[{"_id":"12151","date_updated":"2024-10-09T21:03:37Z","abstract":[{"text":"The k-sample G(k,W) from a graphon W:[0,1]2→[0,1] is the random graph on {1,…,k}, where we sample x1,…,xk∈[0,1] uniformly at random and make each pair {i,j}⊆{1,…,k} an edge with probability W(xi,xj), with all these choices being mutually independent. Let the random variable Xk(W) be the number of edges in  G(k,W). Vera T. Sós asked in 2012 whether two graphons U, W are necessarily weakly isomorphic if the random variables Xk(U) and Xk(W) have the same distribution for every integer k≥2. This question when one of the graphons W is a constant function was answered positively by Endre Csóka and independently by Jacob Fox, Tomasz Łuczak and Vera T. Sós. Here we investigate the question when W is a 2-step graphon and prove that the answer is positive for a 3-dimensional family of such graphons. We also present some related results.","lang":"eng"}],"department":[{"_id":"MaKw"}],"date_published":"2022-11-23T00:00:00Z","page":"1-26","citation":{"ieee":"O. Cooley, M. Kang, and O. Pikhurko, “On a question of Vera T. Sós about size forcing of graphons,” <i>Acta Mathematica Hungarica</i>, vol. 168. Springer Nature, pp. 1–26, 2022.","ama":"Cooley O, Kang M, Pikhurko O. On a question of Vera T. Sós about size forcing of graphons. <i>Acta Mathematica Hungarica</i>. 2022;168:1-26. doi:<a href=\"https://doi.org/10.1007/s10474-022-01265-8\">10.1007/s10474-022-01265-8</a>","ista":"Cooley O, Kang M, Pikhurko O. 2022. On a question of Vera T. Sós about size forcing of graphons. Acta Mathematica Hungarica. 168, 1–26.","chicago":"Cooley, Oliver, M. Kang, and O. Pikhurko. “On a Question of Vera T. Sós about Size Forcing of Graphons.” <i>Acta Mathematica Hungarica</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10474-022-01265-8\">https://doi.org/10.1007/s10474-022-01265-8</a>.","mla":"Cooley, Oliver, et al. “On a Question of Vera T. Sós about Size Forcing of Graphons.” <i>Acta Mathematica Hungarica</i>, vol. 168, Springer Nature, 2022, pp. 1–26, doi:<a href=\"https://doi.org/10.1007/s10474-022-01265-8\">10.1007/s10474-022-01265-8</a>.","short":"O. Cooley, M. Kang, O. Pikhurko, Acta Mathematica Hungarica 168 (2022) 1–26.","apa":"Cooley, O., Kang, M., &#38; Pikhurko, O. (2022). On a question of Vera T. Sós about size forcing of graphons. <i>Acta Mathematica Hungarica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10474-022-01265-8\">https://doi.org/10.1007/s10474-022-01265-8</a>"},"language":[{"iso":"eng"}],"isi":1,"oa":1,"oa_version":"Preprint","date_created":"2023-01-12T12:07:59Z","type":"journal_article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"On a question of Vera T. Sós about size forcing of graphons","scopus_import":"1","author":[{"full_name":"Cooley, Oliver","id":"43f4ddd0-a46b-11ec-8df6-ef3703bd721d","last_name":"Cooley","first_name":"Oliver"},{"full_name":"Kang, M.","first_name":"M.","last_name":"Kang"},{"full_name":"Pikhurko, O.","last_name":"Pikhurko","first_name":"O."}],"intvolume":"       168","article_type":"original","article_processing_charge":"No","keyword":["graphon","k-sample","graphon forcing","graph container"],"year":"2022","doi":"10.1007/s10474-022-01265-8","month":"11","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.09114"}],"corr_author":"1","status":"public","day":"23","publication_identifier":{"eissn":["1588-2632"],"issn":["0236-5294"]},"arxiv":1,"volume":168,"publication":"Acta Mathematica Hungarica","publication_status":"published","publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Supported by Austrian Science Fund (FWF) Grant I3747. Supported by ERC Advanced Grant 101020255 and Leverhulme Research Project Grant RPG-2018-424.\r\nAn extended abstract of this paper appeared in the Proceedings of the European Conference\r\non Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.","external_id":{"arxiv":["2103.09114"],"isi":["000886839900006"]}},{"volume":212,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication":"Journal of Structural Biology","publication_status":"published","publisher":"Elsevier","status":"public","pmid":1,"day":"01","publication_identifier":{"issn":["1047-8477"]},"file":[{"date_created":"2020-12-10T14:01:10Z","relation":"main_file","file_id":"8937","creator":"dernst","date_updated":"2020-12-10T14:01:10Z","content_type":"application/pdf","checksum":"c48cbf594e84fc2f91966ffaafc0918c","file_size":7076870,"file_name":"2020_JourStrucBiology_Faessler.pdf","access_level":"open_access","success":1}],"quality_controlled":"1","acknowledgement":"This work was supported by the Austrian Science Fund (FWF, P33367) to FKMS. BZ acknowledges support by the Niederösterreich Fond. This research was also supported by the Scientific Service Units (SSU) of IST Austria through resources provided by Scientific Computing (SciComp), the Life Science Facility (LSF), the BioImaging Facility (BIF) and the Electron Microscopy Facility (EMF). We thank Georgi Dimchev (IST Austria) and Sonja Jacob (Vienna Biocenter Core Facilities) for testing our grid holders in different experimental setups and Daniel Gütl and the Kondrashov group (IST Austria) for granting us repeated access