TY - JOUR AB - Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression and machine learning. Since the choice of the regularization parameter is crucial but often difficult, path-following methods are used to approximate the entire regularization path, i.e., the set of all possible solutions for all regularization parameters. Due to their nature, the development of these methods requires structural results about the regularization path. The goal of this article is to derive these results for the case of a smooth objective function which is penalized by a piecewise differentiable regularization term. We do this by treating regularization as a multiobjective optimization problem. Our results suggest that even in this general case, the regularization path is piecewise smooth. Moreover, our theory allows for a classification of the nonsmooth features that occur in between smooth parts. This is demonstrated in two applications, namely support-vector machines and exact penalty methods. AU - Gebken, Bennet AU - Bieker, Katharina AU - Peitz, Sebastian ID - 27426 IS - 3 JF - Journal of Global Optimization TI - On the structure of regularization paths for piecewise differentiable regularization terms VL - 85 ER - TY - CONF AU - Hoffmann, Max AU - Biehler, Rolf ED - Trigueros, Marı́a ED - Barquero, Berta ED - Hochmuth, Reinhard ED - Peters, Jana ID - 31849 KW - Teaching and learning of specific topics in university mathematics KW - Transition to KW - across and from university mathematics KW - Student Teachers KW - Geometry KW - Congruence KW - Double Discontinuity. T2 - Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022) TI - Student Teachers ’ Knowledge of Congruence before a University Course on Geometry ER - TY - CONF AU - Florensa, Ignasio AU - Hoffmann, Max AU - Romo Vázquez, Avenilde AU - Zandieh, Michelle AU - Martínez-Planell, Rafael ED - Trigueros, Marı́a ED - Barquero, Berta ED - Hochmuth, Reinhard ED - Peters, Jana ID - 43097 T2 - Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022) TI - Innovations in university teaching based on mathematic education research ER - TY - JOUR AU - Biehler, Rolf AU - Liebendörfer, Michael AU - Schmitz, A. ID - 43504 JF - Mitteilungen der Gesellschaft für Didaktik der Mathematik TI - Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos VL - 114 ER - TY - JOUR AU - Black, Tobias AU - Fuest, Mario AU - Lankeit, Johannes AU - Mizukami, Masaaki ID - 43105 JF - Nonlinear Analysis: Real World Applications KW - Applied Mathematics KW - Computational Mathematics KW - General Economics KW - Econometrics and Finance KW - General Engineering KW - General Medicine KW - Analysis SN - 1468-1218 TI - Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source VL - 73 ER - TY - CHAP AU - Vitt, Vivian AU - Häsel-Weide, Uta ID - 43227 T2 - Mathematica Didactica, 46 TI - Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen. ER - TY - CHAP AU - Häsel-Weide, Uta AU - Nührenbörger, M. ID - 43226 T2 - Mathematica Didactica, 46 TI - Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht. ER - TY - JOUR AU - Hanusch, Maximilian ID - 34832 IS - 21 JF - Annals of Global Analysis and Geometry KW - Lax equation KW - generalized Baker-Campbell-Dynkin-Hausdorff formula KW - regularity of Lie groups TI - The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups VL - 63 ER - TY - GEN AB - 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. Providing 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. AU - Cappello, Chiara AU - Naserasr, Reza AU - Steffen, Eckhard AU - Wang, Zhouningxin ID - 44501 T2 - arXiv:2304.10243 TI - Critically 3-frustrated signed graphs ER - TY - JOUR AB - 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. AU - Silva, Helmuth O.M. AU - Rubert, Diego P. AU - Araujo, Eloi AU - Steffen, Eckhard AU - Doerr, Daniel AU - Martinez, Fábio V. ID - 44857 IS - 3 JF - RAIRO - Operations Research KW - Management Science and Operations Research KW - Computer Science Applications KW - Theoretical Computer Science SN - 0399-0559 TI - Algorithms for the genome median under a restricted measure of rearrangement VL - 57 ER -