[{"date_updated":"2024-04-24T12:47:49Z","publication_status":"published","intvolume":"       376","title":"The Dunkl-Laplace transform and Macdonald’s hypergeometric series","status":"public","year":"2023","author":[{"id":"55911","first_name":"Dominik","last_name":"Brennecken","full_name":"Brennecken, Dominik"},{"first_name":"Margit","last_name":"Rösler","full_name":"Rösler, Margit","id":"37390"}],"doi":"10.1090/tran/8860","user_id":"37390","volume":376,"page":"2419-2447","_id":"36294","publisher":" American Mathematical Society","language":[{"iso":"eng"}],"issue":"4","publication":"Transactions of the American Mathematical Society","citation":{"bibtex":"@article{Brennecken_Rösler_2023, title={The Dunkl-Laplace transform and Macdonald’s hypergeometric series}, volume={376}, DOI={<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>}, number={4}, journal={Transactions of the American Mathematical Society}, publisher={ American Mathematical Society}, author={Brennecken, Dominik and Rösler, Margit}, year={2023}, pages={2419–2447} }","ama":"Brennecken D, Rösler M. The Dunkl-Laplace transform and Macdonald’s hypergeometric series. <i>Transactions of the American Mathematical Society</i>. 2023;376(4):2419-2447. doi:<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>","mla":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i>, vol. 376, no. 4,  American Mathematical Society, 2023, pp. 2419–47, doi:<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>.","short":"D. Brennecken, M. Rösler, Transactions of the American Mathematical Society 376 (2023) 2419–2447.","chicago":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i> 376, no. 4 (2023): 2419–47. <a href=\"https://doi.org/10.1090/tran/8860\">https://doi.org/10.1090/tran/8860</a>.","ieee":"D. Brennecken and M. Rösler, “The Dunkl-Laplace transform and Macdonald’s hypergeometric series,” <i>Transactions of the American Mathematical Society</i>, vol. 376, no. 4, pp. 2419–2447, 2023, doi: <a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>.","apa":"Brennecken, D., &#38; Rösler, M. (2023). The Dunkl-Laplace transform and Macdonald’s hypergeometric series. <i>Transactions of the American Mathematical Society</i>, <i>376</i>(4), 2419–2447. <a href=\"https://doi.org/10.1090/tran/8860\">https://doi.org/10.1090/tran/8860</a>"},"type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-12T08:32:44Z"},{"publisher":"WTM","_id":"53053","language":[{"iso":"eng"}],"doi":"https://doi.org/10.37626/GA9783959872089.0","user_id":"85819","editor":[{"full_name":"IDMI Primar Goethe-Univeristät Frankfurt, .","first_name":".","last_name":"IDMI Primar Goethe-Univeristät Frankfurt"}],"status":"public","year":"2023","title":"Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung","conference":{"name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","location":"Frankfurt am Main"},"author":[{"id":"85819","full_name":"Kolbe, Tim","first_name":"Tim","last_name":"Kolbe"}],"date_updated":"2024-04-26T08:13:52Z","date_created":"2024-03-27T09:29:20Z","type":"conference_abstract","department":[{"_id":"98"}],"publication":"Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","citation":{"mla":"Kolbe, Tim. “Think-Aloud Beim Hochschulischen Mathematiklernen – Ergebnisse Einer Pilotierung.” <i>Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by . IDMI Primar Goethe-Univeristät Frankfurt, WTM, 2023, doi:<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","ama":"Kolbe T. Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung. In: IDMI Primar Goethe-Univeristät Frankfurt ., ed. <i>Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>. WTM; 2023. doi:<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>","bibtex":"@inproceedings{Kolbe_2023, title={Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung}, DOI={<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>}, booktitle={Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, publisher={WTM}, author={Kolbe, Tim}, editor={IDMI Primar Goethe-Univeristät Frankfurt, .}, year={2023} }","apa":"Kolbe, T. (2023). Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung. In . IDMI Primar Goethe-Univeristät Frankfurt (Ed.), <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>. WTM. <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>","ieee":"T. Kolbe, “Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung,” in <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, Frankfurt am Main, 2023, doi: <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","short":"T. Kolbe, in: . IDMI Primar Goethe-Univeristät Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, WTM, 2023.","chicago":"Kolbe, Tim. “Think-Aloud Beim Hochschulischen Mathematiklernen – Ergebnisse Einer Pilotierung.” In <i>Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by . IDMI Primar Goethe-Univeristät Frankfurt. WTM, 2023. <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>."