--- OA_place: repository _id: '19547' abstract: - lang: eng text: "For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes." acknowledgement: "Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331." article_processing_charge: No arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Volodymyr full_name: Riabov, Volodymyr id: 1949f904-edfb-11eb-afb5-e2dfddabb93b last_name: Riabov citation: ama: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv. doi:10.48550/arXiv.2410.06813 apa: Erdös, L., Henheik, S. J., & Riabov, V. (n.d.). Cusp universality for correlated random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.06813 chicago: Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.06813. ieee: L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” arXiv. . ista: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, 10.48550/arXiv.2410.06813. mla: Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” ArXiv, doi:10.48550/arXiv.2410.06813. short: L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.). corr_author: '1' date_created: 2025-04-11T08:48:21Z date_published: 2024-11-03T00:00:00Z date_updated: 2026-04-07T12:37:11Z day: '03' department: - _id: LaEr doi: 10.48550/arXiv.2410.06813 ec_funded: 1 external_id: arxiv: - '2410.06813' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2410.06813 month: '11' oa: 1 oa_version: Preprint project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: arXiv publication_status: draft related_material: record: - id: '20322' relation: later_version status: public - id: '20575' relation: dissertation_contains status: public - id: '19540' relation: dissertation_contains status: public status: public title: Cusp universality for correlated random matrices type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: publisher _id: '18588' abstract: - lang: eng text: "This thesis is an experimental work about two distinct research projects that evolved from a single project: non-equilibrium dynamics of an acoustically vibrated particle and microfabrication of particles with nano-scale 3D printing. The first project explores non equilibrium dynamics of a particle driven by ultrasonic vibrations. We design an experimental system consisting of an electromechanical vibration scheme to drive the particle’s vibrations and an imaging scheme to track its trajectories. We study the trajectories to determine how the particle’s dynamics evolve under the driven conditions, considering out of equilibrium systems in the context of equilibrium statistical mechanics. Using a Langevin framework and the Boltzmann factor, we characterize the particle’s dynamics as complex; the particle motion\r\nis not purely diffusive. We extract physical parameters like spring constant, effective temperature, damping coefficient and resonance frequency.\r\n\r\nIn the second project, we explore and develop techniques in the design and microfabrication of particles across scales. Microfabrication involves building structures at the micron or submicron scale. These designed miniaturized patterns, objects, or devices are useful in biophysics, pharmacology, medical biology, and nanotechnology. We specifically apply two-photon polymerization, a form of 3D nano printing. We print millimetric particles, characterizing different designs to evaluate and showcase the resolution, aspect ratio integrity and print quality of the printing process. We also design and fabricate a microsensor to deflect under applicable force of order 0.1 pN. We present fundamental concepts needed to design the microsensor, showcasing 3D printing at considerably smaller scales down to the µm or below." acknowledged_ssus: - _id: NanoFab - _id: M-Shop acknowledgement: "I would like to acknowledge Scott Waitukaitis and Jérémie Palacci, for their supervision, and their extensive support of my learning. \r\n\r\nFor the beautiful characterization images used in this work, I would like to thank Dr. Daniel Grober, Samuel Hajek and Felix Pertl.\r\n\r\nThe Palacci group, particularly Malina Strugaru and Dan Grober, for their continuous guidance in decoding and following my streams of thought.\r\n\r\nTo the Waitukaitis group, for helping me find my footing in science, and making me feel at\r\nhome.\r\n\r\nTo the Nanofabrication Facility (NFF) at ISTA, for training me in significant aspects of my research. The MIBA Facility, and particularly Todor Asenov for consistently picking up the phone for my machining and designing needs.\r\n\r\nTo my friends, Mariana, Lenka, Aaron, Rebecca, Eavan who provided an ear, wine, and a lot more when I needed to vent, talk through my crises as well as experiment. For the walks, for the coffees, for reading through my work and providing edits, for dinners to take me out of blocks and binds and for cheering me on when it felt insurmountable. \r\n\r\nFinally, I am grateful to Griff and Fletcher, whose music helped me through several blocks, especially with my writing.\r\n\r\nMy science would not have been possible without the guidance, support and contributions of\r\nall these people, and more." alternative_title: - ISTA Master's Thesis article_processing_charge: No author: - first_name: Cecelia N full_name: Mweka, Cecelia N id: 2a69ab4b-896a-11ed-bdf8-cb8641cf2b21 last_name: Mweka citation: ama: Mweka CN. Non equilibrium dynamics of driven individual particles and 3D printing across scales. 2024. doi:10.15479/at:ista:18588 apa: Mweka, C. N. (2024). Non equilibrium dynamics of driven individual particles and 3D printing across scales. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18588 chicago: Mweka, Cecelia N. “Non Equilibrium Dynamics of Driven Individual Particles and 3D Printing across Scales.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18588. ieee: C. N. Mweka, “Non equilibrium dynamics of driven individual particles and 3D printing across scales,” Institute of Science and Technology Austria, 2024. ista: Mweka CN. 2024. Non equilibrium dynamics of driven individual particles and 3D printing across scales. Institute of Science and Technology Austria. mla: Mweka, Cecelia N. Non Equilibrium Dynamics of Driven Individual Particles and 3D Printing across Scales. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18588. short: C.N. Mweka, Non Equilibrium Dynamics of Driven Individual Particles and 3D Printing across Scales, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-11-27T09:12:02Z date_published: 2024-11-29T00:00:00Z date_updated: 2026-04-07T12:42:13Z day: '29' ddc: - '530' degree_awarded: MS department: - _id: GradSch doi: 10.15479/at:ista:18588 file: - access_level: open_access checksum: 054ed7a5e5ae6e7220e6bb37ea57a3c3 content_type: application/pdf creator: cmweka date_created: 2024-11-28T12:50:32Z date_updated: 2024-11-28T12:50:32Z file_id: '18597' file_name: Cecelia Mweka Master Thesis.pdf file_size: 3836671 relation: main_file success: 1 - access_level: closed checksum: 7d7d9299f090d83e628d65d93116e8c2 content_type: application/vnd.openxmlformats-officedocument.wordprocessingml.document creator: cmweka date_created: 2024-11-28T12:51:43Z date_updated: 2024-12-13T11:30:53Z file_id: '18598' file_name: Cecelia Mweka Master Thesis.docx file_size: 7068210 relation: source_file file_date_updated: 2024-12-13T11:30:53Z has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: '61' publication_identifier: issn: - 2791-4585 publication_status: published publisher: Institute of Science and Technology Austria status: public supervisor: - first_name: Scott R full_name: Waitukaitis, Scott R id: 3A1FFC16-F248-11E8-B48F-1D18A9856A87 last_name: Waitukaitis orcid: 0000-0002-2299-3176 - first_name: Jérémie A full_name: Palacci, Jérémie A id: 8fb92548-2b22-11eb-b7c1-a3f0d08d7c7d last_name: Palacci orcid: 0000-0002-7253-9465 title: Non equilibrium dynamics of driven individual particles and 3D printing across scales type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: publisher _id: '17225' abstract: - lang: eng text: "This thesis describes the development of an atom interferometer designed to exploit the\r\nadvantages of utilizing quantum entanglement for enhanced precision measurements beyond\r\nthe standard quantum limit. While the project remains ongoing, significant progress has been\r\nmade.\r\nA key contribution of this work is the development of Quantrol, an experimental control\r\nsystem leveraging the ARTIQ framework. This software enables precise timing and control\r\nwithout requiring prior knowledge of ARTIQ’s implementation details or coding experience.\r\nThe interface offers user friendly visual comprehension of the experimental sequence and\r\nextended capabilities, allowing researchers to scan variables with a simple click of a mouse.\r\nThe main proposed project is to implement atom interferometric sequence with squeezed input\r\nstates inside of a dipole trap generated by a high finesse cavity. The presence of the dipole\r\ntrap allows one dimensional atomic cloud split while maintaining relatively strong confinement\r\nin other directions.\r\nWe are currently able to trap and cool 87Rb atoms to few micro kelvin temperatures, load\r\nthem into the dipole trap and state prepare them to be used for squeezing and interferometric\r\nsequence." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Vyacheslav full_name: Li, Vyacheslav id: 3A4FAA92-F248-11E8-B48F-1D18A9856A87 last_name: Li citation: ama: Li V. Towards a quantum entanglement enhanced atom interferomter. 2024. doi:10.15479/at:ista:17225 apa: Li, V. (2024). Towards a quantum entanglement enhanced atom interferomter. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17225 chicago: Li, Vyacheslav. “Towards a Quantum Entanglement Enhanced Atom Interferomter.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17225. ieee: V. Li, “Towards a quantum entanglement enhanced atom interferomter,” Institute of Science and Technology Austria, 2024. ista: Li V. 2024. Towards a quantum entanglement enhanced atom interferomter. Institute of Science and Technology Austria. mla: Li, Vyacheslav. Towards a Quantum Entanglement Enhanced Atom Interferomter. