-04795-6. short: M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416. date_created: 2023-07-30T22:01:03Z date_published: 2023-10-01T00:00:00Z date_updated: 2024-01-30T12:16:32Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00220-023-04795-6 external_id: arxiv: - '2303.15949' isi: - '001033655400002' file: - access_level: open_access checksum: cca204e81891270216a0c84eb8bcd398 content_type: application/pdf creator: dernst date_created: 2024-01-30T12:15:11Z date_updated: 2024-01-30T12:15:11Z file_id: '14905' file_name: 2023_CommMathPhysics_Vernooij.pdf file_size: 481209 relation: main_file success: 1 file_date_updated: 2024-01-30T12:15:11Z has_accepted_license: '1' intvolume: ' 403' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 381-416 project: - _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833 grant_number: ESP156_N name: Gradient flow techniques for quantum Markov semigroups publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Derivations and KMS-symmetric quantum Markov semigroups 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 403 year: '2023' ... --- _id: '11916' abstract: - lang: eng text: A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained. acknowledgement: "The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_number: '38' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Wirth M. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 2022;7(3). doi:10.1007/s43036-022-00199-w apa: Wirth, M. (2022). Kac regularity and domination of quadratic forms. Advances in Operator Theory. Springer Nature. https://doi.org/10.1007/s43036-022-00199-w chicago: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances in Operator Theory. Springer Nature, 2022. https://doi.org/10.1007/s43036-022-00199-w. ieee: M. Wirth, “Kac regularity and domination of quadratic forms,” Advances in Operator Theory, vol. 7, no. 3. Springer Nature, 2022. ista: Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38. mla: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances in Operator Theory, vol. 7, no. 3, 38, Springer Nature, 2022, doi:10.1007/s43036-022-00199-w. short: M. Wirth, Advances in Operator Theory 7 (2022). date_created: 2022-08-18T07:22:24Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-02-21T10:08:07Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s43036-022-00199-w file: - access_level: open_access checksum: 913474844a1b38264fb710746d5e2e98 content_type: application/pdf creator: dernst date_created: 2022-08-18T08:02:34Z date_updated: 2022-08-18T08:02:34Z file_id: '11921' file_name: 2022_AdvancesOperatorTheory_Wirth.pdf file_size: 389060 relation: main_file success: 1 file_date_updated: 2022-08-18T08:02:34Z has_accepted_license: '1' intvolume: ' 7' issue: '3' keyword: - Algebra and Number Theory - Analysis language: - iso: eng month: '07' oa: 1 oa_version: Published Version publication: Advances in Operator Theory publication_identifier: eissn: - 2538-225X publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Kac regularity and domination of quadratic forms 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 7 year: '2022' ... --- _id: '12177' abstract: - lang: eng text: Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds. acknowledgement: "The first author was partially supported by the National Science Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester. The second author gratefully acknowledges funding by the Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche Forschungsgemeinschaft through the SPP 2265." article_processing_charge: No article_type: original author: - first_name: Tommaso full_name: Cremaschi, Tommaso last_name: Cremaschi - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 citation: ama: Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134 apa: Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. American Mathematical Society. https://doi.org/10.1090/bproc/134 chicago: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B. American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134. ieee: T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022. ista: Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459. mla: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” Proceedings of the American Mathematical Society, Series B, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134. short: T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459. date_created: 2023-01-12T12:12:17Z date_published: 2022-11-02T00:00:00Z date_updated: 2023-01-26T13:04:13Z day: '02' ddc: - '510' department: - _id: JaMa doi: 10.1090/bproc/134 ec_funded: 1 file: - access_level: open_access checksum: cb4a79937c1f60d4c329a10ee797f0d2 content_type: application/pdf creator: dernst date_created: 2023-01-26T13:02:07Z date_updated: 2023-01-26T13:02:07Z file_id: '12404' file_name: 2022_ProceedingsAMS_Cremaschi.pdf file_size: 326471 relation: main_file success: 1 file_date_updated: 2023-01-26T13:02:07Z has_accepted_license: '1' intvolume: ' 9' issue: '43' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 445-459 project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Proceedings