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HL is partially supported by the MUR-Prin 2022-202244A7YL “Gradient Flows and Non-Smooth Geometric Structures with Applications to Optimization and Machine Learning”, funded by the European Union - Next Generation EU. SI is supported in part by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council. Open access funding provided by Institute of Science and Technology (IST Austria).","date_updated":"2026-10-02T11:17:26Z","ddc":["000"],"publisher":"Springer Nature","_id":"14703","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"has_accepted_license":"1","keyword":["Optimal transport","Hamilton-Jacobi equation","convex optimization"],"corr_author":"1","abstract":[{"text":"We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton-Jacobi equation.","lang":"eng"}],"publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]},"doi":"10.1007/s10208-024-09686-3","file_date_updated":"2026-07-23T05:37:52Z","citation":{"mla":"Ishida, Sadashige, and Hugo Lavenant. “Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.” <i>Foundations of Computational Mathematics</i>, vol. 26, Springer Nature, 2026, pp. 349–84, doi:<a href=\"https://doi.org/10.1007/s10208-024-09686-3\">10.1007/s10208-024-09686-3</a>.","apa":"Ishida, S., &#38; Lavenant, H. (2026). Quantitative convergence of a discretization of dynamic optimal transport using the dual formulation. <i>Foundations of Computational Mathematics</i>. 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Towards a deeper understanding of meroblastic cleavage. Institute of Science and Technology Austria.","ieee":"X. Tong, “Towards a deeper understanding of meroblastic cleavage,” Institute of Science and Technology Austria, 2026.","ama":"Tong X. Towards a deeper understanding of meroblastic cleavage. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22804\">10.15479/AT-ISTA-22804</a>","short":"X. Tong, Towards a Deeper Understanding of Meroblastic Cleavage, Institute of Science and Technology Austria, 2026.","chicago":"Tong, Xin. “Towards a Deeper Understanding of Meroblastic Cleavage.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-22804\">https://doi.org/10.15479/AT-ISTA-22804</a>.","apa":"Tong, X. (2026). <i>Towards a deeper understanding of meroblastic cleavage</i>. 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Because holoblastic cleavage resembles canonical cytokinesis, its biochemical and mechanical basis has been extensively studied — an annular contractile ring forms at the equator and constricts in a purse-string-like manner, leading to the complete separation of two daughter cells. In contrast, although meroblastic cleavage occurs widely across the animal kingdom (e.g. in fish, reptiles, birds, and cephalopod molluscs), its mechanical basis remains largely unclear. During meroblastic cleavage, the cytokinetic furrow forms only at one pole and does not traverse the entire embryo, raising the question of how cytokinesis proceeds in the absence of a closed contractile ring. Moreover, the resulting daughter cells are not fully separated from the underlying yolk compartment, and how these blastomeres are subsequently cellularised remains unknown. This thesis takes the zebrafish as a model organism to address both questions. The first part characterises the biochemical and mechanical mechanisms underlying non-canonical meroblastic cleavage, revealing a two-phase process in which actomyosin cable contraction and cadherin-mediated membrane adhesion act sequentially to drive furrow ingression and invagination. The second part sheds light on the spatiotemporal dynamics by which individual blastomeres become cellularised, and uncovers a previously unrecognised contribution of central blastomeres to the yolk syncytial layer."}],"alternative_title":["ISTA Thesis"],"corr_author":"1","keyword":["meroblastic cleavage","cytokinesis","active gel theory","embryogenesis","zebrafish","adhesion"],"has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"CaHe"}],"_id":"22804","publisher":"Institute of Science and Technology Austria","ddc":["596","532","572"],"date_updated":"2026-10-05T08:56:10Z","acknowledgement":"I gratefully acknowledge the NOMIS Stiftung (Project ID 5061.844, Cytoplasmic\r\nself-organization into cell-like compartments as a common guiding principle in\r\nearly animal development) for funding my doctoral studies.","degree_awarded":"PhD","title":"Towards a deeper understanding of meroblastic cleavage","oa_version":"Published Version","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"07","language":[{"iso":"eng"}],"project":[{"_id":"917c023a-16d5-11f0-9cad-eb5cafc52090","name":"Cytoplasmic self-organization into cell-like compartments as a common guiding principle in early animal development"}]},{"project":[{"name":"NOMIS Fellowship Program","_id":"9B861AAC-BA93-11EA-9121-9846C619BF3A"},{"grant_number":"851288","call_identifier":"H2020","name":"Design Principles of Branching Morphogenesis","_id":"05943252-7A3F-11EA-A408-12923DDC885E"}],"oa_version":"None","user_id":"68b8ca59-c5b3-11ee-8790-cd641c68093d","month":"9","date_updated":"2026-10-05T08:56:09Z","_id":"22777","publisher":"Institute of Science and Technology Austria","title":"Towards a deeper understanding of meroblastic cleavage - supplementary movies","article_processing_charge":"No","doi":"10.15479/AT-ISTA-22777","citation":{"mla":"Tong, Xin. <i>Towards a Deeper Understanding of Meroblastic Cleavage - Supplementary Movies</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22777\">10.15479/AT-ISTA-22777</a>.","apa":"Tong, X. (2026). Towards a deeper understanding of meroblastic cleavage - supplementary movies. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-22777\">https://doi.org/10.15479/AT-ISTA-22777</a>","chicago":"Tong, Xin. “Towards a Deeper Understanding of Meroblastic Cleavage - Supplementary Movies.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-22777\">https://doi.org/10.15479/AT-ISTA-22777</a>.","short":"X. Tong, (2026).","ama":"Tong X. Towards a deeper understanding of meroblastic cleavage - supplementary movies. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22777\">10.15479/AT-ISTA-22777</a>","ieee":"X. 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Here, we show that alkali ions introduced during the solution synthesis of SnSe are retained through particle isolation and continue to influence the material during subsequent thermal processing, where they shape the evolution of the final polycrystalline material. Different SnSe powders were prepared using Li+, Na+, and K+ precursors, as well as tetramethylammonium (TMA+) precursors as a nonalkali reference for comparison, and all samples were consolidated under identical conditions. Although all three alkali ions were found in the matrix, at grain boundaries, and in segregated nanoscale regions, they partitioned differently and resulted in distinct grain sizes, defect distributions, and therefore transport properties. Li induced the strongest grain size heterogeneity and the lowest energy barriers, Na the best overall balance between carrier concentration and mobility, and K the broadest alkali-rich grain boundary regions along with the strongest interfacial penalty to charge carrier transport. These results show that residual alkali ions are not just remnants of solution synthesis but active determinants of microstructure and thermoelectric performance in SnSe.","lang":"eng"}],"publication_identifier":{"eissn":["1520-5002"],"issn":["0897-4756"]},"file_date_updated":"2026-10-06T12:11:04Z","doi":"10.1021/acs.chemmater.6c01284","citation":{"short":"C. Fiedler, S. Horta, N. Jakhar, K. Maji, T. Kleinhanns, J. Llorca, Q. Wang, M.G. Ramon, S. Das, V. Gavini, Y. Liu, M. Ibáñez, Chemistry of Materials 38 (2026) 9323–9332.","chicago":"Fiedler, Christine, Sharona Horta, Navita Jakhar, Krishnendu Maji, Tobias Kleinhanns, Jordi Llorca, Qi Wang, et al. “Alkali Ions Retained from Synthesis Govern Microstructure and Transport in Solution-Processed SnSe.” <i>Chemistry of Materials</i>. American Chemical Society, 2026. <a href=\"https://doi.org/10.1021/acs.chemmater.6c01284\">https://doi.org/10.1021/acs.chemmater.6c01284</a>.","ama":"Fiedler C, Horta S, Jakhar N, et al. Alkali ions retained from synthesis govern microstructure and transport in solution-processed SnSe. <i>Chemistry of Materials</i>. 2026;38(18):9323–9332. doi:<a href=\"https://doi.org/10.1021/acs.chemmater.6c01284\">10.1021/acs.chemmater.6c01284</a>","ieee":"C. Fiedler <i>et al.</i>, “Alkali ions retained from synthesis govern microstructure and transport in solution-processed SnSe,” <i>Chemistry of Materials</i>, vol. 38, no. 18. American Chemical Society, pp. 9323–9332, 2026.","ista":"Fiedler C, Horta S, Jakhar N, Maji K, Kleinhanns T, Llorca J, Wang Q, Ramon MG, Das S, Gavini V, Liu Y, Ibáñez M. 2026. Alkali ions retained from synthesis govern microstructure and transport in solution-processed SnSe. Chemistry of Materials. 38(18), 9323–9332.","mla":"Fiedler, Christine, et al. “Alkali Ions Retained from Synthesis Govern Microstructure and Transport in Solution-Processed SnSe.” <i>Chemistry of Materials</i>, vol. 38, no. 18, American Chemical Society, 2026, pp. 9323–9332, doi:<a href=\"https://doi.org/10.1021/acs.chemmater.6c01284\">10.1021/acs.chemmater.6c01284</a>.","apa":"Fiedler, C., Horta, S., Jakhar, N., Maji, K., Kleinhanns, T., Llorca, J., … Ibáñez, M. (2026). Alkali ions retained from synthesis govern microstructure and transport in solution-processed SnSe. <i>Chemistry of Materials</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acs.chemmater.6c01284\">https://doi.org/10.1021/acs.chemmater.6c01284</a>"},"article_processing_charge":"Yes (via OA deal)","title":"Alkali ions retained from synthesis govern microstructure and transport in solution-processed SnSe","external_id":{"pmid":["42787739"]},"acknowledgement":"ISTA and the Werner Siemens Foundation financially supported this work. The Scientific Service Units (SSU) of ISTA supported this research through resources provided by the Electron Microscopy Facility (EMF), Juan Aguilera Servin from the Nanofabrication facility (NNF). Special acknowledgments to the Ibá\r\nez group for their fruitful discussions and insights. K.M. acknowledges the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101034413 and PETRAIII at DESY for the synchrotron X-ray measurements under proposal No. I-20241048 EC. JL is a Serra Húnter Fellow and is grateful to the Academia Excellence program (Generalitat de Catalunya), project PID2024-156765OB-C21 funded by MICIU/AEI/10.13039/501100011033 and the European Regional Development Fund (FEDER), and María de Maeztu Units of Excellence Programme CEX2023-001300 M, funded by MCIN/AEI 10.13039/501100011033. VG and SD acknowledge the use of resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Y.L. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 754411, the National Natural Science Foundation of China (NSFC) (Grants No. 22209034).","date_updated":"2026-10-06T12:16:03Z","ddc":["540"],"_id":"22967","publisher":"American Chemical Society","scopus_import":"1","month":"09","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","project":[{"name":"HighTE: The Werner Siemens Laboratory for the High Throughput Discovery of Semiconductors for Waste Heat Recovery","_id":"9B8F7476-BA93-11EA-9121-9846C619BF3A"},{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"},{"grant_number":"754411","name":"ISTplus - Postdoctoral 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Sharona"},{"orcid":"0000-0001-7408-8197","id":"6ebe278d-ba0b-11ee-8184-f34cdc671de4","last_name":"Navita","full_name":"Navita, Navita","first_name":"Navita"},{"full_name":"Maji, Krishnendu","first_name":"Krishnendu","id":"76bc9e9f-ba0b-11ee-8184-90edabd17a58","last_name":"Maji"},{"full_name":"Kleinhanns, Tobias","first_name":"Tobias","id":"8BD9DE16-AB3C-11E9-9C8C-2A03E6697425","orcid":"0000-0003-1537-7436","last_name":"Kleinhanns"},{"last_name":"Llorca","first_name":"Jordi","full_name":"Llorca, Jordi"},{"id":"0d37923a-aca1-11ef-951f-fd411b71d5f0","last_name":"Wang","full_name":"Wang, Qi","first_name":"Qi"},{"last_name":"Ramon","id":"1ffff7cd-ed76-11ed-8d5f-be5e7c364eb9","full_name":"Ramon, Maria Garcia","first_name":"Maria Garcia"},{"last_name":"Das","full_name":"Das, Sambit","first_name":"Sambit"},{"full_name":"Gavini, Vikram","first_name":"Vikram","last_name":"Gavini"},{"orcid":"0000-0001-7313-6740","last_name":"Liu","id":"2A70014E-F248-11E8-B48F-1D18A9856A87","first_name":"Yu","full_name":"Liu, Yu"},{"first_name":"Maria","full_name":"Ibáñez, Maria","last_name":"Ibáñez","orcid":"0000-0001-5013-2843","id":"43C61214-F248-11E8-B48F-1D18A9856A87"}],"page":"9323–9332","das_tickbox":"0","OA_place":"publisher","ec_funded":1,"supplementarymaterial":"yes","volume":38,"file":[{"file_name":"2026_ChemistryMaterials_Fiedler.pdf","access_level":"open_access","date_created":"2026-10-06T12:11:04Z","checksum":"15e7866ca4fd57f5526737945651a6f2","relation":"main_file","date_updated":"2026-10-06T12:11:04Z","success":1,"content_type":"application/pdf","file_id":"23063","creator":"dernst","file_size":7461570}],"quality_controlled":"1","pmid":1,"article_type":"original","OA_type":"hybrid"},{"author":[{"first_name":"Zuzana","full_name":"Dunajova, 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B"}],"acknowledged_ssus":[{"_id":"Bio"},{"_id":"LifeSc"}],"day":"09","OA_place":"publisher","das_tickbox":"1","volume":12,"supplementarymaterial":"no","OA_type":"gold","article_type":"original","pmid":1,"quality_controlled":"1","file":[{"access_level":"open_access","date_created":"2026-10-06T11:30:48Z","file_name":"2026_ScienceAdv_Dunajova.pdf","checksum":"79f419b659650a39b3dfa58c782690a8","date_updated":"2026-10-06T11:30:48Z","relation":"main_file","content_type":"application/pdf","file_id":"23062","success":1,"file_size":11691064,"creator":"dernst"}],"publication_status":"published","fulldoi":"https://doi.org/10.1126/sciadv.aed0587","publication":"Science Advances","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2026-09-20T22:01:48Z","oa":1,"date_published":"2026-09-09T00:00:00Z","related_material":{"record":[{"status":"public","id":"21427","relation":"earlier_version"}]},"intvolume":"        12","year":"2026","PlanS_conform":"1","status":"public","researchdata_availability":"yes","issue":"37","type":"journal_article","language":[{"iso":"eng"}],"month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","oa_version":"Published Version","article_number":"eaed0587","dataavailabilitystatement":" All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials and the associated data and code repositories. Source data underlying all figures and supplementary figures have been deposited in a Zenodo repository (DOi: 10.5281/zenodo.21718217) and will be made publicly available upon publication. custom simulation and analysis codes used in this study are available at https://codeocean.com/capsule/1237446/tree. no unique biological materials were generated in this study. Microfluidic mask designs generated for this work are available from the corresponding authors upon reasonable request.","project":[{"_id":"34d75525-11ca-11ed-8bc3-89b6307fee9d","name":"Motile active matter models of migrating cells and chiral filaments","grant_number":"26360"},{"_id":"bd91e723-d553-11ed-ba76-fe7eeb2185fd","name":"Pushing from within: Control of cell shape, integrity and motility by cytoskeletal pushing forces","grant_number":"101071793"}],"corr_author":"1","has_accepted_license":"1","department":[{"_id":"EdHa"},{"_id":"MiSi"},{"_id":"GradSch"},{"_id":"AnSa"},{"_id":"NanoFab"}],"DOAJ_listed":"1","article_processing_charge":"Yes","doi":"10.1126/sciadv.aed0587","citation":{"ieee":"Z. Dunajova <i>et al.</i>, “Substrate heterogeneity promotes cancer cell dissemination through interface roughening,” <i>Science Advances</i>, vol. 12, no. 37. AAAS, 2026.","ista":"Dunajova Z, Tasciyan S, Majek J, Merrin J, Jenkins RP, Sahai E, Sixt MK, Hannezo EB. 2026. Substrate heterogeneity promotes cancer cell dissemination through interface roughening. Science Advances. 12(37), eaed0587.","chicago":"Dunajova, Zuzana, Saren Tasciyan, Juraj Majek, Jack Merrin, Robert P. Jenkins, Erik Sahai, Michael K Sixt, and Edouard B Hannezo. “Substrate Heterogeneity Promotes Cancer Cell Dissemination through Interface Roughening.” <i>Science Advances</i>. AAAS, 2026. <a href=\"https://doi.org/10.1126/sciadv.aed0587\">https://doi.org/10.1126/sciadv.aed0587</a>.","short":"Z. Dunajova, S. Tasciyan, J. Majek, J. Merrin, R.P. Jenkins, E. Sahai, M.K. Sixt, E.B. Hannezo, Science Advances 12 (2026).","ama":"Dunajova Z, Tasciyan S, Majek J, et al. Substrate heterogeneity promotes cancer cell dissemination through interface roughening. <i>Science Advances</i>. 2026;12(37). doi:<a href=\"https://doi.org/10.1126/sciadv.aed0587\">10.1126/sciadv.aed0587</a>","mla":"Dunajova, Zuzana, et al. “Substrate Heterogeneity Promotes Cancer Cell Dissemination through Interface Roughening.” <i>Science Advances</i>, vol. 12, no. 37, eaed0587, AAAS, 2026, doi:<a href=\"https://doi.org/10.1126/sciadv.aed0587\">10.1126/sciadv.aed0587</a>.","apa":"Dunajova, Z., Tasciyan, S., Majek, J., Merrin, J., Jenkins, R. P., Sahai, E., … Hannezo, E. B. (2026). Substrate heterogeneity promotes cancer cell dissemination through interface roughening. <i>Science Advances</i>. AAAS. <a href=\"https://doi.org/10.1126/sciadv.aed0587\">https://doi.org/10.1126/sciadv.aed0587</a>"},"file_date_updated":"2026-10-06T11:30:48Z","abstract":[{"lang":"eng","text":"Although studies of tumor invasion have mainly emphasized the evolution of genetic and epigenetic heterogeneity, cellular behaviors also depend on the physical microenvironment. Yet, the tumor microenvironment is both complex and continuously remodeled, making it hard to rigorously test its causal influence on tumor dissemination. Here, we adopted a reductionist approach to studying tumor cell invasion in microengineered environments of tunable patterned geometries. We find that not only the presence of obstacles but more unexpectedly their spatial disorder causes a drastic shift from a collective to a single-cell mode of invasion—comparable in strength to loss of cell-cell adhesion. Combining live-imaging and perturbation experiments with minimal biophysical modeling, we demonstrate that cell dissemination results both from local geometrical constraints and a global integration of spatial disorder over time. We identify generic universality classes of invasion dynamics dependent on environmental geometry, enabling us to identify quantitative physical principles for tumor dissemination."