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17225. short: V. Li, Towards a Quantum Entanglement Enhanced Atom Interferomter, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-07-11T09:46:48Z date_published: 2024-07-11T00:00:00Z date_updated: 2026-04-07T12:42:28Z day: '11' ddc: - '530' degree_awarded: PhD department: - _id: GradSch - _id: OnHo doi: 10.15479/at:ista:17225 file: - access_level: open_access checksum: 15b2dbe8d2c9ed7ca5dd413827928077 content_type: application/pdf creator: vli date_created: 2024-07-11T10:26:22Z date_updated: 2024-07-11T10:26:22Z file_id: '17228' file_name: PhD_Thesis_Vyacheslav_Li_no_signatures_PDFA.pdf file_size: 6729761 relation: main_file success: 1 - access_level: closed checksum: 16e904a11d8d0ebb167cb654ddfc7fe5 content_type: application/x-zip-compressed creator: vli date_created: 2024-07-11T10:26:22Z date_updated: 2024-07-11T10:26:22Z file_id: '17229' file_name: PhD Thesis Vyacheslav Li.zip file_size: 9542859 relation: source_file file_date_updated: 2024-07-11T10:26:22Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '07' oa: 1 oa_version: Published Version page: '79' project: - _id: bdb2a702-d553-11ed-ba76-f12e3e5a3bc6 grant_number: '101087907' name: 'A quantum hybrid of atoms and milligram-scale pendulums: towards gravitational quantum mechanics' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '11438' relation: part_of_dissertation status: public status: public supervisor: - first_name: Onur full_name: Hosten, Onur id: 4C02D85E-F248-11E8-B48F-1D18A9856A87 last_name: Hosten orcid: 0000-0002-2031-204X title: Towards a quantum entanglement enhanced atom interferomter tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: publisher OA_type: free access _id: '18443' abstract: - lang: eng text: "In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they\r\nconjecture an equivalence between categories of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler structures and the\r\ncorresponding branes on affine torus bundles. We use the techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles and connections. This T-duality in the appropriate context specializes to\r\nT-duality between BBB and BAA-branes.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Maria A full_name: Sisak, Maria A id: 44A03D04-AEA4-11E9-B225-EA2DE6697425 last_name: Sisak citation: ama: Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:10.15479/at:ista:18443 apa: Sisak, M. A. (2024). T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18443 chicago: Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18443. ieee: M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024. ista: Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria. mla: Sisak, Maria A. T-Dual Branes on Hyperkähler Manifolds. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18443. short: M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-10-19T12:00:37Z date_published: 2024-10-24T00:00:00Z date_updated: 2026-04-07T12:42:44Z day: '24' ddc: - '516' degree_awarded: PhD department: - _id: GradSch - _id: TaHa doi: 10.15479/at:ista:18443 file: - access_level: open_access checksum: 8c4893e726aaa4b3efb82758da9b6851 content_type: application/pdf creator: msisak date_created: 2024-10-23T14:42:45Z date_updated: 2024-10-23T14:42:45Z file_id: '18467' file_name: MASisak_dissertation.pdf file_size: 1672547 relation: main_file success: 1 - access_level: closed checksum: 1831b072e861a1e5481024ca9d02b036 content_type: application/x-zip-compressed creator: msisak date_created: 2024-10-23T14:43:56Z date_updated: 2024-10-24T08:09:13Z file_id: '18468' file_name: MASisak_source.zip file_size: 617913 relation: source_file file_date_updated: 2024-10-24T08:09:13Z has_accepted_license: '1' keyword: - hyperkaehler geometry - branes - mirror symmetry - T-duality language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '178' project: - _id: 6286e8c4-2b32-11ec-9570-f5297902f67f grant_number: '26069' name: Branes on hyperkähler manifolds publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria status: public supervisor: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel orcid: 0000-0002-9582-2634 title: T-dual branes on hyperkähler manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: publisher _id: '17485' abstract: - lang: eng text: "Large language models (LLMs) have made tremendous progress in the past few years, from being able to generate coherent text to matching or surpassing humans in a wide variety of creative, knowledge or reasoning tasks. Much of this can be attributed to massively increased scale, both in the size of the model as well as the amount of training data, from 100s of millions to 100s of billions, or even trillions. This trend is expected to continue, which, although exciting, also raises major practical concerns. Already today's 100+ billion parameter LLMs require top-of-the-line hardware just to run. Hence, it is clear that sustaining these developments will require significant efficiency advances.\r\n\r\nHistorically, one of the most practical ways of improving model efficiency has been compression, especially in the form of sparsity or quantization. While this has been studied extensively in the past, existing accurate methods are all designed for models around 100 million parameters; scaling them up to ones literally 1000x larger is highly challenging. In this thesis, we introduce a new unified sparsification and quantization approach OBC, which through additional algorithmic enhancements leads to GPTQ and SparseGPT, the first techniques fast and accurate enough to compress 100+ billion parameter models to 4- or even 3-bit precision and 50% weight-sparsity, respectively. Additionally, we show how weight-only quantizion does not just bring space savings but also up to 4.5x faster generation speed, via custom GPU kernels.\r\n\r\nIn fact, we show for the first time that it is possible to develop an FP16 times INT4 mixed-precision matrix multiplication kernel, called Marlin, which comes close to simultaneously maximizing both memory and compute utilization, making weight-only quantization highly practical even for multi-user serving. Further, we demonstrate that GPTQ can be scaled to widely overparametrized trillion-parameter models, where extreme sub-1-bit compression rates can be achieved without any inference slow-down, by co-designing a bespoke entropy coding scheme together with an efficient kernel.\r\n\r\nFinally, we also study compression from the perspective of someone with access to massive amounts of compute resources for training large models completely from scratch. Here the key questions evolve around the joint scaling behavior between compression, model size, and amount of training data used. Based on extensive experimental results for both vision and text models, we introduce the first scaling law which accurately captures the relationship between weight-sparsity, number of non-zero weights and data. This further allows us to characterize the optimal sparsity, which we find to increase the longer a fixed cost model is being trained.\r\n\r\nOverall, this thesis presents contributions to three different angles of large model efficiency: affordable but accurate algorithms, highly efficient systems implementations, and fundamental scaling laws for compressed training." acknowledged_ssus: - _id: ScienComp alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Elias full_name: Frantar, Elias id: 09a8f98d-ec99-11ea-ae11-c063a7b7fe5f last_name: Frantar citation: ama: 'Frantar E. Compressing large neural networks : Algorithms, systems and scaling laws. 2024. doi:10.15479/at:ista:17485' apa: 'Frantar, E. (2024). Compressing large neural networks : Algorithms, systems and scaling laws. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17485' chicago: 'Frantar, Elias. “Compressing Large Neural Networks : Algorithms, Systems and Scaling Laws.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17485.' ieee: 'E. Frantar, “Compressing large neural networks : Algorithms, systems and scaling laws,” Institute of Science and Technology Austria, 2024.' ista: 'Frantar E. 2024. Compressing large neural networks : Algorithms, systems and scaling laws. Institute of Science and Technology Austria.' mla: 'Frantar, Elias. Compressing Large Neural Networks : Algorithms, Systems and Scaling Laws. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17485.' short: 'E. Frantar, Compressing Large Neural Networks : Algorithms, Systems and Scaling Laws, Institute of Science and Technology Austria, 2024.' corr_author: '1' date_created: 2024-09-02T11:01:48Z date_published: 2024-09-05T00:00:00Z date_updated: 2026-04-07T12:43:04Z day: '05' ddc: - '000' degree_awarded: PhD department: - _id: GradSch - _id: DaAl doi: 10.15479/at:ista:17485 ec_funded: 1 file: - access_level: closed checksum: 5d785645805a78c5b4ce7cc3df557b09 content_type: application/zip creator: efrantar date_created: 2024-09-05T12:04:11Z date_updated: 2024-09-05T12:04:11Z file_id: '17570' file_name: thesis-final.zip file_size: 1615167 relation: source_file - access_level: open_access checksum: a9dd1c2d23734986924eb44ebb55fd8f content_type: application/pdf creator: efrantar date_created: 2024-09-06T16:24:59Z date_updated: 2024-09-06T16:24:59Z file_id: '17880' file_name: frantar_thesis_final.pdf file_size: 2376611 relation: main_file success: 1 file_date_updated: 2024-09-06T16:24:59Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '129' project: - _id: 268A44D6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '805223' name: Elastic Coordination for Scalable Machine Learning publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '18062' relation: part_of_dissertation status: public - id: '18061' relation: part_of_dissertation status: public - id: '17378' relation: part_of_dissertation status: public - id: '17087' relation: part_of_dissertation status: public - id: '14458' relation: part_of_dissertation status: public status: public supervisor: - first_name: Dan-Adrian full_name: Alistarh, Dan-Adrian id: 4A899BFC-F248-11E8-B48F-1D18A9856A87 last_name: Alistarh orcid: 0000-0003-3650-940X title: 'Compressing large neural networks : Algorithms, systems and scaling laws' type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- _id: '18061' abstract: - lang: eng text: 'Mixture-of-Experts (MoE) architectures offer a general solution to the high inference costs of large language models (LLMs) via sparse routing, bringing faster and more accurate models, at the cost of massive parameter counts. For example, the SwitchTransformer-c2048 model has 1.6 trillion parameters, requiring 3.2TB of accelerator memory to run efficiently, which makes practical deployment challenging and expensive. In this paper, we present a solution to this memory problem, in form of a new compression and execution framework called QMoE. Specifically, QMoE consists of a scalable algorithm which accurately compresses trillion-parameter MoEs to less than 1 bit per parameter, in a custom format co-designed with bespoke GPU decoding kernels to facilitate efficient end-to-end compressed inference, with minor runtime overheads relative to uncompressed execution. Concretely, QMoE can compress the 1.6 trillion parameter SwitchTransformer-c2048 model to less than 160GB (20x compression, 0.8 bits per parameter) at only minor accuracy loss, in less than a day on a single GPU. This enables, for the first time, the execution of a trillion-parameter model on affordable commodity hardware, like a single server with 4x NVIDIA A6000 or 8x NVIDIA 3090 GPUs, at less than 5% runtime overhead relative to ideal uncompressed inference. The anonymized code is available at: github.com/mlsys24-qmoe/qmoe.' article_processing_charge: No author: - first_name: Elias full_name: Frantar, Elias id: 09a8f98d-ec99-11ea-ae11-c063a7b7fe5f last_name: Frantar - first_name: Dan-Adrian full_name: Alistarh, Dan-Adrian id: 4A899BFC-F248-11E8-B48F-1D18A9856A87 last_name: Alistarh orcid: 0000-0003-3650-940X citation: ama: 'Frantar E, Alistarh D-A. QMoE: Sub-1-bit compression of trillion parameter models. In: Gibbons P, Pekhimenko G, De Sa C, eds. Proceedings of Machine Learning and Systems. Vol 6. ; 2024.' apa: 'Frantar, E., & Alistarh, D.