[{"type":"dissertation","citation":{"apa":"Sisak, M. A. (2024). <i>T-dual branes on hyperkähler manifolds</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18443\">https://doi.org/10.15479/at:ista:18443</a>","ista":"Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria.","ama":"Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18443\">10.15479/at:ista:18443</a>","ieee":"M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024.","chicago":"Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18443\">https://doi.org/10.15479/at:ista:18443</a>.","mla":"Sisak, Maria A. <i>T-Dual Branes on Hyperkähler Manifolds</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18443\">10.15479/at:ista:18443</a>.","short":"M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024."},"status":"public","date_published":"2024-10-24T00:00:00Z","day":"24","language":[{"iso":"eng"}],"department":[{"_id":"GradSch"},{"_id":"TaHa"}],"ddc":["516"],"file_date_updated":"2024-10-24T08:09:13Z","license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"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","lang":"eng"}],"project":[{"_id":"6286e8c4-2b32-11ec-9570-f5297902f67f","grant_number":"26069","name":"Branes on hyperkähler manifolds"}],"OA_place":"publisher","_id":"18443","article_processing_charge":"No","publication_status":"published","oa":1,"publisher":"Institute of Science and Technology Austria","author":[{"id":"44A03D04-AEA4-11E9-B225-EA2DE6697425","last_name":"Sisak","full_name":"Sisak, Maria A","first_name":"Maria A"}],"title":"T-dual branes on hyperkähler manifolds","oa_version":"Published Version","alternative_title":["ISTA Thesis"],"doi":"10.15479/at:ista:18443","page":"178","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"degree_awarded":"PhD","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","OA_type":"free access","keyword":["hyperkaehler geometry","branes","mirror symmetry","T-duality"],"date_created":"2024-10-19T12:00:37Z","corr_author":"1","date_updated":"2026-04-07T12:42:44Z","file":[{"creator":"msisak","file_size":1672547,"content_type":"application/pdf","access_level":"open_access","success":1,"date_created":"2024-10-23T14:42:45Z","date_updated":"2024-10-23T14:42:45Z","relation":"main_file","file_id":"18467","file_name":"MASisak_dissertation.pdf","checksum":"8c4893e726aaa4b3efb82758da9b6851"},{"creator":"msisak","content_type":"application/x-zip-compressed","file_size":617913,"access_level":"closed","date_created":"2024-10-23T14:43:56Z","file_id":"18468","relation":"source_file","date_updated":"2024-10-24T08:09:13Z","file_name":"MASisak_source.zip","checksum":"1831b072e861a1e5481024ca9d02b036"}],"publication_identifier":{"issn":["2663-337X"]},"has_accepted_license":"1","year":"2024","supervisor":[{"first_name":"Tamás","full_name":"Hausel, Tamás","last_name":"Hausel","orcid":"0000-0002-9582-2634","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"}],"month":"10"},{"oa":1,"publisher":"Institute of Science and Technology Austria","title":"Compressing large neural networks : Algorithms, systems and scaling laws","author":[{"last_name":"Frantar","id":"09a8f98d-ec99-11ea-ae11-c063a7b7fe5f","first_name":"Elias","full_name":"Frantar, Elias"}],"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","doi":"10.15479/at:ista:17485","page":"129","degree_awarded":"PhD","date_created":"2024-09-02T11:01:48Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_updated":"2026-04-07T12:43:04Z","corr_author":"1","has_accepted_license":"1","acknowledged_ssus":[{"_id":"ScienComp"}],"publication_identifier":{"issn":["2663-337X"]},"file":[{"checksum":"5d785645805a78c5b4ce7cc3df557b09","file_name":"thesis-final.zip","file_id":"17570","relation":"source_file","date_updated":"2024-09-05T12:04:11Z","date_created":"2024-09-05T12:04:11Z","access_level":"closed","content_type":"application/zip","file_size":1615167,"creator":"efrantar"},{"creator":"efrantar","content_type":"application/pdf","file_size":2376611,"success":1,"access_level":"open_access","date_created":"2024-09-06T16:24:59Z","file_id":"17880","relation":"main_file","date_updated":"2024-09-06T16:24:59Z","file_name":"frantar_thesis_final.pdf","checksum":"a9dd1c2d23734986924eb44ebb55fd8f"}],"supervisor":[{"first_name":"Dan-Adrian","full_name":"Alistarh, Dan-Adrian","last_name":"Alistarh","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3650-940X"}],"year":"2024","month":"09","type":"dissertation","ec_funded":1,"citation":{"ieee":"E. Frantar, “Compressing large neural networks : Algorithms, systems and scaling laws,” Institute of Science and Technology Austria, 2024.","ama":"Frantar E. Compressing large neural networks : Algorithms, systems and scaling laws. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17485\">10.15479/at:ista:17485</a>","mla":"Frantar, Elias. <i>Compressing Large Neural Networks : Algorithms, Systems and Scaling Laws</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17485\">10.15479/at:ista:17485</a>.","short":"E. Frantar, Compressing Large Neural Networks : Algorithms, Systems and Scaling Laws, Institute of Science and Technology Austria, 2024.","chicago":"Frantar, Elias. “Compressing Large Neural Networks : Algorithms, Systems and Scaling Laws.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17485\">https://doi.org/10.15479/at:ista:17485</a>.","apa":"Frantar, E. (2024). <i>Compressing large neural networks : Algorithms, systems and scaling laws</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17485\">https://doi.org/10.15479/at:ista:17485</a>","ista":"Frantar E. 2024. Compressing large neural networks : Algorithms, systems and scaling laws. Institute of Science and Technology Austria."},"status":"public","day":"05","date_published":"2024-09-05T00:00:00Z","language":[{"iso":"eng"}],"ddc":["000"],"department":[{"_id":"GradSch"},{"_id":"DaAl"}],"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."}],"file_date_updated":"2024-09-06T16:24:59Z","OA_place":"publisher","project":[{"call_identifier":"H2020","name":"Elastic Coordination for Scalable Machine Learning","grant_number":"805223","_id":"268A44D6-B435-11E9-9278-68D0E5697425"}],"_id":"17485","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"18062"},{"id":"18061","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"17378"},{"id":"17087","relation":"part_of_dissertation","status":"public"},{"id":"14458","status":"public","relation":"part_of_dissertation"}]},"article_processing_charge":"No","publication_status":"published"},{"conference":{"end_date":"2024-05-16","start_date":"2024-05-13","name":"MLSys: Machine Learning and Systems","location":"Santa Clara, CA, USA"},"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"17485"}]},"year":"2024","_id":"18061","month":"05","article_processing_charge":"No","publication_status":"published","publication":" Proceedings of Machine Learning and Systems","quality_controlled":"1","language":[{"iso":"eng"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"DaAl"}],"date_created":"2024-09-13T10:01:38Z","volume":6,"corr_author":"1","date_updated":"2026-04-07T12:43:03Z","abstract":[{"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.","lang":"eng"}],"author":[{"id":"09a8f98d-ec99-11ea-ae11-c063a7b7fe5f","last_name":"Frantar","full_name":"Frantar, Elias","first_name":"Elias"},{"last_name":"Alistarh","orcid":"0000-0003-3650-940X","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","first_name":"Dan-Adrian","full_name":"Alistarh, Dan-Adrian"}],"title":"QMoE: Sub-1-bit compression of trillion parameter models","citation":{"chicago":"Frantar, Elias, and Dan-Adrian Alistarh. “QMoE: Sub-1-Bit Compression of Trillion Parameter Models.” In <i> Proceedings of Machine Learning and Systems</i>, edited by P. Gibbons, G. Pekhimenko, and C. De Sa, Vol. 6, 2024.","mla":"Frantar, Elias, and Dan-Adrian Alistarh. “QMoE: Sub-1-Bit Compression of Trillion Parameter Models.” <i> Proceedings of Machine Learning and Systems</i>, 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.","ama":"Frantar E, Alistarh D-A. QMoE: Sub-1-bit compression of trillion parameter models. In: Gibbons P, Pekhimenko G, De Sa C, eds. <i> Proceedings of Machine Learning and Systems</i>. Vol 6. ; 2024.","ieee":"E. Frantar and D.