}],"publication_identifier":{"eissn":["2375-2548"]},"title":"Substrate heterogeneity promotes cancer cell dissemination through interface roughening","publisher":"AAAS","_id":"22963","date_updated":"2026-10-06T11:36:34Z","ddc":["570"],"acknowledgement":"We thank all the members of the Hannezo and Sixt groups for fruitful discussions and t. Kato for advice on the experimental setup. We are also thankful for support from the Scientific Service Units (SSU) of IST Austria through resources provided by the imaging and Optics Facility (iOF) and the Lab Support Facility (lSF). We used chatGPt (GPt- 5,OpenAi, 2025) to make minor grammatical and stylistic revisions to the original manuscript, which was written by us. We carefully reviewed and verified all changes and are solely responsible for all scientific content, data, interpretation, and conclusions. Funding: Z.D. has received funding from the Doctoral Programme of the Austrian Academy of Sciences (OeAW):grant agreement 26360. this work was supported by the European Research council (grant ERC- SyG 101071793 to M.S.). E.S. and R.P.J. are supported by the Francis Crick Institute, which receives its core funding from cancer Research UK (cc2040), the UK Medical Research council(cc2040), and the Wellcome trust (cc2040) and the European Research council (ERC Advanced Grant cAn_ORGAniSe, grant agreement number 101019366).","external_id":{"pmid":["42715298"]}},{"article_processing_charge":"Yes","citation":{"mla":"Babashah, Negar, et al. “Distortion of Multi-Winner Elections on the Line Metric: The Polar Comparison Rule.” <i>ACM Transactions on Economics and Computation</i>, 3843232, ACM, 2026, doi:<a href=\"https://doi.org/10.1145/3843232\">10.1145/3843232</a>.","apa":"Babashah, N., Karimi, H., Seddighin, M., &#38; Shahkarami, G. (2026). Distortion of multi-winner elections on the line metric: The polar comparison rule. <i>ACM Transactions on Economics and Computation</i>. ACM. <a href=\"https://doi.org/10.1145/3843232\">https://doi.org/10.1145/3843232</a>","ieee":"N. Babashah, H. Karimi, M. Seddighin, and G. Shahkarami, “Distortion of multi-winner elections on the line metric: The polar comparison rule,” <i>ACM Transactions on Economics and Computation</i>. ACM, 2026.","ista":"Babashah N, Karimi H, Seddighin M, Shahkarami G. 2026. Distortion of multi-winner elections on the line metric: The polar comparison rule. ACM Transactions on Economics and Computation., 3843232.","chicago":"Babashah, Negar, Hasti Karimi, Masoud Seddighin, and Golnoosh Shahkarami. “Distortion of Multi-Winner Elections on the Line Metric: The Polar Comparison Rule.” <i>ACM Transactions on Economics and Computation</i>. ACM, 2026. <a href=\"https://doi.org/10.1145/3843232\">https://doi.org/10.1145/3843232</a>.","short":"N. Babashah, H. Karimi, M. Seddighin, G. Shahkarami, ACM Transactions on Economics and Computation (2026).","ama":"Babashah N, Karimi H, Seddighin M, Shahkarami G. Distortion of multi-winner elections on the line metric: The polar comparison rule. <i>ACM Transactions on Economics and Computation</i>. 2026. doi:<a href=\"https://doi.org/10.1145/3843232\">10.1145/3843232</a>"},"doi":"10.1145/3843232","abstract":[{"lang":"eng","text":"We study the problem of minimizing metric distortion in multi-winner elections, where a committee of size k is selected from a set of candidates based on voters’ ordinal preferences. We assume that voters and candidates are embedded on a line metric, and social cost is determined by the underlying metric distances.\r\nThe distortion of a voting rule is the worst-case ratio between the social cost of the elected committee and an optimal committee. Previous work has focused on the q-cost model, in which a voter’s cost is given by the distance to their qth closest committee member. Here, we study the additive cost, where a voter’s cost is the sum of distances to all committee members.\r\nWe introduce the Polar Comparison Rule and analyze its distortion under utilitarian additive cost. We show that it achieves a distortion upper bound of almost 2.33 for all committee sizes k > 4, improving upon the previously best-known upper bound of 3. Moreover, for k = 2 and k = 3, we establish tight distortion bounds of 2.41 and 2.33, respectively. We also derive lower bounds that depend on the parity of k and analyze the behavior of distortion for small and large committee sizes. Finally, we extend our results to the egalitarian additive cost."}],"publication_identifier":{"eissn":["2167-8383"],"issn":["2167-8375"]},"corr_author":"1","has_accepted_license":"1","department":[{"_id":"GradSch"}],"_id":"22971","publisher":"ACM","ddc":["000"],"date_updated":"2026-10-06T12:38:17Z","title":"Distortion of multi-winner elections on the line metric: The polar comparison rule","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1145/3843232"}],"oa_version":"Published Version","month":"09","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","article_number":"3843232","publication_status":"epub_ahead","fulldoi":"https://doi.org/10.1145/3843232","publication":"ACM Transactions on Economics and Computation","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","year":"2026","PlanS_conform":"1","type":"journal_article","date_created":"2026-09-22T05:37:33Z","oa":1,"date_published":"2026-09-01T00:00:00Z","OA_place":"publisher","author":[{"orcid":"0009-0007-0203-9725","last_name":"Babashah","id":"95f4864e-6ec9-11f0-b3f6-b8422c64859e","full_name":"Babashah, Negar","first_name":"Negar"},{"full_name":"Karimi, Hasti","first_name":"Hasti","last_name":"Karimi"},{"last_name":"Seddighin","full_name":"Seddighin, Masoud","first_name":"Masoud"},{"first_name":"Golnoosh","full_name":"Shahkarami, Golnoosh","last_name":"Shahkarami"}],"day":"01","article_type":"original","OA_type":"gold","quality_controlled":"1"},{"pmid":1,"article_type":"original","OA_type":"hybrid","quality_controlled":"1","supplementarymaterial":"yes","volume":172,"OA_place":"publisher","page":"48-55","das_tickbox":"1","author":[{"orcid":"0000-0002-6246-1465","last_name":"Khudiakova","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","first_name":"Kseniia","full_name":"Khudiakova, Kseniia"},{"orcid":"0000-0002-8548-5240","last_name":"Barton","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","full_name":"Barton, Nicholas H"},{"last_name":"Arnqvist","first_name":"Göran","full_name":"Arnqvist, Göran"}],"day":"17","PlanS_conform":"1","year":"2026","researchdata_availability":"no","status":"public","intvolume":"       172","related_material":{"record":[{"relation":"earlier_version","id":"21968","status":"public"}]},"type":"journal_article","date_created":"2026-09-27T22:01:51Z","date_published":"2026-09-17T00:00:00Z","oa":1,"fulldoi":"https://doi.org/10.1016/j.tpb.2026.09.001","publication_status":"epub_ahead","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication":"Theoretical Population Biology","project":[{"name":"The impact of deleterious mutations on small populations","_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293"}],"dataavailabilitystatement":"The Python code used for the numerical analyses is available online at https://github.com/khudyakovaks/Sign-epistasis-extends-the-effects-of-balancing-selection-on-genetic-diversity.","main_file_link":[{"url":"https://doi.org/10.1016/j.tpb.2026.09.001","open_access":"1"}],"oa_version":"Published Version","month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"scopus_import":"1","ddc":["500","570"],"date_updated":"2026-10-07T06:38:02Z","_id":"22998","external_id":{"pmid":["42722132"],"biorxivid":["10.1101/2025.04.09.647826"]},"acknowledgement":"This work was funded by grants from the Swedish Research Council (2023-03730 to G.A.) and the DOC fellowship from the Austrian Academy of Science (26293 to K.K.). We thank L. Rowe for valuable discussions.","title":"Sign epistasis extends the effects of balancing selection on genetic diversity","biorxivid":1,"article_processing_charge":"Yes (via OA deal)","abstract":[{"text":"Balancing selection, a form of selection that maintains genetic diversity, is difficult to detect, and the importance of balancing selection for the maintenance of genetic variation may be larger than often assumed. We model the possibility that the diversity-promoting effects of balancing selection extend to other loci that show sign epistasis with a locus under balancing selection. Rather than focusing on overdominance, as was done in previous efforts, we explore the effects of negative frequency dependence and show that this has important effects on the conditions under which the diversity-promoting effect of epistasis can occur in diploids. Our results show that not only recombination rate but also the dominance of sign epistasis are key parameters that determine the maintenance of polymorphism beyond the locus under direct balancing selection. We suggest that the effect we explore may play a significant role, especially when balancing selection acts on major effect loci.","lang":"eng"}],"publication_identifier":{"eissn":["1096-0325"],"issn":["0040-5809"]},"citation":{"mla":"Khudiakova, Kseniia, et al. “Sign Epistasis Extends the Effects of Balancing Selection on Genetic Diversity.” <i>Theoretical Population Biology</i>, vol. 172, 2026, pp. 48–55, doi:<a href=\"https://doi.org/10.1016/j.tpb.2026.09.001\">10.1016/j.tpb.2026.09.001</a>.","apa":"Khudiakova, K., Barton, N. H., &#38; Arnqvist, G. (2026). Sign epistasis extends the effects of balancing selection on genetic diversity. <i>Theoretical Population Biology</i>. <a href=\"https://doi.org/10.1016/j.tpb.2026.09.001\">https://doi.org/10.1016/j.tpb.2026.09.001</a>","chicago":"Khudiakova, Kseniia, Nicholas H Barton, and Göran Arnqvist. “Sign Epistasis Extends the Effects of Balancing Selection on Genetic Diversity.” <i>Theoretical Population Biology</i>, 2026. <a href=\"https://doi.org/10.1016/j.tpb.2026.09.001\">https://doi.org/10.1016/j.tpb.2026.09.001</a>.","short":"K. Khudiakova, N.H. Barton, G. Arnqvist, Theoretical Population Biology 172 (2026) 48–55.","ama":"Khudiakova K, Barton NH, Arnqvist G. Sign epistasis extends the effects of balancing selection on genetic diversity. <i>Theoretical Population Biology</i>. 2026;172:48-55. doi:<a href=\"https://doi.org/10.1016/j.tpb.2026.09.001\">10.1016/j.tpb.2026.09.001</a>","ieee":"K. Khudiakova, N. H. Barton, and G. Arnqvist, “Sign epistasis extends the effects of balancing selection on genetic diversity,” <i>Theoretical Population Biology</i>, vol. 172. pp. 48–55, 2026.","ista":"Khudiakova K, Barton NH, Arnqvist G. 2026. Sign epistasis extends the effects of balancing selection on genetic diversity. Theoretical Population Biology. 172, 48–55."},"doi":"10.1016/j.tpb.2026.09.001","keyword":["Sign epistasis","Balancing selection","Within-population genetic variation"],"corr_author":"1","department":[{"_id":"JaMa"},{"_id":"GradSch"},{"_id":"NiBa"}],"has_accepted_license":"1"},{"oa_version":"Published Version","scopus_import":"1","month":"09","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777"}],"article_number":"e70095","citation":{"mla":"Hollom, Lawrence, et al. “Approximate Itai–Zehavi Conjecture for Random Graphs.” <i>Random Structures and Algorithms</i>, vol. 69, no. 2, e70095, Wiley, 2026, doi:<a href=\"https://doi.org/10.1002/rsa.70095\">10.1002/rsa.70095</a>.","apa":"Hollom, L., Lichev, L., Mond, A., Portier, J., &#38; Wang, Y. (2026). Approximate Itai–Zehavi conjecture for random graphs. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.70095\">https://doi.org/10.1002/rsa.70095</a>","ieee":"L. Hollom, L. Lichev, A. Mond, J. Portier, and Y. Wang, “Approximate Itai–Zehavi conjecture for random graphs,” <i>Random Structures and Algorithms</i>, vol. 69, no. 2. Wiley, 2026.","ista":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. 2026. Approximate Itai–Zehavi conjecture for random graphs. Random Structures and Algorithms. 69(2), e70095.","short":"L. Hollom, L. Lichev, A. Mond, J. Portier, Y. Wang, Random Structures and Algorithms 69 (2026).","chicago":"Hollom, Lawrence, Lyuben Lichev, Adva Mond, Julien Portier, and Yiting Wang. “Approximate Itai–Zehavi Conjecture for Random Graphs.” <i>Random Structures and Algorithms</i>. Wiley, 2026. <a href=\"https://doi.org/10.1002/rsa.70095\">https://doi.org/10.1002/rsa.70095</a>.","ama":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. Approximate Itai–Zehavi conjecture for random graphs. <i>Random Structures and Algorithms</i>. 2026;69(2). doi:<a href=\"https://doi.org/10.1002/rsa.70095\">10.1002/rsa.70095</a>"},"doi":"10.1002/rsa.70095","file_date_updated":"2026-10-07T07:10:43Z","publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"abstract":[{"lang":"eng","text":"A famous conjecture by Itai and Zehavi states that, for every 𝑑\r\n-vertex-connected graph 𝐺\r\n and every vertex 𝑟\r\n in 𝐺\r\n, there are 𝑑\r\n spanning trees of 𝐺\r\n such that, for every vertex 𝑣\r\n in 𝐺 ∖{𝑟}\r\n, the paths between 𝑟\r\n and 𝑣\r\n in different trees are internally vertex-disjoint. We show that with high probability the Itai–Zehavi conjecture holds asymptotically for the Erdős–Rényi random graph 𝐺⁡(𝑛,𝑝)\r\n when 𝑛⁢𝑝 =𝜔⁡(log⁡𝑛)\r\n and for random regular graphs 𝐺⁡(𝑛,𝑑)\r\n when 𝑑 =𝜔⁡(log⁡𝑛)\r\n. Moreover, we essentially confirm the conjecture up to a constant factor for sparser random regular graphs. This answers a question of Draganić and Krivelevich positively. Our proof makes use of recent developments on sprinkling techniques in random regular graphs."}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","department":[{"_id":"MaKw"},{"_id":"GradSch"}],"acknowledgement":"Hollom was supported by the Internal Graduate Studentship of Trinity College, Cambridge. Mond was supported by UK Research and Innovation grant MR/W007320/2. Wang was supported by the ERC Starting Grant “RANDSTRUCT” No. 101076777. Lichev was supported by the Austrian Science Fund (FWF) [10.55776/ESP624]. For open access purposes, the authors have applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission. Open Access funding provided by Technische Universitat Wien.\r\n\r\nPart of this research was done during a visit of the fourth author to IST Austria. We thank IST Austria for its hospitality. We also thank the anonymous referees for their comments and suggestions. Open Access funding provided by Technische Universitat Wien. This work was supported by the European Research Council, UK Research and Innovation, the Austrian Science Fund, and Trinity College.","external_id":{"arxiv":["2506.23970"]},"publisher":"Wiley","_id":"23001","date_updated":"2026-10-07T07:13:30Z","ddc":["500"],"title":"Approximate Itai–Zehavi conjecture for random graphs","das_tickbox":"0","OA_place":"publisher","day":"01","author":[{"full_name":"Hollom, Lawrence","first_name":"Lawrence","last_name":"Hollom"},{"id":"9aa8388e-d003-11ee-8458-c4c1d7447977","last_name":"Lichev","full_name":"Lichev, Lyuben","first_name":"Lyuben"},{"last_name":"Mond","first_name":"Adva","full_name":"Mond, Adva"},{"first_name":"Julien","full_name":"Portier, Julien","last_name":"Portier"},{"full_name":"Wang, Yiting","first_name":"Yiting","last_name":"Wang","id":"1917d194-076e-11ed-97cd-837255f88785"}],"quality_controlled":"1","file":[{"date_updated":"2026-10-07T07:10:43Z","relation":"main_file","checksum":"9a786460a47542f24576e947987e558a","file_name":"2026_RandomStructAlgorithms_Hollom.pdf","date_created":"2026-10-07T07:10:43Z","access_level":"open_access","creator":"dernst","file_size":457581,"success":1,"file_id":"23068","content_type":"application/pdf"}],"OA_type":"hybrid","article_type":"original","volume":69,"supplementarymaterial":"yes","publication":"Random Structures and Algorithms","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.1002/rsa.70095","issue":"2","type":"journal_article","intvolume":"        69","year":"2026","researchdata_availability":"no","status":"public","PlanS_conform":"1","oa":1,"date_published":"2026-09-01T00:00:00Z","date_created":"2026-09-27T22:01:52Z"},{"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"10","language":[{"iso":"eng"}],"oa_version":"Published Version","project":[{"grant_number":"949120","_id":"0aa60e99-070f-11eb-9043-a6de6bdc3afa","name":"Tribocharge: a multi-scale approach to an enduring problem in physics","call_identifier":"H2020"},{"grant_number":"805041","call_identifier":"H2020","name":"Organization of CLoUdS, and implications of Tropical  cyclones and for the Energetics of the tropics, in current and waRming climate","_id":"629205d8-2b32-11ec-9570-e1356ff73576"}],"corr_author":"1","alternative_title":["ISTA Thesis"],"OA_embargo":"6","keyword":["aerosol physics","electrostatics","optics","optical tweezers","atmospheric electricity"],"has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"ScWa"},{"_id":"CaMu"}],"article_processing_charge":"No","citation":{"ista":"Stöllner A. 2026. Microscale electrical behavior of highly charged individual aerosol particles using optical tweezers. Institute of Science and Technology Austria.","ieee":"A. Stöllner, “Microscale electrical behavior of highly charged individual aerosol particles using optical tweezers,” Institute of Science and Technology Austria, 2026.","ama":"Stöllner A. Microscale electrical behavior of highly charged individual aerosol particles using optical tweezers. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-23033\">10.15479/AT-ISTA-23033</a>","chicago":"Stöllner, Andrea. “Microscale Electrical Behavior of Highly Charged Individual Aerosol Particles Using Optical Tweezers.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-23033\">https://doi.org/10.15479/AT-ISTA-23033</a>.","short":"A. Stöllner, Microscale Electrical Behavior of Highly Charged Individual Aerosol Particles Using Optical Tweezers, Institute of Science and Technology Austria, 2026.","apa":"Stöllner, A. (2026). <i>Microscale electrical behavior of highly charged individual aerosol particles using optical tweezers</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-23033\">https://doi.org/10.15479/AT-ISTA-23033</a>","mla":"Stöllner, Andrea. <i>Microscale Electrical Behavior of Highly Charged Individual Aerosol Particles Using Optical Tweezers</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-23033\">10.15479/AT-ISTA-23033</a>."},"file_date_updated":"2026-10-05T12:06:04Z","doi":"10.15479/AT-ISTA-23033","publication_identifier":{"issn":["2663-337X"]},"title":"Microscale electrical behavior of highly charged individual aerosol particles using optical tweezers","publisher":"Institute of Science and Technology Austria","_id":"23033","date_updated":"2026-10-09T11:09:10Z","ddc":["530"],"degree_awarded":"PhD","acknowledgement":"This project has received funding from the European Research Council (ERC) under \r\nthe European Union’s Horizon 2020 research and innovation programme (Grant \r\nagreements No. 949120 and No. 805041). This research was supported by the \r\nScientific Service Units of The Institute of Science and Technology Austria (ISTA) \r\nthrough resources provided by the Miba Machine Shop and the Imaging & Optics \r\nFacility. 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De Zordo, C.N. Borja Espinosa, R. Al Hyder, J. Li, W. Kersten, A. Kanagin, G. Koutentakis, F. Kluibenschedl, M. Lemeshko, J.M. Fink, J. Schmiedmayer, E. Redchenko, in:, Quantum 2.0 Conference and Exhibition, Optica Publishing Group, 2026.","chicago":"De Zordo, Nikolaus, Carla N Borja Espinosa, Ragheed Al Hyder, Jinglun Li, Wenzel Kersten, Andrew Kanagin, Georgios Koutentakis, et al. “Detecting Polar Molecules with Superconducting Microwave Resonators.” In <i>Quantum 2.0 Conference and Exhibition</i>. Optica Publishing Group, 2026.","ama":"De Zordo N, Borja Espinosa CN, Al Hyder R, et al. Detecting polar molecules with superconducting microwave resonators. In: <i>Quantum 2.0 Conference and Exhibition</i>. Optica Publishing Group; 2026.","ieee":"N. De Zordo <i>et al.</i>, “Detecting polar molecules with superconducting microwave resonators,” in <i>Quantum 2.0 Conference and Exhibition</i>, Glasgow, United Kingdom, 2026.","ista":"De Zordo N, Borja Espinosa CN, Al Hyder R, Li J, Kersten W, Kanagin A, Koutentakis G, Kluibenschedl F, Lemeshko M, Fink JM, Schmiedmayer J, Redchenko E. 2026. Detecting polar molecules with superconducting microwave resonators. Quantum 2.0 Conference and Exhibition. Quantum 2.0, Technical Digest Series, , QM4D.3.","mla":"De Zordo, Nikolaus, et al. “Detecting Polar Molecules with Superconducting Microwave Resonators.” <i>Quantum 2.0 Conference and Exhibition</i>, QM4D.3, Optica Publishing Group, 2026.","apa":"De Zordo, N., Borja Espinosa, C. N., Al Hyder, R., Li, J., Kersten, W., Kanagin, A., … Redchenko, E. (2026). Detecting polar molecules with superconducting microwave resonators. In <i>Quantum 2.0 Conference and Exhibition</i>. Glasgow, United Kingdom: Optica Publishing Group."