[{"title":"On the structure of regularization paths for piecewise differentiable regularization terms","volume":85,"author":[{"full_name":"Gebken, Bennet","id":"32643","last_name":"Gebken","first_name":"Bennet"},{"first_name":"Katharina","last_name":"Bieker","id":"32829","full_name":"Bieker, Katharina"},{"last_name":"Peitz","first_name":"Sebastian","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"}],"_id":"27426","doi":"10.1007/s10898-022-01223-2","date_updated":"2023-03-11T17:16:33Z","user_id":"47427","citation":{"bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.","short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","apa":"Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2"},"language":[{"iso":"eng"}],"department":[{"_id":"101"},{"_id":"655"}],"abstract":[{"lang":"eng","text":"Regularization is used in many different areas of optimization when solutions\r\nare sought which not only minimize a given function, but also possess a certain\r\ndegree of regularity. Popular applications are image denoising, sparse\r\nregression and machine learning. Since the choice of the regularization\r\nparameter is crucial but often difficult, path-following methods are used to\r\napproximate the entire regularization path, i.e., the set of all possible\r\nsolutions for all regularization parameters. Due to their nature, the\r\ndevelopment of these methods requires structural results about the\r\nregularization path. The goal of this article is to derive these results for\r\nthe case of a smooth objective function which is penalized by a piecewise\r\ndifferentiable regularization term. We do this by treating regularization as a\r\nmultiobjective optimization problem. Our results suggest that even in this\r\ngeneral case, the regularization path is piecewise smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features that occur in between\r\nsmooth parts. This is demonstrated in two applications, namely support-vector\r\nmachines and exact penalty methods."}],"publication":"Journal of Global Optimization","status":"public","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf","open_access":"1"}],"issue":"3","year":"2023","page":"709-741","intvolume":" 85","date_created":"2021-11-15T09:24:59Z","oa":"1","type":"journal_article"},{"quality_controlled":"1","date_updated":"2023-03-25T10:11:35Z","department":[{"_id":"97"}],"language":[{"iso":"eng"}],"citation":{"apa":"Hoffmann, M., & Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). University of Hannover and INDRUM.","bibtex":"@inproceedings{Hoffmann_Biehler_2023, place={Hannover}, title={Student Teachers ’ Knowledge of Congruence before a University Course on Geometry}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, publisher={University of Hannover and INDRUM.}, author={Hoffmann, Max and Biehler, Rolf}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","short":"M. Hoffmann, R. Biehler, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), University of Hannover and INDRUM., Hannover, 2023.","ama":"Hoffmann M, Biehler R. Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). University of Hannover and INDRUM.; 2023.","chicago":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover: University of Hannover and INDRUM., 2023.","ieee":"M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry,” in Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023.","mla":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., University of Hannover and INDRUM., 2023."},"has_accepted_license":"1","user_id":"32202","file_date_updated":"2023-03-25T10:01:03Z","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","author":[{"first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max","id":"32202"},{"full_name":"Biehler, Rolf","id":"16274","last_name":"Biehler","first_name":"Rolf"}],"ddc":["370","510"],"_id":"31849","year":"2023","place":"Hannover","publisher":"University of Hannover and INDRUM.","oa":"1","date_created":"2022-06-12T11:07:34Z","publication_status":"published","type":"conference","file":[{"date_created":"2023-03-25T10:01:03Z","success":1,"access_level":"closed","file_id":"43096","creator":"maxh","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","date_updated":"2023-03-25T10:01:03Z","relation":"main_file","file_size":201942,"content_type":"application/pdf"}],"status":"public","main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"editor":[{"last_name":"Trigueros","first_name":"Marı́a","full_name":"Trigueros, Marı́a"},{"last_name":"Barquero","first_name":"Berta","full_name":"Barquero, Berta"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"full_name":"Peters, Jana","last_name":"Peters","first_name":"Jana"}]},{"date_updated":"2023-03-25T10:10:58Z","quality_controlled":"1","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","file_date_updated":"2023-03-25T10:07:54Z","user_id":"32202","citation":{"bibtex":"@inproceedings{Florensa_Hoffmann_Romo Vázquez_Zandieh_Martínez-Planell_2023, place={Hannover}, title={Innovations in university teaching based on mathematic education research}, booktitle={Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}, author={Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde and Zandieh, Michelle and Martínez-Planell, Rafael}, editor={Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}, year={2023} }","mla":"Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic Education Research.” Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros et al., 2023.","chicago":"Florensa, Ignasio, Max Hoffmann, Avenilde Romo Vázquez, Michelle Zandieh, and Rafael Martínez-Planell. “Innovations in University Teaching Based on Mathematic Education Research.” In Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover, 2023.","ieee":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, and R. Martínez-Planell, “Innovations in university teaching based on mathematic education research,” in Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), 2023.","ama":"Florensa I, Hoffmann M, Romo Vázquez A, Zandieh M, Martínez-Planell R. Innovations in university teaching based on mathematic education research. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022). ; 2023.","short":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, R. Martínez-Planell, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022), Hannover, 2023.","apa":"Florensa, I., Hoffmann, M., Romo Vázquez, A., Zandieh, M., & Martínez-Planell, R. (2023). Innovations in university teaching based on mathematic education research. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)."},"has_accepted_license":"1","department":[{"_id":"97"}],"language":[{"iso":"eng"}],"title":"Innovations in university teaching based on mathematic education research","_id":"43097","ddc":["370","510"],"author":[{"first_name":"Ignasio","last_name":"Florensa","full_name":"Florensa, Ignasio"},{"full_name":"Hoffmann, Max","id":"32202","first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123"},{"first_name":"Avenilde","last_name":"Romo Vázquez","full_name":"Romo Vázquez, Avenilde"},{"full_name":"Zandieh, Michelle","last_name":"Zandieh","first_name":"Michelle"},{"full_name":"Martínez-Planell, Rafael","last_name":"Martínez-Planell","first_name":"Rafael"}],"place":"Hannover","year":"2023","type":"conference","date_created":"2023-03-25T10:09:06Z","oa":"1","status":"public","file":[{"date_created":"2023-03-25T10:07:54Z","success":1,"access_level":"closed","content_type":"application/pdf","file_size":642388,"relation":"main_file","date_updated":"2023-03-25T10:07:54Z","file_id":"43098","file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf","creator":"maxh"}],"editor":[{"last_name":"Trigueros","first_name":"Marı́a","full_name":"Trigueros, Marı́a"},{"full_name":"Barquero, Berta","last_name":"Barquero","first_name":"Berta"},{"first_name":"Reinhard","last_name":"Hochmuth","full_name":"Hochmuth, Reinhard"},{"full_name":"Peters, Jana","first_name":"Jana","last_name":"Peters"}],"main_file_link":[{"open_access":"1","url":"https://hal.univ-reims.fr/INDRUM2022/"}]},{"status":"public","volume":114,"title":"Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos","_id":"43504","author":[{"full_name":"Biehler, Rolf","id":"16274","first_name":"Rolf","last_name":"Biehler"},{"orcid":"0000-0001-9887-2074","first_name":"Michael","last_name":"Liebendörfer","id":"30933","full_name":"Liebendörfer, Michael"},{"full_name":"Schmitz, A.","last_name":"Schmitz","first_name":"A."}],"date_updated":"2023-04-14T09:25:27Z","intvolume":" 114","page":"8-12","year":"2023","publication":"Mitteilungen der Gesellschaft für Didaktik der Mathematik","type":"journal_article","language":[{"iso":"ger"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"date_created":"2023-04-14T09:25:18Z","user_id":"37888","citation":{"bibtex":"@article{Biehler_Liebendörfer_Schmitz_2023, title={Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos}, volume={114}, journal={Mitteilungen der Gesellschaft für Didaktik der Mathematik}, author={Biehler, Rolf and Liebendörfer, Michael and Schmitz, A.}, year={2023}, pages={8–12} }","ieee":"R. Biehler, M. Liebendörfer, and A. Schmitz, “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos,” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, pp. 8–12, 2023.","chicago":"Biehler, Rolf, Michael Liebendörfer, and A. Schmitz. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023): 8–12.","ama":"Biehler R, Liebendörfer M, Schmitz A. Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik. 2023;114:8-12.","mla":"Biehler, Rolf, et al. “Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos.” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 114, 2023, pp. 8–12.","apa":"Biehler, R., Liebendörfer, M., & Schmitz, A. (2023). Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos. Mitteilungen der Gesellschaft für Didaktik der Mathematik, 114, 8–12.","short":"R. Biehler, M. Liebendörfer, A. Schmitz, Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023) 8–12."}},{"_id":"43105","author":[{"id":"23686","full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias"},{"full_name":"Fuest, Mario","first_name":"Mario","last_name":"Fuest"},{"last_name":"Lankeit","first_name":"Johannes","full_name":"Lankeit, Johannes"},{"full_name":"Mizukami, Masaaki","first_name":"Masaaki","last_name":"Mizukami"}],"keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"publication_identifier":{"issn":["1468-1218"]},"status":"public","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","volume":73,"type":"journal_article","publication":"Nonlinear Analysis: Real World Applications","publication_status":"published","citation":{"apa":"Black, T., Fuest, M., Lankeit, J., & Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real World Applications, 73, Article 103868. https://doi.org/10.1016/j.nonrwa.2023.103868","mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications, vol. 73, 103868, Elsevier BV, 2023, doi:10.1016/j.nonrwa.2023.103868.","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” Nonlinear Analysis: Real World Applications, vol. 73, Art. no. 103868, 2023, doi: 10.1016/j.nonrwa.2023.103868.","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. Nonlinear Analysis: Real World Applications. 