-A. Alistarh, “QMoE: Sub-1-bit compression of trillion parameter models,” in <i> Proceedings of Machine Learning and Systems</i>, 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.","apa":"Frantar, E., &#38; Alistarh, D.-A. (2024). QMoE: Sub-1-bit compression of trillion parameter models. In P. Gibbons, G. Pekhimenko, &#38; C. De Sa (Eds.), <i> Proceedings of Machine Learning and Systems</i> (Vol. 6). Santa Clara, CA, USA."},"editor":[{"full_name":"Gibbons, P.","first_name":"P.","last_name":"Gibbons"},{"last_name":"Pekhimenko","full_name":"Pekhimenko, G.","first_name":"G."},{"first_name":"C.","full_name":"De Sa, C.","last_name":"De Sa"}],"oa_version":"Published Version","status":"public","date_published":"2024-05-01T00:00:00Z","day":"01","type":"conference","oa":1,"main_file_link":[{"url":"https://proceedings.mlsys.org/paper_files/paper/2024/hash/c74b624843218d9b6713fcf299d6d5e4-Abstract-Conference.html","open_access":"1"}],"intvolume":"         6"},{"_id":"18062","year":"2024","related_material":{"record":[{"id":"17485","relation":"dissertation_contains","status":"public"}]},"conference":{"end_date":"2024-05-07","start_date":"2024-05-07","location":"Vienna, Austria","name":"ICLR: International Conference on Learning Representations"},"publication_status":"published","publication":"The Twelfth International Conference on Learning Representations","article_processing_charge":"No","month":"01","language":[{"iso":"eng"}],"quality_controlled":"1","scopus_import":"1","external_id":{"arxiv":["2309.08520"]},"abstract":[{"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.","lang":"eng"}],"date_updated":"2026-04-07T12:43:03Z","corr_author":"1","date_created":"2024-09-13T10:31:08Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"DaAl"}],"oa_version":"Published Version","citation":{"ama":"Frantar E, Ruiz CR, Houlsby N, Alistarh D-A, Evci U. Scaling laws for sparsely-connected foundation models. In: <i>The Twelfth International Conference on Learning Representations</i>. ; 2024.","ieee":"E. Frantar, C. R. Ruiz, N. Houlsby, D.-A. Alistarh, and U. Evci, “Scaling laws for sparsely-connected foundation models,” in <i>The Twelfth International Conference on Learning Representations</i>, Vienna, Austria, 2024.","chicago":"Frantar, Elias, Carlos Riquelme Ruiz, Neil Houlsby, Dan-Adrian Alistarh, and Utku Evci. “Scaling Laws for Sparsely-Connected Foundation Models.” In <i>The Twelfth International Conference on Learning Representations</i>, 2024.","mla":"Frantar, Elias, et al. “Scaling Laws for Sparsely-Connected Foundation Models.” <i>The Twelfth International Conference on Learning Representations</i>, 2024.","short":"E. Frantar, C.R. Ruiz, N. Houlsby, D.-A. Alistarh, U. Evci, in:, The Twelfth International Conference on Learning Representations, 2024.","apa":"Frantar, E., Ruiz, C. R., Houlsby, N., Alistarh, D.-A., &#38; Evci, U. (2024). Scaling laws for sparsely-connected foundation models. In <i>The Twelfth International Conference on Learning Representations</i>. Vienna, Austria.","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."},"title":"Scaling laws for sparsely-connected foundation models","author":[{"id":"09a8f98d-ec99-11ea-ae11-c063a7b7fe5f","last_name":"Frantar","full_name":"Frantar, Elias","first_name":"Elias"},{"first_name":"Carlos Riquelme","full_name":"Ruiz, Carlos Riquelme","last_name":"Ruiz"},{"last_name":"Houlsby","first_name":"Neil","full_name":"Houlsby, Neil"},{"last_name":"Alistarh","orcid":"0000-0003-3650-940X","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","first_name":"Dan-Adrian","full_name":"Alistarh, Dan-Adrian"},{"first_name":"Utku","full_name":"Evci, Utku","last_name":"Evci"}],"day":"16","date_published":"2024-01-16T00:00:00Z","status":"public","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://openreview.net/forum?id=i9K2ZWkYIP"}],"oa":1,"type":"conference"},{"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","title":"Exploring the optimization landscape of variational quantum algorithms","author":[{"full_name":"Medina Ramos, Raimel A","first_name":"Raimel A","orcid":"0000-0002-5383-2869","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos"}],"page":"133","doi":"10.15479/at:ista:17208","publisher":"Institute of Science and Technology Austria","oa":1,"supervisor":[{"id":"47809E7E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2399-5827","last_name":"Serbyn","full_name":"Serbyn, Maksym","first_name":"Maksym"}],"year":"2024","acknowledged_ssus":[{"_id":"ScienComp"}],"publication_identifier":{"issn":["2663-337X"]},"has_accepted_license":"1","file":[{"date_updated":"2024-07-10T11:34:09Z","file_id":"17212","relation":"source_file","date_created":"2024-07-09T09:21:44Z","checksum":"6f45273d04f4418bc2adc018baed0525","file_name":"Raimel_Thesis-Final.zip","creator":"rmedinar","access_level":"closed","file_size":"14218691","content_type":"application/zip"},{"creator":"rmedinar","access_level":"open_access","success":1,"file_size":11253627,"content_type":"application/pdf","date_updated":"2024-07-17T09:23:24Z","file_id":"17275","relation":"main_file","date_created":"2024-07-17T09:23:24Z","checksum":"6724a95bec772dbabc0111b9f08a805e","file_name":"Raimel_Thesis-20_pdfa.pdf"}],"month":"07","degree_awarded":"PhD","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2026-04-07T12:43:22Z","corr_author":"1","date_created":"2024-07-09T09:14:24Z","keyword":["Quantum computing","Variational Quantum Algorithms","Optimization"],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","citation":{"short":"R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum Algorithms, Institute of Science and Technology Austria, 2024.","mla":"Medina Ramos, Raimel A. <i>Exploring the Optimization Landscape of Variational Quantum Algorithms</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17208\">10.15479/at:ista:17208</a>.","chicago":"Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational Quantum Algorithms.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17208\">https://doi.org/10.15479/at:ista:17208</a>.","ieee":"R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum algorithms,” Institute of Science and Technology Austria, 2024.","ama":"Medina Ramos RA. Exploring the optimization landscape of variational quantum algorithms. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17208\">10.15479/at:ista:17208</a>","ista":"Medina Ramos RA. 2024. Exploring the optimization landscape of variational quantum algorithms. Institute of Science and Technology Austria.","apa":"Medina Ramos, R. A. (2024). <i>Exploring the optimization landscape of variational quantum algorithms</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17208\">https://doi.org/10.15479/at:ista:17208</a>"},"day":"09","date_published":"2024-07-09T00:00:00Z","status":"public","ec_funded":1,"type":"dissertation","_id":"17208","related_material":{"record":[{"id":"10545","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"10067"},{"id":"17222","relation":"part_of_dissertation","status":"public"},{"id":"13125","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"11471"}]},"project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","grant_number":"850899","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","call_identifier":"H2020"}],"OA_place":"publisher","publication_status":"published","article_processing_charge":"No","language":[{"iso":"eng"}],"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."}],"file_date_updated":"2024-07-17T09:23:24Z","department":[{"_id":"GradSch"},{"_id":"MaSe"}],"ddc":["539"]},{"corr_author":"1","date_updated":"2026-04-07T12:43:22Z","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"MaSe"}],"date_created":"2024-07-10T13:12:09Z","language":[{"iso":"eng"}],"external_id":{"arxiv":["2405.10125"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"draft","publication":"arXiv","month":"05","article_processing_charge":"No","year":"2024","related_material":{"record":[{"id":"17208","relation":"dissertation_contains","status":"public"}]},"_id":"17222","OA_place":"repository","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.10125"}],"type":"preprint","oa":1,"date_published":"2024-05-16T00:00:00Z","day":"16","article_number":"2405.10125","arxiv":1,"doi":"10.48550/arXiv.2405.10125","status":"public","citation":{"ista":"Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. arXiv, 2405.10125.","apa":"Medina Ramos, R. A., &#38; Serbyn, M. (n.d.). A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2405.10125\">https://doi.org/10.48550/arXiv.2405.10125</a>","short":"R.A. Medina Ramos, M. Serbyn, ArXiv (n.d.).","mla":"Medina Ramos, Raimel A., and Maksym Serbyn. “A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm.” <i>ArXiv</i>, 2405.10125, doi:<a href=\"https://doi.org/10.48550/arXiv.2405.10125\">10.48550/arXiv.2405.10125</a>.","chicago":"Medina Ramos, Raimel A, and Maksym Serbyn. “A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2405.10125\">https://doi.org/10.48550/arXiv.2405.10125</a>.","ieee":"R. A. Medina Ramos and M. Serbyn, “A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm,” <i>arXiv</i>. .","ama":"Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2405.10125\">10.48550/arXiv.2405.10125</a>"},"oa_version":"Preprint","author":[{"first_name":"Raimel A","full_name":"Medina Ramos, Raimel A","last_name":"Medina Ramos","id":"CE680B90-D85A-11E9-B684-C920E6697425","orcid":"0000-0002-5383-2869"},{"first_name":"Maksym","full_name":"Serbyn, Maksym","last_name":"Serbyn","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"title":"A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm"},{"date_created":"2024-09-23T18:58:08Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_updated":"2026-04-07T12:53:54Z","corr_author":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)"},"degree_awarded":"PhD","month":"09","publication_identifier":{"issn":["2663-337X"]},"has_accepted_license":"1","file":[{"date_created":"2024-09-23T18:49:22Z","file_id":"18133","relation":"source_file","date_updated":"2024-09-23T18:49:22Z","file_name":"PhDthesis (3).zip","checksum":"2f8cf5cefdab108b1979caa8146cae9a","creator":"jglas","content_type":"application/x-zip-compressed","file_size":5382106,"access_level":"closed"},{"checksum":"08bb6f14c42b47ff25882a2ce3ea0d8a","file_name":"example-phd.pdf","file_id":"18140","relation":"main_file","date_updated":"2024-09-25T14:08:57Z","date_created":"2024-09-25T14:08:57Z","success":1,"access_level":"open_access","content_type":"application/pdf","file_size":2380127,"creator":"jglas"}],"supervisor":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D"}],"year":"2024","publisher":"Institute of Science and Technology Austria","oa":1,"doi":"10.15479/at:ista:18132","page":"195","title":"Counting rational points over function fields","author":[{"first_name":"Jakob","full_name":"Glas, Jakob","last_name":"Glas","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb"}],"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","ddc":["512"],"department":[{"_id":"GradSch"},{"_id":"TiBr"}],"license":"https://creativecommons.org/licenses/by-nc/4.0/","abstract":[{"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","lang":"eng"}],"file_date_updated":"2024-09-25T14:08:57Z","language":[{"iso":"eng"}],"article_processing_charge":"No","publication_status":"published","OA_place":"publisher","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}],"_id":"18132","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","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"}]},"type":"dissertation","status":"public","day":"23","date_published":"2024-09-23T00:00:00Z","citation":{"ieee":"J. Glas, “Counting rational points over function fields,” Institute of Science and Technology Austria, 2024.","ama":"Glas J. Counting rational points over function fields. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18132\">10.15479/at:ista:18132</a>","short":"J. Glas, Counting Rational Points over Function Fields, Institute of Science and Technology Austria, 2024.","mla":"Glas, Jakob. <i>Counting Rational Points over Function Fields</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18132\">10.15479/at:ista:18132</a>.","chicago":"Glas, Jakob. “Counting Rational Points over Function Fields.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18132\">https://doi.org/10.15479/at:ista:18132</a>.","apa":"Glas, J. (2024). <i>Counting rational points over function fields</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18132\">https://doi.org/10.15479/at:ista:18132</a>","ista":"Glas J. 2024. Counting rational points over function fields. Institute of Science and Technology Austria."}},{"author":[{"id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas","full_name":"Glas, Jakob","first_name":"Jakob"}],"title":"Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)","oa_version":"Published Version","doi":"10.1112/jlms.12991","publisher":"London Mathematical Society","oa":1,"file":[{"relation":"main_file","file_id":"18181","date_updated":"2024-10-07T08:51:01Z","date_created":"2024-10-07T08:51:01Z","checksum":"11ebf690363151026ce81f91f2220855","file_name":"2024_JLondonMathSoc_Glas.pdf","creator":"dernst","success":1,"access_level":"open_access","content_type":"application/pdf","file_size":579601}],"has_accepted_license":"1","article_type":"original","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"year":"2024","month":"10","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-10-06T22:01:11Z","corr_author":"1","date_updated":"2026-04-07T12:53:53Z","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).","citation":{"mla":"Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12991\">10.1112/jlms.12991</a>.","short":"J. Glas, Journal of the London Mathematical Society 110 (2024).","chicago":"Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” <i>Journal of the London Mathematical Society</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/jlms.12991\">https://doi.org/10.1112/jlms.12991</a>.","ieee":"J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t),” <i>Journal of the London Mathematical Society</i>, vol. 110, no. 4. London Mathematical Society, 2024.","ama":"Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). <i>Journal of the London Mathematical Society</i>. 