},"abstract":[{"text":"We report progress toward strong electric-dipole coupling of polar molecules in cryogenic crystals to superconducting microwave resonators for hybrid quantum computing. We detect crystal-shifted inversion transitions of ammonia in neon using a multimode resonator.","lang":"eng"}],"publication_identifier":{"isbn":["9781957171616"]},"alternative_title":["Technical Digest Series"],"conference":{"location":"Glasgow, United Kingdom","end_date":"2026-06-18","name":"Quantum 2.0","start_date":"2026-06-15"},"department":[{"_id":"JoFi"},{"_id":"GradSch"},{"_id":"MiLe"}],"OA_type":"closed access","quality_controlled":"1","article_number":"QM4D.3","das_tickbox":"0","oa_version":"None","author":[{"last_name":"De Zordo","first_name":"Nikolaus","full_name":"De Zordo, Nikolaus"},{"first_name":"Carla N","full_name":"Borja Espinosa, Carla N","last_name":"Borja Espinosa","id":"18777c01-896a-11ed-bdf8-e4851dc07d16"},{"full_name":"Al Hyder, Ragheed","first_name":"Ragheed","id":"d1c405be-ae15-11ed-8510-ccf53278162e","last_name":"Al Hyder"},{"id":"ff19510a-0d2c-11ef-b018-c338ad2f4325","last_name":"Li","full_name":"Li, Jinglun","first_name":"Jinglun"},{"last_name":"Kersten","full_name":"Kersten, Wenzel","first_name":"Wenzel"},{"last_name":"Kanagin","first_name":"Andrew","full_name":"Kanagin, Andrew"},{"full_name":"Koutentakis, Georgios","first_name":"Georgios","last_name":"Koutentakis","id":"d7b23d3a-9e21-11ec-b482-f76739596b95"},{"id":"7499e70e-eb2c-11ec-b98b-f925648bc9d9","last_name":"Kluibenschedl","orcid":"0000-0003-4695-5526","full_name":"Kluibenschedl, Florian","first_name":"Florian"},{"full_name":"Lemeshko, Mikhail","first_name":"Mikhail","last_name":"Lemeshko","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802"},{"orcid":"0000-0001-8112-028X","id":"4B591CBA-F248-11E8-B48F-1D18A9856A87","last_name":"Fink","first_name":"Johannes M","full_name":"Fink, Johannes M"},{"last_name":"Schmiedmayer","full_name":"Schmiedmayer, Jörg","first_name":"Jörg"},{"id":"2C21D6E8-F248-11E8-B48F-1D18A9856A87","last_name":"Redchenko","first_name":"Elena","full_name":"Redchenko, Elena"}],"language":[{"iso":"eng"}],"month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","day":"01"},{"citation":{"ieee":"A. Militaru <i>et al.</i>, “Electro-optic conversion of itinerant Fock states,” in <i>Quantum 2.0 Conference and Exhibition</i>, Glasgow, United Kingdom, 2026.","ista":"Militaru A, Werner T, Riyazi E, Hawaldar S, Sahu R, Arnold GM, Falthansl-Scheinecker P, Sanchez Naranjo JA, Loi D, Kapoor L, Zemlicka M, Qiu L, Fink JM. 2026. Electro-optic conversion of itinerant Fock states. Quantum 2.0 Conference and Exhibition. Quantum 2.0, Technical Digest Series, , QM2A.1.","short":"A. Militaru, T. Werner, E. Riyazi, S. Hawaldar, R. Sahu, G.M. Arnold, P. Falthansl-Scheinecker, J.A. Sanchez Naranjo, D. Loi, L. Kapoor, M. Zemlicka, L. Qiu, J.M. Fink, in:, Quantum 2.0 Conference and Exhibition, Optica Publishing Group, 2026.","chicago":"Militaru, Andrei, Thomas Werner, Erfan Riyazi, Samarth Hawaldar, Rishabh Sahu, Georg M Arnold, Paul Falthansl-Scheinecker, et al. “Electro-Optic Conversion of Itinerant Fock States.” In <i>Quantum 2.0 Conference and Exhibition</i>. Optica Publishing Group, 2026.","ama":"Militaru A, Werner T, Riyazi E, et al. Electro-optic conversion of itinerant Fock states. In: <i>Quantum 2.0 Conference and Exhibition</i>. Optica Publishing Group; 2026.","mla":"Militaru, Andrei, et al. “Electro-Optic Conversion of Itinerant Fock States.” <i>Quantum 2.0 Conference and Exhibition</i>, QM2A.1, Optica Publishing Group, 2026.","apa":"Militaru, A., Werner, T., Riyazi, E., Hawaldar, S., Sahu, R., Arnold, G. M., … Fink, J. M. (2026). Electro-optic conversion of itinerant Fock states. In <i>Quantum 2.0 Conference and Exhibition</i>. Glasgow, United Kingdom: Optica Publishing Group."},"publication":"Quantum 2.0 Conference and Exhibition","abstract":[{"lang":"eng","text":"Superconducting qubits face scaling challenges due to millikelvin temperature requirements. Here we demonstrate the generation and low-noise upconversion of single microwave photons to telecom frequencies, paving the way for quantum networks with superconducting qubits."}],"publication_identifier":{"isbn":["9781957171616"]},"publication_status":"published","article_processing_charge":"No","department":[{"_id":"JoFi"},{"_id":"GradSch"},{"_id":"GeKa"}],"alternative_title":["Technical Digest Series"],"corr_author":"1","conference":{"start_date":"2026-06-15","end_date":"2026-06-18","name":"Quantum 2.0","location":"Glasgow, United Kingdom"},"type":"conference","publisher":"Optica Publishing Group","_id":"23056","status":"public","year":"2026","date_updated":"2026-10-12T08:53:25Z","date_published":"2026-09-01T00:00:00Z","title":"Electro-optic conversion of itinerant Fock states","date_created":"2026-10-04T22:01:57Z","oa_version":"None","scopus_import":"1","day":"01","author":[{"id":"d67706f8-8eb1-11ee-ad1b-9c30dfa19e0b","last_name":"Militaru","full_name":"Militaru, Andrei","first_name":"Andrei"},{"id":"1fcd8497-dba3-11ea-a45e-c6fbd715f7c7","last_name":"Werner","orcid":"0009-0001-2346-5236","full_name":"Werner, Thomas","first_name":"Thomas"},{"id":"53322f94-5355-11ee-ae5a-ff6f81c87d51","last_name":"Riyazi","first_name":"Erfan","full_name":"Riyazi, Erfan"},{"first_name":"Samarth","full_name":"Hawaldar, Samarth","last_name":"Hawaldar","orcid":"0000-0002-1965-4309","id":"221708e1-1ff6-11ee-9fa6-85146607433e"},{"last_name":"Sahu","id":"47D26E34-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6264-2162","full_name":"Sahu, Rishabh","first_name":"Rishabh"},{"first_name":"Georg M","full_name":"Arnold, Georg M","last_name":"Arnold","orcid":"0000-0003-1397-7876","id":"3770C838-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Falthansl-Scheinecker, Paul","first_name":"Paul","last_name":"Falthansl-Scheinecker","id":"85b43b21-15b2-11ec-abd3-e2c252cc2285"},{"full_name":"Sanchez Naranjo, Jennifer Anais","first_name":"Jennifer Anais","last_name":"Sanchez Naranjo","id":"0fd10295-ebd4-11ec-b0f1-c1c8465143f9"},{"last_name":"Loi","id":"a24803ec-c619-11f1-873b-95804e96f22f","full_name":"Loi, Dante","first_name":"Dante"},{"full_name":"Kapoor, Lucky","first_name":"Lucky","last_name":"Kapoor","id":"84b9700b-15b2-11ec-abd3-831089e67615","orcid":"0000-0001-8319-2148"},{"full_name":"Zemlicka, Martin","first_name":"Martin","orcid":"0009-0005-0878-3032","id":"2DCF8DE6-F248-11E8-B48F-1D18A9856A87","last_name":"Zemlicka"},{"id":"45e99c0d-1eb1-11eb-9b96-ed8ab2983cac","orcid":"0000-0003-4345-4267","last_name":"Qiu","full_name":"Qiu, Liu","first_name":"Liu"},{"full_name":"Fink, Johannes M","first_name":"Johannes M","orcid":"0000-0001-8112-028X","last_name":"Fink","id":"4B591CBA-F248-11E8-B48F-1D18A9856A87"}],"month":"09","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"closed access","article_number":"QM2A.1"},{"year":"2026","status":"public","researchdata_availability":"yes","intvolume":"        17","type":"journal_article","date_created":"2026-10-11T22:02:04Z","date_published":"2026-09-01T00:00:00Z","oa":1,"fulldoi":"https://doi.org/10.1038/s41467-026-77117-8","publication_status":"published","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication":"Nature Communications","pmid":1,"article_type":"original","OA_type":"gold","file":[{"file_name":"2026_NatureComm_Wang.pdf","date_created":"2026-10-12T10:57:42Z","access_level":"open_access","relation":"main_file","date_updated":"2026-10-12T10:57:42Z","checksum":"f39b50a550623a65aea2405b527e068c","success":1,"file_id":"23107","content_type":"application/pdf","creator":"dernst","file_size":1559219}],"quality_controlled":"1","supplementarymaterial":"yes","volume":17,"OA_place":"publisher","das_tickbox":"1","author":[{"id":"8dff9c62-32b0-11ee-9fa8-fc73025e10f3","last_name":"Wang","first_name":"Xiaoyu","full_name":"Wang, Xiaoyu"},{"full_name":"Hamel, Sebastien","first_name":"Sebastien","last_name":"Hamel"},{"last_name":"Cheng","id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","orcid":"0000-0002-3584-9632","first_name":"Bingqing","full_name":"Cheng, Bingqing"}],"day":"01","acknowledged_ssus":[{"_id":"ScienComp"}],"ddc":["540"],"date_updated":"2026-10-12T11:00:16Z","_id":"23089","publisher":"Springer Nature","external_id":{"pmid":["42816492"]},"acknowledgement":"The authors are thankful to Armin Bergermann and Ronald Redmer for generously sharing AIMD trajectories and data, and for valuable discussions and feedback on the manuscript. The authors also acknowledge the research computing facilities provided by the high-performance computing (HPC) cluster at the Institute of Science and Technology Austria (ISTA), Berkeley Research Computing (BRC) at the University of California, Berkeley (UCB), and Lawrence Livermore National Laboratory (LLNL). B.C. was supported by the Laboratory Directed Research and Development (LDRD) Program at Lawrence Berkeley National Laboratory (LBNL) under project ID 110990-001. Part of this work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344. S.H. was supported by the LDRD Program at LLNL under project tracking code 23-SI-006.","title":"Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics","article_processing_charge":"Yes","DOAJ_listed":"1","abstract":[{"text":"The location of the hydrogen-helium (H/He) immiscibility boundary controls whether and where helium rain occurs in giant planets, yet it remains uncertain because high-pressure experiments are challenging and ab initio simulations are limited in system size and simulation time. We map this boundary by computing composition-dependent chemical potentials from large-scale molecular dynamics driven by machine learning potentials trained on three density functional approximations (PBE, vdW-DF, and the hybrid HSE). Across the pressure range of 100-1000 GPa, the demixing temperatures are typically  ~ 2000 K lower than previous ab initio simulations using small system sizes, and this discrepancy is larger than the estimated error from the chosen density functionals, machine learning potentials, neglect of nuclear quantum effects, and statistical uncertainties. Fitting the H/He mixing free energy to a Redlich-Kister regular solution model rationalizes the thermodynamic driving force for phase separation, and provides a predictive representation of the boundary. Comparing with current planetary interior profiles indicates that helium rain is plausible in Saturn but unlikely in the warmer interior of Jupiter. Our results narrow the uncertainty in the H/He immiscibility boundary and provide inputs for planetary models that couple demixing, heat transport, and composition gradients in gas giants.","lang":"eng"}],"publication_identifier":{"eissn":["2041-1723"]},"citation":{"apa":"Wang, X., Hamel, S., &#38; Cheng, B. (2026). Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-026-77117-8\">https://doi.org/10.1038/s41467-026-77117-8</a>","mla":"Wang, Xiaoyu, et al. “Hydrogen-Helium Immiscibility Boundary in Gas-Giant Planetary Interiors from Machine-Learning Molecular Dynamics.” <i>Nature Communications</i>, vol. 17, 10382, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1038/s41467-026-77117-8\">10.1038/s41467-026-77117-8</a>.","ama":"Wang X, Hamel S, Cheng B. Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics. <i>Nature Communications</i>. 2026;17. doi:<a href=\"https://doi.org/10.1038/s41467-026-77117-8\">10.1038/s41467-026-77117-8</a>","short":"X. Wang, S. Hamel, B. Cheng, Nature Communications 17 (2026).","chicago":"Wang, Xiaoyu, Sebastien Hamel, and Bingqing Cheng. “Hydrogen-Helium Immiscibility Boundary in Gas-Giant Planetary Interiors from Machine-Learning Molecular Dynamics.” <i>Nature Communications</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1038/s41467-026-77117-8\">https://doi.org/10.1038/s41467-026-77117-8</a>.","ista":"Wang X, Hamel S, Cheng B. 2026. Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics. Nature Communications. 17, 10382.","ieee":"X. Wang, S. Hamel, and B. Cheng, “Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics,” <i>Nature Communications</i>, vol. 17. Springer Nature, 2026."},"file_date_updated":"2026-10-12T10:57:42Z","doi":"10.1038/s41467-026-77117-8","corr_author":"1","department":[{"_id":"GradSch"},{"_id":"BiCh"}],"has_accepted_license":"1","dataavailabilitystatement":"The training data, fitted MLPs, MLP molecular dynamics results, and source data underlying all figures and tables in the main text and Supplementary Information have been deposited in the Zenodo repository: https://doi.org/10.5281/zenodo.21632034. The data-analysis and plotting scripts used to generate the figures and tables in the main text and Supplementary Information are available in the GitHub repository: https://github.com/ChengUCB/HighPressure_HHe.","article_number":"10382","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"month":"09","scopus_import":"1"},{"publication_status":"published","fulldoi":"https://doi.org/10.15479/AT-ISTA-23072","oa":1,"date_published":"2026-10-08T00:00:00Z","date_created":"2026-10-07T11:20:26Z","type":"dissertation","related_material":{"record":[{"id":"14459","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"12540","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"17469"}]},"year":"2026","status":"public","acknowledged_ssus":[{"_id":"ScienComp"}],"day":"08","doi_confirm":"1","author":[{"last_name":"Kögler","id":"94ec913c-dc85-11ea-9058-e5051ab2428b","first_name":"Kevin","full_name":"Kögler, Kevin"}],"page":"222","OA_place":"publisher","supervisor":[{"orcid":"0000-0002-3242-7020","id":"27EB676C-8706-11E9-9510-7717E6697425","last_name":"Mondelli","full_name":"Mondelli, Marco","first_name":"Marco"}],"file":[{"relation":"source_file","date_updated":"2026-10-09T12:22:55Z","checksum":"5fb2ff02dc9d8c659b2fb5e0802b06ff","date_created":"2026-10-09T11:20:09Z","access_level":"closed","file_name":"2026_Koegler_Kevin_Thesis.zip","file_size":8504109,"creator":"kkoegler","content_type":"application/zip","file_id":"23084"},{"file_size":6692605,"creator":"kkoegler","file_id":"23085","content_type":"application/pdf","success":1,"date_updated":"2026-10-09T13:25:49Z","relation":"main_file","checksum":"a6df3b04c97628a1703f63356fb56f96","date_created":"2026-10-09T13:25:49Z","access_level":"open_access","file_name":"2026_Koegler_Kevin_Thesis.pdf"}],"has_accepted_license":"1","department":[{"_id":"MaMo"},{"_id":"GradSch"}],"corr_author":"1","alternative_title":["ISTA Thesis"],"citation":{"ista":"Kögler K. 2026. Compression and inference in high dimensions: An approximate message passing perspective. Institute of Science and Technology Austria.","ieee":"K. Kögler, “Compression and inference in high dimensions: An approximate message passing perspective,” Institute of Science and Technology Austria, 2026.","ama":"Kögler K. Compression and inference in high dimensions: An approximate message passing perspective. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-23072\">10.15479/AT-ISTA-23072</a>","short":"K. Kögler, Compression and Inference in High Dimensions: An Approximate Message Passing Perspective, Institute of Science and Technology Austria, 2026.","chicago":"Kögler, Kevin. “Compression and Inference in High Dimensions: An Approximate Message Passing Perspective.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-23072\">https://doi.org/10.15479/AT-ISTA-23072</a>.","apa":"Kögler, K. (2026). <i>Compression and inference in high dimensions: An approximate message passing perspective</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-23072\">https://doi.org/10.15479/AT-ISTA-23072</a>","mla":"Kögler, Kevin. <i>Compression and Inference in High Dimensions: An Approximate Message Passing Perspective</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-23072\">10.15479/AT-ISTA-23072</a>."},"file_date_updated":"2026-10-09T13:25:49Z","doi":"10.15479/AT-ISTA-23072","publication_identifier":{"issn":["2663-337X"]},"abstract":[{"lang":"eng","text":"Inferring signal from large quantities of data is one of the most important problems in today’s\r\nworld, with neural networks emerging as the most powerful solution. While there have been\r\nmassive breakthroughs in the ML space, there are two main drawbacks. The first is that\r\nmost of these models are “black boxes”, with very little understanding of why they work,\r\nwhich makes it hard to find the correct architecture for a given problem. The architecture is\r\ncrucial, as the widely used training algorithms are “local” and thus rely on the loss landscape\r\nbeing benign enough to find a global optimum. This brings us to the second problem: while\r\nthere is a lot of evidence that this can be overcome with large enough data, this is less clear\r\nfor datasets which are noisy, do not have enough samples, or have a non-standard structure.\r\nHistorically, on a smaller scale, the alternative has been simple (Bayesian) statistical methods,\r\nwhich also have the advantage of being interpretable and adaptable. However, many of the\r\nclassical results cannot be easily extended to the high-dimensional regime in which modern\r\ndata lives.\r\nIn this work we want to consider two different settings relating to the above. The first is\r\napproximate message passing (AMP), an iterative algorithm for high-dimensional (generalized)\r\nlinear models that easily lends itself to Bayesian setups, and which in many cases is provably\r\nBayes-optimal. The second is an autoencoder with a shallow encoder, for which we can\r\nanalyze the weights along the training trajectory of gradient descent. Surprisingly, we will find\r\na connection between the two, as we recover certain structures of AMP.\r\nWe will first introduce the AMP framework by studying an extension that can be applied\r\nto a wider variety of data: rotationally invariant generalized approximate message passing\r\n(RI-GAMP). This shows that one can extend the AMP framework to a much wider class of\r\nalgorithms, relevant to more practical settings. The results are then also confirmed on real\r\ndata that go beyond the theoretical setting.\r\nWe then move to the setup of an autoencoder with a shallow encoder and a Bayesian prior in\r\nthe high-dimensional regime, in which the input and compression dimensions are large and\r\nproportional; this is also a first step towards opening one of the black boxes above, as we\r\ncan say precisely when and why the network works. While autoencoders are widely used in\r\nmodern ML architectures, most fundamental research in this direction has focused on extreme\r\nasymptotic regimes, where the autoencoder is either severely over- or under-parameterized,\r\nand which do not extend to the proportional high-dimensional regime. We show that for\r\nGaussian priors the network finds the global optimum, and these theoretical findings extrapolate\r\nstrikingly well to real image data. Next we extend this analysis to more structured priors and\r\na deeper decoder. For sparse Gaussian inputs in the training regime studied here, the shallow\r\ndecoder does not exploit sparsity and yields the same dynamics as in the Gaussian setting.