-A. (2024). QMoE: Sub-1-bit compression of trillion parameter models. In P. Gibbons, G. Pekhimenko, & C. De Sa (Eds.), Proceedings of Machine Learning and Systems (Vol. 6). Santa Clara, CA, USA.' chicago: 'Frantar, Elias, and Dan-Adrian Alistarh. “QMoE: Sub-1-Bit Compression of Trillion Parameter Models.” In Proceedings of Machine Learning and Systems, edited by P. Gibbons, G. Pekhimenko, and C. De Sa, Vol. 6, 2024.' ieee: 'E. Frantar and D.-A. Alistarh, “QMoE: Sub-1-bit compression of trillion parameter models,” in Proceedings of Machine Learning and Systems, Santa Clara, CA, USA, 2024, vol. 6.' ista: 'Frantar E, Alistarh D-A. 2024. QMoE: Sub-1-bit compression of trillion parameter models. Proceedings of Machine Learning and Systems. MLSys: Machine Learning and Systems vol. 6.' mla: 'Frantar, Elias, and Dan-Adrian Alistarh. “QMoE: Sub-1-Bit Compression of Trillion Parameter Models.” Proceedings of Machine Learning and Systems, edited by P. Gibbons et al., vol. 6, 2024.' short: E. Frantar, D.-A. Alistarh, in:, P. Gibbons, G. Pekhimenko, C. De Sa (Eds.), Proceedings of Machine Learning and Systems, 2024. conference: end_date: 2024-05-16 location: Santa Clara, CA, USA name: 'MLSys: Machine Learning and Systems' start_date: 2024-05-13 corr_author: '1' date_created: 2024-09-13T10:01:38Z date_published: 2024-05-01T00:00:00Z date_updated: 2026-04-07T12:43:03Z day: '01' department: - _id: DaAl editor: - first_name: P. full_name: Gibbons, P. last_name: Gibbons - first_name: G. full_name: Pekhimenko, G. last_name: Pekhimenko - first_name: C. full_name: De Sa, C. last_name: De Sa intvolume: ' 6' language: - iso: eng main_file_link: - open_access: '1' url: https://proceedings.mlsys.org/paper_files/paper/2024/hash/c74b624843218d9b6713fcf299d6d5e4-Abstract-Conference.html month: '05' oa: 1 oa_version: Published Version publication: ' Proceedings of Machine Learning and Systems' publication_status: published quality_controlled: '1' related_material: record: - id: '17485' relation: dissertation_contains status: public status: public title: 'QMoE: Sub-1-bit compression of trillion parameter models' type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 6 year: '2024' ... --- _id: '18062' abstract: - lang: eng text: 'We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements. We provide pruning and scaling law fitting code at: github.com/google-research/jaxpruner/tree/main/jaxpruner/projects/bigsparse.' article_processing_charge: No arxiv: 1 author: - first_name: Elias full_name: Frantar, Elias id: 09a8f98d-ec99-11ea-ae11-c063a7b7fe5f last_name: Frantar - first_name: Carlos Riquelme full_name: Ruiz, Carlos Riquelme last_name: Ruiz - first_name: Neil full_name: Houlsby, Neil last_name: Houlsby - first_name: Dan-Adrian full_name: Alistarh, Dan-Adrian id: 4A899BFC-F248-11E8-B48F-1D18A9856A87 last_name: Alistarh orcid: 0000-0003-3650-940X - first_name: Utku full_name: Evci, Utku last_name: Evci citation: ama: 'Frantar E, Ruiz CR, Houlsby N, Alistarh D-A, Evci U. Scaling laws for sparsely-connected foundation models. In: The Twelfth International Conference on Learning Representations. ; 2024.' apa: Frantar, E., Ruiz, C. R., Houlsby, N., Alistarh, D.-A., & Evci, U. (2024). Scaling laws for sparsely-connected foundation models. In The Twelfth International Conference on Learning Representations. Vienna, Austria. chicago: Frantar, Elias, Carlos Riquelme Ruiz, Neil Houlsby, Dan-Adrian Alistarh, and Utku Evci. “Scaling Laws for Sparsely-Connected Foundation Models.” In The Twelfth International Conference on Learning Representations, 2024. ieee: E. Frantar, C. R. Ruiz, N. Houlsby, D.-A. Alistarh, and U. Evci, “Scaling laws for sparsely-connected foundation models,” in The Twelfth International Conference on Learning Representations, Vienna, Austria, 2024. ista: 'Frantar E, Ruiz CR, Houlsby N, Alistarh D-A, Evci U. 2024. Scaling laws for sparsely-connected foundation models. The Twelfth International Conference on Learning Representations. ICLR: International Conference on Learning Representations.' mla: Frantar, Elias, et al. “Scaling Laws for Sparsely-Connected Foundation Models.” The Twelfth International Conference on Learning Representations, 2024. short: E. Frantar, C.R. Ruiz, N. Houlsby, D.-A. Alistarh, U. Evci, in:, The Twelfth International Conference on Learning Representations, 2024. conference: end_date: 2024-05-07 location: Vienna, Austria name: 'ICLR: International Conference on Learning Representations' start_date: 2024-05-07 corr_author: '1' date_created: 2024-09-13T10:31:08Z date_published: 2024-01-16T00:00:00Z date_updated: 2026-04-07T12:43:03Z day: '16' department: - _id: DaAl external_id: arxiv: - '2309.08520' language: - iso: eng main_file_link: - open_access: '1' url: https://openreview.net/forum?id=i9K2ZWkYIP month: '01' oa: 1 oa_version: Published Version publication: The Twelfth International Conference on Learning Representations publication_status: published quality_controlled: '1' related_material: record: - id: '17485' relation: dissertation_contains status: public scopus_import: '1' status: public title: Scaling laws for sparsely-connected foundation models type: conference user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: publisher _id: '17208' abstract: - lang: eng text: "Can current quantum computers provide a speedup over their classical counterparts for some kinds of problems? In this thesis, with a focus on ground state search/preparation, we address some of the challenges that both quantum annealing and variational quantum algorithms suffer from, hindering any possible practical speedup in comparison to the best classical counterparts. \r\n\r\nIn the first part of the thesis, we study the performance of quantum annealing for solving a particular combinatorial optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$. We consider how modifying the initial problem, by adding more interaction terms to the corresponding Hamiltonian, leads to the emergence of a first-order phase transition during the annealing process. This phenomenon causes the total annealing duration, $T$, required to prepare the ground state of $H_C$ with a high probability to increase exponentially with the size of the problem. Our findings indicate that with the growing complexity of problem instances, the likelihood of encountering first-order phase transitions also increases, making quantum annealing an impractical solution for these types of combinatorial optimization problems.\r\n\r\nIn the second part, we focus on the problem of barren plateaus in generic variational quantum algorithms. Barren plateaus correspond to flat regions in the parameter space where the gradient of the cost function is zero in expectation, and with the variance decaying exponentially with the system size, thus obstructing an efficient parameter optimization. We propose an algorithm to circumvent Barren Plateaus by monitoring the entanglement entropy of k-local reduced density matrices, alongside a method for estimating entanglement entropy via classical shadow tomography. We illustrate the approach with the paradigmatic example of the variational quantum eigensolver, and show that our algorithm effectively avoids barren plateaus in the initialization as well as during the optimization stage. \r\n\r\nLastly, in the last two Chapters of this thesis, we focus on the quantum approximate optimization algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial optimization problems in near-term quantum devices. Specifically, we focus on how to develop rigorous initialization strategies with guarantee improvement. Our motivation for this study lies in that for random initialization, the optimization typically leads to local minima with poor performance. Our main result corresponds to the analytical construction of index-1 saddle points or transition states, stationary points with a single direction of descent, as a tool for systematically exploring the QAOA optimization landscape. This leads us to propose a novel greedy parameter initialization strategy that guarantees for the energy to decrease with an increasing number of circuit layers. Furthermore, with precise estimates for the negative Hessian eigenvalue and its eigenvector, we establish a lower bound for energy improvement following a QAOA iteration." acknowledged_ssus: - _id: ScienComp alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Raimel A full_name: Medina Ramos, Raimel A id: CE680B90-D85A-11E9-B684-C920E6697425 last_name: Medina Ramos orcid: 0000-0002-5383-2869 citation: ama: Medina Ramos RA. Exploring the optimization landscape of variational quantum algorithms. 2024. doi:10.15479/at:ista:17208 apa: Medina Ramos, R. A. (2024). Exploring the optimization landscape of variational quantum algorithms. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17208 chicago: Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational Quantum Algorithms.