[{"publisher":"Institute of Science and Technology Austria","oa":1,"page":"152","doi":"10.15479/at:ista:12094","date_published":"2022-09-19T00:00:00Z","date_created":"2023-01-24T13:09:57Z","has_accepted_license":"1","year":"2022","day":"19","project":[{"name":"Probing development and reversibility of autism spectrum disorders","grant_number":"401299","_id":"254BA948-B435-11E9-9278-68D0E5697425"},{"name":"Critical windows and reversibility of ASD associated with mutations in chromatin remodelers","grant_number":"707964","_id":"9B91375C-BA93-11EA-9121-9846C619BF3A"},{"call_identifier":"H2020","_id":"25444568-B435-11E9-9278-68D0E5697425","grant_number":"715508","name":"Probing the Reversibility of Autism Spectrum Disorders by Employing in vivo and in vitro Models"},{"name":"Identification of converging Molecular Pathways Across Chromatinopathies as Targets for Therapy","grant_number":"I04205","_id":"2690FEAC-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"author":[{"full_name":"Dotter, Christoph","orcid":"0000-0002-9033-9096","last_name":"Dotter","first_name":"Christoph","id":"4C66542E-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"Transcriptional consequences of mutations in genes associated with Autism Spectrum Disorder","citation":{"chicago":"Dotter, Christoph. “Transcriptional Consequences of Mutations in Genes Associated with Autism Spectrum Disorder.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:12094.","ista":"Dotter C. 2022. Transcriptional consequences of mutations in genes associated with Autism Spectrum Disorder. Institute of Science and Technology Austria.","mla":"Dotter, Christoph. Transcriptional Consequences of Mutations in Genes Associated with Autism Spectrum Disorder. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12094.","ama":"Dotter C. Transcriptional consequences of mutations in genes associated with Autism Spectrum Disorder. 2022. doi:10.15479/at:ista:12094","apa":"Dotter, C. (2022). Transcriptional consequences of mutations in genes associated with Autism Spectrum Disorder. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:12094","short":"C. Dotter, Transcriptional Consequences of Mutations in Genes Associated with Autism Spectrum Disorder, Institute of Science and Technology Austria, 2022.","ieee":"C. Dotter, “Transcriptional consequences of mutations in genes associated with Autism Spectrum Disorder,” Institute of Science and Technology Austria, 2022."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","alternative_title":["ISTA Thesis"],"month":"09","abstract":[{"lang":"eng","text":"Autism spectrum disorders (ASDs) are a group of neurodevelopmental disorders character\u0002ized by behavioral symptoms such as problems in social communication and interaction, as\r\nwell as repetitive, restricted behaviors and interests. These disorders show a high degree\r\nof heritability and hundreds of risk genes have been identifed using high throughput\r\nsequencing technologies. This genetic heterogeneity has hampered eforts in understanding\r\nthe pathogenesis of ASD but at the same time given rise to the concept of convergent\r\nmechanisms. Previous studies have identifed that risk genes for ASD broadly converge\r\nonto specifc functional categories with transcriptional regulation being one of the biggest\r\ngroups. In this thesis, I focus on this subgroup of genes and investigate the gene regulatory\r\nconsequences of some of them in the context of neurodevelopment.\r\nFirst, we showed that mutations in the ASD and intellectual disability risk gene Setd5 lead\r\nto perturbations of gene regulatory programs in early cell fate specifcation. In addition,\r\nadult animals display abnormal learning behavior which is mirrored at the transcriptional\r\nlevel by altered activity dependent regulation of postsynaptic gene expression. Lastly,\r\nwe link the regulatory function of Setd5 to its interaction with the Paf1 and the NCoR\r\ncomplex.\r\nSecond, by modeling the heterozygous loss of the top ASD gene CHD8 in human cerebral\r\norganoids we demonstrate profound changes in the developmental trajectories of both\r\ninhibitory and excitatory neurons using single cell RNA-sequencing. While the former\r\nwere generated earlier in CHD8+/- organoids, the generation of the latter was shifted to\r\nlater times in favor of a prolonged progenitor expansion phase and ultimately increased\r\norganoid size.\r\nFinally, by modeling heterozygous mutations for four ASD associated chromatin modifers,\r\nASH1L, KDM6B, KMT5B, and SETD5 in human cortical spheroids we show evidence of\r\nregulatory convergence across three of those genes. We observe a shift from dorsal cortical\r\nexcitatory neuron fates towards partially ventralized cell types resembling cells from the\r\nlateral ganglionic eminence. As this project is still ongoing at the time of writing, future\r\nexperiments will aim at elucidating the regulatory mechanisms underlying this shift with\r\nthe aim of linking these three ASD risk genes through biological convergence."