2024;110(4). doi:<a href=\"https://doi.org/10.1112/jlms.12991\">10.1112/jlms.12991</a>","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.","apa":"Glas, J. (2024). Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). <i>Journal of the London Mathematical Society</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/jlms.12991\">https://doi.org/10.1112/jlms.12991</a>"},"arxiv":1,"status":"public","date_published":"2024-10-01T00:00:00Z","article_number":"e12991","day":"01","type":"journal_article","intvolume":"       110","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}],"related_material":{"record":[{"id":"18132","status":"public","relation":"dissertation_contains"}]},"_id":"18173","issue":"4","article_processing_charge":"Yes (via OA deal)","publication_status":"published","publication":"Journal of the London Mathematical Society","scopus_import":"1","external_id":{"arxiv":["2306.02718"]},"quality_controlled":"1","language":[{"iso":"eng"}],"department":[{"_id":"TiBr"}],"ddc":["510"],"volume":110,"file_date_updated":"2024-10-07T08:51:01Z","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."}]},{"oa":1,"type":"preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.16648"}],"doi":"10.48550/arXiv.2405.16648","arxiv":1,"status":"public","date_published":"2024-05-26T00:00:00Z","day":"26","author":[{"full_name":"Glas, Jakob","first_name":"Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas"}],"title":"Canonical singularities on moduli spaces of rational curves via the  circle method","oa_version":"Preprint","citation":{"ista":"Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2405.16648\">10.48550/arXiv.2405.16648</a>.","apa":"Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves via the  circle method. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2405.16648\">https://doi.org/10.48550/arXiv.2405.16648</a>","chicago":"Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2405.16648\">https://doi.org/10.48550/arXiv.2405.16648</a>.","mla":"Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2405.16648\">10.48550/arXiv.2405.16648</a>.","short":"J. Glas, ArXiv (n.d.).","ama":"Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2405.16648\">10.48550/arXiv.2405.16648</a>","ieee":"J. Glas, “Canonical singularities on moduli spaces of rational curves via the  circle method,” <i>arXiv</i>. ."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"TiBr"}],"date_created":"2024-10-10T13:15:43Z","corr_author":"1","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."}],"date_updated":"2026-04-07T12:53:53Z","external_id":{"arxiv":["2405.16648"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"language":[{"iso":"eng"}],"month":"05","article_processing_charge":"No","publication_status":"submitted","publication":"arXiv","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}],"OA_place":"repository","related_material":{"record":[{"relation":"later_version","status":"public","id":"19013"},{"status":"public","relation":"dissertation_contains","id":"18132"}]},"year":"2024","_id":"18295"},{"status":"public","date_published":"2024-12-17T00:00:00Z","day":"17","citation":{"ieee":"T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024.","ama":"Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>","mla":"Heiss, Teresa. <i>New Methods for Applying Topological Data Analysis to Materials Science</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>.","short":"T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.","chicago":"Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>.","apa":"Heiss, T. (2024). <i>New methods for applying topological data analysis to materials science</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>","ista":"Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria."},"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.","type":"dissertation","ec_funded":1,"article_processing_charge":"No","publication_status":"published","OA_place":"publisher","project":[{"call_identifier":"H2020","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10828"},{"relation":"part_of_dissertation","status":"public","id":"11440"},{"relation":"part_of_dissertation","status":"public","id":"18673"},{"status":"public","relation":"part_of_dissertation","id":"9345"}]},"_id":"18667","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"ddc":["514","516","004"],"file_date_updated":"2024-12-19T10:24:50Z","abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.15479/at:ista:18667","page":"111","author":[{"id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","last_name":"Heiss","full_name":"Heiss, Teresa","first_name":"Teresa"}],"title":"New methods for applying topological data analysis to materials science","oa_version":"Published Version","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","oa":1,"month":"12","file":[{"content_type":"application/pdf","file_size":7752253,"success":1,"access_level":"open_access","creator":"theiss","file_name":"Teresa_Heiss_PhD_Thesis_final.pdf","checksum":"247bb057aed2fba1cd4711917aaa2d77","date_created":"2024-12-19T10:24:46Z","file_id":"18686","relation":"main_file","date_updated":"2024-12-19T10:24:46Z"},{"access_level":"closed","content_type":"application/zip","file_size":17197731,"creator":"theiss","checksum":"9648b45c07a008ee11a07f99856a139d","file_name":"PhD_Thesis.zip","relation":"source_file","file_id":"18687","date_updated":"2024-12-19T10:24:50Z","date_created":"2024-12-19T10:24:50Z"}],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-052-7"]},"has_accepted_license":"1","year":"2024","supervisor":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2024-12-17T16:17:55Z","keyword":["persistent homology","topological data analysis","periodic","crystalline materials","images","fingerprint"],"corr_author":"1","date_updated":"2026-04-07T12:54:10Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"degree_awarded":"PhD"},{"oa_version":"Preprint","title":"Merge trees of periodic filtrations","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Heiss","orcid":"0000-0002-1780-2689","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","first_name":"Teresa","full_name":"Heiss, Teresa"}],"doi":"10.48550/arXiv.2408.16575","oa":1,"year":"2024","month":"08","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2026-04-07T12:54:09Z","corr_author":"1","date_created":"2024-12-18T14:06:57Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","citation":{"chicago":"Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">https://doi.org/10.48550/arXiv.2408.16575</a>.","short":"H. Edelsbrunner, T. Heiss, ArXiv (n.d.).","mla":"Edelsbrunner, Herbert, and Teresa Heiss. “Merge Trees of Periodic Filtrations.