\r\nWe then show how a deeper decoder can break this behavior, and interestingly, if we treat the\r\nproblem as an AMP problem, the network eventually learns the same decoding as AMP. This\r\ntoo extrapolates to real image data.\r\nLastly, we will show that the AMP setup has real practical use, by using a practical variant,\r\ngenetic vector approximate message passing (gVAMP), for predicting plasma protein levels\r\nfrom genetic information using the UKB GWAS data. This is a perfect example of the problems\r\nin the high-dimensional regime: approximately 8.4 million dimensions and 40,000 samples,\r\nwhere the high noise, low sample count, and large size make it hard for ML methods to work.\r\nTo get the optimal prediction accuracy we consider a two-step inference. We first consider a\r\npre-processed version of the data, of about 880,000 dimensions, on which we run the gVAMP\r\nalgorithm; this allows us to find predictive regions, taking into account joint effects between\r\ndifferent regions, and for most proteins we end up selecting only about 0.1% of the dimensions.\r\nWe then consider the analogue of this small subset, on which we can now run a standard tree\r\nalgorithm (XGB) that no longer suffers from the aforementioned problems. This pipeline yields\r\nbetter prediction accuracy than recent nonlinear deep learning approaches applied to this data,\r\nas we are able to handle the pre-processing in a principled Bayesian way."}],"article_processing_charge":"No","title":"Compression and inference in high dimensions: An approximate message passing perspective","acknowledgement":"This project was partially supported by the 2019 Lopez-Loreta Prize and\r\nthe ERC INF2 project (project number 101161364). Furthermore, the candidate acknowledges\r\nthe support from the Scientific Service Units of the Institute of Science and Technology Austria\r\nthrough resources provided by Scientific Computing.","degree_awarded":"PhD","_id":"23072","publisher":"Institute of Science and Technology Austria","ddc":["519"],"date_updated":"2026-10-12T13:04:49Z","language":[{"iso":"eng"}],"month":"10","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Published Version","project":[{"name":"Prix Lopez-Loretta 2019 - Marco Mondelli","_id":"059876FA-7A3F-11EA-A408-12923DDC885E"}]},{"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"month":"09","oa_version":"Published Version","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1038/s41929-026-01616-6"}],"dataavailabilitystatement":"All data are available from the authors upon request.","project":[{"grant_number":"PAT 1250924","_id":"8f1d607d-16d5-11f0-9cad-ab453295ba5e","name":"Photoactive ligands for transformative nickel catalysis"},{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413"}],"department":[{"_id":"BaPi"},{"_id":"GradSch"},{"_id":"RaKl"}],"corr_author":"1","abstract":[{"text":"The formation of C(sp2)–heteroatom bonds through cross-coupling catalysis is central to the synthesis of pharmaceuticals, agrochemicals and materials. Whereas Pd0/PdII catalysis requires substrate-specific ligand optimization to balance the competing demands of oxidative addition and reductive elimination, NiI/NiIII catalysis offers a complementary strategy because the bond-forming step is intrinsically favourable. However, contemporary NiI/NiIII methodologies suffer from insufficient oxidative addition reactivity, restricting the aryl halide scope and requiring high catalyst loadings. Here we show that mechanistically guided ligand design overcomes these limitations. Together with a non-nucleophilic base additive that promotes direct visible-light generation of NiI from a bench-stable NiII precatalyst, this ligand design enables the coupling of electron-rich aryl bromides with N-, O-, S- and P-based nucleophiles at nickel loadings as low as 100 ppm. The method is compatible with sterically encumbered nucleophiles and enables gram-scale synthesis and late-stage functionalization of complex molecules.","lang":"eng"}],"publication_identifier":{"eissn":["2520-1158"]},"citation":{"short":"A. Bena, T. Banik, C. Giannoudis, F. Ortis, D. Bím, H. Baunis, G. Palissery, B. Pieber, Nature Catalysis (2026).","chicago":"Bena, Aleksander, Trisha Banik, Christos Giannoudis, Florian Ortis, Daniel Bím, Haralds Baunis, Gayathri Palissery, and Bartholomäus Pieber. “Ligand Design Broadens NiI-Catalysed C(Sp2)–Heteroatom Couplings of Aryl Bromides at Low Catalyst Loadings.” <i>Nature Catalysis</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1038/s41929-026-01616-6\">https://doi.org/10.1038/s41929-026-01616-6</a>.","ama":"Bena A, Banik T, Giannoudis C, et al. Ligand design broadens NiI-catalysed C(sp2)–heteroatom couplings of aryl bromides at low catalyst loadings. <i>Nature Catalysis</i>. 2026. doi:<a href=\"https://doi.org/10.1038/s41929-026-01616-6\">10.1038/s41929-026-01616-6</a>","ieee":"A. Bena <i>et al.</i>, “Ligand design broadens NiI-catalysed C(sp2)–heteroatom couplings of aryl bromides at low catalyst loadings,” <i>Nature Catalysis</i>. Springer Nature, 2026.","ista":"Bena A, Banik T, Giannoudis C, Ortis F, Bím D, Baunis H, Palissery G, Pieber B. 2026. Ligand design broadens NiI-catalysed C(sp2)–heteroatom couplings of aryl bromides at low catalyst loadings. Nature Catalysis.","mla":"Bena, Aleksander, et al. “Ligand Design Broadens NiI-Catalysed C(Sp2)–Heteroatom Couplings of Aryl Bromides at Low Catalyst Loadings.” <i>Nature Catalysis</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1038/s41929-026-01616-6\">10.1038/s41929-026-01616-6</a>.","apa":"Bena, A., Banik, T., Giannoudis, C., Ortis, F., Bím, D., Baunis, H., … Pieber, B. (2026). Ligand design broadens NiI-catalysed C(sp2)–heteroatom couplings of aryl bromides at low catalyst loadings. <i>Nature Catalysis</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41929-026-01616-6\">https://doi.org/10.1038/s41929-026-01616-6</a>"},"doi":"10.1038/s41929-026-01616-6","article_processing_charge":"Yes (via OA deal)","title":"Ligand design broadens NiI-catalysed C(sp2)–heteroatom couplings of aryl bromides at low catalyst loadings","acknowledgement":"We acknowledge ISTA for generous financial support. This research was supported by the Scientific Service Units (SSU) of ISTA through resources provided by the Lab Support Facility, Mass Spec Facility, NMR facility and the Miba Machine Shop. We specifically thank A. Paraskevopoulou for high-resolution mass spectrometry measurements. B.P. acknowledges the Austrian Science Fund (PAT 1250924) and the ACS GCI Pharmaceutical Roundtable for funding. T.B. thanks the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. D.B. acknowledges funding from the Czech Science Foundation (25-17760M). Open access funding provided by Institute of Science and Technology (IST Austria).","date_updated":"2026-10-14T06:32:42Z","publisher":"Springer Nature","_id":"23094","day":"29","acknowledged_ssus":[{"_id":"LifeSc"},{"_id":"MassSpec"},{"_id":"NMR"},{"_id":"M-Shop"}],"author":[{"full_name":"Bena, Aleksander","first_name":"Aleksander","id":"4197c39e-e8ec-11ed-86cb-afed934cd664","last_name":"Bena"},{"first_name":"Trisha","full_name":"Banik, Trisha","last_name":"Banik","id":"506b8e06-c59a-11ee-a1af-ae470719e7d3"},{"first_name":"Christos","full_name":"Giannoudis, Christos","last_name":"Giannoudis","id":"1bd506c6-e8ec-11ed-86cb-d495f63f2dcd"},{"full_name":"Ortis, Florian","first_name":"Florian","id":"e34c9177-3208-11ee-ac71-a6a15cf2ef29","orcid":"0000-0002-0458-5187","last_name":"Ortis"},{"last_name":"Bím","first_name":"Daniel","full_name":"Bím, Daniel"},{"last_name":"Baunis","id":"2eea55ec-e8ec-11ed-86cb-d9c76787acfe","full_name":"Baunis, Haralds","first_name":"Haralds"},{"last_name":"Palissery","id":"b02c9d47-50c9-11ef-b52e-b2180bf00ccd","first_name":"Gayathri","full_name":"Palissery, Gayathri"},{"first_name":"Bartholomäus","full_name":"Pieber, Bartholomäus","orcid":"0000-0001-8689-388X","id":"93e5e5b2-0da6-11ed-8a41-af589a024726","last_name":"Pieber"}],"das_tickbox":"1","OA_place":"publisher","ec_funded":1,"supplementarymaterial":"yes","quality_controlled":"1","OA_type":"hybrid","article_type":"original","publication":"Nature Catalysis","fulldoi":"https://doi.org/10.1038/s41929-026-01616-6","publication_status":"epub_ahead","date_published":"2026-09-29T00:00:00Z","oa":1,"date_created":"2026-10-11T22:02:06Z","type":"journal_article","year":"2026","researchdata_availability":"upon request","PlanS_conform":"1","status":"public"},{"volume":999,"OA_type":"gold","article_type":"original","quality_controlled":"1","file":[{"file_size":2808503,"creator":"dernst","file_id":"23136","content_type":"application/pdf","success":1,"date_updated":"2026-10-14T07:50:51Z","relation":"main_file","checksum":"1b8caf640c32d0d27a078bfb27ffcf8a","date_created":"2026-10-14T07:50:51Z","access_level":"open_access","file_name":"2026_AstrophysicalJour_Higginson.pdf"}],"author":[{"full_name":"Higginson, Jack","first_name":"Jack","last_name":"Higginson"},{"first_name":"Rongmon","full_name":"Bordoloi, Rongmon","last_name":"Bordoloi"},{"last_name":"Simcoe","full_name":"Simcoe, Robert A.","first_name":"Robert A."},{"full_name":"Matthee, Jorryt J","first_name":"Jorryt J","last_name":"Matthee","id":"7439a258-f3c0-11ec-9501-9df22fe06720","orcid":"0000-0003-2871-127X"},{"full_name":"Kashino, Daichi","first_name":"Daichi","last_name":"Kashino"},{"last_name":"Mackenzie","full_name":"Mackenzie, Ruari","first_name":"Ruari"},{"orcid":"0000-0001-5346-6048","last_name":"Kramarenko","id":"9a9394cb-3200-11ee-973b-f5ba2a8b16e4","first_name":"Ivan","full_name":"Kramarenko, Ivan"},{"first_name":"Simon J.","full_name":"Lilly, Simon J.","last_name":"Lilly"},{"last_name":"Eilers","first_name":"Anna-Christina","full_name":"Eilers, Anna-Christina"},{"last_name":"Naidu","full_name":"Naidu, Rohan P.","first_name":"Rohan P."},{"first_name":"Minghao","full_name":"Yue, Minghao","last_name":"Yue"}],"day":"24","OA_place":"publisher","date_created":"2026-10-12T12:15:27Z","oa":1,"date_published":"2026-02-24T00:00:00Z","intvolume":"       999","year":"2026","PlanS_conform":"1","status":"public","issue":"1","type":"journal_article","arxiv":1,"publication_status":"published","fulldoi":"https://doi.org/10.3847/1538-4357/ae3e81","publication":"The Astrophysical Journal","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_number":"49","project":[{"grant_number":"101076224","_id":"bd9b2118-d553-11ed-ba76-db24564edfea","name":"Young galaxies as tracers and agents of cosmic reionization"}],"month":"02","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","oa_version":"Published Version","title":"EIGER. VIII. First stars signatures in the connection between O I absorption and galaxies in the epoch of reionization","publisher":"IOP Publishing","_id":"23115","ddc":["520"],"date_updated":"2026-10-14T07:58:57Z","acknowledgement":"IOP Science home\r\nAccessibility Help\r\n\r\nJournals\r\nBooks\r\nPublishing Support\r\nLogin\r\nThe Astrophysical Journal\r\nThe American Astronomical Society, find out more.\r\n\r\nThe following article isOpen access\r\nEIGER. VIII. First Stars Signatures in the Connection between O I Absorption and Galaxies in the Epoch of Reionization\r\nJack Higginson, Rongmon Bordoloi, Robert A. Simcoe, Jorryt Matthee, Daichi Kashino, Ruari Mackenzie, Ivan Kramarenko, Simon J. Lilly, Anna-Christina Eilers, Rohan P. NaiduShow full author list\r\n\r\nPublished 2026 February 24 • © 2026. The Author(s). Published by the American Astronomical Society.\r\nThe Astrophysical Journal, Volume 999, Number 1\r\nCitation Jack Higginson et al 2026 ApJ 999 49\r\nDOI 10.3847/1538-4357/ae3e81\r\n\r\nPDFOpens in a new tab.\r\nePub\r\nAuthors\r\nFigures\r\nTables\r\nReferences\r\nArticle data\r\nPDFOpens in a new tab.\r\nePub\r\nArticle metrics\r\n626 Total downloads\r\n\r\n22 total citations on Dimensions.\r\nShare this article\r\nArticle information\r\nAbstract\r\nWe investigate the association between galaxies and neutral O i absorption systems at z ∼ 6, which trace metal-enriched gas during the epoch of reionization. We identify 40 galaxies across six quasar fields, residing in 15 overdensities within 300 kpc of the background sight lines. Five O i absorption systems are associated with five of these overdensities, yielding a covering fraction of \r\n within 300 kpc. The absorption occurs beyond typical virial radii, indicating that the gas traces extended overdensity environments rather than individual galaxy halos, unlike the z ∼ 0 circumgalactic medium (CGM), which is largely bound to halos. These galaxy-associated absorbers account for ∼35% of all O i systems seen in blind quasar surveys, implying the remainder arise in lower-mass galaxies below our detection threshold or in dense neutral intergalactic medium pockets. The CGM around these galaxies contains  ≳  2 × 106 M⊙ of oxygen, comparable to the interstellar medium oxygen mass of the galaxies themselves, suggesting that the surrounding environment holds as much metal mass as the galaxies. All five galaxy-associated systems show significantly higher \r\n ratios than absorbers lacking galaxy associations. Furthermore, relative abundance ratios ([Si/O], [C/O]) reveal that four of the five exhibit enrichment patterns consistent with Population III nucleosynthesis at the outskirts of galaxy overdensities. These rare systems offer a unique window into the role of first-generation stars in shaping the early metal enrichment of galaxies and their environments.\r\n\r\nExport citation and abstract\r\nBibTeX\r\nRIS\r\n\r\nPrevious article in issue\r\nNext article in issue\r\nRelated links\r\n\r\nOriginal content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.\r\n\r\n1. Introduction\r\nThe first generations of stars formed shortly after the Epoch of Recombination within dark matter overdensities, producing the first significant quantities of metals and enriching the intergalactic medium (IGM) while reionizing hydrogen and helium (e.g., R. S. Klessen & S. C. O. Glover 2023). These metals and gas eventually coalesced into the first galaxies, which over cosmic time evolved into Milky Way–like systems today. Studying these young galaxies and their environments provides critical insight into galaxy formation and evolution, constraining models of stellar feedback, gas accretion, and chemical enrichment (C.-A. Faucher-Giguère & S. P. Oh 2023; C. Peroux & D. Nelson 2024).\r\n\r\nAt low redshift, decades of observations using deep ground-based spectroscopy and Hubble Space Telescope (HST) data of background quasars and foreground galaxies have built a rich understanding of the circumgalactic medium (CGM) and its interplay with galaxies (e.g., J. Tumlinson et al. 2017). The CGM plays a crucial role in gas recycling, star formation regulation, and quenching; understanding its structure and composition informs galaxy growth models (Y. Peng et al. 2015; E. Zinger et al. 2020).\r\n\r\nHigh-redshift studies, leveraging ground- and space-based near-infrared (NIR) spectroscopy of quasars, reveal that the early Universe was already chemically enriched by the epoch of reionization (e.g., T. J. Cooper et al. 2019; L. Christensen et al. 2023; R. L. Davies et al. 2023a). Among tracers of neutral and low-ionization gas, O i has emerged as a key probe: surveys report an increase in O i number density at z  ≳  5–6 (G. D. Becker et al. 2019; L. Christensen et al. 2023; A. M. Sebastian et al. 2024; A. Sodini et al. 2024), while higher-ionization species like C iv and Si iv decline, consistent with a softer and evolving UV background at the end of reionization (T. J. Cooper et al. 2019; V. D’Odorico et al. 2022; R. L. Davies et al. 2023a, 2023b).\r\n\r\nHistorically, connecting absorption systems with their host galaxies was challenging due to the difficulty of obtaining deep, high-redshift galaxy spectroscopy. This has changed with the advent of JWST, providing unprecedented views of early galaxies and their impact on surrounding gas through surveys such as EIGER (D. Kashino et al. 2023) and ASPIRE (F. Wang et al. 2023). First systematic studies of cool, low-ionization CGM traced by Mg ii around z ∼ 6 galaxies suggest that high-redshift CGM differs significantly from its low-redshift counterpart: these galaxies typically have low masses, and strong stellar feedback can eject metals far beyond the halo’s gravitational potential (R. Bordoloi et al. 2024). Such pioneering studies now allow systematic investigations of the CGM in the early Universe.\r\n\r\nThe UV background during reionization was inhomogeneous and rapidly evolving (e.g., S. R. Furlanetto & S. P. Oh 2005; B. D. Oppenheimer et al. 2009; K. Finlator et al. 2013; G. D. Becker et al. 2015; S. E. I. Bosman et al. 2022), initially dominated by Population III stars (K. Nakajima & R. Maiolino 2022; K. Nakajima et al. 2025), then by early star-forming galaxies (L. Jiang et al. 2022; J. Matthee et al. 2022), with active galactic nuclei (AGN) contributing significantly by z ∼ 5 (A. D’Aloisio et al. 2017; G. Kulkarni et al. 2019; C.-A. Faucher-Giguère 2020). Modeling indicates that pockets of Population III star formation may persist throughout the Epoch of Reionization (L. Tornatore et al. 2007; R. H. Mebane et al. 2018; J. L. Johnson & A. Aykutalp 2019; A. Venditti et al. 2023; O. Zier et al. 2025).\r\n\r\nThe large reservoir of neutral O i observed in quasar absorption lines at high redshift is typically self-shielded, providing robust estimates of chemical abundances. Studying the association of these absorbers with galaxies offers unique insight into the CGM of early galaxies, and into potential contributions from Population III stars to early chemical enrichment.\r\n\r\nIn this work, we study the cool, neutral CGM around galaxies at z ∼ 6, traced by O i absorption from the EIGER survey (D. Kashino et al. 2023). We focus on O i absorbers associated with [O iii]5008-emitting galaxies at 5.875 <z < 6.378 within 300 kpc of six background quasars. We quantify absorber incidence, column densities, and mass estimates, and analyze ionic abundances to probe chemical enrichment, including potential contributions from Population III stars.\r\n\r\nThis paper is organized as follows. Section 2 describes the observations; Section 3 details our methods for galaxy selection, redshift estimation, galaxy properties, defining galaxy overdensities, absorber measurements, and completeness; Section 4 presents the results, including the association of O i absorption with galaxies, the incidence of galaxy-associated O i absorbers, their chemical abundances, and physical interpretations; Section 5 summarizes our conclusions. Throughout, we adopt a ΛCDM cosmology with H0 = 67.66 km s−1 Mpc−1 (Planck Collaboration et al. 2020).\r\n\r\n2. Observations\r\nEIGER (Program ID 1243; PI: S. J. Lilly) is a large JWST Wide Field Slitless Spectroscopy (WFSS) program totaling 126.5 hr, conducting deep WFSS observations in six extragalactic fields, each centered on an ultraluminous quasar at z ≥ 6. These quasars have also been observed with deep optical and NIR medium- and high-resolution spectroscopy with Magellan/FIRE, Very Large Telescope/X-shooter, and Keck High Resolution Echelle Spectrometer (HIRES)/MOSFIRE, providing over 100 hr of complementary NIR spectroscopy across the six sight lines. We refer the reader to A.-C. Eilers et al. (2023) and A.