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17208. ieee: R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum algorithms,” Institute of Science and Technology Austria, 2024. ista: Medina Ramos RA. 2024. Exploring the optimization landscape of variational quantum algorithms. Institute of Science and Technology Austria. mla: Medina Ramos, Raimel A. Exploring the Optimization Landscape of Variational Quantum Algorithms. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17208. short: R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum Algorithms, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-07-09T09:14:24Z date_published: 2024-07-09T00:00:00Z date_updated: 2026-04-07T12:43:22Z day: '09' ddc: - '539' degree_awarded: PhD department: - _id: GradSch - _id: MaSe doi: 10.15479/at:ista:17208 ec_funded: 1 file: - access_level: closed checksum: 6f45273d04f4418bc2adc018baed0525 content_type: application/zip creator: rmedinar date_created: 2024-07-09T09:21:44Z date_updated: 2024-07-10T11:34:09Z file_id: '17212' file_name: Raimel_Thesis-Final.zip file_size: '14218691' relation: source_file - access_level: open_access checksum: 6724a95bec772dbabc0111b9f08a805e content_type: application/pdf creator: rmedinar date_created: 2024-07-17T09:23:24Z date_updated: 2024-07-17T09:23:24Z file_id: '17275' file_name: Raimel_Thesis-20_pdfa.pdf file_size: 11253627 relation: main_file success: 1 file_date_updated: 2024-07-17T09:23:24Z has_accepted_license: '1' keyword: - Quantum computing - Variational Quantum Algorithms - Optimization language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '133' project: - _id: 23841C26-32DE-11EA-91FC-C7463DDC885E call_identifier: H2020 grant_number: '850899' name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control' publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '10545' relation: part_of_dissertation status: public - id: '10067' relation: part_of_dissertation status: public - id: '17222' relation: part_of_dissertation status: public - id: '13125' relation: part_of_dissertation status: public - id: '11471' relation: part_of_dissertation status: public status: public supervisor: - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 title: Exploring the optimization landscape of variational quantum algorithms tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: repository _id: '17222' abstract: - lang: eng text: "The quantum approximate optimization algorithm (QAOA) uses a quantum computer\r\nto implement a variational method with $2p$ layers of alternating unitary\r\noperators, optimized by a classical computer to minimize a cost function. While\r\nrigorous performance guarantees exist for the QAOA at small depths $p$, the\r\nbehavior at large depths remains less clear, though simulations suggest\r\nexponentially fast convergence for certain problems. In this work, we gain\r\ninsights into the deep QAOA using an analytic expansion of the cost function\r\naround transition states. Transition states are constructed in a recursive\r\nmanner: from the local minima of the QAOA with $p$ layers we obtain transition\r\nstates of the QAOA with $p+1$ layers, which are stationary points characterized\r\nby a unique direction of negative curvature. We construct an analytic estimate\r\nof the negative curvature and the corresponding direction in parameter space at\r\neach transition state. The expansion of the QAOA cost function along the\r\nnegative direction to the quartic order gives a lower bound of the QAOA cost\r\nfunction improvement. We provide physical intuition behind the analytic\r\nexpressions for the local curvature and quartic expansion coefficient. Our\r\nnumerical study confirms the accuracy of our approximations and reveals that\r\nthe obtained bound and the true value of the QAOA cost function gain have a\r\ncharacteristic exponential decrease with the number of layers $p$, with the\r\nbound decreasing more rapidly. Our study establishes an analytical method for\r\nrecursively studying the QAOA that is applicable in the regime of high circuit\r\ndepth." article_number: '2405.10125' article_processing_charge: No arxiv: 1 author: - first_name: Raimel A full_name: Medina Ramos, Raimel A id: CE680B90-D85A-11E9-B684-C920E6697425 last_name: Medina Ramos orcid: 0000-0002-5383-2869 - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 citation: ama: Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. arXiv. doi:10.48550/arXiv.2405.10125 apa: Medina Ramos, R. A., & Serbyn, M. (n.d.). A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. arXiv. https://doi.org/10.48550/arXiv.2405.10125 chicago: Medina Ramos, Raimel A, and Maksym Serbyn. “A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2405.10125. ieee: R. A. Medina Ramos and M. Serbyn, “A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm,” arXiv. . ista: Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. arXiv, 2405.10125. mla: Medina Ramos, Raimel A., and Maksym Serbyn. “A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm.” ArXiv, 2405.10125, doi:10.48550/arXiv.2405.10125. short: R.A. Medina Ramos, M. Serbyn, ArXiv (n.d.). corr_author: '1' date_created: 2024-07-10T13:12:09Z date_published: 2024-05-16T00:00:00Z date_updated: 2026-04-07T12:43:22Z day: '16' department: - _id: MaSe doi: 10.48550/arXiv.2405.10125 external_id: arxiv: - '2405.10125' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.10125 month: '05' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '17208' relation: dissertation_contains status: public status: public title: A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_place: publisher _id: '18132' abstract: - lang: eng text: "In this thesis, we are dealing with both arithmetic and geometric problems coming from the\r\nstudy of rational points with a particular focus on function fields over finite fields:\r\n(1) Using the circle method we produce upper bounds for the number of rational points of\r\nbounded height on diagonal cubic surfaces and fourfolds over Fq(t). This is based on\r\njoint work with Leonhard Hochfilzer.\r\n(2) We study rational points on smooth complete intersections X defined by cubic and\r\nquadratic hypersurfaces over Fq(t). We refine the Farey dissection of the “unit square”\r\ndeveloped by Vishe [202] and use the circle method with a Kloosterman refinement to\r\nestablish an asymptotic formula for the number of rational points of bounded height on\r\nX when dim(X) ≥ 23. Under the same hypotheses, we also verify weak approximation.\r\n(3) In joint work with Hochfilzer, we obtain upper bounds for the number of rational points of\r\nbounded height on del Pezzo surfaces of low degree over any global field. Our approach\r\nis to take hyperplane sections, which reduces the problem to uniform estimates for the\r\nnumber of rational points on curves.\r\n(4) We develop a version of the circle method capable of counting Fq-points on jet schemes\r\nof moduli spaces of rational curves on hypersurfaces. Combining this with a spreading\r\nout argument and a result of Mustaţă [150], this allows us to show that these moduli\r\nspaces only have canonical singularities under suitable assumptions on the degree and the\r\ndimension.\r\nIn addition, we give an overview of guiding questions and conjectures in the field of rational\r\npoints and explain the basic mechanism underlying the circle method.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Counting rational points over function fields. 2024. doi:10.15479/at:ista:18132 apa: Glas, J. (2024). Counting rational points over function fields. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18132 chicago: Glas, Jakob. “Counting Rational Points over Function Fields.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18132. ieee: J. Glas, “Counting rational points over function fields,” Institute of Science and Technology Austria, 2024. ista: Glas J. 2024. Counting rational points over function fields. Institute of Science and Technology Austria. mla: Glas, Jakob. Counting Rational Points over Function Fields. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18132. short: J. Glas, Counting Rational Points over Function Fields, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-09-23T18:58:08Z date_published: 2024-09-23T00:00:00Z date_updated: 2026-04-07T12:53:54Z day: '23' ddc: - '512' degree_awarded: PhD department: - _id: GradSch - _id: TiBr doi: 10.15479/at:ista:18132 file: - access_level: closed checksum: 2f8cf5cefdab108b1979caa8146cae9a content_type: application/x-zip-compressed creator: jglas date_created: 2024-09-23T18:49:22Z date_updated: 2024-09-23T18:49:22Z file_id: '18133' file_name: PhDthesis (3).zip file_size: 5382106 relation: source_file - access_level: open_access checksum: 08bb6f14c42b47ff25882a2ce3ea0d8a content_type: application/pdf creator: jglas date_created: 2024-09-25T14:08:57Z date_updated: 2024-09-25T14:08:57Z file_id: '18140' file_name: example-phd.pdf file_size: 2380127 relation: main_file success: 1 file_date_updated: 2024-09-25T14:08:57Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '195' project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '18293' relation: part_of_dissertation status: public - id: '18294' relation: part_of_dissertation status: public - id: '18295' relation: part_of_dissertation status: public - id: '18173' relation: part_of_dissertation status: public status: public supervisor: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 title: Counting rational points over function fields tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- _id: '18173' abstract: - lang: eng text: Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation. acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and Pankaj Vishe for useful comments. Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise in exponential sums and geometry. While working on this paper, the author was supported by FWF grant (DOI 10.55776/P36278). article_number: e12991 article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 2024;110(4). doi:10.1112/jlms.12991 apa: Glas, J. (2024). Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.12991 chicago: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.12991. ieee: J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t),” Journal of the London Mathematical Society, vol. 110, no. 4. London Mathematical Society, 2024. ista: Glas J. 2024. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4), e12991. mla: Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society, vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:10.1112/jlms.12991. short: J. Glas, Journal of the London Mathematical Society 110 (2024). corr_author: '1' date_created: 2024-10-06T22:01:11Z date_published: 2024-10-01T00:00:00Z date_updated: 2026-04-07T12:53:53Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1112/jlms.12991 external_id: arxiv: - '2306.02718' file: - access_level: open_access checksum: 11ebf690363151026ce81f91f2220855 content_type: application/pdf creator: dernst date_created: 2024-10-07T08:51:01Z date_updated: 2024-10-07T08:51:01Z file_id: '18181' file_name: 2024_JLondonMathSoc_Glas.pdf file_size: 579601 relation: main_file success: 1 file_date_updated: 2024-10-07T08:51:01Z has_accepted_license: '1' intvolume: ' 110' issue: '4' language: - iso: eng month: '10' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: London Mathematical Society quality_controlled: '1' related_material: record: - id: '18132' relation: dissertation_contains status: public scopus_import: '1' status: public title: Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t) tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 110 year: '2024' ... --- OA_place: repository _id: '18295' abstract: - lang: eng text: By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d. article_processing_charge: No arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas citation: ama: Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv. doi:10.48550/arXiv.2405.16648 apa: Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv. https://doi.org/10.48550/arXiv.2405.16648 chicago: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2405.16648. ieee: J. Glas, “Canonical singularities on moduli spaces of rational curves via the  circle method,” arXiv. . ista: Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv, 10.48550/arXiv.2405.16648. mla: Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” ArXiv, doi:10.48550/arXiv.2405.16648. short: J. Glas, ArXiv (n.d.). corr_author: '1' date_created: 2024-10-10T13:15:43Z date_published: 2024-05-26T00:00:00Z date_updated: 2026-04-07T12:53:53Z day: '26' department: - _id: TiBr doi: 10.48550/arXiv.2405.16648 external_id: arxiv: - '2405.16648' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.16648 month: '05' oa: 1 oa_version: Preprint project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: arXiv publication_status: submitted related_material: record: - id: '19013' relation: later_version status: public - id: '18132' relation: dissertation_contains status: public status: public title: Canonical singularities on moduli spaces of rational curves via the circle method tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: publisher _id: '18667' abstract: - lang: eng text: "Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability." acknowledgement: "I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 citation: ama: Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:10.15479/at:ista:18667 apa: Heiss, T. (2024). New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18667 chicago: Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18667. ieee: T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024. ista: Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria. mla: Heiss, Teresa. New Methods for Applying Topological Data Analysis to Materials Science. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18667. short: T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-12-17T16:17:55Z date_published: 2024-12-17T00:00:00Z date_updated: 2026-04-07T12:54:10Z day: '17' ddc: - '514' - '516' - '004' degree_awarded: PhD department: - _id: GradSch - _id: HeEd doi: 10.15479/at:ista:18667 ec_funded: 1 file: - access_level: open_access checksum: 247bb057aed2fba1cd4711917aaa2d77 content_type: application/pdf creator: theiss date_created: 2024-12-19T10:24:46Z date_updated: 2024-12-19T10:24:46Z file_id: '18686' file_name: Teresa_Heiss_PhD_Thesis_final.pdf file_size: 7752253 relation: main_file success: 1 - access_level: closed checksum: 9648b45c07a008ee11a07f99856a139d content_type: application/zip creator: theiss date_created: 2024-12-19T10:24:50Z date_updated: 2024-12-19T10:24:50Z file_id: '18687' file_name: PhD_Thesis.zip file_size: 17197731 relation: source_file file_date_updated: 2024-12-19T10:24:50Z has_accepted_license: '1' keyword: - persistent homology - topological data analysis - periodic - crystalline materials - images - fingerprint language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: '111' project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended publication_identifier: isbn: - 978-3-99078-052-7 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '10828' relation: part_of_dissertation status: public - id: '11440' relation: part_of_dissertation status: public - id: '18673' relation: part_of_dissertation status: public - id: '9345' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: New methods for applying topological data analysis to materials science tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: repository _id: '18673' abstract: - lang: eng text: "Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability under perturbations and provide an algorithm that under mild geometric conditions typically satisfied by crystalline materials takes O((n+m)logn) time, in which n and m are the numbers of vertices and edges in the quotient complex, respectively.\r\n" acknowledgement: "Both authors are partially supported by the European Research Council (ERC) Horizon 2020 project\r\n‘Alpha Shape Theory Extended’, grant no. 788183. The first author is also partially supported by the DFG\r\nCollaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund\r\n(FWF), grant no. I 02979-N35." article_processing_charge: No arxiv: 1 author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 citation: ama: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv. doi:10.48550/arXiv.2408.16575 apa: Edelsbrunner, H., & Heiss, T. (n.d.). Merge trees of periodic filtrations. arXiv. https://doi.org/10.48550/arXiv.2408.16575 chicago: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.16575. ieee: H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” arXiv. . ista: Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, 10.48550/arXiv.2408.16575. mla: Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” ArXiv, doi:10.48550/arXiv.2408.16575. short: H. Edelsbrunner, T. Heiss, ArXiv (n.d.). corr_author: '1' date_created: 2024-12-18T14:06:57Z date_published: 2024-08-29T00:00:00Z date_updated: 2026-04-07T12:54:09Z day: '29' department: - _id: HeEd doi: 10.48550/arXiv.2408.16575 ec_funded: 1 external_id: arxiv: - '2408.16575' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2408.16575 month: '08' oa: 1 oa_version: Preprint project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: arXiv publication_status: draft related_material: record: - id: '18667' relation: dissertation_contains status: public status: public title: Merge trees of periodic filtrations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_place: publisher _id: '14711' abstract: - lang: eng text: "In nature, different species find their niche in a range of environments, each with its unique characteristics. While some thrive in uniform (homogeneous) landscapes where environmental conditions stay relatively consistent across space, others traverse the complexities of spatially heterogeneous terrains. Comprehending how species are distributed and how they interact within these landscapes holds the key to gaining insights into their evolutionary dynamics while also informing conservation and management strategies.\r\n\r\nFor species inhabiting heterogeneous landscapes, when the rate of dispersal is low compared to spatial fluctuations in selection pressure, localized adaptations may emerge. Such adaptation in response to varying selection strengths plays an important role in the persistence of populations in our rapidly changing world. Hence, species in nature are continuously in a struggle to adapt to local environmental conditions, to ensure their continued survival. Natural populations can often adapt in time scales short enough for evolutionary changes to influence ecological dynamics and vice versa, thereby creating a feedback between evolution and demography. The analysis of this feedback and the relative contributions of gene flow, demography, drift, and natural selection to genetic variation and differentiation has remained a recurring theme in evolutionary biology. Nevertheless, the effective role of these forces in maintaining variation and shaping patterns of diversity is not fully understood. Even in homogeneous environments devoid of local adaptations, such understanding remains elusive. Understanding this feedback is crucial, for example in determining the conditions under which extinction risk can be mitigated in peripheral populations subject to deleterious mutation accumulation at the edges of species’ ranges\r\nas well as in highly fragmented populations.\r\n\r\nIn this thesis we explore both uniform and spatially heterogeneous metapopulations, investigating and providing theoretical insights into the dynamics of local adaptation in the latter and examining the dynamics of load and extinction as well as the impact of joint ecological and evolutionary (eco-evolutionary) dynamics in the former. The thesis is divided into 5 chapters.\r\n\r\nChapter 1 provides a general introduction into the subject matter, clarifying concepts and ideas used throughout the thesis. In chapter 2, we explore how fast a species distributed across a heterogeneous landscape adapts to changing conditions marked by alterations in carrying capacity, selection pressure, and migration rate.\r\n\r\nIn chapter 3, we investigate how migration selection and drift influences adaptation and the maintenance of variation in a metapopulation with three habitats, an extension of previous models of adaptation in two habitats. We further develop analytical approximations for the critical threshold required for polymorphism to persist.\r\n\r\nThe focus of chapter 4 of the thesis is on understanding the interplay between ecology and evolution as coupled processes. We investigate how eco-evolutionary feedback between migration, selection, drift, and demography influences eco-evolutionary outcomes in marginal populations subject to deleterious mutation accumulation. Using simulations as well as theoretical approximations of the coupled dynamics of population size and allele frequency, we analyze how gene flow from a large mainland source influences genetic load and population size on an island (i.e., in a marginal population) under genetically realistic assumptions. Analyses of this sort are important because small isolated populations, are repeatedly affected by complex interactions between ecological and evolutionary processes, which can lead to their death. Understanding these interactions can therefore provide an insight into the conditions under which extinction risk can be mitigated in peripheral populations thus, contributing to conservation and restoration efforts.