of the American Mathematical Society, Series B publication_identifier: issn: - 2330-1511 publication_status: published publisher: American Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Effective contraction of Skinning maps tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2022' ... --- _id: '10588' abstract: - lang: eng text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds. acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lorenzo full_name: Dello Schiavo, Lorenzo id: ECEBF480-9E4F-11EA-B557-B0823DDC885E last_name: Dello Schiavo orcid: 0000-0002-9881-6870 - first_name: Kohei full_name: Suzuki, Kohei last_name: Suzuki citation: ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2 apa: Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2 chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature, 2022. https://doi.org/10.1007/s00208-021-02331-2. ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp. 1815–1832, 2022. ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832. mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2. short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832. date_created: 2022-01-02T23:01:35Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T13:39:05Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s00208-021-02331-2 ec_funded: 1 external_id: arxiv: - '2110.05137' isi: - '000734150200001' file: - access_level: open_access checksum: 2593abbf195e38efa93b6006b1e90eb1 content_type: application/pdf creator: alisjak date_created: 2022-01-03T11:08:31Z date_updated: 2022-01-03T11:08:31Z file_id: '10596' file_name: 2021_MathAnn_DelloSchiavo.pdf file_size: 410090 relation: main_file success: 1 file_date_updated: 2022-01-03T11:08:31Z has_accepted_license: '1' intvolume: ' 384' isi: 1 keyword: - quasi curvature-dimension condition - sub-riemannian geometry - Sobolev-to-Lipschitz property - Varadhan short-time asymptotics language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 1815-1832 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Sobolev-to-Lipschitz property on QCD- spaces and applications 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 384 year: '2022' ... --- _id: '11330' abstract: - lang: eng text: In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation. acknowledgement: "The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_number: '19' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Wirth M. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9 apa: Wirth, M. (2022). A dual formula for the noncommutative transport distance. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9 chicago: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9. ieee: M. Wirth, “A dual formula for the noncommutative transport distance,” Journal of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022. ista: Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19. mla: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022, doi:10.1007/s10955-022-02911-9. short: M. Wirth, Journal of Statistical Physics 187 (2022). date_created: 2022-04-24T22:01:43Z date_published: 2022-04-08T00:00:00Z date_updated: 2023-08-03T06:37:49Z day: '08' ddc: - '510' - '530' department: - _id: JaMa doi: 10.1007/s10955-022-02911-9 ec_funded: 1 external_id: isi: - '000780305000001' file: - access_level: open_access checksum: f3e0b00884b7dde31347a3756788b473 content_type: application/pdf creator: dernst date_created: 2022-04-29T11:24:23Z date_updated: 2022-04-29T11:24:23Z file_id: '11338' file_name: 2022_JourStatisticalPhysics_Wirth.pdf file_size: 362119 relation: main_file success: 1 file_date_updated: 2022-04-29T11:24:23Z has_accepted_license: '1' intvolume: ' 187' isi: 1 issue: '2' language: - iso: eng month: '04' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A dual formula for the noncommutative transport distance 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 187 year: '2022' ... --- _id: '11447' abstract: - lang: eng text: Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks. acknowledgement: We are grateful to Herbert Edelsbrunner and Jeferson Zapata for helpful discussions. Open access funding provided by Austrian Science Fund (FWF). Partially supported by the ERC Consolidator (771209–CharFL) and the FWF Austrian Science Fund (I5127-B) grants to FAK. article_number: '74' article_processing_charge: Yes (via OA deal) article_type: original author: - 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 - first_name: Fyodor full_name: Kondrashov, Fyodor id: 44FDEF62-F248-11E8-B48F-1D18A9856A87 last_name: Kondrashov orcid: 0000-0001-8243-4694 - first_name: Kseniia full_name: Khudiakova, Kseniia id: 4E6DC800-AE37-11E9-AC72-31CAE5697425 last_name: Khudiakova orcid: 0000-0002-6246-1465 citation: ama: Saona Urmeneta RJ, Kondrashov F, Khudiakova K. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 2022;84(8). doi:10.1007/s11538-022-01029-z apa: Saona Urmeneta, R. J., Kondrashov, F., & Khudiakova, K. (2022). Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. Springer Nature. https://doi.org/10.1007/s11538-022-01029-z chicago: Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology. Springer Nature, 2022. https://doi.org/10.1007/s11538-022-01029-z. ieee: R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between the number of peaks and the number of reciprocal sign epistatic interactions,” Bulletin of Mathematical Biology, vol. 84, no. 8. Springer Nature, 2022. ista: Saona Urmeneta RJ, Kondrashov F, Khudiakova K. 2022. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 84(8), 74. mla: Saona Urmeneta, Raimundo J., et al. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” Bulletin of Mathematical Biology, vol. 84, no. 8, 74, Springer Nature, 2022, doi:10.1007/s11538-022-01029-z. short: R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical Biology 84 (2022). date_created: 2022-06-17T16:16:15Z date_published: 2022-06-17T00:00:00Z date_updated: 2023-08-03T07:20:53Z day: '17' ddc: - '510' - '570' department: - _id: GradSch - _id: NiBa - _id: JaMa doi: 10.1007/s11538-022-01029-z ec_funded: 1 external_id: isi: - '000812509800001' file: - access_level: open_access checksum: 05a1fe7d10914a00c2bca9b447993a65 content_type: application/pdf creator: dernst date_created: 2022-06-20T07:51:32Z date_updated: 2022-06-20T07:51:32Z file_id: '11455' file_name: 2022_BulletinMathBiology_Saona.pdf file_size: 463025 relation: main_file success: 1 file_date_updated: 2022-06-20T07:51:32Z has_accepted_license: '1' intvolume: ' 84' isi: 1 issue: '8' keyword: - Computational Theory and Mathematics - General Agricultural and Biological Sciences - Pharmacology - General Environmental Science - General Biochemistry - Genetics and Molecular Biology - General Mathematics - Immunology - General Neuroscience language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 26580278-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '771209' name: Characterizing the fitness landscape on population and global scales - _id: c098eddd-5a5b-11eb-8a69-abe27170a68f grant_number: I05127 name: Evolutionary analysis of gene regulation publication: Bulletin of Mathematical Biology publication_identifier: eissn: - 1522-9602 issn: - 0092-8240 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1007/s11538-022-01118-z scopus_import: '1' status: public title: Relation between the number of peaks and the number of reciprocal sign epistatic interactions 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 84 year: '2022' ... --- _id: '11739' abstract: - lang: eng text: We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality. acknowledgement: This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245. article_processing_charge: No article_type: original author: - first_name: Dominik L full_name: Forkert, Dominik L id: 35C79D68-F248-11E8-B48F-1D18A9856A87 last_name: Forkert - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Forkert DL, Maas J, Portinale L. Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 2022;54(4):4297-4333. doi:10.1137/21M1410968 apa: Forkert, D. L., Maas, J., & Portinale, L. (2022). Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21M1410968 chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21M1410968. ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022. ista: Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333. mla: Forkert, Dominik L., et al. “Evolutionary $\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” SIAM Journal on Mathematical Analysis, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:10.1137/21M1410968. short: D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333. date_created: 2022-08-07T22:01:59Z date_published: 2022-07-18T00:00:00Z date_updated: 2023-08-03T12:37:21Z day: '18' department: - _id: JaMa doi: 10.1137/21M1410968 ec_funded: 1 external_id: arxiv: - '2008.10962' isi: - '000889274600001' intvolume: ' 54' isi: 1 issue: '4' keyword: - Fokker--Planck equation - gradient flow - evolutionary $\Gamma$-convergence language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2008.10962' month: '07' oa: 1 oa_version: Preprint page: 4297-4333 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260788DE-B435-11E9-9278-68D0E5697425 call_identifier: FWF name: Dissipation and Dispersion in Nonlinear Partial Differential Equations publication: SIAM Journal on Mathematical Analysis publication_identifier: eissn: - 1095-7154 issn: - 0036-1410 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' related_material: record: - id: '10022' relation: earlier_version status: public scopus_import: '1' status: public title: Evolutionary $\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 54 year: '2022' ... --- _id: '11700' abstract: - lang: eng text: This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space. acknowledgement: "ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG), Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117). JM also acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful reading and useful suggestions." article_processing_charge: No article_type: original author: - first_name: Matthias full_name: Erbar, Matthias last_name: Erbar - first_name: Dominik L full_name: Forkert, Dominik L id: 35C79D68-F248-11E8-B48F-1D18A9856A87 last_name: Forkert - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Delio full_name: Mugnolo, Delio last_name: Mugnolo citation: ama: Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 2022;17(5):687-717. doi:10.3934/nhm.2022023 apa: Erbar, M., Forkert, D. L., Maas, J., & Mugnolo, D. (2022). Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. American Institute of Mathematical Sciences. https://doi.org/10.3934/nhm.2022023 chicago: Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media. American Institute of Mathematical Sciences, 2022. https://doi.org/10.3934/nhm.2022023. ieee: M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” Networks and Heterogeneous Media, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022. ista: Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 17(5), 687–717. mla: Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” Networks and Heterogeneous Media, vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717, doi:10.3934/nhm.2022023. short: M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media 17 (2022) 687–717. date_created: 2022-07-31T22:01:46Z date_published: 2022-10-01T00:00:00Z date_updated: 2023-08-03T12:25:49Z day: '01' department: - _id: JaMa doi: 10.3934/nhm.2022023 ec_funded: 1 external_id: arxiv: - '2105.05677' isi: - '000812422100001' intvolume: ' 17' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.05677 month: '10' oa: 1 oa_version: Preprint page: 687-717 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Networks and Heterogeneous Media publication_identifier: eissn: - 1556-181X issn: - 1556-1801 publication_status: published publisher: American Institute of Mathematical Sciences quality_controlled: '1' scopus_import: '1' status: public title: Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 17 year: '2022' ... --- _id: '12210' abstract: - lang: eng text: "The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution kernel kt of this operator satisfies\r\n∥kt∥1≍t,∥kt∥∞≍1,\r\nso that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density of L and spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ), t>0,γ>0, and (Δ~−z)s, with complex z, s." acknowledgement: "Yu. K. thanks Professor Waldemar Hebisch for valuable discussions on the general context of multipliers on Lie groups. This work was started during an ICL-CNRS fellowship of the second\r\nnamed author at the Imperial College London. Yu. K. is supported by the ANR-19-CE40-0002 grant of the French National Research Agency (ANR). H. Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. R. A. was supported by the EPSRC grant EP/R003025. M. R. is supported by the EPSRC grant EP/R003025/2 and by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations." article_processing_charge: No article_type: original author: - first_name: Rauan full_name: Akylzhanov, Rauan last_name: Akylzhanov - first_name: Yulia full_name: Kuznetsova, Yulia last_name: Kuznetsova - first_name: Michael full_name: Ruzhansky, Michael last_name: Ruzhansky - first_name: Haonan full_name: Zhang, Haonan id: D8F41E38-9E66-11E9-A9E2-65C2E5697425 last_name: Zhang citation: ama: Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 2022;302(4):2327-2352. doi:10.1007/s00209-022-03143-z apa: Akylzhanov, R., Kuznetsova, Y., Ruzhansky, M., & Zhang, H. (2022). Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-022-03143-z chicago: Akylzhanov, Rauan, Yulia Kuznetsova, Michael Ruzhansky, and Haonan Zhang. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” Mathematische Zeitschrift. Springer Nature, 2022. https://doi.org/10.1007/s00209-022-03143-z. ieee: R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, and H. Zhang, “Norms of certain functions of a distinguished Laplacian on the ax + b groups,” Mathematische Zeitschrift, vol. 302, no. 4. Springer Nature, pp. 2327–2352, 2022. ista: Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. 2022. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 302(4), 2327–2352. mla: Akylzhanov, Rauan, et al. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” Mathematische Zeitschrift, vol. 302, no. 4, Springer Nature, 2022, pp. 2327–52, doi:10.1007/s00209-022-03143-z. short: R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang, Mathematische Zeitschrift 302 (2022) 2327–2352. date_created: 2023-01-16T09:45:31Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-04T09:22:14Z day: '01' department: - _id: JaMa doi: 10.1007/s00209-022-03143-z ec_funded: 1 external_id: arxiv: - '2101.00584' isi: - '000859680700001' intvolume: ' 302' isi: 1 issue: '4' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.00584 month: '12' oa: 1 oa_version: Preprint page: 2327-2352 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6 grant_number: M03337 name: Curvature-dimension in noncommutative analysis publication: Mathematische Zeitschrift publication_identifier: eissn: - 1432-1823 issn: - 0025-5874 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Norms of certain functions of a distinguished Laplacian on the ax + b groups type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 302 year: '2022' ...