-C. Ďurovčíková et al. (2025) for data reduction and details of the ground-based quasar spectroscopy. In addition, all fields are covered by deep JWST/NIRCam and HST imaging. A detailed description of the survey design, methodology, and spectroscopic and photometric observation details is provided in D. Kashino et al. (2023), J. Matthee et al. (2023), and R. Bordoloi et al. (2024). In this work, we make use of the complete EIGER survey of z ≥ 5.9 galaxies spanning all six extragalactic fields (D. Kashino et al. 2026).\r\n\r\nWe note that all six quasars were chosen with prior knowledge of metal absorption systems along their lines of sight, which could in principle bias any attempt to associate galaxies with those absorbers. In contrast, a galaxy-centric approach starts with quasar–galaxy pairs without prior knowledge of absorption and then builds statistics systematically (see e.g., R. Bordoloi et al. 2011; J. K. Werk et al. 2013; R. Bordoloi et al. 2014). However, once a blind, well-characterized galaxy survey is in place, the two approaches converge. This is conceptually similar to a program that combines quasar spectroscopy performed without prior absorber selection with a complete galaxy survey. This work employs deep blind galaxy searches in each of the EIGER fields, yielding an emission-line complete sample of spectroscopic galaxies (J. Matthee et al. 2022; R. Bordoloi et al. 2024) and a complete census of absorption lines along these sight lines (Section 3.5). By combining these two elements—a galaxy survey with quantified completeness and an absorption survey with well-defined sensitivity—we establish a robust framework for conducting a census of CGM absorption around galaxies. This combined approach has been successfully demonstrated at low redshifts (J. N. Burchett et al. 2019).\r\n\r\n3. Methods\r\nIn this section, we describe how galaxy redshifts and properties are measured and how absorption lines are identified and measured.\r\n\r\n3.1. Galaxy Redshifts\r\nSince our focus is on galaxies at z ∼ 6 near the quasar sight lines, we begin with the full EIGER catalog of [O iii] emitters (D. Kashino et al. 2026), which contains 948 galaxies detected via [O iii] emission within 5.33 ≤ z ≤ 6.97. From this catalog, we select galaxies that (1) lie at least 10,000 km s−1 in the foreground of each quasar , (2) are within a projected impact parameter of 300 pkpc, and (3) have O i λ1302 coverage in the quasar NIR spectra outside of the Gunn–Peterson trough. This yields a sample of 40 galaxies. Of these, 33 fall within the central of the EIGER spectroscopic footprint (R. Bordoloi et al. 2024), observed with both JWST/NIRCam reverse grism modules (A and B). Because the two modules disperse light in opposite directions, they provide independent moderate-resolution (R ∼ 1500) spectra of the same target, enabling us to assess redshift measurement uncertainties.\r\n\r\nFollowing the procedure in R. Bordoloi et al. (2024), we visually inspect each NIRCam 2D spectrum using the custom Python application programming interface (API) zgui(R. Bordoloi et al. 2025), extract 1D spectra from each module, and fit Gaussians to the emission line to determine redshifts. Redshifts from the two modules are consistent with a mean velocity offset of Δv = 9.3 km s−1 with a standard deviation of 24 km s−1 (Figure 1). We therefore adopt an average redshift uncertainty of ≈24 km s−1 for the [O iii] emitters, sufficient for associating metal absorption systems with their host galaxies. Hereafter, we focus on this sample of 40 galaxies.\r\n\r\nZoom InZoom OutReset image size\r\nFigure 1. Redshift uncertainty distribution of the [O iii] emitter EIGER galaxies. The histogram shows the difference in redshift between emission-line measurements from NIRCam Grism Module A and Module B spectra, expressed in km s−1. Individual redshifts were derived from Gaussian fits to the [O iii] and Hβ lines. The two modules yield consistent results with a mean offset and standard deviation of Δz = 0.0028 ± 0.0073 (Δv = 9.3 ± 24 km s−1).\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\n3.2. Galaxy Stellar Mass, Star formation Rate, Halo Mass\r\nTo estimate galaxy stellar masses and star formation rates (SFRs), we follow the procedure of J. Matthee et al. (2022). We first measure the [O iii] and Hβ emission-line fluxes of each galaxy, and combine these with JWST/NIRCam broadband photometry (F115W, F200W, and F356W) to perform spectral energy distribution fitting at the galaxy redshift using the Prospector code (B. D. Johnson et al. 2021). We assume a G. Chabrier (2003) initial mass function (IMF), adopt MIST isochrones (J. Choi et al. 2016; A. Dotter 2016), a nonparametric star formation history model (R. P. Naidu et al. 2024), and the dust attenuation curve of D. Calzetti et al. (2000). Galaxy SFRs are derived by averaging over the most recent 50 Myr of star formation history from the Prospector posteriors.\r\n\r\nFigure 2 (left) shows the impact parameter distribution of the 40 EIGER galaxies relative to the background quasars (black star symbols). The galaxies are randomly distributed with respect to the quasar sight lines. The right panel shows their stellar masses and SFRs, with symbols color coded by galaxy redshift. Following R. Bordoloi et al. (2024), we estimate halo masses and virial radii (Rvir) using abundance matching from P. Behroozi et al. (2019). Uncertainties in Rvir are propagated from the 16th and 84th percentile stellar mass errors, giving a mean uncertainty of ΔRvir = 1.8 kpc. The galaxies span stellar masses of and SFRs of , with all systems being star-forming by selection.\r\n\r\nZoom InZoom OutReset image size\r\nFigure 2. Properties of 40 spectroscopically confirmed galaxies at 5.9 ≤ z ≤ 6.4 within 300 kpc of background quasars in the EIGER survey. Each square denotes a galaxy and is color coded by redshift. Left: angular positions and impact parameters relative to the background quasar (black star), with dashed concentric rings marking 100, 200, and 300 kpc at z = 6. Right: stellar mass vs. SFR, averaged over the last 50 Myr. Error bars show the 16th–84th percentile uncertainties in stellar mass and SFR.\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\nOne galaxy (z = 5.910384, galaxyID = 15362, qsoID = J159) has an exceptionally high stellar mass of , beyond the calibrated range of the P. Behroozi et al. (2019) relation. This object exhibits a compact, pointlike morphology and likely hosts an obscured AGN, placing it among the recently identified population of little red dots (LRDs; e.g., J. Matthee et al. 2024). We do not detect broad Hβ for this object. However, this is not unexpected, as LRDs can have Hα/Hβ values as high as ∼10 (M. Brooks et al. (2025; A. Torralba et al. 2026, in preparation). As robust AGN modeling at these redshifts is not yet established, we estimated its halo mass by linearly extrapolating the P. Behroozi et al. (2019) relation from the stable stellar mass regime. We explicitly note where this assumption may affect our results in the following sections. Additionally, this galaxy has not been plotted in the right panel of 2.\r\n\r\n3.3. Galaxy Overdensities\r\nA significant fraction of z ≥ 6 galaxies in the EIGER survey are not isolated but are found in overdense environments, either as mergers or members of “protogroups” (see, e.g., D. Kashino et al. 2026). The EIGER [O iii] galaxy catalog already merges individual [O iii] emission clumps within 2″ into a single system, even when they exhibit complex morphologies or merger signatures. To identify larger-scale overdensities, we therefore search for galaxies that lie at similar redshifts but are widely separated on the sky.\r\n\r\nWithin 300 kpc from the QSO sight lines, we identify overdensities around the 40 selected EIGER galaxies using a friends-of-friends algorithm (R. Bordoloi et al. 2025). Galaxies are grouped as an overdensity if they lie within 1 pMpc in projected separation and within ±1000 km s−1 in redshift space. A galaxy is considered part of an overdensity only if all members are “fully” connected, i.e., each galaxy in the overdensity satisfies these conditions with all other members. Around each detected O i absorption system, we further search for overdensities within ±1500 km s−1 of the absorber redshift, and merge these associations to ensure all clustered galaxies are treated as a single overdensity. This conservative approach ensures that we capture the full galaxy environment of O i absorbers. The 40 galaxies studied in this work are part of 15 distinct overdensities, with each grouping containing 1–5 members. The number of galaxies in each grouping is reported in Table 1. The typical velocity dispersion of these overdensities is 449.2 km s−1.\r\n\r\nTable 1. O i Absorption Lines and Associated Galaxy Properties\r\n\r\nLabel\tQuasar\tzgala\tR\t〈v〉b\t#c\tzO I\t\t\t\t\t\r\n \t \t \t(kpc)\t(km s−1)\tGalaxies\t \t(cm−2)\t(cm−2)\t(cm−2)\t(cm−2)\t(cm−2)\r\n(1)\t(2)\t(3)\t(4)\t(5)\t(6)\t(7)\t(8)\t(9)\t(10)\t(11)\t(12)\r\na\tJ0100\t5.941\t119.6\t157\t5\t5.945\t\t\t\t\t\r\nb\tJ1148\t6.008\t157.5\t130\t3\t6.011\t\td\t\t\t\r\nc\tJ159\t5.934\t25.2\t−920\t5\t5.913\t\t\t\t⋯\t⋯\r\nd\tJ159\t6.049\t40.8\t230\t2\t6.054\t\t<13.12\t\t⋯\t⋯\r\ne\tJ1030\t6.075\t147.9\t−131\t2\t6.076\te\t\t\t⋯\t⋯\r\nNotes. The galaxies listed are the primary members of groups with detections at the lowest impact parameter from the host quasar. aRedshift of the primary member of the overdensity. bVelocity offset of O i relative to the primary member galaxy of the overdensity. cNumber of galaxy members in the overdensity. dFor this system, Si II λ1304 was not present, so the value given here is derived from fitting Si II λ1526. eThis system is blended; see discussion in Section 3.4.\r\n\r\nDownload table as: \r\nASCII\r\nTypeset image\r\n\r\nThroughout this work, we define the galaxy with the smallest impact parameter to the background quasar sight line within each galaxy overdensity as the primary member. This convention is adopted solely to simplify the presentation and does not imply a unique physical association between the intervening absorption system and this galaxy. In fact, the concept of a unique absorber–galaxy association at high redshift is significantly less robust than in the low-redshift Universe (e.g., R. Bordoloi et al. 2024). As discussed in Section 4.1, none of the O i absorption systems lie within the virial radius of any individual halo. Even at low redshift, the galaxy with the smallest impact parameter is not necessarily the one with the smallest velocity offset from the absorber, and therefore does not constitute evidence for a unique absorber–galaxy pair (A. Hamanowicz et al. 2020). This behavior is also observed for galaxies residing in groups (R. Bordoloi et al. 2011). Our analysis, therefore, focuses on the broader environment, which we argue is most appropriately characterized by galaxy overdensities, and our choice of a primary galaxy does not affect our main conclusions.\r\n\r\n3.4. Absorption-line Detection and Measurements\r\nWe follow the procedures outlined in R. Bordoloi et al. (2024) to identify and measure the strength of O i absorption systems around EIGER galaxies, and provide a brief summary here. We first use a custom Python-based 1D spectrum viewer to identify and tabulate all intervening absorption lines in the EIGER quasar spectra. A semiautomated CGM absorption-line analysis pipeline is then used to perform the measurements. For each galaxy, we extract a ±1500 km s−1 spectral window centered on its systemic redshift, for all transitions of interest. In this work, we analyze slices around O i λ1302, Si ii λ1260, Si ii λ1304, Si ii λ1527, C ii λ1334, Si iv λ1393, Si iv λ1402, C iv λ1548, and C iv λ1550. Each slice is locally continuum-normalized using an automated Legendre polynomial fit, with the polynomial order chosen via the Bayesian Information Criterion. The continuum fits and absorption features are visually inspected, and both rest-frame equivalent widths (Wr) and apparent optical depth (AOD) column densities are measured. We define a detection as any absorption system with Wr ≥ 3σw, where σw is the 1σ uncertainty in Wr. We note that this uncertainty contains both the statistical uncertainty due to the signal-to-noise ratio of the data and the continuum-fitting uncertainty. Nondetections are reported as 2σw upper limits measured within ±100 km s−1 of the systemic redshift of the galaxy. For column density, we report the 2σ uncertainty on AOD column density as an upper limit on nondetections. When a transition is detected in multiple instruments, each spectrum is analyzed independently, and the inverse-variance-weighted mean is adopted as the final Wr. The details of this automated approach and full documentation of the APIs used can be found in R. Bordoloi et al. (2025).\r\n\r\nFor all detections, we perform Voigt profile fitting using the rbvfit package, which employs Markov Chain Monte Carlo (MCMC) sampling to simultaneously fit multiple absorption systems across different instruments (R. Bordoloi & J. Higginson 2025). This approach yields robust column densities, resolves the kinematic structure, and enables accurate modeling of blended lines. Additionally, since we obtain a marginalized posterior distribution for the fitted parameters, the results yield accurate column density estimates even if the Doppler b parameter or velocity centroids are not well constrained in moderate-resolution spectra (see discussion in R. Bordoloi et al. 2024). In our case, most of the O i Si ii C ii transitions are all covered by higher-resolution HIRES spectroscopy and thus their properties are well constrained. rbvfit supports two MCMC samplers, emcee (D. Foreman-Mackey et al. 2013) and zeus (M. Karamanis et al. 2021; M. Karamanis & F. Beutler 2020), both of which are used in this work depending on the complexity of the fit. We typically adopt 50 walkers with initial perturbations of either 10−3 or 10−6, and default chain lengths of 8000–20,000 steps, ensuring the total number of steps exceeds 50 times the autocorrelation time. Additional steps are run as needed to achieve convergence. In each case, a flat prior is assumed with reasonable physical bounds.\r\n\r\nFigure 3 shows an example of Voigt profile fits to O i λ1302 and Si ii λ1304 lines simultaneously modeled across FIRE, X-shooter, and HIRES. We fit a two-component Voigt profile with a mean velocity offset from the host galaxy of voffset =  157 km s−1 . This joint fitting maximizes information from all instruments while preserving the kinematic detail provided by higher-resolution data. Galaxy overdensities associated with this system are marked with green vertical ticks. This system has a total O i column density 13.46. All other O i fits are presented in Figure 8. All absorption-line measurements are presented in Table 1.\r\n\r\nZoom InZoom OutReset image size\r\nFigure 3. Voigt profile fits to O i and Si ii absorption profiles at z = 5.945 toward the quasar SDSS J0100+2802. Shown are the flux (black), error spectrum (red), best-fit Voigt model (orange/black), and individual Voigt components (thin blue), using data from FIRE, X-shooter, and HIRES. Vertical green lines mark galaxy members of the associated overdensity. Spectra from all instruments and all transitions are simultaneously fit using the rbvfit Bayesian absorption-line fitter.\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\nWe note that an O i and Si ii absorption system is detected along the J1030 quasar sight line at z ∼ 6.075, blended with an intervening C iv absorber at z ∼ 4.948 (Figure 8, top left panels; see also C. G. Díaz et al. 2021). The z ∼ 6.076 system is confirmed by the independent detection of Si ii, Mg ii, C ii, and Fe ii absorption in FIRE and X-shooter data, and we simultaneously fit the C iv, O i, and Si ii systems across three instruments. Although the proximity of the C iv doublet in wavelength space introduces an inherent degeneracy with the O i and Si ii pair, high-resolution HIRES data reveal sufficient kinematic substructure to warrant an additional component at a mean velocity offset of voffset = –85.4 km s−1. We interpret this component as O i, supported by the aforementioned coincident detections. To constrain the system, we use the secondary lines to fix the velocity centroid of the O i component and perform simultaneous Voigt profile fitting across all three instruments, including both C iv transitions and single-component O i and Si ii models. The column density reported in this work corresponds to this singular O i component, and the system is marked with an asterisk in Table 1.\r\n\r\n3.5. O i Absorption Detection Completeness\r\nWe quantify the completeness of O i absorption detection around each galaxy as follows. For each galaxy overdensity, we compute the detection sensitivity on a pixel-by-pixel basis following the general framework of, e.g., K. M. Lanzetta et al. (1987), M. L. Bernet et al. (2010), and N. L. Mathes et al. (2017). In particular, we use a continuum-normalized spectral slice of ±1500 km s−1 centered on the expected O i absorption at the redshift of each galaxy overdensity.\r\n\r\nWe define the completeness in O i absorption detection in a single instrument as\r\n\r\nwhere H is the Heaviside step function, and is the equivalent-width cutoff at which completeness is defined. We adopt Å to facilitate comparison with the literature (see Section 4.2). Nσ is the detection threshold, which we set to Nσ = 3 by convention. The equivalent-width error, σEW(z), is given by\r\n\r\nwhere Δλj is the wavelength spacing between adjacent pixels (set by the spectrograph), and npix is the number of pixels over which the equivalent width is computed. We adopt the typical width of an O i absorber as npix for our analysis, yielding npix, X-shooter = 10, npix, HIRES = 50, and npix, FIRE = 11, respectively. This is a conservative approach to calculating completeness, as the typical width of the absorbers is larger than the resolving power of the instruments. We neglect continuum-fitting errors, so σEW(z) reflects only statistical uncertainties from the spectra. Any chip gaps or sky lines are masked. σI and Ic are the flux uncertainty and continuum levels of the spectrum.\r\n\r\nFor galaxy overdensities observed with multiple spectrographs, we define the combined completeness as requiring detection in at least one instrument across the relevant wavelength range. For example, with three or more instruments available,\r\n\r\nwhere the logical OR (∨) runs over all instruments i ∈ X-shooter, FIRE, HIRES. We then compute the mean completeness for each overdensity, and obtain the overall mean completeness, , by averaging over all overdensities weighted by their wavelength coverage. This yields a mean completeness of 91.4% for O i absorption around galaxy overdensities in the EIGER survey for 0.05 Å.\r\n\r\n4. Results\r\nIn this section, we present the variation of O i absorption around z ∼ 6 galaxies, the incidence of O i absorption per comoving path length that is due to O i absorption around galaxies, and the chemical abundance of these systems.\r\n\r\n4.1. Variation of O i Absorption around Galaxies\r\nSince all 40 galaxies in our sample reside within 15 identified overdensities (Section 3.3), we investigate whether O i absorption is preferentially detected in these environments. For clarity, we show the primary galaxy in each overdensity (as defined in Section 3.3) when presenting the radial distribution of O i absorption. Out of the 15 overdensities, 5 show associated O i absorption.