[{"doi":"10.54330/afm.181562","date_updated":"2026-04-28T12:06:00Z","date_created":"2026-04-26T22:01:47Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","arxiv":1,"oa_version":"Published Version","ddc":["510"],"month":"04","project":[{"name":"Spectra and topology of graphs and of simplicial complexes","_id":"fc35eaa2-9c52-11eb-aca3-88501ab155e9","grant_number":"M03100"}],"page":"237-260","type":"journal_article","department":[{"_id":"UlWa"}],"OA_place":"publisher","scopus_import":"1","oa":1,"fulldoi":"https://doi.org/10.54330/afm.181562","citation":{"ieee":"M. Dymond and V. Kaluza, “Extending bilipschitz mappings between separated nets,” <i>Annales Fennici Mathematici</i>, vol. 51, no. 1. Finnish Mathematical Society, pp. 237–260, 2026.","mla":"Dymond, Michael, and Vojtech Kaluza. “Extending Bilipschitz Mappings between Separated Nets.” <i>Annales Fennici Mathematici</i>, vol. 51, no. 1, Finnish Mathematical Society, 2026, pp. 237–60, doi:<a href=\"https://doi.org/10.54330/afm.181562\">10.54330/afm.181562</a>.","apa":"Dymond, M., &#38; Kaluza, V. (2026). Extending bilipschitz mappings between separated nets. <i>Annales Fennici Mathematici</i>. Finnish Mathematical Society. <a href=\"https://doi.org/10.54330/afm.181562\">https://doi.org/10.54330/afm.181562</a>","ama":"Dymond M, Kaluza V. Extending bilipschitz mappings between separated nets. <i>Annales Fennici Mathematici</i>. 2026;51(1):237-260. doi:<a href=\"https://doi.org/10.54330/afm.181562\">10.54330/afm.181562</a>","short":"M. Dymond, V. Kaluza, Annales Fennici Mathematici 51 (2026) 237–260.","chicago":"Dymond, Michael, and Vojtech Kaluza. “Extending Bilipschitz Mappings between Separated Nets.” <i>Annales Fennici Mathematici</i>. Finnish Mathematical Society, 2026. <a href=\"https://doi.org/10.54330/afm.181562\">https://doi.org/10.54330/afm.181562</a>.","ista":"Dymond M, Kaluza V. 2026. Extending bilipschitz mappings between separated nets. Annales Fennici Mathematici. 51(1), 237–260."},"publication_identifier":{"issn":["2737-0690"],"eissn":["2737-114X"]},"tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png"},"file_date_updated":"2026-04-28T12:03:13Z","file":[{"checksum":"442023926a3803d5d6ca8db8dbc4af1c","creator":"dernst","content_type":"application/pdf","date_updated":"2026-04-28T12:03:13Z","date_created":"2026-04-28T12:03:13Z","relation":"main_file","file_id":"21772","file_name":"2026_AnnalesFenniciMath_Dymond.pdf","file_size":342082,"access_level":"open_access","success":1}],"day":"17","article_type":"original","OA_type":"hybrid","year":"2026","has_accepted_license":"1","publication_status":"published","date_published":"2026-04-17T00:00:00Z","title":"Extending bilipschitz mappings between separated nets","author":[{"first_name":"Michael","last_name":"Dymond","full_name":"Dymond, Michael"},{"id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","full_name":"Kaluza, Vojtech","first_name":"Vojtech","orcid":"0000-0002-2512-8698","last_name":"Kaluza"}],"publisher":"Finnish Mathematical Society","article_processing_charge":"Yes (in subscription journal)","_id":"21766","quality_controlled":"1","keyword":["Lipschitz","bilipschitz","extension","separated net."],"external_id":{"arxiv":["2507.22007"]},"issue":"1","license":"https://creativecommons.org/licenses/by-nc/4.0/","intvolume":"        51","acknowledgement":"The present work developed from a research visit of M.D. to V.K. at IST Austria, funded by\r\na London Mathematical Society Research in Pairs grant. This work was done while V.K. was fully funded by the Austria Science Fund (FWF) [M 3100-N].","status":"public","language":[{"iso":"eng"}],"abstract":[{"text":"We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete positive solution of the open problem in dimension two. Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces.","lang":"eng"}],"publication":"Annales Fennici Mathematici","volume":51},{"ddc":["515","516"],"oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"month":"03","date_updated":"2023-08-14T11:26:34Z","date_created":"2021-07-14T07:01:28Z","doi":"10.1007/s11856-022-2448-6","type":"journal_article","department":[{"_id":"UlWa"}],"page":"501-554","citation":{"mla":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” <i>Israel Journal of Mathematics</i>, vol. 253, Springer Nature, 2023, pp. 501–54, doi:<a href=\"https://doi.org/10.1007/s11856-022-2448-6\">10.1007/s11856-022-2448-6</a>.","apa":"Dymond, M., &#38; Kaluza, V. (2023). Highly irregular separated nets. <i>Israel Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11856-022-2448-6\">https://doi.org/10.1007/s11856-022-2448-6</a>","ieee":"M. Dymond and V. Kaluza, “Highly irregular separated nets,” <i>Israel Journal of Mathematics</i>, vol. 253. Springer Nature, pp. 501–554, 2023.","ama":"Dymond M, Kaluza V. Highly irregular separated nets. <i>Israel Journal of Mathematics</i>. 2023;253:501-554. doi:<a href=\"https://doi.org/10.1007/s11856-022-2448-6\">10.1007/s11856-022-2448-6</a>","chicago":"Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” <i>Israel Journal of Mathematics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11856-022-2448-6\">https://doi.org/10.1007/s11856-022-2448-6</a>.","ista":"Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal of Mathematics. 253, 501–554.","short":"M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554."},"fulldoi":"https://doi.org/10.1007/s11856-022-2448-6","publication_identifier":{"eissn":["1565-8511"]},"oa":1,"scopus_import":"1","day":"01","article_type":"original","file_date_updated":"2021-07-14T07:41:50Z","file":[{"file_name":"separated_nets.pdf","file_size":900422,"file_id":"9653","relation":"main_file","date_updated":"2021-07-14T07:41:50Z","date_created":"2021-07-14T07:41:50Z","content_type":"application/pdf","creator":"vkaluza","checksum":"6fa0a3207dd1d6467c309fd1bcc867d1","access_level":"open_access"}],"has_accepted_license":"1","year":"2023","publication_status":"published","isi":1,"title":"Highly irregular separated nets","author":[{"last_name":"Dymond","first_name":"Michael","full_name":"Dymond, Michael"},{"orcid":"0000-0002-2512-8698","first_name":"Vojtech","last_name":"Kaluza","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","full_name":"Kaluza, Vojtech"}],"date_published":"2023-03-01T00:00:00Z","quality_controlled":"1","keyword":["Lipschitz","bilipschitz","bounded displacement","modulus of continuity","separated net","non-realisable density","Burago--Kleiner construction"],"external_id":{"isi":["000904950300003"],"arxiv":["1903.05923"]},"article_processing_charge":"No","publisher":"Springer Nature","_id":"9652","volume":253,"publication":"Israel Journal of Mathematics","abstract":[{"lang":"eng","text":"In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such notions also give rise to distinct equivalence classes. Put differently, we find occurrences of particularly strong divergence of separated nets from the integer lattice. Our approach generalises that of Burago and Kleiner and McMullen which takes place largely in a continuous setting. Existence of irregular separated nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞). In the present work we obtain stronger types of non-realisable densities."