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>.","ama":"Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>","ieee":"H. Edelsbrunner and T. Heiss, “Merge trees of periodic filtrations,” <i>arXiv</i>. .","ista":"Edelsbrunner H, Heiss T. Merge trees of periodic filtrations. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">10.48550/arXiv.2408.16575</a>.","apa":"Edelsbrunner, H., &#38; Heiss, T. (n.d.). Merge trees of periodic filtrations. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2408.16575\">https://doi.org/10.48550/arXiv.2408.16575</a>"},"day":"29","date_published":"2024-08-29T00:00:00Z","status":"public","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2408.16575"}],"ec_funded":1,"type":"preprint","_id":"18673","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"18667"}]},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"call_identifier":"FWF","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"OA_place":"repository","publication":"arXiv","publication_status":"draft","article_processing_charge":"No","language":[{"iso":"eng"}],"external_id":{"arxiv":["2408.16575"]},"abstract":[{"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","lang":"eng"}],"department":[{"_id":"HeEd"}]},{"_id":"14711","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"10787"},{"id":"10658","status":"public","relation":"part_of_dissertation"},{"id":"14732","relation":"part_of_dissertation","status":"public"}]},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"},{"grant_number":"P32896","_id":"c08d3278-5a5b-11eb-8a69-fdb09b55f4b8","name":"Causes and consequences of population fragmentation"},{"name":"Polygenic Adaptation in a Metapopulation","_id":"34c872fe-11ca-11ed-8bc3-8534b82131e6","grant_number":"26380"}],"OA_place":"publisher","publication_status":"published","article_processing_charge":"No","language":[{"iso":"eng"}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2024-01-03T18:31:34Z","department":[{"_id":"NiBa"},{"_id":"GradSch"}],"ddc":["576"],"citation":{"ista":"Olusanya OO. 2024. Local adaptation, genetic load and extinction in metapopulations. Institute of Science and Technology Austria.","apa":"Olusanya, O. O. (2024). <i>Local adaptation, genetic load and extinction in metapopulations</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:14711\">https://doi.org/10.15479/at:ista:14711</a>","mla":"Olusanya, Oluwafunmilola O. <i>Local Adaptation, Genetic Load and Extinction in Metapopulations</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:14711\">10.15479/at:ista:14711</a>.","short":"O.O. Olusanya, Local Adaptation, Genetic Load and Extinction in Metapopulations, Institute of Science and Technology Austria, 2024.","chicago":"Olusanya, Oluwafunmilola O. “Local Adaptation, Genetic Load and Extinction in Metapopulations.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:14711\">https://doi.org/10.15479/at:ista:14711</a>.","ieee":"O. O. Olusanya, “Local adaptation, genetic load and extinction in metapopulations,” Institute of Science and Technology Austria, 2024.","ama":"Olusanya OO. Local adaptation, genetic load and extinction in metapopulations. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:14711\">10.15479/at:ista:14711</a>"},"day":"19","date_published":"2024-01-19T00:00:00Z","status":"public","ec_funded":1,"type":"dissertation","supervisor":[{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","last_name":"Barton","full_name":"Barton, Nicholas H","first_name":"Nicholas H"},{"last_name":"Polechova","full_name":"Polechova, Jitka","first_name":"Jitka"},{"full_name":"Sachdeva, Himani","first_name":"Himani","last_name":"Sachdeva"}],"year":"2024","publication_identifier":{"issn":["2663-337X"]},"has_accepted_license":"1","acknowledged_ssus":[{"_id":"SSU"}],"file":[{"date_created":"2024-01-03T18:30:13Z","date_updated":"2024-01-03T18:30:13Z","relation":"source_file","file_id":"14730","file_name":"FinalSubmission_Thesis_OLUSANYA.zip","checksum":"de179b1c6758f182ff0c70d8b38c1501","creator":"oolusany","file_size":16986244,"content_type":"application/zip","access_level":"closed"},{"success":1,"access_level":"open_access","content_type":"application/pdf","file_size":6460403,"creator":"oolusany","checksum":"0e331585e3cd4823320aab4e69e64ccf","file_name":"FinalSubmission2_Thesis_OLUSANYA.pdf","relation":"main_file","file_id":"14731","date_updated":"2024-01-03T18:31:34Z","date_created":"2024-01-03T18:31:34Z"}],"month":"01","degree_awarded":"PhD","tmp":{"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)","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"date_updated":"2026-04-07T12:54:29Z","corr_author":"1","date_created":"2023-12-26T22:49:53Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","title":"Local adaptation, genetic load and extinction in metapopulations","author":[{"last_name":"Olusanya","orcid":"0000-0003-1971-8314","id":"41AD96DC-F248-11E8-B48F-1D18A9856A87","first_name":"Oluwafunmilola O","full_name":"Olusanya, Oluwafunmilola O"}],"page":"183","doi":"10.15479/at:ista:14711","oa":1,"publisher":"Institute of Science and Technology Austria"},{"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2024-06-26T21:00:14Z","department":[{"_id":"TaHa"},{"_id":"GradSch"}],"ddc":["516"],"language":[{"iso":"eng"}],"publication_status":"published","article_processing_charge":"No","_id":"17156","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"17157"}]},"OA_place":"publisher","project":[{"name":"Topology of open smooth varieties with a torus action","_id":"34cd0f74-11ca-11ed-8bc3-bf0492a14a24","grant_number":"26525"}],"type":"dissertation","day":"25","date_published":"2024-06-25T00:00:00Z","status":"public","citation":{"apa":"Rychlewicz, K. P. (2024). <i>Equivariant cohomology and rings of functions</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17156\">https://doi.org/10.15479/at:ista:17156</a>","ista":"Rychlewicz KP. 2024. Equivariant cohomology and rings of functions. Institute of Science and Technology Austria.","ieee":"K. P. Rychlewicz, “Equivariant cohomology and rings of functions,” Institute of Science and Technology Austria, 2024.","ama":"Rychlewicz KP. Equivariant cohomology and rings of functions. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17156\">10.15479/at:ista:17156</a>","short":"K.P. Rychlewicz, Equivariant Cohomology and Rings of Functions, Institute of Science and Technology Austria, 2024.","mla":"Rychlewicz, Kamil P. <i>Equivariant Cohomology and Rings of Functions</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17156\">10.15479/at:ista:17156</a>.","chicago":"Rychlewicz, Kamil P. “Equivariant Cohomology and Rings of Functions.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17156\">https://doi.org/10.15479/at:ista:17156</a>."