}},{"publisher":"Springer Science and Business Media LLC","_id":"46569","language":[{"iso":"eng"}],"doi":"10.1007/s11858-023-01494-3","user_id":"99409","year":"2023","status":"public","title":"Characterizing external visualization in mathematics education research: a scoping review","author":[{"full_name":"Schoenherr, Johanna","last_name":"Schoenherr","first_name":"Johanna"},{"full_name":"Schukajlow, Stanislaw","last_name":"Schukajlow","first_name":"Stanislaw"}],"publication_identifier":{"issn":["1863-9690","1863-9704"]},"date_updated":"2024-04-30T13:43:22Z","publication_status":"published","date_created":"2023-08-17T10:11:45Z","type":"journal_article","keyword":["General Mathematics","Education"],"department":[{"_id":"913"}],"publication":"ZDM – Mathematics Education","citation":{"chicago":"Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” <i>ZDM – Mathematics Education</i>, 2023. <a href=\"https://doi.org/10.1007/s11858-023-01494-3\">https://doi.org/10.1007/s11858-023-01494-3</a>.","short":"J. Schoenherr, S. Schukajlow, ZDM – Mathematics Education (2023).","apa":"Schoenherr, J., &#38; Schukajlow, S. (2023). Characterizing external visualization in mathematics education research: a scoping review. <i>ZDM – Mathematics Education</i>. <a href=\"https://doi.org/10.1007/s11858-023-01494-3\">https://doi.org/10.1007/s11858-023-01494-3</a>","ieee":"J. Schoenherr and S. Schukajlow, “Characterizing external visualization in mathematics education research: a scoping review,” <i>ZDM – Mathematics Education</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>.","ama":"Schoenherr J, Schukajlow S. Characterizing external visualization in mathematics education research: a scoping review. <i>ZDM – Mathematics Education</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>","bibtex":"@article{Schoenherr_Schukajlow_2023, title={Characterizing external visualization in mathematics education research: a scoping review}, DOI={<a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schoenherr, Johanna and Schukajlow, Stanislaw}, year={2023} }","mla":"Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” <i>ZDM – Mathematics Education</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>."},"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.</jats:p>"}]},{"date_created":"2024-04-17T12:23:18Z","department":[{"_id":"100"}],"type":"journal_article","keyword":["General Mathematics"],"publication":"Mathematical Proceedings of the Cambridge Philosophical Society","issue":"1","language":[{"iso":"eng"}],"doi":"10.1017/s0305004123000075","author":[{"last_name":"Ernst","first_name":"Alena","full_name":"Ernst, Alena","id":"46953"},{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","first_name":"Kai-Uwe"}],"publication_identifier":{"issn":["0305-0041","1469-8064"]},"year":"2023","title":"Intersection theorems for finite general linear groups","intvolume":"       175","date_updated":"2024-05-07T08:29:59Z","publication_status":"published","citation":{"mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","ama":"Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2023;175(1):129-160. doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>","bibtex":"@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160} }","apa":"Ernst, A., &#38; Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>175</i>(1), 129–160. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>","ieee":"A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, pp. 129–160, 2023, doi: <a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i> 175, no. 1 (2023): 129–60. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>.","short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160."},"publisher":"Cambridge University Press (CUP)","_id":"53533","page":"129-160","volume":175,"user_id":"46953","status":"public"},{"language":[{"iso":"ger"}],"_id":"48596","page":"215-229","volume":5,"user_id":"26718","author":[{"full_name":"Häsel-Weide, Uta","first_name":"Uta","last_name":"Häsel-Weide","id":"60267"},{"first_name":"R.","last_name":"Schmidt","full_name":"Schmidt, R."},{"first_name":"Petra","last_name":"Büker","full_name":"Büker, Petra","id":"21978"}],"title":"„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung","status":"public","year":"2023","intvolume":"         5","date_updated":"2024-07-23T13:05:48Z","date_created":"2023-11-02T11:22:34Z","department":[{"_id":"543"},{"_id":"458"}],"type":"journal_article","citation":{"mla":"Häsel-Weide, Uta, et al. “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung.” <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>, vol. 5, no. 1, 2023, pp. 215–29.","bibtex":"@article{Häsel-Weide_Schmidt_Büker_2023, title={„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung}, volume={5}, number={1}, journal={Zeitschrift für Schul- und Professionsentwicklung (PFLB)}, author={Häsel-Weide, Uta and Schmidt, R. and Büker, Petra}, year={2023}, pages={215–229} }","ama":"Häsel-Weide U, Schmidt R, Büker P. „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung. <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>. 2023;5(1):215-229.","ieee":"U. Häsel-Weide, R. Schmidt, and P. Büker, “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung,” <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>, vol. 5, no. 1, pp. 215–229, 2023.","apa":"Häsel-Weide, U., Schmidt, R., &#38; Büker, P. (2023). „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung. <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>, <i>5</i>(1), 215–229.","short":"U. Häsel-Weide, R. Schmidt, P. Büker, Zeitschrift für Schul- und Professionsentwicklung (PFLB) 5 (2023) 215–229.","chicago":"Häsel-Weide, Uta, R. Schmidt, and Petra Büker. “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung.” <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i> 5, no. 1 (2023): 215–29."