2023;73. doi:10.1016/j.nonrwa.2023.103868","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” Nonlinear Analysis: Real World Applications 73 (2023). https://doi.org/10.1016/j.nonrwa.2023.103868.","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={10.1016/j.nonrwa.2023.103868}, number={103868}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}, year={2023} }"},"date_created":"2023-03-27T07:25:58Z","user_id":"23686","article_number":"103868","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"language":[{"iso":"eng"}],"publisher":"Elsevier BV","intvolume":" 73","date_updated":"2023-03-27T07:27:03Z","doi":"10.1016/j.nonrwa.2023.103868","year":"2023"},{"_id":"43227","author":[{"first_name":"Vivian","last_name":"Vitt","full_name":"Vitt, Vivian"},{"full_name":"Häsel-Weide, Uta","id":"60267","last_name":"Häsel-Weide","first_name":"Uta"}],"status":"public","title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","publication":"Mathematica Didactica, 46","type":"book_chapter","language":[{"iso":"eng"}],"department":[{"_id":"543"}],"user_id":"44184","date_created":"2023-03-30T10:06:24Z","citation":{"ama":"Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1671","ieee":"V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46, 2023.","chicago":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1671.","mla":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1671.","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.","bibtex":"@inbook{Vitt_Häsel-Weide_2023, title={Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}, DOI={https://doi.org/10.18716/ojs/md/2023.1671}, booktitle={Mathematica Didactica, 46}, author={Vitt, Vivian and Häsel-Weide, Uta}, year={2023} }","apa":"Vitt, V., & Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1671"},"doi":"https://doi.org/10.18716/ojs/md/2023.1671","date_updated":"2023-03-30T10:06:53Z","year":"2023"},{"date_updated":"2023-03-30T10:06:49Z","doi":"https://doi.org/10.18716/ojs/md/2023.1670","year":"2023","type":"book_chapter","publication":"Mathematica Didactica, 46","citation":{"bibtex":"@inbook{Häsel-Weide_Nührenbörger_2023, title={Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.}, DOI={https://doi.org/10.18716/ojs/md/2023.1670}, booktitle={Mathematica Didactica, 46}, author={Häsel-Weide, Uta and Nührenbörger, M.}, year={2023} }","mla":"Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter Förderung Im Mathematikunterricht.” Mathematica Didactica, 46, 2023, doi:https://doi.org/10.18716/ojs/md/2023.1670.","ama":"Häsel-Weide U, Nührenbörger M. Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. In: Mathematica Didactica, 46. ; 2023. doi:https://doi.org/10.18716/ojs/md/2023.1670","ieee":"U. Häsel-Weide and M. Nührenbörger, “Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.,” in Mathematica Didactica, 46, 2023.","chicago":"Häsel-Weide, Uta, and M. Nührenbörger. “Inklusive Praktiken Unterrichtsintegrierter Förderung Im Mathematikunterricht.” In Mathematica Didactica, 46, 2023. https://doi.org/10.18716/ojs/md/2023.1670.","short":"U. Häsel-Weide, M. Nührenbörger, in: Mathematica Didactica, 46, 2023.","apa":"Häsel-Weide, U., & Nührenbörger, M. (2023). Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. In Mathematica Didactica, 46. https://doi.org/10.18716/ojs/md/2023.1670"},"user_id":"44184","date_created":"2023-03-30T10:04:31Z","language":[{"iso":"eng"}],"department":[{"_id":"543"}],"status":"public","title":"Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.","_id":"43226","author":[{"first_name":"Uta","last_name":"Häsel-Weide","id":"60267","full_name":"Häsel-Weide, Uta"},{"last_name":"Nührenbörger","first_name":"M.","full_name":"Nührenbörger, M."}]},{"project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"citation":{"apa":"Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. Annals of Global Analysis and Geometry, 63(21). https://doi.org/10.1007/s10455-023-09888-y","short":"M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).","mla":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023, doi:10.1007/s10455-023-09888-y.","ieee":"M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups,” Annals of Global Analysis and Geometry, vol. 63, no. 21, 2023, doi: 10.1007/s10455-023-09888-y.","chicago":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” Annals of Global Analysis and Geometry 63, no. 21 (2023). https://doi.org/10.1007/s10455-023-09888-y.","ama":"Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. Annals of Global Analysis and Geometry. 