}],"intvolume":"       253","acknowledgement":"This work was done while both authors were employed at the University of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.","language":[{"iso":"eng"}],"status":"public"},{"year":"2022","publication_status":"published","isi":1,"title":"Transcriptional analysis in the Arabidopsis roots reveals new regulators that link rac-GR24 treatment with changes in flavonol accumulation, root hair elongation and lateral root density","author":[{"last_name":"Struk","first_name":"Sylwia","full_name":"Struk, Sylwia"},{"full_name":"Braem, Lukas","first_name":"Lukas","last_name":"Braem"},{"first_name":"Cedrick","last_name":"Matthys","full_name":"Matthys, Cedrick"},{"last_name":"Walton","first_name":"Alan","full_name":"Walton, Alan"},{"full_name":"Vangheluwe, Nick","first_name":"Nick","last_name":"Vangheluwe"},{"full_name":"Van Praet, Stan","last_name":"Van Praet","first_name":"Stan"},{"first_name":"Lingxiang","last_name":"Jiang","full_name":"Jiang, Lingxiang"},{"id":"3028BD74-F248-11E8-B48F-1D18A9856A87","full_name":"Baster, Pawel","first_name":"Pawel","last_name":"Baster"},{"full_name":"De Cuyper, Carolien","first_name":"Carolien","last_name":"De Cuyper"},{"full_name":"Boyer, Francois-Didier","last_name":"Boyer","first_name":"Francois-Didier"},{"full_name":"Stes, Elisabeth","first_name":"Elisabeth","last_name":"Stes"},{"last_name":"Beeckman","first_name":"Tom","full_name":"Beeckman, Tom"},{"first_name":"Jiří","orcid":"0000-0002-8302-7596","last_name":"Friml","id":"4159519E-F248-11E8-B48F-1D18A9856A87","full_name":"Friml, Jiří"},{"full_name":"Gevaert, Kris","last_name":"Gevaert","first_name":"Kris"},{"first_name":"Sofie","last_name":"Goormachtig","full_name":"Goormachtig, Sofie"}],"date_published":"2022-01-21T00:00:00Z","keyword":["flavonols","MAX2","rac-Gr24","RNA-seq","root development","transcriptional regulation"],"quality_controlled":"1","external_id":{"isi":["000877899400009"],"pmid":["34791413"]},"issue":"1","article_processing_charge":"No","publisher":"Oxford University Press","_id":"10583","publication":"Plant & Cell Physiology","volume":63,"intvolume":"        63","language":[{"iso":"eng"}],"acknowledgement":"The authors thank Ralf Stracke (Bielefeld University, Bielefeld, Germany) for providing the myb mutants and their colleagues Bert De Rybel for the tmo5t;mo5l1 double mutant, Boris Parizot for tips on the RNA-seq analysis, Veronique Storme for statistical help on both the RNA-seq and lateral root density, and Martine De Cock for help in preparing the manuscript.","status":"public","abstract":[{"text":"The synthetic strigolactone (SL) analog, rac-GR24, has been instrumental in studying the role of SLs as well as karrikins because it activates the receptors DWARF14 (D14) and KARRIKIN INSENSITIVE 2 (KAI2) of their signaling pathways, respectively. Treatment with rac-GR24 modifies the root architecture at different levels, such as decreasing the lateral root density (LRD), while promoting root hair elongation or flavonol accumulation. Previously, we have shown that the flavonol biosynthesis is transcriptionally activated in the root by rac-GR24 treatment, but, thus far, the molecular players involved in that response have remained unknown. To get an in-depth insight into the changes that occur after the compound is perceived by the roots, we compared the root transcriptomes of the wild type and the more axillary growth2 (max2) mutant, affected in both SL and karrikin signaling pathways, with and without rac-GR24 treatment. Quantitative reverse transcription (qRT)-PCR, reporter line analysis and mutant phenotyping indicated that the flavonol response and the root hair elongation are controlled by the ELONGATED HYPOCOTYL 5 (HY5) and MYB12 transcription factors, but HY5, in contrast to MYB12, affects the LRD as well. Furthermore, we identified the transcription factors TARGET OF MONOPTEROS 5 (TMO5) and TMO5 LIKE1 as negative and the Mediator complex as positive regulators of the rac-GR24 effect on LRD. Altogether, hereby, we get closer toward understanding the molecular mechanisms that underlay the rac-GR24 responses in the root.