--- _id: '27426' 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." author: - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X citation: 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 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 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} }' 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.' 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.' 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. date_created: 2021-11-15T09:24:59Z date_updated: 2023-03-11T17:16:33Z department: - _id: '101' - _id: '655' doi: 10.1007/s10898-022-01223-2 intvolume: ' 85' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf oa: '1' page: 709-741 publication: Journal of Global Optimization status: public title: On the structure of regularization paths for piecewise differentiable regularization terms type: journal_article user_id: '47427' volume: 85 year: '2023' ... --- _id: '31849' author: - first_name: Max full_name: Hoffmann, Max id: '32202' last_name: Hoffmann orcid: 0000-0002-6964-7123 - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler citation: 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.' 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} }' 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. 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.' date_created: 2022-06-12T11:07:34Z date_updated: 2023-03-25T10:11:35Z ddc: - '370' - '510' department: - _id: '97' editor: - first_name: Marı́a full_name: Trigueros, Marı́a last_name: Trigueros - first_name: Berta full_name: Barquero, Berta last_name: Barquero - first_name: Reinhard full_name: Hochmuth, Reinhard last_name: Hochmuth - first_name: Jana full_name: Peters, Jana last_name: Peters file: - access_level: closed content_type: application/pdf creator: maxh date_created: 2023-03-25T10:01:03Z date_updated: 2023-03-25T10:01:03Z file_id: '43096' file_name: HoffmannBiehler2022_indrum_congruence.pdf file_size: 201942 relation: main_file success: 1 file_date_updated: 2023-03-25T10:01:03Z has_accepted_license: '1' keyword: - Teaching and learning of specific topics in university mathematics - Transition to - across and from university mathematics - Student Teachers - Geometry - Congruence - Double Discontinuity. language: - iso: eng main_file_link: - open_access: '1' url: https://hal.univ-reims.fr/INDRUM2022/ oa: '1' place: Hannover publication: Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022) publication_status: published publisher: University of Hannover and INDRUM. quality_controlled: '1' status: public title: Student Teachers ’ Knowledge of Congruence before a University Course on Geometry type: conference user_id: '32202' year: '2023' ... --- _id: '43097' author: - first_name: Ignasio full_name: Florensa, Ignasio last_name: Florensa - first_name: Max full_name: Hoffmann, Max id: '32202' last_name: Hoffmann orcid: 0000-0002-6964-7123 - first_name: Avenilde full_name: Romo Vázquez, Avenilde last_name: Romo Vázquez - first_name: Michelle full_name: Zandieh, Michelle last_name: Zandieh - first_name: Rafael full_name: Martínez-Planell, Rafael last_name: Martínez-Planell citation: 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.' 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). 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} }' 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. 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. 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.' date_created: 2023-03-25T10:09:06Z date_updated: 2023-03-25T10:10:58Z ddc: - '370' - '510' department: - _id: '97' editor: - first_name: Marı́a full_name: Trigueros, Marı́a last_name: Trigueros - first_name: Berta full_name: Barquero, Berta last_name: Barquero - first_name: Reinhard full_name: Hochmuth, Reinhard last_name: Hochmuth - first_name: Jana full_name: Peters, Jana last_name: Peters file: - access_level: closed content_type: application/pdf creator: maxh date_created: 2023-03-25T10:07:54Z date_updated: 2023-03-25T10:07:54Z file_id: '43098' file_name: 2022_FlorensaEtAl_indrum_panelInnovations.pdf file_size: 642388 relation: main_file success: 1 file_date_updated: 2023-03-25T10:07:54Z has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://hal.univ-reims.fr/INDRUM2022/ oa: '1' place: Hannover publication: Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022) quality_controlled: '1' status: public title: Innovations in university teaching based on mathematic education research type: conference user_id: '32202' year: '2023' ... --- _id: '43504' author: - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler - first_name: Michael full_name: Liebendörfer, Michael id: '30933' last_name: Liebendörfer orcid: 0000-0001-9887-2074 - first_name: A. full_name: Schmitz, A. last_name: Schmitz citation: 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. 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. 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} }' 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.' 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. 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. short: R. Biehler, M. Liebendörfer, A. Schmitz, Mitteilungen der Gesellschaft für Didaktik der Mathematik 114 (2023) 8–12. date_created: 2023-04-14T09:25:18Z date_updated: 2023-04-14T09:25:27Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '363' intvolume: ' 114' language: - iso: ger page: 8-12 publication: Mitteilungen der Gesellschaft für Didaktik der Mathematik status: public title: Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos type: journal_article user_id: '37888' volume: 114 year: '2023' ... --- _id: '43105' article_number: '103868' author: - first_name: Tobias full_name: Black, Tobias id: '23686' last_name: Black orcid: 0000-0001-9963-0800 - first_name: Mario full_name: Fuest, Mario last_name: Fuest - first_name: Johannes full_name: Lankeit, Johannes last_name: Lankeit - first_name: Masaaki full_name: Mizukami, Masaaki last_name: Mizukami citation: 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' 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' 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} }' 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.' 