},"publication":"Zeitschrift für Schul- und Professionsentwicklung (PFLB)","issue":"1","related_material":{"link":[{"url":"https://doi.org/10.11576/pflb-6763 ","relation":"original"}]}},{"date_created":"2024-07-16T11:09:01Z","department":[{"_id":"102"}],"type":"journal_article","citation":{"apa":"Klahn, B., &#38; Technau, M. (2023). Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>. <i>Int. J. Number Theory</i>, <i>19</i>(10), 2443–2450. <a href=\"https://doi.org/10.1142/S1793042123501208\">https://doi.org/10.1142/S1793042123501208</a>","ieee":"B. Klahn and M. Technau, “Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>,” <i>Int. J. Number Theory</i>, vol. 19, no. 10, pp. 2443–2450, 2023, doi: <a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>.","short":"B. Klahn, M. Technau, Int. J. Number Theory 19 (2023) 2443–2450.","chicago":"Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.” <i>Int. J. Number Theory</i> 19, no. 10 (2023): 2443–2450. <a href=\"https://doi.org/10.1142/S1793042123501208\">https://doi.org/10.1142/S1793042123501208</a>.","mla":"Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.” <i>Int. J. Number Theory</i>, vol. 19, no. 10, 2023, pp. 2443–2450, doi:<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>.","ama":"Klahn B, Technau M. Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>. <i>Int J Number Theory</i>. 2023;19(10):2443–2450. doi:<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>","bibtex":"@article{Klahn_Technau_2023, title={Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>}, volume={19}, DOI={<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>}, number={10}, journal={Int. J. Number Theory}, author={Klahn, B. and Technau, Marc}, year={2023}, pages={2443–2450} }"},"issue":"10","publication":"Int. J. Number Theory","extern":"1","language":[{"iso":"eng"}],"_id":"55277","page":"2443–2450","volume":19,"user_id":"106108","doi":"10.1142/S1793042123501208","author":[{"full_name":"Klahn, B.","last_name":"Klahn","first_name":"B."},{"orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc","full_name":"Technau, Marc","id":"106108"}],"year":"2023","title":"Galois groups of (ⁿ₀)+(ⁿ₁)X+…+(ⁿ₆)X⁶","status":"public","intvolume":"        19","date_updated":"2024-07-24T07:23:33Z"},{"_id":"55279","language":[{"iso":"eng"}],"page":"291–320","volume":387,"doi":"10.1007/s00208-022-02452-2","user_id":"106108","author":[{"last_name":"Minelli","first_name":"P.","full_name":"Minelli, P."},{"last_name":"Sourmelidis","first_name":"A.","full_name":"Sourmelidis, A."},{"id":"106108","full_name":"Technau, Marc","first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau"}],"year":"2023","title":"Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums","status":"public","intvolume":"       387","date_updated":"2024-07-24T07:26:05Z","date_created":"2024-07-16T11:09:01Z","department":[{"_id":"102"}],"type":"journal_article","citation":{"ama":"Minelli P, Sourmelidis A, Technau M. Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math Ann</i>. 2023;387:291–320. doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>","bibtex":"@article{Minelli_Sourmelidis_Technau_2023, title={Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}, volume={387}, DOI={<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>}, journal={Math. Ann.}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc}, year={2023}, pages={291–320} }","mla":"Minelli, P., et al. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i>, vol. 387, 2023, pp. 291–320, doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","short":"P. Minelli, A. Sourmelidis, M. Technau, Math. Ann. 387 (2023) 291–320.","chicago":"Minelli, P., A. Sourmelidis, and Marc Technau. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i> 387 (2023): 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>.","apa":"Minelli, P., Sourmelidis, A., &#38; Technau, M. (2023). Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math. Ann.</i>, <i>387</i>, 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>","ieee":"P. Minelli, A. Sourmelidis, and M. Technau, “Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums,” <i>Math. Ann.</i>, vol. 387, pp. 291–320, 2023, doi: <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>."},"publication":"Math. Ann.","extern":"1"},{"user_id":"178","doi":"10.1007/s10543-023-00989-05","volume":63,"article_number":"50","publisher":"Springer","_id":"34803","language":[{"iso":"eng"}],"date_updated":"2024-08-09T08:48:06Z","intvolume":"        63","status":"public","title":"Deep neural networks on diffeomorphism groups for optimal shape reparametrization","year":"2023","author":[{"first_name":"Elena","last_name":"Celledoni","full_name":"Celledoni, Elena"},{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"},{"first_name":"Jørgen","last_name":"Riseth","full_name":"Riseth, Jørgen"},{"full_name":"Schmeding, Alexander","last_name":"Schmeding","first_name":"Alexander"}],"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2207.11141"]},"date_created":"2022-12-22T07:37:20Z","quality_controlled":"1","publication":"BIT Numerical Mathematics","citation":{"mla":"Celledoni, Elena, et al. “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.” <i>BIT Numerical Mathematics</i>, vol. 63, 50, Springer, 2023, doi:<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>.","ama":"Celledoni E, Glöckner H, Riseth J, Schmeding A. Deep neural networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>. 