\r\n\r\nFigure 4 shows the 2D spatial distribution of galaxies around these five detected systems, with the size depicting the virial radii of the galaxies. The galaxies are randomly distributed around the absorbers, and we do not find correlations with stellar mass, star formation, or other galaxy properties. In all five cases where we have O i detection, the galaxy member with the minimum impact parameter is also the member with the lowest R/Rvir.\r\n\r\nZoom InZoom OutReset image size\r\nFigure 4. Galaxy overdensities around z ∼ 6 O i absorbers in the EIGER survey. Each panel shows the background quasar (red star) at the center, with foreground galaxies associated with O i absorption marked as circles. Circles are color coded by the velocity offset between the galaxy and the O i absorber, and circle sizes are scaled to their virial radii. Only galaxies within 300 kpc of the quasar are shown, highlighting the overdensities nearest the absorbers. Dashed circles denote projected impact parameters of 50, 100, 200, and 300 pkpc from the quasar.\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\nFigure 5 presents 1D the radial profiles around the primary galaxies in these systems. The marker size indicates the number of member galaxies in each overdensity, while the color encodes the velocity offset from the corresponding O i absorption. Panels (a) and (c) show impact parameter (R), and panels (b) and (d) show the same distribution normalized by the halo virial radius (R/Rvir).\r\n\r\nZoom InZoom OutReset image size\r\nFigure 5. Radial absorption profiles of O i absorption at z ∼ 6. Each point marks the impact parameter to the nearest galaxy in a galaxy overdensity, with all detected O i absorption arising in such environments. Overdensities with O i absorption are shown as circles, while nondetections (2σ limits) are indicated by downward arrows. Points are color coded by the velocity offset between the galaxy redshift and the O i absorber, and their size scales with the number of members in the overdensity. The mean uncertainty on the virial radius is ΔRvir = 1.81 kpc. Top panels: rest-frame equivalent width vs. impact parameter (R, left) and normalized impact parameter (R/Rvir, right). Bottom panels: same as above, but for O i column densities.\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\nMost of the O i detections occur within R ≲ 175 kpc of the primary galaxy, corresponding to an incidence rate of , estimated using 68% Wilson score confidence intervals. Within 100 kpc, the incidence is , increasing to for R ≤ 50 kpc. Conversely, at R  >  150 kpc, an incidence of is measured. Within 300 kpc of the primary galaxy, the overall incidence is , with values of for 50 ≤ R ≤ 300 kpc and for 100 ≤ R ≤ 300 kpc. These rates are substantially weaker than the incidence of strong Mg ii absorption at z ∼ 6 (R. Bordoloi et al. 2024), indicating that neutral oxygen preferentially traces a different phase of the circumgalactic environment.\r\n\r\nPanels (b) and (d) reveal that O i absorbers are typically located at much larger R/Rvir than strong low-ionization tracers such as Mg ii. This distinction suggests that O i absorption at z ∼ 6 is not confined to the CGM of an individual galaxy but instead reflects the larger-scale gaseous environment of galaxy overdensities—what might be described as “cosmic ecosystems” rather than isolated halos.\r\n\r\nComparing the stellar mass distributions of overdensities with and without O i absorption, we find no statistically significant differences. The mean stellar mass of galaxies in overdensities with absorption is , compared to for those without.\r\n\r\nWe emphasize that at z ∼ 6, the large R/Rvir values of these halos imply that O i absorption typically arises at scales well beyond the typical CGM [R/Rvir ≲ 1] (J. Tumlinson et al. 2017) probed by low-ionization lines at lower redshift. Unlike the low-z CGM, where metal absorbers are closely tied to the halo of a single massive galaxy, the O i absorbers studied here appear to be linked to extended networks of low-mass, young galaxies embedded in shared overdensities. Over cosmic time, these small systems and their diffuse gaseous environments are expected to merge and evolve into more massive systems, eventually forming Milky Way–like galaxies by z = 0. Thus, neutral O i at reionization is best understood not as a tracer of isolated galactic halos, but as a probe of the extended environments that connect galaxies, gas, and structure growth in the early Universe.\r\n\r\nBecause O i absorption traces dense, neutral gas and requires only minimal ionization corrections, we can place a conservative lower limit on the total oxygen mass associated with the EIGER galaxies. These estimates are intended as simple, order-of-magnitude calculations to provide intuition about the amount of neutral oxygen relative to the observed galaxy properties. Following the formalism of R. Bordoloi et al. (2014), the oxygen mass contained in an annulus bounded by Rin and Rout is\r\n\r\nwhere Rin and Rout are the inner and outer radii of the annulus, fc is the covering fraction (the incidence of O i detections in that bin), 〈NOI〉 is the mean O i column density in the annulus, and mO = 16 mp is the mass of an oxygen atom, with mp being the mass of a proton. For a conservative lower limit, we adopt fion = 1, where fion is the ionization fraction (i.e., we assume that all of the oxygen mass is in the neutral phase). We justify this assumption as follows: O i is tightly coupled to H i through charge exchange, and in dense gas, the required ionization correction is minor, even under strong radiation fields such as the Fermi Bubbles (R. Bordoloi et al. 2017; T. Ashley et al. 2022). Under a typical metagalactic UV background, it is generally less than 10% and does not significantly alter the inferred oxygen abundance. In addition, oxygen does not deplete onto dust grains, unlike Si or C. For these reasons, we consider the approximation NO,total ≈ NOI to be valid for our analysis.\r\n\r\nWe compute masses in two radial bins: 0–100 kpc and 100–300 kpc, respectively. The total oxygen mass within radius is obtained by summing the masses of the constituent annuli. This yields a strict lower limit of  ≳  2 ×106M⊙ on the total oxygen mass within = 300 kpc.\r\n\r\nWe compare the inferred oxygen mass in the extended environment of our sample with the total oxygen content in the interstellar medium (ISM) of a typical z ∼ 6 galaxy. In computing this quantity, we make the following assumptions. First, we assume that all galaxies in this work lie on the typical z ∼ 6 mass–metallicity relation, derived by stacking [O iii] emitter galaxies (J. Matthee et al. 2022), and we adopt the gas-phase metallicity from this relation for each galaxy.\r\n\r\nBecause direct measurements of the total H2 and H i gas content are not available at these redshifts, we extrapolate the molecular gas fraction from L. J. Tacconi et al. (2018) to z ∼ 6 and adopt a conservative H i gas fraction based on local observations (S. Huang et al. 2012). We note that high-z galaxies are likely more gas-rich than their local counterparts; therefore, the inferred ISM gas masses should be considered lower limits.\r\n\r\nWith these caveats in mind, we estimate the total ISM oxygen mass as\r\n\r\nwhere we define . Here, XO is the gas-phase oxygen abundance derived from the mass–metallicity relation, and and MHI are the molecular and atomic gas masses derived as described above. For our galaxy sample, the mean stellar mass is , corresponding to an ISM oxygen mass of MO,ISM  ≳  6.8 × 105 M⊙. Remarkably, this indicates that the typical ISM oxygen content is comparable to the oxygen mass in the extended environment around these galaxies, implying that the circumgalactic or intergalactic medium at z ∼ 6 contains a substantial reservoir of oxygen. While these estimates depend on several specific assumptions, the inferred ISM and CGM oxygen masses appear to be of similar magnitude.\r\n\r\nAt low redshift, both L* and sub-L* galaxies similarly exhibit substantial metal content in their circumgalactic medium (CGM), with the CGM containing at least as much metal as the ISM of their host galaxies (J. Tumlinson et al. 2011; R. Bordoloi et al. 2014). A key difference is that, whereas the low-z CGM is typically gravitationally bound to its host galaxy, at high redshift much of the gas exists in the extended environment of galaxy overdensities rather than being bound to individual galaxies (see also R. Bordoloi et al. 2024).\r\n\r\n4.2. Expected Incidence of O i Absorbers\r\nIn this section, we report the expected redshift-path incidence of O i absorbers around [O iii] emitting galaxies detected in the EIGER survey. We define the number of O i absorbers associated with each galaxy overdensity per unit absorption distance above a detection threshold (WOI ≥ 0.05Å ) as\r\n\r\n\r\nHere, Rmax = 300 kpc is the survey radius adopted in this work, and is the mean O i absorber detection completeness (see Section 3.5; 91.4% for WOI ≥ 0.05 Å). nOD is defined as\r\n\r\n\r\nngal is the number density of [O iii] emitting galaxies per unit comoving volume, estimated from the [O iii] luminosity function at z ∼ 6. And 〈overdensity size〉 is simply the mean number of galaxies in each galaxy overdensity empirically measured to be 〈overdensity size〉 = 2.67. fc is the O i absorption covering fraction within 300 kpc for WOI ≥ 0.05 Å (). (The covering fraction within 300 kpc is independent of the definition of the primary member.)\r\n\r\nTo estimate the number density of galaxies per unit comoving volume (ngal), we integrate the z ∼ 6 [O iii] luminosity function derived from the EIGER survey, with a minimum luminosity of Lmin = 1042.2 ergs−1 (J. Matthee et al. 2022):\r\n\r\n\r\nwhere Φ(L) is the [O iii] luminosity function defined as\r\n\r\n\r\nHere, Φ* is the characteristic number density, L* is the characteristic luminosity, and α is the faint-end slope. We adopt Φ* = 10−4.02 Mpc−3, L* = 1043.33 ergs−1, and α = −1.92, values derived from detailed completeness calculations of the EIGER [O iii]-emitting galaxies (R. Mackenzie et al. 2026, in preparation). This results in ngal = 8.586 × 10−04 Mpc−3. Using these values in Equation (6) yields , for O i absorption around galaxies at a mean galaxy redshift of 6.001.\r\n\r\nAll calculations in this section are performed with a detection threshold of WOI > 0.05Å, since the survey is highly complete down to this equivalent-width limit and because most of the literature surveys we compare against adopt the same threshold.\r\n\r\nWe emphasize that this approach differs from blind QSO absorption-line surveys (e.g., G. D. Becker et al. 2006; L. Christensen et al. 2023; A. M. Sebastian et al. 2024; A. Sodini et al. 2024), where all O i absorption-line systems along the full quasar redshift path are counted to compute dN/dX directly, under the assumption that the absorber cross section is contributed by all galaxies. In contrast, our method begins by defining the absorber cross section around galaxy overdensities and then estimating the corresponding contribution to dN/dX from the galaxy overdensities under study. Comparing these two approaches constrains the fraction of O i (or other metal) absorption systems that arise in the extended halos of these galaxies. Figure 6 shows these literature measurements as colored circles, while the contribution to dN/dX around z ∼ 6 galaxy overdensities is indicated by an orange square. To quantify the relative contribution of galaxy overdensities, we fit a single power law to all literature values at z  >  4 (blue dashed line with shaded region). Comparing the dN/dX inferred from quasar absorption-line surveys at z ∼ 6 to our measured value, we find that O i dN/dX around z ∼ 6 EIGER galaxy environments account for 35% ± 16% of all O i absorption-line systems detected in blind quasar surveys. This implies that [O iii] emitting galaxy environments at z ∼ 6 contribute roughly one-third of the O i absorption systems at that epoch. Although the EIGER QSOs were selected to have known absorption systems along their sight lines, the EIGER galaxy survey around these sight lines is highly complete and independent of this selection. Therefore, we can create an unbiased measurement of the absorption cross section (dN/dX) around these galaxy overdensities. We justify this comparison to blind absorption surveys in Section 2.\r\n\r\nZoom InZoom OutReset image size\r\nFigure 6. Incidence of O i absorbers per comoving path length, dN/dX. Values are derived from all O i absorption lines along high-z quasar sight lines. Literature measurements are shown from G. D. Becker et al. (2019; blue circles), L. Christensen et al. (2023; purple circles), and A. M. Sebastian et al. (2024; red circles). The blue dashed line shows a power-law fit to the z  > 4 literature data, with the shaded region marking the 1σ uncertainty. The orange square gives the inferred dN/dX when including only O i absorption associated with host galaxies (see Section 4.2), indicating that only ∼35% of O i absorbers at z ∼ 6 arise in galaxy environments.\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\nThis in turn suggests that ∼65% of the O i absorption systems detected along quasar sight lines at the epoch of reionization are not associated with [O iii] emitter galaxy overdensities. Either the bulk of O i absorption resides in isolated pockets of neutral IGM gas outside extended galaxy halos, or it is contributed by even lower-luminosity, less massive galaxies () that fall below the EIGER detection limits. Such systems may also be detected in galaxy halos that are oxygen-poor or lack strong [O iii] emission features, since our galaxy identifications primarily rely on [O iii] and Hβ emission lines.\r\n\r\nSimulations suggest that O i absorption should primarily arise in galactic halos rather than in the diffuse IGM, since metals are not widely distributed and ionization fronts propagate more quickly than metals (B. D. Oppenheimer et al. 2009; K. Finlator et al. 2013). Very low-mass protogalaxies forming their first stars may blur the boundary between IGM and CGM, enriching their surroundings with metals, especially if their star formation is bursty and prolific. If sufficiently numerous, such systems could contribute a nonnegligible fraction of oxygen in the early Universe.\r\n\r\nRecent observations support this possibility. K. Nakajima et al. (2025) reported a strongly lensed (μ = 98) galaxy at z ≈ 6.6 with a stellar mass upper limit of only ∼2700 M⊙ and a dynamical mass ∼100 times larger. The source shows emission and may be dominated by Population III stars. This provides direct evidence of oxygen production in extremely low-mass systems. A population of such ultralow-mass dwarf galaxies could plausibly account for the ∼65% of O i absorbers detected along quasar sight lines that are not associated with galaxies in our survey. Our sensitivity limit of (J. Matthee et al. 2022) means such dwarfs remain undetected. However, these galaxies may lack a dense enough CGM to shield neutral O i from the UV background; thus, even if they produce oxygen, neutral O i may not survive (K. Finlator et al. 2013). Interestingly, simulations by S. Kušmić et al. (2024) showed that the contribution of metal ions, including O i, is only weakly correlated with the stellar mass of the galaxy, and the contribution is indistinguishable when comparing across galaxy luminosities. Additionally, they argue that due to the steep slope of the stellar mass function, lower-mass, lower-luminosity galaxies contribute the majority of absorbing metal ions in the CGM and IGM.\r\n\r\nLater simulation works by C. Doughty et al. (2018); C. Doughty & K. Finlator (2019) suggest that as the Epoch of Reionization continues, O i will reduce overall but be preferentially found in higher column density regions close to halos, as they have a better ability to self-shield from ionizing photons. In fact, C. Doughty & K. Finlator (2019) found that at z = 6 the majority of O i mass was located in the ISM of galaxies and only ∼30% of O i mass was found in the CGM and IGM. In contrast, in this work, we find that a substantial (comparable to ISM mass) oxygen mass exists outside galaxies; however, we stress that our mass measurements are order-of-magnitude estimates. A more direct comparison between these simulations and this work is the covering fraction. They report ∼5%–25% covering fraction at z = 6 for O i with out to 102 pkpc. In the EIGER survey, we report a covering fraction using a minimum threshold of WOI ≥ 0.05 Å (or approximately logNOI > 13.7 cm−2) out to 300 kpc. Given the large measurement uncertainties and different definitions of associated galaxies, the covering fractions are qualitatively consistent between the two works.\r\n\r\nThe simulations of K. Finlator et al. (2013) suggest that O i absorbers with are most likely associated with halos of mass ∼109 M⊙, where self-shielding is efficient. They further predict that only ∼13% of all O i absorption systems should reside in halos of 1010–1011.5 M⊙, the mass range of galaxies probed in this work. By contrast, we measure a higher dN/dX of ∼35%, but qualitatively our results remain consistent with the idea that roughly two-thirds of O i absorbers are associated with undetected ∼109 M⊙ halos. Future observations targeting lower-luminosity galaxies and higher redshifts will be essential to test these predictions.\r\n\r\nAfter the initial posting of this manuscript, G. Pruto et al. (2026) presented a simulation-based study that adopts the observational compilation shown in Figure 6 as a reference and explores the corresponding behavior in numerical models. Our minimum Wr threshold corresponds to ; therefore, the most appropriate comparison is with their sample. Qualitatively, the two sets of results are in agreement. A key distinction lies in the definition of galactic environment. We characterize environments in terms of galaxy overdensities, which we argue is the most appropriate description of where O i absorbers reside at z ≈ 6, whereas G. Pruto et al. (2026) define the CGM based on the virial radii of halos with . As a result, a direct quantitative comparison is not straightforward. Nevertheless, their inferred dN/dX corresponds to an incidence rate of O i absorbers of ∼58% ± 11%, which is consistent with our measurements within the uncertainties. This agreement may depend on their tighter constraints on absorber location and on the adopted minimum Wr or threshold. G. Pruto et al. (2026) further report that ∼80% of O i absorbers with are predicted to lie outside the CGM, also in qualitative agreement with our findings.\r\n\r\n4.3. Metal Abundances in O i absorber population\r\nIn this section, we examine the relative abundances and metal column density ratios of O i absorbers associated with galaxy overdensities, and compare them to O i absorbers without any associated galaxies. To enable a fair comparison, we restrict our analysis to the six quasar sight lines from the EIGER survey and identify all O i absorption systems in the redshift range where an [O iii]-emitting galaxy could be detected (5.9 ≤ zOI ≤ zQSO). We detect 10 O i absorption systems in total, 5 of which have associated galaxy overdensities (Table 1) and 5 are without any identified galaxy association.