},"date_updated":"2026-04-07T12:55:46Z","corr_author":"1","keyword":["equivariant cohomology","zero schemes","algebraic groups","Lie algebras"],"date_created":"2024-06-23T15:07:06Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","degree_awarded":"PhD","tmp":{"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)","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"month":"06","supervisor":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9582-2634","first_name":"Tamás","full_name":"Hausel, Tamás"}],"year":"2024","has_accepted_license":"1","publication_identifier":{"issn":["2663-337X"]},"file":[{"access_level":"closed","file_size":2761814,"content_type":"application/zip","creator":"krychlew","checksum":"1610063569f5452f8a5acef728c2fc26","file_name":"thesis.zip","date_updated":"2024-06-26T21:00:14Z","file_id":"17179","relation":"source_file","date_created":"2024-06-26T20:56:27Z"},{"creator":"krychlew","file_size":3695952,"content_type":"application/pdf","access_level":"open_access","date_created":"2024-06-26T20:58:24Z","date_updated":"2024-06-26T20:58:24Z","file_id":"17180","relation":"main_file","file_name":"thesis.pdf","checksum":"7bbadb1fbc9ed2a1ecf54597f88af99c"}],"publisher":"Institute of Science and Technology Austria","oa":1,"page":"117","doi":"10.15479/at:ista:17156","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","title":"Equivariant cohomology and rings of functions","author":[{"first_name":"Kamil P","full_name":"Rychlewicz, Kamil P","last_name":"Rychlewicz","id":"85A07246-A8BF-11E9-B4FA-D9E3E5697425"}]},{"status":"public","day":"07","date_published":"2024-11-07T00:00:00Z","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.","citation":{"chicago":"Surendranadh, Parvathy. “Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18515\">https://doi.org/10.15479/at:ista:18515</a>.","short":"P. Surendranadh, Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange, Institute of Science and Technology Austria, 2024.","mla":"Surendranadh, Parvathy. <i>Effect of Population Structure on Neutral Genetic Variation and Barriers to Gene Exchange</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18515\">10.15479/at:ista:18515</a>.","ama":"Surendranadh P. Effect of population structure on neutral genetic variation and barriers to gene exchange. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18515\">10.15479/at:ista:18515</a>","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.","apa":"Surendranadh, P. (2024). <i>Effect of population structure on neutral genetic variation and barriers to gene exchange</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18515\">https://doi.org/10.15479/at:ista:18515</a>"},"type":"dissertation","article_processing_charge":"No","publication_status":"published","project":[{"grant_number":"P32166","_id":"05959E1C-7A3F-11EA-A408-12923DDC885E","name":"Snapdragon Speciation"},{"name":"Understanding the evolution of continuous genomes","_id":"bd6958e0-d553-11ed-ba76-86eba6a76c00","grant_number":"101055327"}],"OA_place":"publisher","_id":"18515","ddc":["576"],"department":[{"_id":"GradSch"},{"_id":"NiBa"}],"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2024-11-07T10:59:42Z","language":[{"iso":"eng"}],"doi":"10.15479/at:ista:18515","page":"219","title":"Effect of population structure on neutral genetic variation and barriers to gene exchange","author":[{"full_name":"Surendranadh, Parvathy","first_name":"Parvathy","orcid":"0000-0001-6395-386X","id":"455235B8-F248-11E8-B48F-1D18A9856A87","last_name":"Surendranadh"}],"alternative_title":["ISTA Thesis"],"oa_version":"Published Version","oa":1,"publisher":"Institute of Science and Technology 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H","orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","last_name":"Barton"}],"year":"2024","date_created":"2024-11-06T21:25:37Z","OA_type":"gold","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_updated":"2026-04-07T12:56:52Z","corr_author":"1","tmp":{"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)","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"degree_awarded":"PhD"},{"acknowledged_ssus":[{"_id":"Bio"},{"_id":"LifeSc"},{"_id":"M-Shop"},{"_id":"E-Lib"}],"year":"2024","month":"02","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-12-19T12:28:00Z","corr_author":"1","date_updated":"2026-04-07T12:56:36Z","author":[{"orcid":"0000-0003-1286-7368","id":"35A03822-F248-11E8-B48F-1D18A9856A87","last_name":"Gallei","full_name":"Gallei, Michelle C","first_name":"Michelle C"},{"last_name":"Truckenbrodt","id":"45812BD4-F248-11E8-B48F-1D18A9856A87","first_name":"Sven M","full_name":"Truckenbrodt, Sven M"},{"full_name":"Kreuzinger, Caroline","first_name":"Caroline","id":"382077BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kreuzinger"},{"orcid":"0009-0002-5890-120X","id":"F8660870-D756-11E9-98C5-34DFE5697425","last_name":"Inumella","full_name":"Inumella, Syamala","first_name":"Syamala"},{"first_name":"Vitali","full_name":"Vistunou, Vitali","last_name":"Vistunou","id":"7e146587-8972-11ed-ae7b-d7a32ea86a81"},{"full_name":"Sommer, Christoph M","first_name":"Christoph M","orcid":"0000-0003-1216-9105","id":"4DF26D8C-F248-11E8-B48F-1D18A9856A87","last_name":"Sommer"},{"orcid":"0000-0002-7667-6854","id":"3A0A06F4-F248-11E8-B48F-1D18A9856A87","last_name":"Tavakoli","full_name":"Tavakoli, Mojtaba","first_name":"Mojtaba"},{"last_name":"Agudelo Duenas","id":"40E7F008-F248-11E8-B48F-1D18A9856A87","first_name":"Nathalie","full_name":"Agudelo Duenas, Nathalie"},{"last_name":"Vorlaufer","orcid":"0009-0000-7590-3501","id":"937696FA-C996-11E9-8C7C-CF13E6697425","first_name":"Jakob","full_name":"Vorlaufer, Jakob"},{"last_name":"Jahr","id":"425C1CE8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0201-2315","first_name":"Wiebke","full_name":"Jahr, Wiebke"},{"first_name":"Marek","full_name":"Randuch, Marek","last_name":"Randuch","id":"6ac4636d-15b2-11ec-abd3-fb8df79972ae"},{"first_name":"Alexander J","full_name":"Johnson, Alexander J","last_name":"Johnson","orcid":"0000-0002-2739-8843","id":"46A62C3A-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Eva","full_name":"Benková, Eva","last_name":"Benková","id":"38F4F166-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8510-9739"},{"id":"4159519E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8302-7596","last_name":"Friml","full_name":"Friml, Jiří","first_name":"Jiří"},{"full_name":"Danzl, Johann G","first_name":"Johann G","orcid":"0000-0001-8559-3973","id":"42EFD3B6-F248-11E8-B48F-1D18A9856A87","last_name":"Danzl"}],"title":"Super-resolution expansion microscopy in plant roots","oa_version":"Preprint","doi":"10.1101/2024.02.21.581330","oa":1,"project":[{"call_identifier":"H2020","name":"Tracing Evolution of Auxin Transport and Polarity in Plants","grant_number":"742985","_id":"261099A6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"26AA4EF2-B435-11E9-9278-68D0E5697425","grant_number":"W1232-B24","name":"Molecular Drug Targets"},{"name":"UltraX - achieving sub-nanometer resolution in light microscopy using iterative X10 microscopy in combination with nanobodies and STED","grant_number":"ALTF 679-2018","_id":"269B5B22-B435-11E9-9278-68D0E5697425"}],"OA_place":"repository","related_material":{"record":[{"status":"public","relation":"later_version","id":"19003"},{"relation":"dissertation_contains","status":"public","id":"18681"}]},"_id":"18689","article_processing_charge":"No","publication_status":"draft","publication":"bioRxiv","language":[{"iso":"eng"}],"department":[{"_id":"EvBe"},{"_id":"JoDa"},{"_id":"JiFr"}],"abstract":[{"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.","lang":"eng"}],"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.","citation":{"ieee":"M. C. Gallei <i>et al.