2023;63. doi:<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>","bibtex":"@article{Celledoni_Glöckner_Riseth_Schmeding_2023, title={Deep neural networks on diffeomorphism groups for optimal shape reparametrization}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>}, number={50}, journal={BIT Numerical Mathematics}, publisher={Springer}, author={Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}, year={2023} }","apa":"Celledoni, E., Glöckner, H., Riseth, J., &#38; Schmeding, A. (2023). Deep neural networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>, <i>63</i>, Article 50. <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">https://doi.org/10.1007/s10543-023-00989-05</a>","ieee":"E. Celledoni, H. Glöckner, J. Riseth, and A. Schmeding, “Deep neural networks on diffeomorphism groups for optimal shape reparametrization,” <i>BIT Numerical Mathematics</i>, vol. 63, Art. no. 50, 2023, doi: <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>.","chicago":"Celledoni, Elena, Helge Glöckner, Jørgen Riseth, and Alexander Schmeding. “Deep Neural Networks on Diffeomorphism Groups for Optimal Shape Reparametrization.” <i>BIT Numerical Mathematics</i> 63 (2023). <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">https://doi.org/10.1007/s10543-023-00989-05</a>.","short":"E. Celledoni, H. Glöckner, J. Riseth, A. Schmeding, BIT Numerical Mathematics 63 (2023)."}},{"date_created":"2022-12-22T07:45:13Z","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_article","issue":"1","publication":"Journal of Convex Analysis","abstract":[{"lang":"eng","text":"Let $E$ be a finite-dimensional real vector space and $M\\subseteq E$ be a\r\nconvex polytope with non-empty interior. We turn the group of all\r\n$C^\\infty$-diffeomorphisms of $M$ into a regular Lie group."}],"language":[{"iso":"eng"}],"author":[{"last_name":"Glöckner","first_name":"Helge","full_name":"Glöckner, Helge","id":"178"}],"title":"Diffeomorphism groups of convex polytopes","year":"2023","intvolume":"        30","date_updated":"2024-08-09T08:49:17Z","external_id":{"arxiv":["2203.09285"]},"citation":{"apa":"Glöckner, H. (2023). Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>, <i>30</i>(1), 343–358.","ieee":"H. Glöckner, “Diffeomorphism groups of convex polytopes,” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, pp. 343–358, 2023.","chicago":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i> 30, no. 1 (2023): 343–58.","short":"H. Glöckner, Journal of Convex Analysis 30 (2023) 343–358.","mla":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, Heldermann, 2023, pp. 343–58.","ama":"Glöckner H. Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>. 2023;30(1):343-358.","bibtex":"@article{Glöckner_2023, title={Diffeomorphism groups of convex polytopes}, volume={30}, number={1}, journal={Journal of Convex Analysis}, publisher={Heldermann}, author={Glöckner, Helge}, year={2023}, pages={343–358} }"},"quality_controlled":"1","publisher":"Heldermann","_id":"34805","page":"343-358","volume":30,"user_id":"178","status":"public"},{"quality_controlled":"1","publication":"Journal of Lie Theory","issue":"1","citation":{"ama":"Glöckner H, Tárrega L. Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>. 2023;33(1):271-296.","short":"H. Glöckner, L. Tárrega, Journal of Lie Theory 33 (2023) 271–296.","chicago":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i> 33, no. 1 (2023): 271–96.","bibtex":"@article{Glöckner_Tárrega_2023, title={Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }, volume={33}, number={1}, journal={Journal of Lie Theory}, publisher={Heldermann}, author={Glöckner, Helge and Tárrega, Luis}, year={2023}, pages={271–296} }","apa":"Glöckner, H., &#38; Tárrega, L. (2023). Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>, <i>33</i>(1), 271–296.","mla":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i>, vol. 33, no. 1, Heldermann, 2023, pp. 271–96.","ieee":"H. Glöckner and L. Tárrega, “Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ,” <i>Journal of Lie Theory</i>, vol. 33, no. 1, pp. 271–296, 2023."},"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2210.01246"]},"date_created":"2022-12-22T07:23:57Z","date_updated":"2024-08-09T08:48:51Z","intvolume":"        33","title":"Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ","year":"2023","status":"public","author":[{"full_name":"Glöckner, Helge","first_name":"Helge","last_name":"Glöckner","id":"178"},{"last_name":"Tárrega","first_name":"Luis","full_name":"Tárrega, Luis"}],"user_id":"178","volume":33,"page":"271-296","publisher":"Heldermann","_id":"34801","language":[{"iso":"eng"}]},{"date_updated":"2024-08-09T09:27:43Z","title":"Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen","year":"2023","status":"public","author":[{"last_name":"Jakob","first_name":"Johanna","full_name":"Jakob, Johanna"}],"user_id":"178","language":[{"iso":"eng"}],"_id":"55575","citation":{"short":"J. Jakob, (2023).","chicago":"Jakob, Johanna. “Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen,” 2023.","ieee":"J. Jakob, “Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen.” 2023.","apa":"Jakob, J. (2023). <i>Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen</i>.","bibtex":"@article{Jakob_2023, title={Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen}, author={Jakob, Johanna}, year={2023} }","ama":"Jakob J. Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen. Published online 2023.","mla":"Jakob, Johanna. <i>Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen</i>. 2023."},"type":"preprint","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2307.03473"]},"date_created":"2024-08-09T09:15:06Z"},{"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","year":"2023","author":[{"id":"85279","full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"publication_status":"published","date_updated":"2024-08-12T13:46:29Z","intvolume":"     14071","series_title":"Lecture Notes in Computer Science (LNCS)","language":[{"iso":"eng"}],"doi":"10.1007/978-3-031-38271-0_57","publication":"Geometric Science of Information","abstract":[{"lang":"eng","text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE."}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML","description":"GitHub"}]},"file":[{"file_id":"46273","content_type":"application/pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","file_name":"LDensityLearning.pdf","file_size":1938962,"access_level":"open_access","relation":"main_file","date_updated":"2023-08-02T12:04:17Z","date_created":"2023-08-02T12:04:17Z","description":"The article shows how to learn models of dynamical systems\nfrom data which are governed by an unknown variational PDE. Rather\nthan employing reduction techniques, we learn a discrete field theory\ngoverned by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is\nnecessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of\nthe discrete Euler–Lagrange equations. Secondly, we develop a method to\nfind solutions to machine learned discrete field theories which constitute\ntravelling waves of the underlying continuous PDE.","creator":"coffen"}],"date_created":"2023-02-16T11:32:48Z","type":"conference","keyword":["System identification","discrete Lagrangians","travelling waves"],"department":[{"_id":"636"}],"status":"public","conference":{"location":"Saint-Malo, Palais du Grand Large, France","start_date":"2023-08-30","name":"  GSI'23 6th International Conference on Geometric Science of Information","end_date":"2023-09-01"},"has_accepted_license":"1","page":"569-579","_id":"42163","publisher":"Springer, Cham.","user_id":"85279","ddc":["510"],"volume":14071,"editor":[{"first_name":"F","last_name":"Nielsen","full_name":"Nielsen, F"},{"first_name":"F","last_name":"Barbaresco","full_name":"Barbaresco, F"}],"file_date_updated":"2023-08-02T12:04:17Z","citation":{"ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in <i>Geometric Science of Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen &#38; F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp. 569–579). Springer, Cham. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>"},"quality_controlled":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"external_id":{"arxiv":["2302.08232 "]},"oa":"1"},{"publisher":"Springer International Publishing","_id":"37469","user_id":"30933","doi":"10.1007/978-3-031-14175-1","editor":[{"full_name":"Biehler, Rolf","last_name":"Biehler","first_name":"Rolf"},{"last_name":"Liebendörfer","first_name":"Michael","full_name":"Liebendörfer, Michael"},{"last_name":"Gueudet","first_name":"Ghislaine","full_name":"Gueudet, Ghislaine"},{"last_name":"Rasmussen","first_name":"Chris","full_name":"Rasmussen, Chris"},{"full_name":"Winsløw, Carl","last_name":"Winsløw","first_name":"Carl"}],"status":"public","year":"2023","title":"Practice-Oriented Research in Tertiary Mathematics Education","publication_identifier":{"isbn":["9783031141744","9783031141751"],"issn":["1869-4918","1869-4926"]},"publication_status":"published","date_updated":"2023-01-18T22:47:41Z","date_created":"2023-01-18T22:17:58Z","place":"Cham","type":"book_editor","department":[{"_id":"10"}],"citation":{"short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-14175-1\">https://doi.org/10.1007/978-3-031-14175-1</a>.","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., &#38; Winsløw, C. (Eds.). (2023). <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-14175-1\">https://doi.org/10.1007/978-3-031-14175-1</a>","ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Cham: Springer International Publishing, 2023.","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing; 2023. doi:<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>","bibtex":"@book{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>}, publisher={Springer International Publishing}, year={2023} }","mla":"Biehler, Rolf, et al., editors. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing, 2023, doi:<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>."