\r\n\r\nChapter 5 extends the analysis in chapter 4 to consider the dynamics of load (due to deleterious mutation accumulation) and extinction risk in a metapopulation. We explore the role of gene flow, selection, and dominance on load and extinction risk and further pinpoint critical thresholds required for metapopulation persistence.\r\n\r\nOverall this research contributes to our understanding of ecological and evolutionary mechanisms that shape species’ persistence in fragmented landscapes, a crucial foundation for successful conservation efforts and biodiversity management." acknowledged_ssus: - _id: SSU alternative_title: - ISTA Thesis 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 citation: ama: Olusanya OO. Local adaptation, genetic load and extinction in metapopulations. 2024. doi:10.15479/at:ista:14711 apa: Olusanya, O. O. (2024). Local adaptation, genetic load and extinction in metapopulations. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14711 chicago: Olusanya, Oluwafunmilola O. “Local Adaptation, Genetic Load and Extinction in Metapopulations.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:14711. ieee: O. O. Olusanya, “Local adaptation, genetic load and extinction in metapopulations,” Institute of Science and Technology Austria, 2024. ista: Olusanya OO. 2024. Local adaptation, genetic load and extinction in metapopulations. Institute of Science and Technology Austria. mla: Olusanya, Oluwafunmilola O. Local Adaptation, Genetic Load and Extinction in Metapopulations. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:14711. short: O.O. Olusanya, Local Adaptation, Genetic Load and Extinction in Metapopulations, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2023-12-26T22:49:53Z date_published: 2024-01-19T00:00:00Z date_updated: 2026-04-07T12:54:29Z day: '19' ddc: - '576' degree_awarded: PhD department: - _id: NiBa - _id: GradSch doi: 10.15479/at:ista:14711 ec_funded: 1 file: - access_level: closed checksum: de179b1c6758f182ff0c70d8b38c1501 content_type: application/zip creator: oolusany date_created: 2024-01-03T18:30:13Z date_updated: 2024-01-03T18:30:13Z file_id: '14730' file_name: FinalSubmission_Thesis_OLUSANYA.zip file_size: 16986244 relation: source_file - access_level: open_access checksum: 0e331585e3cd4823320aab4e69e64ccf content_type: application/pdf creator: oolusany date_created: 2024-01-03T18:31:34Z date_updated: 2024-01-03T18:31:34Z file_id: '14731' file_name: FinalSubmission2_Thesis_OLUSANYA.pdf file_size: 6460403 relation: main_file success: 1 file_date_updated: 2024-01-03T18:31:34Z has_accepted_license: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: '183' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program - _id: c08d3278-5a5b-11eb-8a69-fdb09b55f4b8 grant_number: P32896 name: Causes and consequences of population fragmentation - _id: 34c872fe-11ca-11ed-8bc3-8534b82131e6 grant_number: '26380' name: Polygenic Adaptation in a Metapopulation publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '10787' relation: part_of_dissertation status: public - id: '10658' relation: part_of_dissertation status: public - id: '14732' relation: part_of_dissertation status: public status: public supervisor: - first_name: Nicholas H full_name: Barton, Nicholas H id: 4880FE40-F248-11E8-B48F-1D18A9856A87 last_name: Barton orcid: 0000-0002-8548-5240 - first_name: Jitka full_name: Polechova, Jitka last_name: Polechova - first_name: Himani full_name: Sachdeva, Himani last_name: Sachdeva title: Local adaptation, genetic load and extinction in metapopulations tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: publisher _id: '17156' abstract: - lang: eng text: "This dissertation is the summary of the author’s work, concerning the relations between\r\ncohomology rings of algebraic varieties and rings of functions on zero schemes and fixed\r\npoint schemes. For most of the thesis, the focus is on smooth complex varieties with\r\nan action of a principally paired group, e.g. a parabolic subgroup of a reductive group.\r\nThe fundamental theorem 5.2.11 from co-authored article [66] says that if the principal\r\nnilpotent has a unique zero, then the zero scheme over the Kostant section is isomorphic\r\nto the spectrum of the equivariant cohomology ring, remembering the grading in terms of\r\na C^* action. A similar statement is proved also for the G-invariant functions on the total\r\nzero scheme over the whole Lie algebra. Additionally, we are able to prove an analogous\r\nresult for the GKM spaces, which poses the question on a joint generalisation.\r\nWe also tackle the situation of a singular variety. As long as it is embedded in a smooth\r\nvariety with regular action, we are able to study its cohomology as well by means of\r\nthe zero scheme. In case of e.g. Schubert varieties this determines the cohomology ring\r\ncompletely. In largest generality, this allows us to see a significant part of the cohomology\r\nring.\r\nWe also show (Theorem 6.2.1) that the cohomology ring of spherical varieties appears as\r\nthe ring of functions on the zero scheme. The computational aspect is not easy, but one\r\ncan hope that this can bring some concrete information about such cohomology rings.\r\nLastly, the K-theory conjecture 6.3.1 is studied, with some results attained for GKM\r\nspaces.\r\nThe thesis includes also an introduction to group actions on algebraic varieties. In\r\nparticular, the vector fields associated to the actions are extensively studied. We also\r\nprovide a version of the Kostant section for arbitrary principally paired group, which\r\nparametrises the regular orbits in the Lie algebra of an algebraic group. Before proving\r\nthe main theorem, we also include a historical overview of the field. In particular we bring\r\ntogether the results of Akyildiz, Carrell and Lieberman on non-equivariant cohomology\r\nrings." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Kamil P full_name: Rychlewicz, Kamil P id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425 last_name: Rychlewicz citation: ama: Rychlewicz KP. Equivariant cohomology and rings of functions. 2024. doi:10.15479/at:ista:17156 apa: Rychlewicz, K. P. (2024). Equivariant cohomology and rings of functions. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17156 chicago: Rychlewicz, Kamil P. “Equivariant Cohomology and Rings of Functions.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17156. ieee: K. P. Rychlewicz, “Equivariant cohomology and rings of functions,” Institute of Science and Technology Austria, 2024. ista: Rychlewicz KP. 2024. Equivariant cohomology and rings of functions. Institute of Science and Technology Austria. mla: Rychlewicz, Kamil P. Equivariant Cohomology and Rings of Functions. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17156. short: K.P. Rychlewicz, Equivariant Cohomology and Rings of Functions, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-06-23T15:07:06Z date_published: 2024-06-25T00:00:00Z date_updated: 2026-04-07T12:55:46Z day: '25' ddc: - '516' degree_awarded: PhD department: - _id: TaHa - _id: GradSch doi: 10.15479/at:ista:17156 file: - access_level: closed checksum: 1610063569f5452f8a5acef728c2fc26 content_type: application/zip creator: krychlew date_created: 2024-06-26T20:56:27Z date_updated: 2024-06-26T21:00:14Z file_id: '17179' file_name: thesis.zip file_size: 2761814 relation: source_file - access_level: open_access checksum: 7bbadb1fbc9ed2a1ecf54597f88af99c content_type: application/pdf creator: krychlew date_created: 2024-06-26T20:58:24Z date_updated: 2024-06-26T20:58:24Z file_id: '17180' file_name: thesis.pdf file_size: 3695952 relation: main_file file_date_updated: 2024-06-26T21:00:14Z has_accepted_license: '1' keyword: - equivariant cohomology - zero schemes - algebraic groups - Lie algebras language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: '117' project: - _id: 34cd0f74-11ca-11ed-8bc3-bf0492a14a24 grant_number: '26525' name: Topology of open smooth varieties with a torus action publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '17157' relation: part_of_dissertation status: public status: public supervisor: - first_name: Tamás full_name: Hausel, Tamás id: 4A0666D8-F248-11E8-B48F-1D18A9856A87 last_name: Hausel orcid: 0000-0002-9582-2634 title: Equivariant cohomology and rings of functions tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: publisher OA_type: gold _id: '18515' abstract: - lang: eng text: "Understanding the role of evolutionary processes in shaping genetic variation has been a\r\nprimary goal in evolutionary genetics. In this regard, a key question is how genetically\r\ndistinct populations evolve in the face of gene flow, thereby generating genetic and\r\nphenotypic divergence and reproductive isolation (RI). This requires quantifying the role\r\nand relative contributions of prezygotic and postzygotic isolating mechanisms on the\r\nreduction of gene exchange between populations, and identifying regions in the genome\r\nthat mediate RI, which is often polygenic. Further, this needs distinguishing neutral and\r\nselected regions in the genome, and discerning how selection influences patterns of neutral\r\ndivergence.\r\nPopulation structure, defined as any deviation from panmixia, such as geographic distribution, movement and mating patterns of individuals, influences how genetic variation is\r\nstructured in space and shapes the neutral null model. Availability of large scale spatial\r\ngenomic datasets now enables us to detect signatures of population structure in genetic\r\ndata and infer population genetic parameters. Such inferences are crucial and have wide\r\napplications in biodiversity, conservation genetics, population management and medical\r\ngenetics. However, inferences are based on assumptions that do not always match the\r\ncomplex reality, thus leading to erroneous conclusions. Moreover, the role and interaction\r\nof heterogeneous population density and dispersal, which are ubiquitous in nature, has\r\nbeen challenging to study owing to their mathematical complexity. In such scenarios,\r\nfeedback between theory, data and simulations can prove to be useful.