}],"oa_version":"Published Version","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"3"},{"id":"11160","status":"public","relation":"part_of_dissertation"}]},"ec_funded":1,"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","embargo":"2023-09-19","file_id":"12365","checksum":"896f4cac9adb6d3f26a6605772f4e1a3","file_size":20457465,"date_updated":"2023-09-20T22:30:03Z","creator":"cchlebak","file_name":"220923_Thesis_CDotter_Final.pdf","date_created":"2023-01-24T13:15:45Z"},{"file_name":"latex_source_CDotter_Thesis_2022.zip","date_created":"2023-02-02T09:15:35Z","file_size":22433512,"date_updated":"2023-09-20T22:30:03Z","creator":"cchlebak","checksum":"ad01bb20da163be6893b7af832e58419","file_id":"12482","embargo_to":"open_access","content_type":"application/x-zip-compressed","relation":"source_file","access_level":"closed"}],"language":[{"iso":"eng"}],"type":"dissertation","status":"public","_id":"12364","file_date_updated":"2023-09-20T22:30:03Z","department":[{"_id":"GradSch"},{"_id":"GaNo"}],"supervisor":[{"last_name":"Novarino","orcid":"0000-0002-7673-7178","full_name":"Novarino, Gaia","id":"3E57A680-F248-11E8-B48F-1D18A9856A87","first_name":"Gaia"}],"date_updated":"2023-11-16T13:10:22Z","ddc":["570"]},{"supervisor":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"}],"date_updated":"2023-09-07T13:29:01Z","ddc":["006","514","516"],"file_date_updated":"2021-02-03T10:37:28Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"_id":"9056","type":"dissertation","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","file":[{"file_name":"thesis_source.zip","date_created":"2021-02-02T14:09:25Z","file_size":13446994,"date_updated":"2021-02-03T10:37:28Z","creator":"patrickd","checksum":"bcf27986147cab0533b6abadd74e7629","file_id":"9063","content_type":"application/zip","relation":"source_file","access_level":"closed"},{"creator":"patrickd","file_size":5210329,"date_updated":"2021-02-02T14:09:18Z","file_name":"thesis_pdfA2b.pdf","date_created":"2021-02-02T14:09:18Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"9064","checksum":"9cc8af266579a464385bbe2aff6af606"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"187"},{"status":"public","id":"8703","relation":"part_of_dissertation"}]},"abstract":[{"text":"In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations. The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,\r\nand thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics. We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration\r\nfunction on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss the implications on persistence for periodic data sets.","lang":"eng"}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"month":"02","place":"Klosterneuburg","citation":{"chicago":"Osang, Georg F. “Multi-Cover Persistence and Delaunay Mosaics.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9056.","ista":"Osang GF. 2021. Multi-cover persistence and Delaunay mosaics. Klosterneuburg: Institute of Science and Technology Austria.","mla":"Osang, Georg F. Multi-Cover Persistence and Delaunay Mosaics. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9056.","apa":"Osang, G. F. (2021). Multi-cover persistence and Delaunay mosaics. Institute of Science and Technology Austria, Klosterneuburg. https://doi.org/10.15479/AT:ISTA:9056","ama":"Osang GF. Multi-cover persistence and Delaunay mosaics. 2021. doi:10.15479/AT:ISTA:9056","ieee":"G. F. Osang, “Multi-cover persistence and Delaunay mosaics,” Institute of Science and Technology Austria, Klosterneuburg, 2021.","short":"G.F. Osang, Multi-Cover Persistence and Delaunay Mosaics, Institute of Science and Technology Austria, 2021."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"full_name":"Osang, Georg F","orcid":"0000-0002-8882-5116","last_name":"Osang","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","first_name":"Georg F"}],"article_processing_charge":"No","title":"Multi-cover persistence and Delaunay mosaics","has_accepted_license":"1","year":"2021","day":"01","page":"134","date_published":"2021-02-01T00:00:00Z","doi":"10.15479/AT:ISTA:9056","date_created":"2021-02-02T14:11:06Z","publisher":"Institute of Science and Technology Austria","oa":1},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","apa":"Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022."},"title":"Fluctuations in the spectrum of random matrices","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"},{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"day":"25","has_accepted_license":"1","year":"2021","date_published":"2021-01-25T00:00:00Z","doi":"10.15479/AT:ISTA:9022","date_created":"2021-01-21T18:16:54Z","page":"380","acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","publisher":"Institute of Science and Technology Austria","oa":1,"ddc":["510"],"supervisor":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"date_updated":"2023-09-07T13:29:32Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2021-01-25T14:19:10Z","_id":"9022","status":"public","type":"dissertation","file":[{"file_name":"thesis.pdf","date_created":"2021-01-25T14:19:03Z","file_size":4127796,"date_updated":"2021-01-25T14:19:03Z","creator":"gcipollo","success":1,"checksum":"5a93658a5f19478372523ee232887e2b","file_id":"9043","content_type":"application/pdf","relation":"main_file","access_level":"open_access"},{"file_size":12775206,"date_updated":"2021-01-25T14:19:10Z","creator":"gcipollo","file_name":"Thesis_files.zip","date_created":"2021-01-25T14:19:10Z","content_type":"application/zip","relation":"source_file","access_level":"closed","file_id":"9044","checksum":"e8270eddfe6a988e92a53c88d1d19b8c"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","ec_funded":1,"oa_version":"Published Version","abstract":[{"lang":"eng","text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices."}],"month":"01","alternative_title":["ISTA Thesis"]},{"publisher":"Institute of Science and Technology Austria","oa":1,"has_accepted_license":"1","year":"2021","day":"14","page":"300","doi":"10.15479/at:ista:10007","date_published":"2021-09-14T00:00:00Z","date_created":"2021-09-13T11:12:34Z","project":[{"name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"citation":{"short":"S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts, Institute of Science and Technology Austria, 2021.","ieee":"S. Hensel, “Curvature driven interface evolution: Uniqueness properties of weak solution concepts,” Institute of Science and Technology Austria, 2021.","apa":"Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007","ama":"Hensel S. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. 2021. doi:10.15479/at:ista:10007","mla":"Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10007.","ista":"Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria.","chicago":"Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10007."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian"}],"article_processing_charge":"No","title":"Curvature driven interface evolution: Uniqueness properties of weak solution concepts","abstract":[{"lang":"eng","text":"The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis."}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"month":"09","publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"content_type":"application/x-zip-compressed","relation":"source_file","access_level":"closed","file_id":"10008","checksum":"c8475faaf0b680b4971f638f1db16347","file_size":15022154,"date_updated":"2021-09-15T14:37:30Z","creator":"shensel","file_name":"thesis_final_Hensel.zip","date_created":"2021-09-13T11:03:24Z"},{"date_created":"2021-09-13T14:18:56Z","file_name":"thesis_final_Hensel.pdf","date_updated":"2021-09-14T09:52:47Z","file_size":6583638,"creator":"shensel","checksum":"1a609937aa5275452822f45f2da17f07","file_id":"10014","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10012"},{"relation":"part_of_dissertation","id":"10013","status":"public"},{"id":"7489","status":"public","relation":"part_of_dissertation"}]},"ec_funded":1,"_id":"10007","type":"dissertation","status":"public","supervisor":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"}],"date_updated":"2023-09-07T13:30:45Z","ddc":["515"],"department":[{"_id":"GradSch"},{"_id":"JuFi"}],"file_date_updated":"2021-09-15T14:37:30Z"},{"project":[{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","article_processing_charge":"No","author":[{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Portinale, Lorenzo. Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10030.","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021.","apa":"Portinale, L. (2021). Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10030","ama":"Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:10.15479/at:ista:10030","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10030.","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria."},"oa":1,"publisher":"Institute of Science and Technology Austria","acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","date_created":"2021-09-21T09:14:15Z","doi":"10.15479/at:ista:10030","date_published":"2021-09-22T00:00:00Z","day":"22","year":"2021","has_accepted_license":"1","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","_id":"10030","file_date_updated":"2022-03-10T12:14:42Z","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"ddc":["515"],"date_updated":"2023-09-07T13:31:06Z","supervisor":[{"last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan"}],"month":"09","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"abstract":[{"text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces.","lang":"eng"}],"related_material":{"record":[{"id":"10022","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"9792"},{"relation":"part_of_dissertation","id":"7573","status":"public"}]},"language":[{"iso":"eng"}],"file":[{"file_id":"10032","checksum":"8cd60dcb8762e8f21867e21e8001e183","access_level":"closed","relation":"source_file","content_type":"application/x-zip-compressed","date_created":"2021-09-21T09:17:34Z","file_name":"tex_and_pictures.zip","creator":"cchlebak","date_updated":"2022-03-10T12:14:42Z","file_size":3876668},{"creator":"cchlebak","file_size":2532673,"date_updated":"2021-09-27T11:14:31Z","file_name":"thesis_portinale_Final (1).pdf","date_created":"2021-09-27T11:14:31Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"10047","checksum":"9789e9d967c853c1503ec7f307170279"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]}}]