}},{"user_id":"30905","volume":75,"page":"170-201","_id":"34814","publisher":"Canadian Mathematical Society","status":"public","project":[{"name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)","_id":"161"}],"citation":{"short":"M. Hanusch, Canadian Journal of Mathematics 75 (2023) 170–201.","chicago":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” <i>Canadian Journal of Mathematics</i> 75, no. 1 (2023): 170–201. <a href=\"https://doi.org/10.4153/s0008414x21000596\">https://doi.org/10.4153/s0008414x21000596</a>.","ieee":"M. Hanusch, “A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus,” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, pp. 170–201, 2023, doi: <a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>.","apa":"Hanusch, M. (2023). A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. <i>Canadian Journal of Mathematics</i>, <i>75</i>(1), 170–201. <a href=\"https://doi.org/10.4153/s0008414x21000596\">https://doi.org/10.4153/s0008414x21000596</a>","bibtex":"@article{Hanusch_2023, title={A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}, volume={75}, DOI={<a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>}, number={1}, journal={Canadian Journal of Mathematics}, publisher={Canadian Mathematical Society}, author={Hanusch, Maximilian}, year={2023}, pages={170–201} }","ama":"Hanusch M. A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus. <i>Canadian Journal of Mathematics</i>. 2023;75(1):170-201. doi:<a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>","mla":"Hanusch, Maximilian. “A $C^k$-Seeley-Extension-Theorem for Bastiani’s Differential Calculus.” <i>Canadian Journal of Mathematics</i>, vol. 75, no. 1, Canadian Mathematical Society, 2023, pp. 170–201, doi:<a href=\"https://doi.org/10.4153/s0008414x21000596\">10.4153/s0008414x21000596</a>."},"doi":"10.4153/s0008414x21000596","language":[{"iso":"eng"}],"date_updated":"2023-02-22T11:38:32Z","publication_status":"published","intvolume":"        75","article_type":"original","year":"2023","title":"A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus","publication_identifier":{"issn":["0008-414X","1496-4279"]},"author":[{"id":"30905","last_name":"Hanusch","first_name":"Maximilian","full_name":"Hanusch, Maximilian"}],"type":"journal_article","keyword":["extension of differentiable maps"],"department":[{"_id":"93"}],"date_created":"2022-12-22T09:16:48Z","issue":"1","publication":"Canadian Journal of Mathematics"},{"volume":85,"user_id":"47427","_id":"27426","page":"709-741","status":"public","oa":"1","citation":{"short":"B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741.","chicago":"Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” <i>Journal of Global Optimization</i> 85, no. 3 (2023): 709–41. <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">https://doi.org/10.1007/s10898-022-01223-2</a>.","apa":"Gebken, B., Bieker, K., &#38; Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. <i>Journal of Global Optimization</i>, <i>85</i>(3), 709–741. <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">https://doi.org/10.1007/s10898-022-01223-2</a>","ieee":"B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” <i>Journal of Global Optimization</i>, vol. 85, no. 3, pp. 709–741, 2023, doi: <a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>.","ama":"Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. <i>Journal of Global Optimization</i>. 2023;85(3):709-741. doi:<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>","bibtex":"@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }","mla":"Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” <i>Journal of Global Optimization</i>, vol. 85, no. 3, 2023, pp. 709–41, doi:<a href=\"https://doi.org/10.1007/s10898-022-01223-2\">10.1007/s10898-022-01223-2</a>."},"doi":"10.1007/s10898-022-01223-2","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf"}],"intvolume":"        85","date_updated":"2023-03-11T17:16:33Z","author":[{"full_name":"Gebken, Bennet","first_name":"Bennet","last_name":"Gebken","id":"32643"},{"id":"32829","first_name":"Katharina","last_name":"Bieker","full_name":"Bieker, Katharina"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427"}],"title":"On the structure of regularization paths for piecewise differentiable regularization terms","year":"2023","department":[{"_id":"101"},{"_id":"655"}],"type":"journal_article","date_created":"2021-11-15T09:24:59Z","abstract":[{"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.","lang":"eng"}],"publication":"Journal of Global Optimization","issue":"3"},{"editor":[{"last_name":"Trigueros","first_name":"Marı́a","full_name":"Trigueros, Marı́a"},{"first_name":"Berta","last_name":"Barquero","full_name":"Barquero, Berta"},{"full_name":"Hochmuth, Reinhard","last_name":"Hochmuth","first_name":"Reinhard"},{"first_name":"Jana","last_name":"Peters","full_name":"Peters, Jana"}],"ddc":["370","510"],"user_id":"32202","_id":"31849","publisher":"University of Hannover and INDRUM.","has_accepted_license":"1","status":"public","oa":"1","place":"Hannover","quality_controlled":"1","citation":{"chicago":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” In <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover: 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.","ieee":"M. Hoffmann and R. Biehler, “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry,” in <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, 2023.","apa":"Hoffmann, M., &#38; Biehler, R. (2023). Student Teachers ’ Knowledge of Congruence before a University Course on Geometry. In M. Trigueros, B. Barquero, R. Hochmuth, &#38; J. Peters (Eds.), <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>. 