\r\nIn this thesis, I examine the effect of population structure on neutral genetic variation\r\nand barriers to gene exchange in hybridising populations, thereby bridging together the\r\nfields of spatial population genetics and speciation.\r\nDespite being a key concept in speciation, reproductive isolation (RI) lacks a quantitative\r\ndefinition and has been used and measured differently across different fields. Chapter 2\r\ngives a quantitative definition of RI, in terms of the effect of genetic differences on gene\r\nflow. We give analytical predictions for RI in a range of scenarios, in terms of effective migration rates for discrete populations and barrier strength for continuous populations.\r\nIn addition to this, we discuss current measures of RI and their limitations, and propose\r\nthe need for new measures that combine organismal and genetic perspectives of RI.\r\nIn chapter 3, I examine the combined effect of assortative mating, sexual selection\r\nand viability selection on RI. For this, we consider a polygenic ‘magic’ trait under a\r\nmainland-island model. We obtain novel theoretical predictions for molecular divergence\r\nin terms of effective migration rates, which bears a simple relationship to measurable\r\nfitness components of migrants and various early generation hybrids. We explore the\r\nconditions under which local adaptation can be maintained despite maladaptive gene flow\r\nand quantify the relative contributions of viability and sexual selection to genome-wide\r\nbarriers to gene flow.\r\nThe next two chapters of the thesis focus on a hybrid zone of Antirrhinum majus that\r\nconsist of two subspecies- the magenta flowered A. m. pseudomajus and the yellow\r\nflowered A.m. striatum. Previous studies have suggested that flower colour is target of\r\npollinator mediated selection and is influenced only by few genes. While these regions\r\nshow high genetic differentiation between the subspecies, the rest of the genome is seen\r\nto be well mixed. Chapter 4 examines the effects of heterogeneous population density\r\nand leptokurtic dispersal on isolation by distance and the distribution of heterozygosity\r\nby focusing on non-flower colour markers.\r\nChapter 5 analyses cline shapes and associations among 6 focal flower colour markers to\r\nunderstand how selection and dispersal maintain this hybrid zone. We see sharp coincident\r\nstepped clines at all loci and positive associations throughout the hybrid zone, contrary to\r\nthe expected patterns from diffusive gene flow. With a novel scheme of inferring dispersal\r\ncombined with multilocus simulations, we show that stepped clines do not reflect genetic\r\nbarriers to gene flow, but are rather a result of long-distance migration. This framework\r\nallows us to get realistic estimates gene flow and selection and shows how traditional cline\r\nanalysis may lead to inaccurate conclusions when assumptions of the theory are not met.\r\nOverall, this thesis investigates how different features of population structure leave\r\ndetectable signatures in genetic variation, namely in patterns of isolation by distance,\r\nlinkage disequilibrium and genetic divergence. It also highlights how effective migration\r\nrates provide useful way of analysing polygenic architectures and shed new light into\r\nhybrid zones. In doing so, I identify scenarios when simple models become insufficient\r\nand suggest possibe directions by combining genetic data with simulations." acknowledged_ssus: - _id: ScienComp acknowledgement: "I also acknowledge the funding agencies Marie Curie COFUND Doctoral Fellowship,\r\nAustrian Science Fund FWF (grant P32166) and ERC (grant PR1000ERC02) for financially\r\nsupporting my research over the years." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Parvathy full_name: Surendranadh, Parvathy id: 455235B8-F248-11E8-B48F-1D18A9856A87 last_name: Surendranadh orcid: 0000-0001-6395-386X citation: ama: Surendranadh P. Effect of population structure on neutral genetic variation and barriers to gene exchange. 2024. doi:10.15479/at:ista:18515 apa: Surendranadh, P. (2024). Effect of population structure on neutral genetic variation and barriers to gene exchange. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18515 chicago: Surendranadh, Parvathy. “Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18515. ieee: P. Surendranadh, “Effect of population structure on neutral genetic variation and barriers to gene exchange,” Institute of Science and Technology Austria, 2024. ista: Surendranadh P. 2024. Effect of population structure on neutral genetic variation and barriers to gene exchange. Institute of Science and Technology Austria. mla: Surendranadh, Parvathy. Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18515. short: P. Surendranadh, Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-11-06T21:25:37Z date_published: 2024-11-07T00:00:00Z date_updated: 2026-04-07T12:56:52Z day: '07' ddc: - '576' degree_awarded: PhD department: - _id: GradSch - _id: NiBa doi: 10.15479/at:ista:18515 file: - access_level: open_access checksum: c32cf7bc75748d9c551d8eb70178bbec content_type: application/pdf creator: psurendr date_created: 2024-11-07T10:59:29Z date_updated: 2024-11-07T10:59:29Z file_id: '18519' file_name: PhD_Thesis__Parvathy_071124_PDFA.pdf file_size: 37019760 relation: main_file success: 1 - access_level: closed checksum: 4417e02d54084d89e75734e18caaa96d content_type: application/zip creator: psurendr date_created: 2024-11-07T10:59:42Z date_updated: 2024-11-07T10:59:42Z file_id: '18520' file_name: PhD Thesis- Parvathy_071124.zip file_size: 41198857 relation: source_file file_date_updated: 2024-11-07T10:59:42Z has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: '219' project: - _id: 05959E1C-7A3F-11EA-A408-12923DDC885E grant_number: P32166 name: Snapdragon Speciation - _id: bd6958e0-d553-11ed-ba76-86eba6a76c00 grant_number: '101055327' name: Understanding the evolution of continuous genomes publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria status: public supervisor: - first_name: Nicholas H full_name: Barton, Nicholas H id: 4880FE40-F248-11E8-B48F-1D18A9856A87 last_name: Barton orcid: 0000-0002-8548-5240 title: Effect of population structure on neutral genetic variation and barriers to gene exchange tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: repository _id: '18689' abstract: - lang: eng text: Multiplexed fluorescence microscopy imaging is widely used in biomedical applications. However, simultaneous imaging of multiple fluorophores can result in spectral leaks and overlapping, which greatly degrades image quality and subsequent analysis. Existing popular spectral unmixing methods are mainly based on computational intensive linear models and the performance is heavily dependent on the reference spectra, which may greatly preclude its further applications. In this paper, we propose a deep learning-based blindly spectral unmixing method, termed AutoUnmix, to imitate the physical spectral mixing process. A tranfer learning framework is further devised to allow our AutoUnmix adapting to a variety of imaging systems without retraining the network. Our proposed method has demonstrated real-time unmixing capabilities, surpassing existing methods by up to 100-fold in terms of unmixing speed. We further validate the reconstruction performance on both synthetic datasets and biological samples. The unmixing results of AutoUnmix achieve a highest SSIM of 0.99 in both three- and four-color imaging, with nearly up to 20% higher than other popular unmixing methods. Due to the desirable property of data independency and superior blind unmixing performance, we believe AutoUnmix is a powerful tool to study the interaction process of different organelles labeled by multiple fluorophores. acknowledged_ssus: - _id: Bio - _id: LifeSc - _id: M-Shop - _id: E-Lib acknowledgement: "We gratefully acknowledge support by the Scientific Service Units at ISTA, including the Imaging and Optics and Lab Support facilities and the mechanical workshop and Library. We thank Philipp Velicky for STED microscope alignment.\r\n\r\nThis project has received funding from the Austrian Science Fund (FWF): I 3630-B25 (J.G.D) and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 742985, J.F.). It has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385. S.T. has received funding as an ISTplus Fellow from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skłodowska-Curie grant agreement no. 754411 and from an EMBO Long-Term Fellowship (grant number ALTF 679-2018). It has further received funding from the Austrian Science Fund (FWF) grant DK W1232 (M.T, N.A-D., J.G.D). W.J. received funding via a Human Frontier Science Program postdoctoral fellowship LT000557/2018.