\r\n\r\nWe first compare the ionic column density ratios in these two populations. Figure 7 (top panels) shows the ratios of NSiII/NOI and NCII/NOI as functions of NOI. Systems located near galaxy overdensities (blue squares) systematically show higher Si ii/O i and C ii/O i ratios compared to systems without associated overdensities (green crosses). This offset could reflect differences in metallicity, or alternatively, the effects of ionization. However, since the majority of these O i systems lack detectable high-ionization transitions, it is reasonable to assume that neutral oxygen and singly ionized silicon and carbon dominate the elemental reservoirs (see also L. Christensen et al. 2023). In those cases, the observed ionic ratios provide direct tracers of relative abundances. Two exceptions are found along the J0100 and J1148 sight lines, which do exhibit Si iv and C iv absorption; for these systems, the degeneracy between chemical composition and ionization corrections cannot be resolved. It is plausible that, on average, O i absorption found near galaxy overdensities has higher elemental abundance ratios as the non-galaxy-associated absorbers either have significantly lower-luminosity and less massive galaxies, which would be expected to produce less metal, or there are truly no galaxies associated with this population.\r\n\r\nZoom InZoom OutReset image size\r\nFigure 7. Top panels: ion column density ratios of Si ii to O i (left) and C ii to O i (right) as a function of the detected O i column densities, shown in logarithmic units. Absorbers associated with galaxy overdensities (blue squares) and those not associated with galaxy overdensities (green crosses) exhibit clear variations in their column density ratios. One sight line with no detected Si ii absorption is indicated with a downward arrow, where a 2σ upper limit on the column density is assumed. Bottom panel: relative abundance ratios [Si/O] vs. [C/O] with respect to solar abundance. The background contours show the IMF-weighted abundance distributions from Population II and Population III SN models. Orange and pink circles indicate abundance ratios predicted by low-metallicity Population II SN models. The abundance ratios of several O i absorbers associated with galaxy overdensities are consistent with a significant contribution from Population III SNe.\r\n\r\nDownload figure:\r\n\r\nStandard image\r\nHigh-resolution image\r\nWe next compute the relative abundances [Si/O] and [C/O], presented in the bottom panel of Figure 7. These abundances are defined as\r\n\r\n\r\nwhere NSi,tot and NC,tot represent the summed ionic column densities. For systems with detected high-ionization absorption (C iv or Si iv), we include both low- and high-ionization states (NSiII + NSiIV and NCII + NCIV), marking these measurements as lower limits (blue upward arrows in the figure) since additional undetected ionization states may be present. We note that in the two systems (a and b) exhibiting high-ionization absorption (see Table 1), the low- and high-ionization absorption components are offset in velocity by Δv = –66 km s−1 and –69 km s−1, respectively. These offsets are within ≲1.5 resolution elements of the instrument, and therefore we cannot statistically distinguish whether the low- and high-ionization components are kinematically distinct. This is suggestive of a complex, potentially multiphase gaseous environment in the outskirts of these galaxies. For systems without detected high-ionization transitions, we adopt NSiII and NCII as the dominant contributions. We assume NO,tot ≈ NOI, as ionization corrections for O i are typically very small at high O i column densities (see Section 4.1 for discussion). We adopt solar reference abundances of = −1.18 ± 0.05 and (M. Asplund et al. 2021).\r\n\r\nFigure 7 (bottom panel) reveals a striking separation between O i absorbers associated with galaxy overdensities (blue squares) and those without galaxy associations (green crosses). Systems near galaxies are found in the upper left of the [Si/O]–[C/O] diagram, with two cases exhibiting high-ionization absorption (lower abundance limits, blue arrows), which will offset them even farther from the locus of nongalaxy absorbers.\r\n\r\nWe place these abundance patterns in the context of chemical enrichment models from different stellar populations (see also L. Christensen et al. 2023). The contours and colored circles in Figure 7 highlight predicted [C/O] and [Si/O] yields from representative Population II and Population III supernova (SN) models, weighted by a Salpeter IMF. The weighting by number of stars predicted by an IMF is done to represent the typical observational relative abundance distribution in these models. These are not exhaustive but span the dominant theoretical expectations.\r\n\r\nPopulation III pair-instability SNe (PISNe; 140–260M⊙; light green contours) predict narrow [C/O] ≃ –0.7 and high [Si/O] values, inconsistent with any of our observed systems. Such PISNe are also expected to produce substantial amounts of iron-peak elements, leading to elevated Fe/O ratios (J. Tumlinson et al. 2004). We will investigate Mg ii and Fe ii absorption associated with z ∼ 6 galaxies in an upcoming work (J. Higginson et al. 2026, in preparation). Models of massive Population III stars (10–100 M⊙) produce both hypernovae (gray contours; E > 1052 erg) and standard core-collapse SNe (light blue contours; A. Heger & S. E. Woosley 2010), spanning a broader region overlapping some of our measurements. We also consider Population II models: low-metallicity core-collapse SNe from M. Limongi & A. Chieffi (2018; orange contours, Population II SNe (L18)) occupy −0.25 ≲ [C/O] ≲ 0.5 and −0.4 ≲ [Si/O] ≲ 0.4, overlapping parts of the Population III range, while the C. Kobayashi et al. (2006) yields (pink and orange circles for hypernovae and SNe, respectively) tend toward lower [Si/O] and [C/O].\r\n\r\nAgainst these predictions, the contrast between the two absorber populations is clear. All nongalaxy O i systems (green crosses) fall at the lower left of the diagram, consistent with enrichment from both Population II and/or Population III SNe models. This regime also overlaps with ultra-metal-poor damped Lyman-α absorbers (DLAs) at z ∼ 3 (−0.5 ≲ [Si/O] ≲ 0, −0.5 ≲ [C/O] ≲ 0; R. Cooke et al. 2011; R. J. Cooke et al. 2017). By contrast, three of the five galaxy-associated absorbers lie well outside both the locus of Population II predictions and the locus of ultra-metal-poor DLA relative abundances. These systems are best explained if Population III enrichment played a major role, suggesting that they may represent a distinct population from ultra-metal-poor DLA host galaxies (see also A. Sodini et al. 2024).\r\n\r\nSimilarly, A. Sodini et al. (2024) found that the [C/O] and [Si/O] abundance ratios for high-redshift O i absorber systems are consistent with significant enrichment from Population III, with the majority explained by ≥ 30% contributions. They also find a large spread in the implied Population III contribution; several systems require ≥ 60% contributions, while others fall significantly below the average. This is a strong indication of heterogeneous chemical enrichment by Population III stars during the epoch of reionization.\r\n\r\nThe absorber toward J159 at z = 5.91 shows [C/O] = 0.20, [Si/O] = 0.55 (labeled c), and no evidence of high-ionization absorption. These abundance ratios are best explained by contributions from Population III SNe or hypernovae. The absorber toward J1030 at z = 6.07 ([C/O] = −0.38, [Si/O] = 0.65, labeled e) also shows no high-ionization absorption. The relative abundances in these two predominantly neutral systems are therefore quite robust. Interestingly, the J1030 system is not reproduced by any single Population II or Population III model, suggesting that it may have experienced multiple enrichment episodes, producing unusually high [Si/O] coupled with low [C/O].\r\n\r\nTwo cases require special mention. The absorber toward J0100 at z = 5.94 shows [C/O] ≥ 0.42 and [Si/O] ≥ 0.67 (labeled a), with strong C iv and Si iv absorption. Since these are lower limits, ionization corrections (for carbon and silicon) would push this system further upward, strengthening the case for Population III contributions. This observation is best explained by contributions from Population III hypernovae models. The J1148 absorber at z = 6.01 shows [C/O] ≥ 0.02 and [Si/O] ≥ 0.20 (labeled b), again with high-ionization lines; correcting for ionization would shift it diagonally upward in the diagram. Taken together, four of the five galaxy-associated absorbers show relative abundances that cannot be explained by Population II models alone, pointing instead to significant enrichment from Population III SNe or hypernovae.\r\n\r\nThus, most galaxy-associated O i systems carry signatures of Population III enrichment. These results suggest that O i systems tracing galaxy overdensities at z ∼ 6 carry chemical signatures of Population III enrichment, likely from multiple SNe events rather than a single explosion. The elevated [Si/O] and [C/O] ratios in these environments imply that [O iii]—emitting galaxies at this epoch may retain significant Population III contributions, and that metal-line absorbers around such overdensities provide a powerful probe of the first generations of stars.\r\n\r\n4.4. Comparison to the z ≈ 0 Universe\r\nAt z ∼ 6, we cannot directly detect the local environments where O i absorption systems arise. However, at z ∼ 0, there are instances where the environments giving rise to O i absorption are well understood. Here, we discuss several such instances and compare them with z ∼ 6 observations. Such comparisons can provide useful insights regarding the nature of local environments within which O i systems exist at high z. We focus on O i absorption associated with local blue compact dwarf (BCD) galaxies and the Magellanic Stream (MS), owing to their low metallicities and well-characterized local environments.\r\n\r\nThere is evidence that O i is found preferentially in the H ii regions of local BCDs, with their H i regions being pristine or showing very low levels of enrichment (D. Kunth et al. 1994; M. Pettini & K. Lipman 1995; T. X. Thuan & Y. I. Izotov 1997). In particular, T. X. Thuan & Y. I. Izotov (1997) report that, to varying degrees, low-ionization metal lines (e.g., O i and Si ii) reside in the ionized hydrogen regions of BCDs rather than the neutral hydrogen regions. They report . Compared to the z ∼ 6 measurements in panel (b) of Figure 7, the O i column density of the BCD is comparable, but the Si ii-to-O i ratio is inconsistent with the z ∼ 6 values. On the other hand, V. Lebouteiller et al. (2004) find that the H ii region of the BCD I Zw 36 has significantly higher metallicity than its H i region. However, inferred from velocity offsets, O i in that system is associated with the H i region. The reported O i column density of that BCD () is approximately 2 orders of magnitude higher than the z ∼ 6 sample. Given the available evidence, we conclude that the observed z ∼ 6 O i absorption systems are not similar to local BCD systems and are unlikely to originate in H ii regions.\r\n\r\nThe MS is a filamentary trail of gas in the Local Group. Multiphase absorption-line observations from A. J. Fox et al. (2013) and P. Richter et al. (2013) support the argument that the MS was tidally stripped from the Magellanic Clouds approximately 2 Gyr ago. Inferences from the abundance ratios of alpha elements in the MS are best explained by contributions from massive stars via Type II SNe when the MS was still part of the Magellanic Clouds, although the presence of significant dust depletion makes further inferences into enrichment history difficult. An additional study of the MS (N. Kumari et al. 2015) reports abundance ratios in a compact high-velocity cloud (CHVC) that is believed to be associated with the MS. They find [Si/O] = −0.04 ± 0.25 and [C/O] = −0.09 ± 0.23. When comparing these with the z ∼ 6 observations presented in panel (c) of Figure 7, we see that the CHVC abundance ratios occupy a different region of parameter space than the z ≈ 6 O i absorbers within identified galactic overdensities showing Population III enrichment signatures (points a, c, e). This discrepancy provides evidence that these z ∼ 6 O i absorbers with Population III enrichment signatures are unlikely to arise in environments similar to the MS. However, the ionic ratios of O i absorption systems not associated with galaxy overdensities (green crosses) are consistent with this measurement. With the caveat that MS measurements do contain dust depletion effects, it is plausible that such O i systems may trace IGM structures with densities comparable to those of the MS at high z.\r\n\r\n5. Conclusion\r\nWe have conducted a survey of neutral O i absorption systems associated with galaxies during the Epoch of Reionization in the EIGER survey, using six high-redshift quasars as background sight lines. Our study focuses on the distribution of neutral oxygen around -emitting galaxies within 300 kpc and their connection to galaxy overdensities. The main results are as follows:\r\n\r\n1.  \r\nFive O i absorbers are detected among 15 galaxy overdensities, spanning z = 5.91–6.16 with a mean redshift 〈z〉 = 6.001.\r\n2.  \r\nThe O i covering fraction within 300 kpc of the closest galaxy is , with for R ≤ 50 kpc and for 50 ≤ R ≤ 300 kpc, where the covering fraction is calculated using the galaxy in an overdensity with the lowest impact parameter.\r\n3.  \r\nWe find  ≳ 2 × 106 M⊙ of oxygen within 300 kpc, a mass comparable to the ISM oxygen content of z ∼ 6 galaxies—assuming minimal ionization correction (see Section 4.1 for justification)—suggesting that the circumgalactic environment already holds metal reservoirs rivaling those inside galaxies.\r\n4.  \r\nO i absorbers are detected as far as ∼8 R/Rvir from galaxies, in sharp contrast to low-ionization tracers such as Mg ii, which are typically confined within ≲R/Rvir.\r\n5.  \r\nThe incidence of galaxy-associated O i absorbers is \r\n \r\n. Comparison with blind quasar absorption-line surveys indicates that these systems represent only ∼35% of all O i absorbers at z ∼ 6, implying that the majority likely arise in lower-mass galaxies below current detection limits or in dense neutral IGM pockets that survived reionization.\r\n6.  \r\nRelative abundance and ionization ratios ([Si/O], [C/O]) show that galaxy-associated O i systems are chemically enriched, with signatures in several systems consistent with contributions from Population III stars. In particular, we identify four galaxy overdensities whose outskirts exhibit absorption-line abundance ratios consistent with contributions from Population III nucleosynthesis.\r\n\r\nOverall, these results indicate that neutral O i at z ∼ 6 primarily traces extended overdensity environments rather than the CGM of individual halos. Moreover, the chemical abundance patterns of galaxy-associated O i systems suggest contributions from Population III stars, likely arising from multiple SNe events rather than a single explosion. The elevated [Si/O] and [C/O] ratios imply that [O iii]-emitting galaxies at this epoch may retain significant Population III enrichment. Consequently, metal-line absorbers around such overdensities offer a powerful probe of the first generations of stars, providing insight into early chemical enrichment and the role of primordial stellar populations in shaping galaxy evolution during the Epoch of Reionization.\r\n\r\nAcknowledgments\r\nThis work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. These observations are associated with program #1243. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. This work was supported by a NASA Keck PI Data Award, administered by the NASA Exoplanet Science Institute. Data presented herein were obtained at the W. M. Keck Observatory from telescope time allocated to the National Aeronautics and Space Administration (NASA) through the agency’s scientific partnership with the California Institute of Technology and the University of California. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The JWST data presented in this article were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via DOI: 10.17909/y94q-h212. This work was partially supported by the National Science Foundation under grant No. AST-2108931. Jorryt Matthee and Ivan Kramarenko acknowledge funding from the European Union (ERC, AGENTS, 101076224).\r\n\r\nFacilities: JWST - James Webb Space Telescope (NIRCam), Magellan: Baade - (FIRE), VLT: Kueyen - (X-shooter), and Keck: I - (HIRES, MOSFIRE).\r\n\r\nSoftware: astropy (Astropy Collaboration et al. 2013, 2018, 2022), rbcodes (R. Bordoloi et al. 2025), rbvfit (R. Bordoloi & J. Higginson 2025).","external_id":{"arxiv":["2510.05220"]},"has_accepted_license":"1","department":[{"_id":"JoMa"},{"_id":"GradSch"}],"article_processing_charge":"Yes","DOAJ_listed":"1","doi":"10.3847/1538-4357/ae3e81","citation":{"ieee":"J. Higginson <i>et al.</i>, “EIGER. VIII. First stars signatures in the connection between O I absorption and galaxies in the epoch of reionization,” <i>The Astrophysical Journal</i>, vol. 999, no. 1. IOP Publishing, 2026.","ista":"Higginson J, Bordoloi R, Simcoe RA, Matthee JJ, Kashino D, Mackenzie R, Kramarenko I, Lilly SJ, Eilers A-C, Naidu RP, Yue M. 2026. EIGER. VIII. First stars signatures in the connection between O I absorption and galaxies in the epoch of reionization. The Astrophysical Journal. 999(1), 49.","chicago":"Higginson, Jack, Rongmon Bordoloi, Robert A. Simcoe, Jorryt J Matthee, Daichi Kashino, Ruari Mackenzie, Ivan Kramarenko, et al. “EIGER. VIII. First Stars Signatures in the Connection between O I Absorption and Galaxies in the Epoch of Reionization.” <i>The Astrophysical Journal</i>. IOP Publishing, 2026. <a href=\"https://doi.org/10.3847/1538-4357/ae3e81\">https://doi.org/10.3847/1538-4357/ae3e81</a>.","short":"J. Higginson, R. Bordoloi, R.A. Simcoe, J.J. Matthee, D. Kashino, R. Mackenzie, I. Kramarenko, S.J. Lilly, A.-C. Eilers, R.P. Naidu, M. Yue, The Astrophysical Journal 999 (2026).","ama":"Higginson J, Bordoloi R, Simcoe RA, et al. EIGER. VIII. First stars signatures in the connection between O I absorption and galaxies in the epoch of reionization. <i>The Astrophysical Journal</i>. 2026;999(1). doi:<a href=\"https://doi.org/10.3847/1538-4357/ae3e81\">10.3847/1538-4357/ae3e81</a>","mla":"Higginson, Jack, et al. “EIGER. VIII. First Stars Signatures in the Connection between O I Absorption and Galaxies in the Epoch of Reionization.” <i>The Astrophysical Journal</i>, vol. 999, no. 1, 49, IOP Publishing, 2026, doi:<a href=\"https://doi.org/10.3847/1538-4357/ae3e81\">10.3847/1538-4357/ae3e81</a>.","apa":"Higginson, J., Bordoloi, R., Simcoe, R. A., Matthee, J. J., Kashino, D., Mackenzie, R., … Yue, M. (2026). EIGER. VIII. First stars signatures in the connection between O I absorption and galaxies in the epoch of reionization. <i>The Astrophysical Journal</i>. IOP Publishing. <a href=\"https://doi.org/10.3847/1538-4357/ae3e81\">https://doi.org/10.3847/1538-4357/ae3e81</a>"},"file_date_updated":"2026-10-14T07:50:51Z","abstract":[{"lang":"eng","text":"We investigate the association between galaxies and neutral O I absorption systems at z ∼ 6, which trace metalenriched gas during the epoch of reionization. We identify 40 galaxies across six quasar fields, residing in 15\r\noverdensities within 300 kpc of the background sight lines. Five O I absorption systems are associated with five of\r\nthese overdensities, yielding a covering fraction of\r\n0.27 0.10\r\n+0.13\r\nwithin 300 kpc. The absorption occurs beyond typical\r\nvirial radii, indicating that the gas traces extended overdensity environments rather than individual galaxy halos,\r\nunlike the z ∼ 0 circumgalactic medium (CGM), which is largely bound to halos. These galaxy-associated\r\nabsorbers account for ∼35% of all O I systems seen in blind quasar surveys, implying the remainder arise in\r\nlower-mass galaxies below our detection threshold or in dense neutral intergalactic medium pockets. The CGM\r\naround these galaxies contains ≳ 2 × 106 M⊙ of oxygen, comparable to the interstellar medium oxygen mass of\r\nthe galaxies themselves, suggesting that the surrounding environment holds as much metal mass as the galaxies.