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["580"],"oa_version":"Published Version","month":"01","date_created":"2021-12-28T11:44:18Z","doi":"10.1093/pcp/pcab149","date_updated":"2026-07-28T12:02:02Z","type":"journal_article","department":[{"_id":"JiFr"}],"page":"104-119","pmid":1,"fulldoi":"https://doi.org/10.1093/pcp/pcab149","publication_identifier":{"eissn":["1471-9053"],"issn":["0032-0781"]},"citation":{"ama":"Struk S, Braem L, Matthys C, et al. Transcriptional analysis in the Arabidopsis roots reveals new regulators that link rac-GR24 treatment with changes in flavonol accumulation, root hair elongation and lateral root density. <i>Plant &#38; Cell Physiology</i>. 2022;63(1):104-119. doi:<a href=\"https://doi.org/10.1093/pcp/pcab149\">10.1093/pcp/pcab149</a>","mla":"Struk, Sylwia, et al. “Transcriptional Analysis in the Arabidopsis Roots Reveals New Regulators That Link Rac-GR24 Treatment with Changes in Flavonol Accumulation, Root Hair Elongation and Lateral Root Density.” <i>Plant &#38; Cell Physiology</i>, vol. 63, no. 1, Oxford University Press, 2022, pp. 104–19, doi:<a href=\"https://doi.org/10.1093/pcp/pcab149\">10.1093/pcp/pcab149</a>.","ieee":"S. Struk <i>et al.</i>, “Transcriptional analysis in the Arabidopsis roots reveals new regulators that link rac-GR24 treatment with changes in flavonol accumulation, root hair elongation and lateral root density,” <i>Plant &#38; Cell Physiology</i>, vol. 63, no. 1. Oxford University Press, pp. 104–119, 2022.","apa":"Struk, S., Braem, L., Matthys, C., Walton, A., Vangheluwe, N., Van Praet, S., … Goormachtig, S. (2022). Transcriptional analysis in the Arabidopsis roots reveals new regulators that link rac-GR24 treatment with changes in flavonol accumulation, root hair elongation and lateral root density. <i>Plant &#38; Cell Physiology</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/pcp/pcab149\">https://doi.org/10.1093/pcp/pcab149</a>","ista":"Struk S, Braem L, Matthys C, Walton A, Vangheluwe N, Van Praet S, Jiang L, Baster P, De Cuyper C, Boyer F-D, Stes E, Beeckman T, Friml J, Gevaert K, Goormachtig S. 2022. Transcriptional analysis in the Arabidopsis roots reveals new regulators that link rac-GR24 treatment with changes in flavonol accumulation, root hair elongation and lateral root density. Plant &#38; Cell Physiology. 63(1), 104–119.","chicago":"Struk, Sylwia, Lukas Braem, Cedrick Matthys, Alan Walton, Nick Vangheluwe, Stan Van Praet, Lingxiang Jiang, et al. “Transcriptional Analysis in the Arabidopsis Roots Reveals New Regulators That Link Rac-GR24 Treatment with Changes in Flavonol Accumulation, Root Hair Elongation and Lateral Root Density.” <i>Plant &#38; Cell Physiology</i>. Oxford University Press, 2022. <a href=\"https://doi.org/10.1093/pcp/pcab149\">https://doi.org/10.1093/pcp/pcab149</a>.","short":"S. Struk, L. Braem, C. Matthys, A. Walton, N. Vangheluwe, S. Van Praet, L. Jiang, P. Baster, C. De Cuyper, F.-D. Boyer, E. Stes, T. Beeckman, J. Friml, K. Gevaert, S. Goormachtig, Plant &#38; Cell Physiology 63 (2022) 104–119."