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} }","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. <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>. University of Hannover and INDRUM.; 2023.","mla":"Hoffmann, Max, and Rolf Biehler. “Student Teachers ’ Knowledge of Congruence before a University Course on Geometry.” <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros et al., University of Hannover and INDRUM., 2023."},"file_date_updated":"2023-03-25T10:01:03Z","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"date_updated":"2023-03-25T10:11:35Z","publication_status":"published","author":[{"orcid":"0000-0002-6964-7123","last_name":"Hoffmann","first_name":"Max","full_name":"Hoffmann, Max","id":"32202"},{"id":"16274","first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"}],"title":"Student Teachers ’ Knowledge of Congruence before a University Course on Geometry","year":"2023","department":[{"_id":"97"}],"type":"conference","keyword":["Teaching and learning of specific topics in university mathematics","Transition to","across and from university mathematics","Student Teachers","Geometry","Congruence","Double Discontinuity."],"date_created":"2022-06-12T11:07:34Z","file":[{"date_created":"2023-03-25T10:01:03Z","creator":"maxh","file_id":"43096","content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2023-03-25T10:01:03Z","file_name":"HoffmannBiehler2022_indrum_congruence.pdf","file_size":201942,"access_level":"closed"}],"publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)"},{"type":"conference","department":[{"_id":"97"}],"file":[{"date_created":"2023-03-25T10:07:54Z","creator":"maxh","content_type":"application/pdf","success":1,"file_id":"43098","date_updated":"2023-03-25T10:07:54Z","relation":"main_file","file_size":642388,"access_level":"closed","file_name":"2022_FlorensaEtAl_indrum_panelInnovations.pdf"}],"date_created":"2023-03-25T10:09:06Z","publication":"Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)","main_file_link":[{"url":"https://hal.univ-reims.fr/INDRUM2022/","open_access":"1"}],"language":[{"iso":"eng"}],"date_updated":"2023-03-25T10:10:58Z","year":"2023","title":"Innovations in university teaching based on mathematic education research","author":[{"first_name":"Ignasio","last_name":"Florensa","full_name":"Florensa, Ignasio"},{"id":"32202","first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max"},{"first_name":"Avenilde","last_name":"Romo Vázquez","full_name":"Romo Vázquez, Avenilde"},{"last_name":"Zandieh","first_name":"Michelle","full_name":"Zandieh, Michelle"},{"first_name":"Rafael","last_name":"Martínez-Planell","full_name":"Martínez-Planell, Rafael"}],"oa":"1","place":"Hannover","quality_controlled":"1","file_date_updated":"2023-03-25T10:07:54Z","citation":{"apa":"Florensa, I., Hoffmann, M., Romo Vázquez, A., Zandieh, M., &#38; Martínez-Planell, R. (2023). Innovations in university teaching based on mathematic education research. In M. Trigueros, B. Barquero, R. Hochmuth, &#38; J. Peters (Eds.), <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>.","ieee":"I. Florensa, M. Hoffmann, A. Romo Vázquez, M. Zandieh, and R. Martínez-Planell, “Innovations in university teaching based on mathematic education research,” in <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, 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 <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros, Berta Barquero, Reinhard Hochmuth, and Jana Peters. Hannover, 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.","mla":"Florensa, Ignasio, et al. “Innovations in University Teaching Based on Mathematic Education Research.” <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>, edited by Marı́a Trigueros et al., 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. <i>Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)</i>. ; 2023.","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} }"},"ddc":["370","510"],"user_id":"32202","editor":[{"full_name":"Trigueros, Marı́a","first_name":"Marı́a","last_name":"Trigueros"},{"first_name":"Berta","last_name":"Barquero","full_name":"Barquero, Berta"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"first_name":"Jana","last_name":"Peters","full_name":"Peters, Jana"}],"_id":"43097","has_accepted_license":"1","status":"public"},{"citation":{"mla":"Black, Tobias, et al. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, 103868, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","bibtex":"@article{Black_Fuest_Lankeit_Mizukami_2023, title={Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}, volume={73}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>}, 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} }","ama":"Black T, Fuest M, Lankeit J, Mizukami M. Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>. 2023;73. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>","ieee":"T. Black, M. Fuest, J. Lankeit, and M. Mizukami, “Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 73, Art. no. 103868, 2023, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">10.1016/j.nonrwa.2023.103868</a>.","apa":"Black, T., Fuest, M., Lankeit, J., &#38; Mizukami, M. (2023). Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source. <i>Nonlinear Analysis: Real World Applications</i>, <i>73</i>, Article 103868. <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>","short":"T. Black, M. Fuest, J. Lankeit, M. Mizukami, Nonlinear Analysis: Real World Applications 73 (2023).","chicago":"Black, Tobias, Mario Fuest, Johannes Lankeit, and Masaaki Mizukami. “Possible Points of Blow-up in Chemotaxis Systems with Spatially Heterogeneous Logistic Source.” <i>Nonlinear Analysis: Real World Applications</i> 73 (2023). <a href=\"https://doi.org/10.1016/j.nonrwa.2023.103868\">https://doi.org/10.1016/j.nonrwa.2023.103868</a>."},"status":"public","user_id":"23686","volume":73,"_id":"43105","publisher":"Elsevier BV","publication":"Nonlinear Analysis: Real World Applications","keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2023-03-27T07:25:58Z","publication_status":"published","date_updated":"2023-03-27T07:27:03Z","intvolume":"        73","title":"Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source","year":"2023","publication_identifier":{"issn":["1468-1218"]},"author":[{"full_name":"Black, Tobias","first_name":"Tobias","last_name":"Black","orcid":"0000-0001-9963-0800","id":"23686"},{"full_name":"Fuest, Mario","first_name":"Mario","last_name":"Fuest"},{"full_name":"Lankeit, Johannes","first_name":"Johannes","last_name":"Lankeit"},{"last_name":"Mizukami","first_name":"Masaaki","full_name":"Mizukami, Masaaki"}],"doi":"10.1016/j.nonrwa.2023.103868","article_number":"103868","language":[{"iso":"eng"}]},{"date_updated":"2023-03-30T10:06:53Z","author":[{"full_name":"Vitt, Vivian","last_name":"Vitt","first_name":"Vivian"},{"full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta","id":"60267"}],"status":"public","title":"Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.","year":"2023","user_id":"44184","doi":"https://doi.org/10.18716/ojs/md/2023.1671","_id":"43227","language":[{"iso":"eng"}],"citation":{"chicago":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” In <i>Mathematica Didactica, 46</i>, 2023. <a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>.","short":"V. Vitt, U. Häsel-Weide, in: Mathematica Didactica, 46, 2023.","ieee":"V. Vitt and U. Häsel-Weide, “Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.,” in <i>Mathematica Didactica, 46</i>, 2023.","apa":"Vitt, V., &#38; Häsel-Weide, U. (2023). Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In <i>Mathematica Didactica, 46</i>. <a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>","bibtex":"@inbook{Vitt_Häsel-Weide_2023, title={Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}, DOI={<a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>}, booktitle={Mathematica Didactica, 46}, author={Vitt, Vivian and Häsel-Weide, Uta}, year={2023} }","ama":"Vitt V, Häsel-Weide U. Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. In: <i>Mathematica Didactica, 46</i>. ; 2023. doi:<a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>","mla":"Vitt, Vivian, and Uta Häsel-Weide. “Reziprokes Peer-Tutoring Zur Förderung von Schüler*innen Mit Schwierigkeiten Beim Mathematiklernen.” <i>Mathematica Didactica, 46</i>, 2023, doi:<a href=\"https://doi.org/10.18716/ojs/md/2023.1671\">https://doi.org/10.18716/ojs/md/2023.1671</a>."},"publication":"Mathematica Didactica, 46","department":[{"_id":"543"}],"type":"book_chapter","date_created":"2023-03-30T10:06:24Z"},{"title":"The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups","status":"public","year":"2023","author":[{"first_name":"Maximilian","last_name":"Hanusch","full_name":"Hanusch, Maximilian","id":"30905"}],"date_updated":"2023-04-05T18:18:24Z","publication_status":"published","intvolume":"        63","language":[{"iso":"eng"}],"_id":"34832","doi":"10.1007/s10455-023-09888-y","user_id":"30905","volume":63,"issue":"21","publication":"Annals of Global Analysis and Geometry","citation":{"bibtex":"@article{Hanusch_2023, title={The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>}, number={21}, journal={Annals of Global Analysis and Geometry}, author={Hanusch, Maximilian}, year={2023} }","ama":"Hanusch M. The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. <i>Annals of Global Analysis and Geometry</i>. 2023;63(21). doi:<a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>","mla":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 21, 2023, doi:<a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>.","chicago":"Hanusch, Maximilian. “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups.” <i>Annals of Global Analysis and Geometry</i> 63, no. 21 (2023). <a href=\"https://doi.org/10.1007/s10455-023-09888-y\">https://doi.org/10.1007/s10455-023-09888-y</a>.","short":"M. Hanusch, Annals of Global Analysis and Geometry 63 (2023).","ieee":"M. Hanusch, “The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups,” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 21, 2023, doi: <a href=\"https://doi.org/10.1007/s10455-023-09888-y\">10.1007/s10455-023-09888-y</a>.","apa":"Hanusch, M. (2023). The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups. <i>Annals of Global Analysis and Geometry</i>, <i>63</i>(21). <a href=\"https://doi.org/10.1007/s10455-023-09888-y\">https://doi.org/10.1007/s10455-023-09888-y</a>"},"project":[{"_id":"161","name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)"}],"date_created":"2022-12-22T09:45:34Z","type":"journal_article","keyword":["Lax equation","generalized Baker-Campbell-Dynkin-Hausdorff formula","regularity of Lie groups"],"department":[{"_id":"93"}]}]