2023;63(21). doi:10.1007/s10455-023-09888-y","bibtex":"@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}, volume={63}, DOI={10.1007/s10455-023-09888-y}, number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch, Maximilian}, year={2023} }"},"date_created":"2022-12-22T09:45:34Z","user_id":"30905","language":[{"iso":"eng"}],"department":[{"_id":"93"}],"type":"journal_article","publication":"Annals of Global Analysis and Geometry","publication_status":"published","year":"2023","intvolume":" 63","date_updated":"2023-04-05T18:18:24Z","doi":"10.1007/s10455-023-09888-y","keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"author":[{"id":"30905","full_name":"Hanusch, Maximilian","last_name":"Hanusch","first_name":"Maximilian"}],"issue":"21","_id":"34832","title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups","volume":63,"status":"public"},{"title":"Critically 3-frustrated signed graphs","status":"public","author":[{"id":"72874","full_name":"Cappello, Chiara","last_name":"Cappello","first_name":"Chiara"},{"last_name":"Naserasr","first_name":"Reza","full_name":"Naserasr, Reza"},{"orcid":"0000-0002-9808-7401","first_name":"Eckhard","last_name":"Steffen","id":"15548","full_name":"Steffen, Eckhard"},{"full_name":"Wang, Zhouningxin","last_name":"Wang","first_name":"Zhouningxin"}],"_id":"44501","year":"2023","date_updated":"2023-05-05T06:53:47Z","user_id":"15540","date_created":"2023-05-05T06:52:39Z","citation":{"bibtex":"@article{Cappello_Naserasr_Steffen_Wang_2023, title={Critically 3-frustrated signed graphs}, journal={arXiv:2304.10243}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2023} }","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. arXiv:230410243. Published online 2023.","chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” arXiv:2304.10243. 2023.","mla":"Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023).","apa":"Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically 3-frustrated signed graphs. In arXiv:2304.10243."},"abstract":[{"lang":"eng","text":"Extending the notion of maxcut, the study of the frustration index of signed graphs is one of the basic questions in the theory of signed graphs. Recently two of the authors initiated the study of critically frustrated signed graphs. That is a signed graph whose frustration index decreases with the removal of any edge. The main focus of this study is on critical signed graphs which are not edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable signed graphs) and which are not built from other critically frustrated signed graphs by subdivision. We conjecture that for any given k there are only finitely many critically k-frustrated signed graphs of this kind.\r\nProviding support for this conjecture we show that there are only two of such critically 3-frustrated signed graphs where there is no pair of edge-disjoint negative cycles. Similarly, we show that there are exactly ten critically 3-frustrated signed planar graphs that are neither decomposable nor subdivisions of other critically frustrated signed graphs. We present a method for building non-decomposable critically frustrated signed graphs based on two given such signed graphs. We also show that the condition of being non-decomposable is necessary for our conjecture. "}],"language":[{"iso":"eng"}],"department":[{"_id":"542"}],"publication":"arXiv:2304.10243","type":"preprint","external_id":{"arxiv":["2304.10243"]}},{"issue":"3","keyword":["Management Science and Operations Research","Computer Science Applications","Theoretical Computer Science"],"status":"public","type":"journal_article","publication_status":"published","date_created":"2023-05-16T08:48:22Z","publisher":"EDP Sciences","intvolume":" 57","page":"1045-1058","year":"2023","_id":"44857","author":[{"full_name":"Silva, Helmuth O.M.","first_name":"Helmuth O.M.","last_name":"Silva"},{"full_name":"Rubert, Diego P.","first_name":"Diego P.","last_name":"Rubert"},{"first_name":"Eloi","last_name":"Araujo","full_name":"Araujo, Eloi"},{"first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard","id":"15548"},{"last_name":"Doerr","first_name":"Daniel","full_name":"Doerr, Daniel"},{"full_name":"Martinez, Fábio V.","first_name":"Fábio V.","last_name":"Martinez"}],"publication_identifier":{"issn":["0399-0559","2804-7303"]},"title":"Algorithms for the genome median under a restricted measure of rearrangement","volume":57,"publication":"RAIRO - Operations Research","citation":{"apa":"Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052","bibtex":"@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms for the genome median under a restricted measure of rearrangement}, volume={57}, DOI={10.1051/ro/2023052}, number={3}, journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }","chicago":"Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023): 1045–58. https://doi.org/10.1051/ro/2023052.","ieee":"H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V. Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,” RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi: 10.1051/ro/2023052.","ama":"Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052","mla":"Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3, EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052.","short":"H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058."},"user_id":"15540","language":[{"iso":"eng"}],"department":[{"_id":"542"}],"abstract":[{"text":"Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives.","lang":"eng"}],"date_updated":"2023-05-16T08:49:30Z","doi":"10.1051/ro/2023052"}]