},"scopus_import":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/pcp/pcab149"}],"day":"21","OA_type":"free access","article_type":"original"},{"keyword":["transcription","pausing","backtracking","polymerase","RNA","NET-seq","nucleosome","basepairing"],"fulldoi":"https://doi.org/10.15479/AT:ISTA:45","citation":{"ieee":"M. Lukacisin, M. Landon, and R. Jajoo, “MATLAB analysis code for ‘Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast.’” Institute of Science and Technology Austria, 2016.","apa":"Lukacisin, M., Landon, M., &#38; Jajoo, R. (2016). MATLAB analysis code for “Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast.” Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:45\">https://doi.org/10.15479/AT:ISTA:45</a>","mla":"Lukacisin, Martin, et al. <i>MATLAB Analysis Code for “Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast.”</i> Institute of Science and Technology Austria, 2016, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:45\">10.15479/AT:ISTA:45</a>.","ama":"Lukacisin M, Landon M, Jajoo R. MATLAB analysis code for “Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast.” 2016. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:45\">10.15479/AT:ISTA:45</a>","short":"M. Lukacisin, M. Landon, R. Jajoo, (2016).","chicago":"Lukacisin, Martin, Matthieu Landon, and Rishi Jajoo. “MATLAB Analysis Code for ‘Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast.’” Institute of Science and Technology Austria, 2016. <a href=\"https://doi.org/10.15479/AT:ISTA:45\">https://doi.org/10.15479/AT:ISTA:45</a>.","ista":"Lukacisin M, Landon M, Jajoo R. 2016. MATLAB analysis code for ‘Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast’, Institute of Science and Technology Austria, <a href=\"https://doi.org/10.15479/AT:ISTA:45\">10.15479/AT:ISTA:45</a>."},"tmp":{"name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode"},"article_processing_charge":"No","publisher":"Institute of Science and Technology Austria","oa":1,"_id":"5556","day":"25","license":"https://creativecommons.org/licenses/by-sa/4.0/","status":"public","abstract":[{"text":"MATLAB code and processed datasets available for reproducing the results in: \r\nLukačišin, M.*, Landon, M.*, Jajoo, R*. (2016) Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast.\r\n*equal contributions","lang":"eng"}],"file_date_updated":"2020-07-14T12:47:02Z","file":[{"access_level":"open_access","checksum":"ee697f2b1ade4dc14d6ac0334dd832ab","creator":"system","content_type":"application/zip","relation":"main_file","date_updated":"2020-07-14T12:47:02Z","date_created":"2018-12-12T13:02:58Z","file_id":"5616","file_size":296722548,"file_name":"IST-2016-45-v1+1_PaperCode.zip"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2016","oa_version":"Published Version","has_accepted_license":"1","ddc":["571"],"month":"08","datarep_id":"45","date_updated":"2025-07-10T11:49:51Z","doi":"10.15479/AT:ISTA:45","date_created":"2018-12-12T12:31:31Z","type":"research_data","title":"MATLAB analysis code for 'Sequence-Specific Thermodynamic Properties of Nucleic Acids Influence Both Transcriptional Pausing and Backtracking in Yeast'","author":[{"full_name":"Lukacisin, Martin","id":"298FFE8C-F248-11E8-B48F-1D18A9856A87","last_name":"Lukacisin","first_name":"Martin","orcid":"0000-0001-6549-4177"},{"full_name":"Landon, Matthieu","last_name":"Landon","first_name":"Matthieu"},{"last_name":"Jajoo","first_name":"Rishi","full_name":"Jajoo, Rishi"}],"department":[{"_id":"ToBo"}],"date_published":"2016-08-25T00:00:00Z","related_material":{"record":[{"status":"deleted","relation":"used_in_publication","id":"8431"},{"relation":"research_paper","status":"public","id":"1029"}]}}]