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.' 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.' short: 'T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).' date_created: 2023-03-27T07:25:58Z date_updated: 2023-03-27T07:27:03Z department: - _id: '34' - _id: '10' - _id: '90' doi: 10.1016/j.nonrwa.2023.103868 intvolume: ' 73' keyword: - Applied Mathematics - Computational Mathematics - General Economics - Econometrics and Finance - General Engineering - General Medicine - Analysis language: - iso: eng publication: 'Nonlinear Analysis: Real World Applications' publication_identifier: issn: - 1468-1218 publication_status: published publisher: Elsevier BV status: public title: Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source type: journal_article user_id: '23686' volume: 73 year: '2023' ... --- _id: '43227' author: - first_name: Vivian full_name: Vitt, Vivian last_name: Vitt - first_name: Uta full_name: Häsel-Weide, Uta id: '60267' last_name: Häsel-Weide 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' 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 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} }' 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. ieee: V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in Mathematica Didactica, 46, 2023. 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.' date_created: 2023-03-30T10:06:24Z date_updated: 2023-03-30T10:06:53Z department: - _id: '543' doi: https://doi.org/10.18716/ojs/md/2023.1671 language: - iso: eng publication: Mathematica Didactica, 46 status: public title: Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. type: book_chapter user_id: '44184' year: '2023' ... --- _id: '43226' author: - first_name: Uta full_name: Häsel-Weide, Uta id: '60267' last_name: Häsel-Weide - first_name: M. full_name: Nührenbörger, M. last_name: Nührenbörger citation: 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' 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 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} }' 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. ieee: U. Häsel-Weide and M. Nührenbörger, “Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.,” in Mathematica Didactica, 46, 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. short: 'U. Häsel-Weide, M. Nührenbörger, in: Mathematica Didactica, 46, 2023.' date_created: 2023-03-30T10:04:31Z date_updated: 2023-03-30T10:06:49Z department: - _id: '543' doi: https://doi.org/10.18716/ojs/md/2023.1670 language: - iso: eng publication: Mathematica Didactica, 46 status: public title: Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. type: book_chapter user_id: '44184' year: '2023' ... --- _id: '34832' author: - first_name: Maximilian full_name: Hanusch, Maximilian id: '30905' last_name: Hanusch citation: 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 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 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} }' 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. 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.' 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. short: M. Hanusch, Annals of Global Analysis and Geometry 63 (2023). date_created: 2022-12-22T09:45:34Z date_updated: 2023-04-05T18:18:24Z department: - _id: '93' doi: 10.1007/s10455-023-09888-y intvolume: ' 63' issue: '21' keyword: - Lax equation - generalized Baker-Campbell-Dynkin-Hausdorff formula - regularity of Lie groups language: - iso: eng project: - _id: '161' name: 'RegLie: Regularität von Lie-Gruppen und Lie''s Dritter Satz (RegLie)' publication: Annals of Global Analysis and Geometry publication_status: published status: public title: The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups type: journal_article user_id: '30905' volume: 63 year: '2023' ... --- _id: '44501' 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. " author: - first_name: Chiara full_name: Cappello, Chiara id: '72874' last_name: Cappello - first_name: Reza full_name: Naserasr, Reza last_name: Naserasr - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 - first_name: Zhouningxin full_name: Wang, Zhouningxin last_name: Wang citation: ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. arXiv:230410243. Published online 2023. apa: Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically 3-frustrated signed graphs. In arXiv:2304.10243. 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} }' 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). date_created: 2023-05-05T06:52:39Z date_updated: 2023-05-05T06:53:47Z department: - _id: '542' external_id: arxiv: - '2304.10243' language: - iso: eng publication: arXiv:2304.10243 status: public title: Critically 3-frustrated signed graphs type: preprint user_id: '15540' year: '2023' ... --- _id: '44857' abstract: - lang: eng 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. author: - first_name: Helmuth O.M. full_name: Silva, Helmuth O.M. last_name: Silva - first_name: Diego P. full_name: Rubert, Diego P. last_name: Rubert - first_name: Eloi full_name: Araujo, Eloi last_name: Araujo - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 - first_name: Daniel full_name: Doerr, Daniel last_name: Doerr - first_name: Fábio V. full_name: Martinez, Fábio V. last_name: Martinez citation: 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 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.' 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. date_created: 2023-05-16T08:48:22Z date_updated: 2023-05-16T08:49:30Z department: - _id: '542' doi: 10.1051/ro/2023052 intvolume: ' 57' issue: '3' keyword: - Management Science and Operations Research - Computer Science Applications - Theoretical Computer Science language: - iso: eng page: 1045-1058 publication: RAIRO - Operations Research publication_identifier: issn: - 0399-0559 - 2804-7303 publication_status: published publisher: EDP Sciences status: public title: Algorithms for the genome median under a restricted measure of rearrangement type: journal_article user_id: '15540' volume: 57 year: '2023' ...