to their 3D printers. We also thank Jonna Alanko and the Sixt lab (IST Austria) for providing us HeLa cells, primary BL6 mouse tail fibroblasts, NIH 3T3 fibroblasts and human telomerase immortalised foreskin fibroblasts for our experiments. We are thankful to Ori Avinoam and William Wan for helpful comments on the manuscript and also thank Dorotea Fracchiolla (Art&Science) for illustrating the graphical abstract.","ddc":["570"],"external_id":{"pmid":["32987119"],"isi":["000600997800008"]},"month":"12","file_date_updated":"2020-12-10T14:01:10Z","doi":"10.1016/j.jsb.2020.107633","project":[{"grant_number":"P33367","name":"Structure and isoform diversity of the Arp2/3 complex","_id":"9B954C5C-BA93-11EA-9121-9846C619BF3A"},{"name":"NÖ-Fonds Preis für die Jungforscherin des Jahres am IST Austria","_id":"059B463C-7A3F-11EA-A408-12923DDC885E"}],"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","keyword":["electron microscopy","cryo-EM","EM sample preparation","3D printing","cell culture"],"year":"2020","intvolume":"       212","author":[{"orcid":"0000-0001-7149-769X","last_name":"Fäßler","first_name":"Florian","id":"404F5528-F248-11E8-B48F-1D18A9856A87","full_name":"Fäßler, Florian"},{"first_name":"Bettina","last_name":"Zens","orcid":"0000-0002-9561-1239","id":"45FD126C-F248-11E8-B48F-1D18A9856A87","full_name":"Zens, Bettina"},{"first_name":"Robert","orcid":"0000-0001-9843-3522","last_name":"Hauschild","full_name":"Hauschild, Robert","id":"4E01D6B4-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Florian KM","last_name":"Schur","orcid":"0000-0003-4790-8078","id":"48AD8942-F248-11E8-B48F-1D18A9856A87","full_name":"Schur, Florian KM"}],"related_material":{"record":[{"id":"14592","status":"public","relation":"used_in_publication"},{"relation":"dissertation_contains","id":"12491","status":"public"}]},"article_type":"original","_id":"8586","date_updated":"2026-04-25T22:30:39Z","abstract":[{"text":"Cryo-electron microscopy (cryo-EM) of cellular specimens provides insights into biological processes and structures within a native context. However, a major challenge still lies in the efficient and reproducible preparation of adherent cells for subsequent cryo-EM analysis. This is due to the sensitivity of many cellular specimens to the varying seeding and culturing conditions required for EM experiments, the often limited amount of cellular material and also the fragility of EM grids and their substrate. Here, we present low-cost and reusable 3D printed grid holders, designed to improve specimen preparation when culturing challenging cellular samples directly on grids. The described grid holders increase cell culture reproducibility and throughput, and reduce the resources required for cell culturing. We show that grid holders can be integrated into various cryo-EM workflows, including micro-patterning approaches to control cell seeding on grids, and for generating samples for cryo-focused ion beam milling and cryo-electron tomography experiments. Their adaptable design allows for the generation of specialized grid holders customized to a large variety of applications.","lang":"eng"}],"date_published":"2020-12-01T00:00:00Z","department":[{"_id":"FlSc"}],"citation":{"ieee":"F. Fäßler, B. Zens, R. Hauschild, and F. K. Schur, “3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy,” <i>Journal of Structural Biology</i>, vol. 212, no. 3. Elsevier, 2020.","ama":"Fäßler F, Zens B, Hauschild R, Schur FK. 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy. <i>Journal of Structural Biology</i>. 2020;212(3). doi:<a href=\"https://doi.org/10.1016/j.jsb.2020.107633\">10.1016/j.jsb.2020.107633</a>","ista":"Fäßler F, Zens B, Hauschild R, Schur FK. 2020. 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy. Journal of Structural Biology. 212(3), 107633.","chicago":"Fäßler, Florian, Bettina Zens, Robert Hauschild, and Florian KM Schur. “3D Printed Cell Culture Grid Holders for Improved Cellular Specimen Preparation in Cryo-Electron Microscopy.” <i>Journal of Structural Biology</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jsb.2020.107633\">https://doi.org/10.1016/j.jsb.2020.107633</a>.","short":"F. Fäßler, B. Zens, R. Hauschild, F.K. Schur, Journal of Structural Biology 212 (2020).","mla":"Fäßler, Florian, et al. “3D Printed Cell Culture Grid Holders for Improved Cellular Specimen Preparation in Cryo-Electron Microscopy.” <i>Journal of Structural Biology</i>, vol. 212, no. 3, 107633, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jsb.2020.107633\">10.1016/j.jsb.2020.107633</a>.","apa":"Fäßler, F., Zens, B., Hauschild, R., &#38; Schur, F. K. (2020). 3D printed cell culture grid holders for improved cellular specimen preparation in cryo-electron microscopy. <i>Journal of Structural Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsb.2020.107633\">https://doi.org/10.1016/j.jsb.2020.107633</a>"},"acknowledged_ssus":[{"_id":"ScienComp"},{"_id":"LifeSc"},{"_id":"Bio"},{"_id":"EM-Fac"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","oa_version":"Published Version","date_created":"2020-09-29T13:24:06Z","article_number":"107633","type":"journal_article","issue":"3","oa":1,"isi":1}]