\r\n\r\nThe funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript." article_processing_charge: No author: - first_name: Michelle C full_name: Gallei, Michelle C id: 35A03822-F248-11E8-B48F-1D18A9856A87 last_name: Gallei orcid: 0000-0003-1286-7368 - first_name: Sven M full_name: Truckenbrodt, Sven M id: 45812BD4-F248-11E8-B48F-1D18A9856A87 last_name: Truckenbrodt - first_name: Caroline full_name: Kreuzinger, Caroline id: 382077BA-F248-11E8-B48F-1D18A9856A87 last_name: Kreuzinger - first_name: Syamala full_name: Inumella, Syamala id: F8660870-D756-11E9-98C5-34DFE5697425 last_name: Inumella orcid: 0009-0002-5890-120X - first_name: Vitali full_name: Vistunou, Vitali id: 7e146587-8972-11ed-ae7b-d7a32ea86a81 last_name: Vistunou - first_name: Christoph M full_name: Sommer, Christoph M id: 4DF26D8C-F248-11E8-B48F-1D18A9856A87 last_name: Sommer orcid: 0000-0003-1216-9105 - first_name: Mojtaba full_name: Tavakoli, Mojtaba id: 3A0A06F4-F248-11E8-B48F-1D18A9856A87 last_name: Tavakoli orcid: 0000-0002-7667-6854 - first_name: Nathalie full_name: Agudelo Duenas, Nathalie id: 40E7F008-F248-11E8-B48F-1D18A9856A87 last_name: Agudelo Duenas - first_name: Jakob full_name: Vorlaufer, Jakob id: 937696FA-C996-11E9-8C7C-CF13E6697425 last_name: Vorlaufer orcid: 0009-0000-7590-3501 - first_name: Wiebke full_name: Jahr, Wiebke id: 425C1CE8-F248-11E8-B48F-1D18A9856A87 last_name: Jahr orcid: 0000-0003-0201-2315 - first_name: Marek full_name: Randuch, Marek id: 6ac4636d-15b2-11ec-abd3-fb8df79972ae last_name: Randuch - first_name: Alexander J full_name: Johnson, Alexander J id: 46A62C3A-F248-11E8-B48F-1D18A9856A87 last_name: Johnson orcid: 0000-0002-2739-8843 - first_name: Eva full_name: Benková, Eva id: 38F4F166-F248-11E8-B48F-1D18A9856A87 last_name: Benková orcid: 0000-0002-8510-9739 - first_name: Jiří full_name: Friml, Jiří id: 4159519E-F248-11E8-B48F-1D18A9856A87 last_name: Friml orcid: 0000-0002-8302-7596 - first_name: Johann G full_name: Danzl, Johann G id: 42EFD3B6-F248-11E8-B48F-1D18A9856A87 last_name: Danzl orcid: 0000-0001-8559-3973 citation: ama: Gallei MC, Truckenbrodt SM, Kreuzinger C, et al. Super-resolution expansion microscopy in plant roots. bioRxiv. doi:10.1101/2024.02.21.581330 apa: Gallei, M. C., Truckenbrodt, S. M., Kreuzinger, C., Inumella, S., Vistunou, V., Sommer, C. M., … Danzl, J. G. (n.d.). Super-resolution expansion microscopy in plant roots. bioRxiv. https://doi.org/10.1101/2024.02.21.581330 chicago: Gallei, Michelle C, Sven M Truckenbrodt, Caroline Kreuzinger, Syamala Inumella, Vitali Vistunou, Christoph M Sommer, Mojtaba Tavakoli, et al. “Super-Resolution Expansion Microscopy in Plant Roots.” BioRxiv, n.d. https://doi.org/10.1101/2024.02.21.581330. ieee: M. C. Gallei et al., “Super-resolution expansion microscopy in plant roots,” bioRxiv. . ista: Gallei MC, Truckenbrodt SM, Kreuzinger C, Inumella S, Vistunou V, Sommer CM, Tavakoli M, Agudelo Duenas N, Vorlaufer J, Jahr W, Randuch M, Johnson AJ, Benková E, Friml J, Danzl JG. Super-resolution expansion microscopy in plant roots. bioRxiv, 10.1101/2024.02.21.581330. mla: Gallei, Michelle C., et al. “Super-Resolution Expansion Microscopy in Plant Roots.” BioRxiv, doi:10.1101/2024.02.21.581330. short: M.C. Gallei, S.M. Truckenbrodt, C. Kreuzinger, S. Inumella, V. Vistunou, C.M. Sommer, M. Tavakoli, N. Agudelo Duenas, J. Vorlaufer, W. Jahr, M. Randuch, A.J. Johnson, E. Benková, J. Friml, J.G. Danzl, BioRxiv (n.d.). corr_author: '1' date_created: 2024-12-19T12:28:00Z date_published: 2024-02-21T00:00:00Z date_updated: 2026-04-07T12:56:36Z day: '21' department: - _id: EvBe - _id: JoDa - _id: JiFr doi: 10.1101/2024.02.21.581330 ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1101/2024.02.21.581330 month: '02' oa: 1 oa_version: Preprint project: - _id: 261099A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '742985' name: Tracing Evolution of Auxin Transport and Polarity in Plants - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 26AA4EF2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: W1232-B24 name: Molecular Drug Targets - _id: 269B5B22-B435-11E9-9278-68D0E5697425 grant_number: ALTF 679-2018 name: UltraX - achieving sub-nanometer resolution in light microscopy using iterative X10 microscopy in combination with nanobodies and STED publication: bioRxiv publication_status: draft related_material: record: - id: '19003' relation: later_version status: public - id: '18681' relation: dissertation_contains status: public status: public title: Super-resolution expansion microscopy in plant roots tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- OA_embargo: '20' OA_place: publisher _id: '18681' acknowledged_ssus: - _id: Bio - _id: PreCl - _id: LifeSc alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Mojtaba full_name: Tavakoli, Mojtaba id: 3A0A06F4-F248-11E8-B48F-1D18A9856A87 last_name: Tavakoli orcid: 0000-0002-7667-6854 citation: ama: 'Tavakoli M. Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy. 2024. doi:10.15479/at:ista:18681' apa: 'Tavakoli, M. (2024). Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:18681' chicago: 'Tavakoli, Mojtaba. “Developing Molecular and Structural Tools for Studying Brain Architecture with Super Resolution Expansion Microscopy. LICONN: Molecularly-Informed Connectomics Reconstruction with Light Microscopy.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:18681.' ieee: 'M. Tavakoli, “Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy,” Institute of Science and Technology Austria, 2024.' ista: 'Tavakoli M. 2024. Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy. Institute of Science and Technology Austria.' mla: 'Tavakoli, Mojtaba. Developing Molecular and Structural Tools for Studying Brain Architecture with Super Resolution Expansion Microscopy. LICONN: Molecularly-Informed Connectomics Reconstruction with Light Microscopy. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:18681.' short: 'M. Tavakoli, Developing Molecular and Structural Tools for Studying Brain Architecture with Super Resolution Expansion Microscopy. LICONN: Molecularly-Informed Connectomics Reconstruction with Light Microscopy, Institute of Science and Technology Austria, 2024.' corr_author: '1' date_created: 2024-12-19T02:30:39Z date_published: 2024-12-20T00:00:00Z date_updated: 2026-04-07T12:56:37Z day: '20' ddc: - '600' - '570' degree_awarded: PhD department: - _id: GradSch - _id: JoDa doi: 10.15479/at:ista:18681 file: - access_level: closed checksum: b61651d417cafddd740a8528f46068c5 content_type: application/vnd.openxmlformats-officedocument.wordprocessingml.document creator: mtavakol date_created: 2024-12-20T10:23:17Z date_updated: 2024-12-20T10:31:37Z file_id: '18699' file_name: Thesis_Mojtaba Tavakoli_.docx file_size: 118593521 relation: source_file - access_level: closed checksum: c80bcfd1a34c23afc3538052325283e5 content_type: application/pdf creator: mtavakol date_created: 2024-12-20T10:25:12Z date_updated: 2024-12-20T10:25:12Z embargo: 2026-08-01 embargo_to: open_access file_id: '18700' file_name: Thesis_Mojtaba Tavakoli_.pdf file_size: 63885521 relation: main_file file_date_updated: 2024-12-20T10:31:37Z has_accepted_license: '1' language: - iso: eng month: '12' oa_version: Published Version page: '230' project: - _id: 6285a163-2b32-11ec-9570-8e204ca2dba5 grant_number: '26137' name: Studying Organelle Structure and Function at Nanoscale Resolution with Expansion Microscopy - _id: 26AA4EF2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: W1232-B24 name: Molecular Drug Targets publication_identifier: isbn: - 978-3-99078-048-0 issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '11160' relation: part_of_dissertation status: public - id: '18688' relation: part_of_dissertation status: public - id: '18677' relation: part_of_dissertation status: public - id: '18689' relation: part_of_dissertation status: public status: public supervisor: - first_name: Johann G full_name: Danzl, Johann G id: 42EFD3B6-F248-11E8-B48F-1D18A9856A87 last_name: Danzl orcid: 0000-0001-8559-3973 title: 'Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy' 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: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ... --- OA_place: publisher _id: '15094' abstract: - lang: eng text: "Point sets, geometric networks, and arrangements of hyperplanes are fundamental objects in\r\ndiscrete geometry that have captivated mathematicians for centuries, if not millennia. This\r\nthesis seeks to cast new light on these structures by illustrating specific instances where a\r\ntopological perspective, specifically through discrete Morse theory and persistent homology,\r\nprovides valuable insights.\r\n\r\nAt first glance, the topology of these geometric objects might seem uneventful: point sets\r\nessentially lack of topology, arrangements of hyperplanes are a decomposition of Rd, which\r\nis a contractible space, and the topology of a network primarily involves the enumeration\r\nof connected components and cycles within the network. However, beneath this apparent\r\nsimplicity, there lies an array of intriguing structures, a small subset of which will be uncovered\r\nin this thesis.\r\n\r\nFocused on three case studies, each addressing one of the mentioned objects, this work\r\nwill showcase connections that intertwine topology with diverse fields such as combinatorial\r\ngeometry, algorithms and data structures, and emerging applications like spatial biology.\r\n\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Sebastiano full_name: Cultrera di Montesano, Sebastiano id: 34D2A09C-F248-11E8-B48F-1D18A9856A87 last_name: Cultrera di Montesano orcid: 0000-0001-6249-0832 citation: ama: Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:10.15479/at:ista:15094 apa: Cultrera di Montesano, S. (2024). Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:15094 chicago: Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:15094. ieee: S. Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024. ista: Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria. mla: Cultrera di Montesano, Sebastiano. Persistence and Morse Theory for Discrete Geometric Structures. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:15094. short: S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024. corr_author: '1' date_created: 2024-03-08T15:28:10Z date_published: 2024-03-08T00:00:00Z date_updated: 2026-04-07T12:58:48Z day: '08' ddc: - '514' - '500' - '516' degree_awarded: PhD department: - _id: GradSch - _id: HeEd doi: 10.15479/at:ista:15094 ec_funded: 1 file: - access_level: open_access checksum: 1e468bfa42a7dcf04d89f4dadc621c87 content_type: application/pdf creator: scultrer date_created: 2024-03-14T08:55:07Z date_updated: 2024-03-14T08:55:07Z file_id: '15112' file_name: Thesis Sebastiano.pdf file_size: 4106872 relation: main_file success: 1 - access_level: closed checksum: bcbd213490f5a7e68855a092bbce93f1 content_type: application/zip creator: scultrer date_created: 2024-03-14T08:56:24Z date_updated: 2024-03-14T14:14:35Z file_id: '15113' file_name: Thesis (1).zip file_size: 4746234 relation: source_file file_date_updated: 2024-03-14T14:14:35Z has_accepted_license: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: '108' project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: Mathematics, Computer Science - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Persistent Homology, Algorithms and Stochastic Geometry - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '15091' relation: part_of_dissertation status: public - id: '11660' relation: part_of_dissertation status: public - id: '15090' relation: part_of_dissertation status: public - id: '15093' relation: part_of_dissertation status: public - id: '13182' relation: part_of_dissertation status: public - id: '11658' relation: part_of_dissertation status: public status: public supervisor: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 title: Persistence and Morse theory for discrete geometric structures tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd year: '2024' ...