</i>, “Super-resolution expansion microscopy in plant roots,” <i>bioRxiv</i>. .","ama":"Gallei MC, Truckenbrodt SM, Kreuzinger C, et al. Super-resolution expansion microscopy in plant roots. <i>bioRxiv</i>. doi:<a href=\"https://doi.org/10.1101/2024.02.21.581330\">10.1101/2024.02.21.581330</a>","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.).","mla":"Gallei, Michelle C., et al. “Super-Resolution Expansion Microscopy in Plant Roots.” <i>BioRxiv</i>, doi:<a href=\"https://doi.org/10.1101/2024.02.21.581330\">10.1101/2024.02.21.581330</a>.","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.” <i>BioRxiv</i>, n.d. <a href=\"https://doi.org/10.1101/2024.02.21.581330\">https://doi.org/10.1101/2024.02.21.581330</a>.","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. <i>bioRxiv</i>. <a href=\"https://doi.org/10.1101/2024.02.21.581330\">https://doi.org/10.1101/2024.02.21.581330</a>","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, <a href=\"https://doi.org/10.1101/2024.02.21.581330\">10.1101/2024.02.21.581330</a>."},"status":"public","date_published":"2024-02-21T00:00:00Z","day":"21","type":"preprint","ec_funded":1,"main_file_link":[{"url":"https://doi.org/10.1101/2024.02.21.581330","open_access":"1"}]},{"publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","alternative_title":["ISTA Thesis"],"author":[{"id":"3A0A06F4-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7667-6854","last_name":"Tavakoli","full_name":"Tavakoli, Mojtaba","first_name":"Mojtaba"}],"title":"Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. 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(2024). <i>Developing molecular and structural tools for studying brain architecture with super resolution expansion microscopy. LICONN: Molecularly-informed connectomics reconstruction with light microscopy</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18681\">https://doi.org/10.15479/at:ista:18681</a>","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. 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Cultrera di Montesano, “Persistence and Morse theory for discrete geometric structures,” Institute of Science and Technology Austria, 2024.","ama":"Cultrera di Montesano S. Persistence and Morse theory for discrete geometric structures. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:15094\">10.15479/at:ista:15094</a>","short":"S. Cultrera di Montesano, Persistence and Morse Theory for Discrete Geometric Structures, Institute of Science and Technology Austria, 2024.","mla":"Cultrera di Montesano, Sebastiano. <i>Persistence and Morse Theory for Discrete Geometric Structures</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:15094\">10.15479/at:ista:15094</a>.","chicago":"Cultrera di Montesano, Sebastiano. “Persistence and Morse Theory for Discrete Geometric Structures.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:15094\">https://doi.org/10.15479/at:ista:15094</a>.","apa":"Cultrera di Montesano, S. (2024). <i>Persistence and Morse theory for discrete geometric structures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:15094\">https://doi.org/10.15479/at:ista:15094</a>","ista":"Cultrera di Montesano S. 2024. Persistence and Morse theory for discrete geometric structures. Institute of Science and Technology Austria."},"status":"public","date_published":"2024-03-08T00:00:00Z","day":"08","type":"dissertation","ec_funded":1,"OA_place":"publisher","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"},{"grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316","name":"Persistent Homology, Algorithms and Stochastic Geometry"},{"name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","call_identifier":"FWF"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"15091"},{"status":"public","relation":"part_of_dissertation","id":"11660"},{"id":"15090","status":"public","relation":"part_of_dissertation"},{"id":"15093","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"13182"},{"status":"public","relation":"part_of_dissertation","id":"11658"}]},"_id":"15094","article_processing_charge":"No","publication_status":"published","language":[{"iso":"eng"}],"ddc":["514","500","516"],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"file_date_updated":"2024-03-14T14:14:35Z","abstract":[{"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","lang":"eng"}]},{"pmid":1,"department":[{"_id":"HeEd"}],"ddc":["000"],"abstract":[{"text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram.","lang":"eng"}],"file_date_updated":"2025-01-09T07:39:41Z","volume":8,"scopus_import":"1","external_id":{"pmid":["39678706"]},"language":[{"iso":"eng"}],"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Journal of Applied and Computational Topology","publication_status":"published","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"Persistent Homology, Algorithms and Stochastic Geometry","grant_number":"I4887","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"call_identifier":"FWF","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science"}],"OA_place":"publisher","_id":"13182","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"intvolume":"         8","type":"journal_article","ec_funded":1,"status":"public","day":"01","date_published":"2024-10-01T00:00:00Z","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","citation":{"apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 8, 1101–1119.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 1101–1119, 2024.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. 2024;8:1101-1119. doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>","mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 1101–19, doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>."},"date_created":"2023-07-02T22:00:44Z","OA_type":"hybrid","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-04-07T12:58:47Z","corr_author":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"10","has_accepted_license":"1","publication_identifier":{"issn":["2367-1726"],"eissn":["2367-1734"]},"article_type":"original","file":[{"date_updated":"2025-01-09T07:39:41Z","relation":"main_file","file_id":"18783","date_created":"2025-01-09T07:39:41Z","checksum":"d493df5088c222b88d9ca46b623ad0ee","file_name":"2024_JourApplCompTopo_Biswas.pdf","creator":"dernst","access_level":"open_access","success":1,"file_size":476896,"content_type":"application/pdf"}],"year":"2024","publisher":"Springer Nature","oa":1,"doi":"10.1007/s41468-023-00126-9","page":"1101-1119","title":"Geometric characterization of the persistence of 1D maps","author":[{"full_name":"Biswas, Ranita","first_name":"Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"full_name":"Cultrera Di Montesano, Sebastiano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza"}],"oa_version":"Published Version"},{"publisher":"Society for Industrial and Applied Mathematics","oa":1,"doi":"10.1137/1.9781611977912.11","page":"243 - 295","author":[{"full_name":"Cultrera di Montesano, Sebastiano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"full_name":"Henzinger, Monika H","first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger"},{"first_name":"Lara","full_name":"Ost, Lara","last_name":"Ost"}],"title":"Dynamically maintaining the persistent homology of time series","oa_version":"Preprint","editor":[{"full_name":"Woodruff, David P.","first_name":"David P.","last_name":"Woodruff"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-03-08T10:27:39Z","corr_author":"1","date_updated":"2026-04-07T12:58:47Z","month":"01","publication_identifier":{"eisbn":["9781611977912"]},"year":"2024","type":"conference","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2311.01115"}],"arxiv":1,"status":"public","date_published":"2024-01-04T00:00:00Z","day":"04","acknowledgement":"The  first  and  second  authors  are  funded  by  the  European  Research  Council  under  the European Union’s Horizon 2020 research and innovation programme, ERC grant no. 788183,“Alpha Shape Theory Extended (Alpha)”, by the Wittgenstein Prize, FWF grant no. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, FWF grant no. I 02979-N35.The third author received funding by the European Research Council under the European Union’s Horizon 2020research  and  innovation  programme,  ERC  grant  no.  101019564,  “The  Design  of  Modern  Fully  Dynamic  DataStructures (MoDynStruct)”, and by the Austrian Science Fund through the Wittgenstein Prize with FWF grant no. Z 422-N, and also by FWF grant no. I 5982-N, and by FWF grant no. P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.  The fourth author is funded by the Vienna Graduate School on Computational Optimization, FWF project no. W1260-N35.","citation":{"ieee":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, and L. Ost, “Dynamically maintaining the persistent homology of time series,” in <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, Alexandria, VA, USA, 2024, pp. 243–295.","ama":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. Dynamically maintaining the persistent homology of time series. In: Woodruff DP, ed. <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>. Society for Industrial and Applied Mathematics; 2024:243-295. doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>","mla":"Cultrera di Montesano, Sebastiano, et al. “Dynamically Maintaining the Persistent Homology of Time Series.” <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, Society for Industrial and Applied Mathematics, 2024, pp. 243–95, doi:<a href=\"https://doi.org/10.1137/1.9781611977912.11\">10.1137/1.9781611977912.11</a>.","short":"S. Cultrera di Montesano, H. Edelsbrunner, M. Henzinger, L. Ost, in:, D.P. Woodruff (Ed.), Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Society for Industrial and Applied Mathematics, 2024, pp. 243–295.","chicago":"Cultrera di Montesano, Sebastiano, Herbert Edelsbrunner, Monika Henzinger, and Lara Ost. “Dynamically Maintaining the Persistent Homology of Time Series.” In <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i>, edited by David P. Woodruff, 243–95. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>.","apa":"Cultrera di Montesano, S., Edelsbrunner, H., Henzinger, M., &#38; Ost, L. (2024). Dynamically maintaining the persistent homology of time series. In D. P. Woodruff (Ed.), <i>Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)</i> (pp. 243–295). Alexandria, VA, USA: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611977912.11\">https://doi.org/10.1137/1.9781611977912.11</a>","ista":"Cultrera di Montesano S, Edelsbrunner H, Henzinger M, Ost L. 2024. Dynamically maintaining the persistent homology of time series. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SODA: Symposium on Discrete Algorithms, 243–295."},"department":[{"_id":"HeEd"},{"_id":"MoHe"}],"abstract":[{"lang":"eng","text":"We present a dynamic data structure for maintaining the persistent homology of a time series of real numbers. The data structure supports local operations, including the insertion and deletion of an item and the cutting and concatenating of lists, each in time O(log n + k), in which n counts the critical items and k the changes in the augmented persistence diagram. To achieve this, we design a tailor-made tree structure with an unconventional representation, referred to as banana tree, which may be useful in its own right."}],"scopus_import":"1","external_id":{"arxiv":["2311.01115"]},"quality_controlled":"1","language":[{"iso":"eng"}],"article_processing_charge":"No","publication_status":"published","publication":"Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","conference":{"end_date":"2024-01-10","start_date":"2024-01-07","location":"Alexandria, VA, USA","name":"SODA: Symposium on Discrete Algorithms"},"project":[{"name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"Mathematics, Computer Science","call_identifier":"FWF"},{"name":"The design and evaluation of modern fully dynamic data structures","grant_number":"101019564","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020"},{"name":"Efficient algorithms","grant_number":"Z00422","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer"}],"related_material":{"record":[{"id":"15094","relation":"dissertation_contains","status":"public"}]},"_id":"15093"},{"related_material":{"record":[{"relation":"later_version","status":"public","id":"20585"},{"id":"18979","status":"public","relation":"dissertation_contains"},{"relation":"dissertation_contains","status":"public","id":"15094"}]},"year":"2024","_id":"15091","OA_place":"repository","publication":"arXiv","publication_status":"draft","month":"02","article_processing_charge":"No","language":[{"iso":"eng"}],"external_id":{"arxiv":["2212.03128"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"corr_author":"1","abstract":[{"text":"Motivated by applications in the medical sciences, we study finite chromatic\r\nsets in Euclidean space from a topological perspective. Based on the persistent\r\nhomology for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers that describe the geometric micro- and macro-structure\r\nof how the color classes mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay and alpha complexes, and code that does these\r\ncomputations is provided.","lang":"eng"}],"date_updated":"2026-04-07T12:58:47Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"HeEd"}],"date_created":"2024-03-08T10:13:59Z","citation":{"ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>arXiv</i>. .","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2212.03128\">10.48550/arXiv.2212.03128</a>","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>ArXiv</i>, 2212.03128, doi:<a href=\"https://doi.org/10.48550/arXiv.2212.03128\">10.48550/arXiv.2212.03128</a>.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2212.03128\">https://doi.org/10.48550/arXiv.2212.03128</a>.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). Chromatic alpha complexes. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2212.03128\">https://doi.org/10.48550/arXiv.2212.03128</a>","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv, 2212.03128."},"oa_version":"Preprint","author":[{"last_name":"Cultrera di Montesano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano"},{"full_name":"Draganov, Ondrej","first_name":"Ondrej","orcid":"0000-0003-0464-3823","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","last_name":"Draganov"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"title":"Chromatic alpha complexes","date_published":"2024-02-07T00:00:00Z","day":"07","article_number":"2212.03128","doi":"10.48550/arXiv.2212.03128","arxiv":1,"status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2212.03128"}],"type":"preprint","oa":1}]