\r\nAll five galaxy-associated systems show significantly higher\r\nlog NCII NOI ( / )\r\nratios than absorbers lacking galaxy\r\nassociations. Furthermore, relative abundance ratios ([Si/O], [C/O]) reveal that four of the five exhibit\r\nenrichment patterns consistent with Population III nucleosynthesis at the outskirts of galaxy overdensities. These\r\nrare systems offer a unique window into the role of first-generation stars in shaping the early metal enrichment of\r\ngalaxies and their environments."}],"publication_identifier":{"eissn":["1538-4357"],"issn":["0004-637X"]}},{"das_tickbox":"0","OA_place":"publisher","day":"01","author":[{"id":"776468ec-50b0-11ef-861e-96ad19e894f3","last_name":"Grebennikov","first_name":"Aleksandr","full_name":"Grebennikov, Aleksandr"},{"full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan"}],"quality_controlled":"1","file":[{"success":1,"content_type":"application/pdf","file_id":"23139","creator":"dernst","file_size":284851,"file_name":"2026_BulletinLondonMathSoc_Grebennikov.pdf","date_created":"2026-10-14T08:37:16Z","access_level":"open_access","date_updated":"2026-10-14T08:37:16Z","relation":"main_file","checksum":"cce830e3fc66174803b91103f5b88a29"}],"article_type":"original","OA_type":"hybrid","volume":58,"supplementarymaterial":"no","publication":"Bulletin of the London Mathematical Society","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","fulldoi":"https://doi.org/10.1112/blms.70510","issue":"10","type":"journal_article","intvolume":"        58","mathsc":["05D40","52C10","52C35"],"PlanS_conform":"1","year":"2026","researchdata_availability":"no","status":"public","oa":1,"date_published":"2026-10-01T00:00:00Z","date_created":"2026-10-12T13:57:47Z","oa_version":"Published Version","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"10","language":[{"iso":"eng"}],"project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"article_number":"e70510","file_date_updated":"2026-10-14T08:37:16Z","doi":"10.1112/blms.70510","citation":{"ama":"Grebennikov A, Kwan MA. No‐(k+1)‐in‐line problem for large constant k. <i>Bulletin of the London Mathematical Society</i>. 2026;58(10). doi:<a href=\"https://doi.org/10.1112/blms.70510\">10.1112/blms.70510</a>","short":"A. Grebennikov, M.A. Kwan, Bulletin of the London Mathematical Society 58 (2026).","chicago":"Grebennikov, Aleksandr, and Matthew Alan Kwan. “No‐(K+1)‐in‐line Problem for Large Constant K.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2026. <a href=\"https://doi.org/10.1112/blms.70510\">https://doi.org/10.1112/blms.70510</a>.","ista":"Grebennikov A, Kwan MA. 2026. No‐(k+1)‐in‐line problem for large constant k. Bulletin of the London Mathematical Society. 58(10), e70510.","ieee":"A. Grebennikov and M. A. Kwan, “No‐(k+1)‐in‐line problem for large constant k,” <i>Bulletin of the London Mathematical Society</i>, vol. 58, no. 10. Wiley, 2026.","apa":"Grebennikov, A., &#38; Kwan, M. A. (2026). No‐(k+1)‐in‐line problem for large constant k. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.70510\">https://doi.org/10.1112/blms.70510</a>","mla":"Grebennikov, Aleksandr, and Matthew Alan Kwan. “No‐(K+1)‐in‐line Problem for Large Constant K.” <i>Bulletin of the London Mathematical Society</i>, vol. 58, no. 10, e70510, Wiley, 2026, doi:<a href=\"https://doi.org/10.1112/blms.70510\">10.1112/blms.70510</a>."},"publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"abstract":[{"lang":"eng","text":"How many points can be placed in an 𝑛 × 𝑛 grid sothat every (affine) line contains at most 𝑘 points? Weprove that for 𝑛 ⩾ 𝑘 ⩾ 1037 the maximum number ofpoints is exactly 𝑘𝑛. Our proof builds on the recent workof Kovács, Nagy and Szabó (who proved an analogousresult when 𝑘 is at least about √𝑛 log 𝑛), incorporat-ing ideas of Jain and Pham. Using the same approach,we also obtain new bounds for higher-dimensionalextensions of this problem"}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","department":[{"_id":"MaKw"},{"_id":"GradSch"}],"corr_author":"1","acknowledgement":"We would like to thank Huy Pham for insightful discussions about the proof approach, and wewould like to thank the anonymous referees for their careful reading and helpful comments. Bothauthors are supported by ERC Starting Grant “RANDSTRUCT” No. 101076777.Open Access funding provided by Institute of Science and Technology Austria.","publisher":"Wiley","_id":"23123","date_updated":"2026-10-14T08:41:00Z","ddc":["510"],"title":"No‐(k+1)‐in‐line problem for large constant k"},{"oa_version":"Published Version","month":"09","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","language":[{"iso":"eng"}],"article_processing_charge":"No","publication_identifier":{"issn":["2663-337X "],"isbn":["978-3-99078-093-0"]},"doi":"10.15479/AT-ISTA-22984","file_date_updated":"2026-09-25T09:25:56Z","citation":{"apa":"Teplova, A. (2026). <i>Chasing the elusive: Investigating nucleotide cyclase activity in gibberellin and strigolactone signalling; Cellular mechanisms of gravity sensing and response in roots</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-22984\">https://doi.org/10.15479/AT-ISTA-22984</a>","mla":"Teplova, Anastasiia. <i>Chasing the Elusive: Investigating Nucleotide Cyclase Activity in Gibberellin and Strigolactone Signalling; Cellular Mechanisms of Gravity Sensing and Response in Roots</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22984\">10.15479/AT-ISTA-22984</a>.","ista":"Teplova A. 2026. Chasing the elusive: Investigating nucleotide cyclase activity in gibberellin and strigolactone signalling; Cellular mechanisms of gravity sensing and response in roots. Institute of Science and Technology Austria.","ieee":"A. Teplova, “Chasing the elusive: Investigating nucleotide cyclase activity in gibberellin and strigolactone signalling; Cellular mechanisms of gravity sensing and response in roots,” Institute of Science and Technology Austria, 2026.","ama":"Teplova A. Chasing the elusive: Investigating nucleotide cyclase activity in gibberellin and strigolactone signalling; Cellular mechanisms of gravity sensing and response in roots. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-22984\">10.15479/AT-ISTA-22984</a>","chicago":"Teplova, Anastasiia. “Chasing the Elusive: Investigating Nucleotide Cyclase Activity in Gibberellin and Strigolactone Signalling; Cellular Mechanisms of Gravity Sensing and Response in Roots.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-22984\">https://doi.org/10.15479/AT-ISTA-22984</a>.","short":"A. Teplova, Chasing the Elusive: Investigating Nucleotide Cyclase Activity in Gibberellin and Strigolactone Signalling; Cellular Mechanisms of Gravity Sensing and Response in Roots, Institute of Science and Technology Austria, 2026."},"alternative_title":["ISTA Thesis"],"corr_author":"1","department":[{"_id":"GradSch"},{"_id":"JiFr"}],"has_accepted_license":"1","date_updated":"2026-10-15T08:30:03Z","ddc":["570"],"publisher":"Institute of Science and Technology Austria","_id":"22984","degree_awarded":"PhD","title":"Chasing the elusive: Investigating nucleotide cyclase activity in gibberellin and strigolactone signalling; Cellular mechanisms of gravity sensing and response in roots","OA_place":"publisher","page":"190","author":[{"full_name":"Teplova, Anastasiia","first_name":"Anastasiia","last_name":"Teplova","id":"e3736151-106c-11ec-b916-c2558e2762c6"}],"doi_confirm":"1","day":"23","acknowledged_ssus":[{"_id":"Bio"},{"_id":"LifeSc"},{"_id":"MassSpec"}],"file":[{"access_level":"closed","date_created":"2026-09-25T09:19:25Z","file_name":"2026-Teplova-Anastasia-Thesis-final.docx","checksum":"ae6e37780e4a8d07cfabf0a899c6c6bf","date_updated":"2026-09-25T09:19:25Z","relation":"source_file","file_id":"22996","content_type":"application/vnd.openxmlformats-officedocument.wordprocessingml.document","file_size":106736394,"creator":"ateplova"},{"file_id":"22997","content_type":"application/pdf","creator":"ateplova","file_size":39343452,"file_name":"2026-Teplova-Anastasia-Thesis-final-pdfA.pdf","embargo_to":"open_access","access_level":"closed","date_created":"2026-09-25T09:25:56Z","embargo":"2027-09-30","checksum":"305099d360d30bd596af946171d19c3b","relation":"main_file","date_updated":"2026-09-25T09:25:56Z"}],"supervisor":[{"last_name":"Friml","id":"4159519E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8302-7596","first_name":"Jiří","full_name":"Friml, Jiří"}],"fulldoi":"https://doi.org/10.15479/AT-ISTA-22984","publication_status":"published","year":"2026","status":"public","related_material":{"record":[{"id":"15257","relation":"part_of_dissertation","status":"public"}]},"type":"dissertation","date_created":"2026-09-23T15:29:42Z","date_published":"2026-09-23T00:00:00Z"},{"ec_funded":1,"OA_place":"publisher","page":"83","author":[{"id":"02d96aae-000e-11ec-b801-cadd0a5eefbb","last_name":"Asadi","first_name":"Ali","full_name":"Asadi, Ali"}],"doi_confirm":"1","day":"09","file":[{"date_created":"2026-10-09T11:12:08Z","access_level":"open_access","file_name":"2026_Asadi_Ali_Thesis.pdf","date_updated":"2026-10-12T13:13:51Z","relation":"main_file","checksum":"c6b368f342409de884eafdd3af7867c5","content_type":"application/pdf","file_id":"23081","file_size":694682,"creator":"aasadi"},{"file_size":1538723,"creator":"aasadi","content_type":"application/zip","file_id":"23082","checksum":"71ecb0b666438f395a92b395e315f904","relation":"source_file","date_updated":"2026-10-09T11:47:47Z","access_level":"closed","date_created":"2026-10-09T11:12:56Z","file_name":"2026_Asadi_Ali_Thesis.zip"}],"supervisor":[{"orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"}],"publication_status":"published","fulldoi":"https://doi.org/10.15479/AT-ISTA-23079","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"21281"},{"relation":"part_of_dissertation","status":"public","id":"17099"}]},"status":"public","year":"2026","type":"dissertation","date_created":"2026-10-08T09:07:53Z","oa":1,"date_published":"2026-10-09T00:00:00Z","oa_version":"Published Version","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","month":"10","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"grant_number":"COE12","name":"Bilateral Artificial Intelligence (Chatterjee)","_id":"4029cfc7-b034-11f1-9e55-88ab2ff3b6ee"},{"call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093"}],"article_processing_charge":"No","citation":{"ista":"Asadi A. 2026. Approximation of values and equilibria in stochastic games: Complexity and algorithms. Institute of Science and Technology Austria.","ieee":"A. Asadi, “Approximation of values and equilibria in stochastic games: Complexity and algorithms,” Institute of Science and Technology Austria, 2026.","ama":"Asadi A. Approximation of values and equilibria in stochastic games: Complexity and algorithms. 2026. doi:<a href=\"https://doi.org/10.15479/AT-ISTA-23079\">10.15479/AT-ISTA-23079</a>","chicago":"Asadi, Ali. “Approximation of Values and Equilibria in Stochastic Games: Complexity and Algorithms.” Institute of Science and Technology Austria, 2026. <a href=\"https://doi.org/10.15479/AT-ISTA-23079\">https://doi.org/10.15479/AT-ISTA-23079</a>.","short":"A. Asadi, Approximation of Values and Equilibria in Stochastic Games: Complexity and Algorithms, Institute of Science and Technology Austria, 2026.","apa":"Asadi, A. (2026). <i>Approximation of values and equilibria in stochastic games: Complexity and algorithms</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT-ISTA-23079\">https://doi.org/10.15479/AT-ISTA-23079</a>","mla":"Asadi, Ali. <i>Approximation of Values and Equilibria in Stochastic Games: Complexity and Algorithms</i>. Institute of Science and Technology Austria, 2026, doi:<a href=\"https://doi.org/10.15479/AT-ISTA-23079\">10.15479/AT-ISTA-23079</a>."},"doi":"10.15479/AT-ISTA-23079","file_date_updated":"2026-10-12T13:13:51Z","abstract":[{"text":"We study the computational aspects of the two central solution concepts of stochastic games\r\nplayed on finite graphs for an infinite number of steps: the value in two-player zero-sum\r\ngames, and Nash equilibria in multi-player games. In both settings, exact solutions are in\r\ntractable. Fortwo-playerzero-sumconcurrentstochasticgames,valuescanbeirrational,and\r\nthe associated decision problem is SQRT-SUM hard. For multi-player turn-based stochastic\r\ngames,theequilibriumprobabilitiescanbeirrational,anddecidingtheconstrainedexistence\r\nof a Nash equilibrium is undecidable in the presence of memory, and ∃R-complete when the\r\nplayers are restricted to stationary strategies. Hence, in both settings, the natural computational problem is the approximation of the solution within an arbitrary additive error. In\r\nthis thesis, we present improved complexity results and algorithms for such approximation\r\nproblems.\r\nThe first part of the thesis considers two-player zero-sum concurrent stochastic games\r\nwith two classic objectives: (a) stateful-discounted objectives, which are similar to the classic\r\ndiscounted-sum objectives, but states are associated with different discount factors rather\r\nthan a single discount factor; and (b) parity objectives, which are a canonical representation\r\nfor ω-regular objectives. For stateful-discounted objectives, given an ordering of the discount\r\nfactors, the limit value is the limit of the value of the stateful-discounted objectives, as\r\nthe discount factors approach zero according to the given order. The value-approximation\r\nproblem is known to be in EXPSPACE for the limit value of stateful-discounted objectives and\r\nin PSPACEforparityobjectives,andthebest-knownalgorithmsforbothproblemsareatleast\r\nexponential time, with an exponential dependence on the number of states and actions. Our\r\nmain results for the value-approximation problem for the limit value of stateful-discounted\r\nobjectives and parity objectives areas follows: (a)we establish TFNPNP complexity; and (b)we\r\npresent algorithms that improve the dependency on the number of actions in the exponent\r\nfrom linear to logarithmic. In particular, if the number of states is constant, our algorithms\r\nrun in polynomial time.\r\nThe second part of the thesis considers multi-player turn-based stochastic games with\r\nterminal payoffs, where the players are restricted to stationary strategies. We study the\r\napproximate constrained existence problem of Nash equilibria: given a game that has a Nash\r\nequilibrium in which the payoff of every player lies in a given interval, compute a strategy\r\nprofile that is an ε-Nash equilibrium and that satisfies the same constraints up to an additive\r\nerror ε. Our main results are as follows: (a) we present an FNPNP algorithm for the problem;\r\nand(b)we establish that its decision version is NP-hard, already with two players. For the\r\nupperbound,weshowthatifaconstrainedNashequilibriumexists,thenthereexists one\r\nin which the non-zero probabilities are at least an inverse of a double-exponential in the\r\ni\r\ninput size, and that such a strategy profile can be represented, up to an additive error ε, with\r\nfloating-point numbers of polynomial size. We complement the upper bound with a lower\r\nbound on this approach: we present a game with only five players in which every constrained\r\nNash equilibrium requires double-exponentially small probabilities.\r\nThe two parts share a common technical toolkit: bounds on solutions of systems of\r\npolynomial inequalities that arise from real algebraic geometry, the floating-point representation of doubly-exponentially small numbers, and guess-and-verify procedures that resolve\r\nsingle-player games with an NP oracle.","lang":"eng"}],"publication_identifier":{"issn":["2791-4585"]},"corr_author":"1","alternative_title":["ISTA Master’s Thesis"],"has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"KrCh"}],"_id":"23079","publisher":"Institute of Science and Technology Austria","ddc":["000"],"date_updated":"2026-10-16T08:00:45Z","acknowledgement":"The research reported in Part I was partially supported by the European Research\r\nCouncil (ERC) Consolidator Grant 863818 (ForM-SMArt), by the Austrian Science Fund\r\n(FWF) 10.55776/COE12, and by the French Agence Nationale de la Recherche (ANR) grant\r\nANR-21-CE40-0020 (CONVERGENCE project). The research reported in Part II is a part of\r\nproject VAMOS, which has received funding from the European Research Council (ERC) under\r\ngrant agreement No.101020093.","degree_awarded":"MS","title":"Approximation of values and equilibria in stochastic games: Complexity and algorithms"},{"related_material":{"record":[{"id":"12237","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"17124"},{"relation":"part_of_dissertation","status":"public","id":"17052"}]},"status":"public","year":"2026","type":"dissertation","date_created":"2026-08-03T07:55:16Z","date_published":"2026-08-05T00:00:00Z","publication_status":"published","fulldoi":"https://doi.org/10.15479/AT-ISTA-22626","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"date_updated":"2026-08-07T10:02:41Z","relation":"source_file","checksum":"4f357f3c0f5ee3d679dd0395dbafc4bb","file_name":"2026_Fiedler_Christine_Thesis.docx","date_created":"2026-08-07T09:10:56Z","access_level":"closed","creator":"cfiedler","file_size":625541367,"content_type":"application/vnd.openxmlformats-officedocument.wordprocessingml.document","file_id":"22659"},{"date_created":"2026-08-07T09:10:45Z","access_level":"closed","embargo_to":"open_access","file_name":"2026_Fiedler_Christine_Thesis.pdf","relation":"main_file","date_updated":"2026-08-07T10:16:07Z","checksum":"69784d2e7b9ef3d3a0fbe134f3bba089","embargo":"2027-02-07","file_id":"22660","content_type":"application/pdf","file_size":16646551,"creator":"cfiedler"}],"supervisor":[{"orcid":"0000-0001-5013-2843","last_name":"Ibáñez","id":"43C61214-F248-11E8-B48F-1D18A9856A87","first_name":"Maria","full_name":"Ibáñez, Maria"}],"OA_place":"publisher","page":"141","doi_confirm":"1","author":[{"full_name":"Fiedler, Christine","first_name":"Christine","last_name":"Fiedler","id":"bd3fceba-dc74-11ea-a0a7-c17f71817366"}],"day":"05","_id":"22626","publisher":"Institute of Science and Technology Austria","ddc":["540","546","530"],"date_updated":"2026-10-16T09:30:26Z","acknowledgement":"This thesis and the publications within, were financially supported by the Institute of Science and Technology Austria and the Werner Siemens Foundation under the project “High Thermoelectric Materials: The Werner Siemens Laboratory for the High Throughput Discovery of Semiconductors for Waste Heat Recovery”.","degree_awarded":"PhD","title":"Mechanistic insight into solution-processed p-type tin chalcogenides as a basis for designing their n-type analogs","article_processing_charge":"No","doi":"10.15479/AT-ISTA-22626","citation":{"ama":"Fiedler C. 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