@misc{GrafGrossSponagel1987, author = {Graf, G{\"u}nter and Groß, Heinz and Sponagel, Stefan}, title = {Verfahren zur Herstellung eines Dichtringes mit einer Dichtlippe : Patentschrift DE3621241C1 ; Ver{\"o}ffentlichungstag der Patenterteilung : 25.06.1987}, publisher = {Deutsches Patent- und Markenamt}, address = {M{\"u}nchen}, pages = {5 S. : Ill.}, year = {1987}, language = {de} } @book{GrafGrossSponagel1988, author = {Graf, G{\"u}nter and Groß, Heinz and Sponagel, Stefan}, title = {Verfahren zur Herstellung eines Dichtringes : Europ{\"a}ische Patentschrift EP0250642B1 ; Ver{\"o}ffentlichungstag der Patentschrift: 11.02.1988}, publisher = {Europ{\"a}isches Patentamt}, address = {[M{\"u}nchen u.a.]}, pages = {5 S. : Ill.}, year = {1988}, language = {de} } @article{GrajewskiHronTurek2006, author = {Grajewski, Matthias and Hron, Jaroslav and Turek, Stefan}, title = {Numerical analysis for a new non-conforming linear finite element on quadrilaterals}, series = {Journal of Computational and Applied Mathematics}, volume = {193}, journal = {Journal of Computational and Applied Mathematics}, number = {1}, issn = {0377-0427}, doi = {10.1016/j.cam.2005.05.024}, pages = {38 -- 50}, year = {2006}, language = {en} } @article{GrajewskiHronTurek2005, author = {Grajewski, Matthias and Hron, Jaroslav and Turek, Stefan}, title = {Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals}, series = {Applied Numerical Mathematics}, volume = {54}, journal = {Applied Numerical Mathematics}, number = {3-4}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0168-9274}, doi = {10.1016/j.apnum.2004.09.016}, pages = {504 -- 518}, year = {2005}, abstract = {After a short introduction of a new nonconforming linear finite element on quadrilaterals recently developed by Park, we derive a dual weighted residual-based a posteriori error estimator (in the sense of Becker and Rannacher) for this finite element. By computing a corresponding dual solution we estimate the error with respect to a given target error functional. The reliability and efficiency of this estimator is analyzed in several numerical experiments.}, language = {en} } @article{GrajewskiKleefeld2023, author = {Grajewski, Matthias and Kleefeld, Andreas}, title = {Detecting and approximating decision boundaries in low-dimensional spaces}, series = {Numerical Algorithms}, volume = {93}, journal = {Numerical Algorithms}, number = {4}, publisher = {Springer Science+Business Media}, address = {Dordrecht}, issn = {1572-9265}, pages = {35 Seiten}, year = {2023}, abstract = {A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of scattered points along with the corresponding classification algorithm to construct a representation of a decision curve by points with prescribed maximal distance to the true decision curve. Hereby, our algorithm ensures that the representing point set covers the decision curve in its entire extent and features local refinement based on the geometric properties of the decision curve. We demonstrate applications of our method to problems related to the detection of faults, to multi-criteria decision aid and, in combination with Kirsch's factorization method, to solving an inverse acoustic scattering problem. In all applications we considered in this work, our method requires significantly less pointwise classifications than previously employed algorithms.}, language = {en} } @article{GrajewskiKoesterTurek2010, author = {Grajewski, Matthias and K{\"o}ster, Michael and Turek, Stefam}, title = {Numerical analysis and implementational aspects of a new multilevel grid deformation method}, series = {Applied Numerical Mathematics}, volume = {60}, journal = {Applied Numerical Mathematics}, number = {8}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0168-9274}, doi = {10.1016/j.apnum.2010.03.017}, pages = {767 -- 781}, year = {2010}, abstract = {Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.}, language = {en} } @article{GrajewskiKoesterTurek2009, author = {Grajewski, Matthias and K{\"o}ster, Michael and Turek, Stefan}, title = {Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context}, series = {SIAM Journal on Scientific Computing}, volume = {31}, journal = {SIAM Journal on Scientific Computing}, number = {2}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, Pa.}, doi = {10.1137/050639387}, pages = {1539 -- 1557}, year = {2009}, language = {en} } @unpublished{GriegerMehrkanoonBialonski2024, author = {Grieger, Niklas and Mehrkanoon, Siamak and Bialonski, Stephan}, title = {Preprint: Data-efficient sleep staging with synthetic time series pretraining}, series = {arXiv}, journal = {arXiv}, pages = {10 Seiten}, year = {2024}, abstract = {Analyzing electroencephalographic (EEG) time series can be challenging, especially with deep neural networks, due to the large variability among human subjects and often small datasets. To address these challenges, various strategies, such as self-supervised learning, have been suggested, but they typically rely on extensive empirical datasets. Inspired by recent advances in computer vision, we propose a pretraining task termed "frequency pretraining" to pretrain a neural network for sleep staging by predicting the frequency content of randomly generated synthetic time series. Our experiments demonstrate that our method surpasses fully supervised learning in scenarios with limited data and few subjects, and matches its performance in regimes with many subjects. Furthermore, our results underline the relevance of frequency information for sleep stage scoring, while also demonstrating that deep neural networks utilize information beyond frequencies to enhance sleep staging performance, which is consistent with previous research. We anticipate that our approach will be advantageous across a broad spectrum of applications where EEG data is limited or derived from a small number of subjects, including the domain of brain-computer interfaces.}, language = {en} } @article{GriegerSchwabedalWendeletal.2021, author = {Grieger, Niklas and Schwabedal, Justus T. C. and Wendel, Stefanie and Ritze, Yvonne and Bialonski, Stephan}, title = {Automated scoring of pre-REM sleep in mice with deep learning}, series = {Scientific Reports}, volume = {11}, journal = {Scientific Reports}, number = {Art. 12245}, publisher = {Springer Nature}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-021-91286-0}, year = {2021}, abstract = {Reliable automation of the labor-intensive manual task of scoring animal sleep can facilitate the analysis of long-term sleep studies. In recent years, deep-learning-based systems, which learn optimal features from the data, increased scoring accuracies for the classical sleep stages of Wake, REM, and Non-REM. Meanwhile, it has been recognized that the statistics of transitional stages such as pre-REM, found between Non-REM and REM, may hold additional insight into the physiology of sleep and are now under vivid investigation. We propose a classification system based on a simple neural network architecture that scores the classical stages as well as pre-REM sleep in mice. When restricted to the classical stages, the optimized network showed state-of-the-art classification performance with an out-of-sample F1 score of 0.95 in male C57BL/6J mice. When unrestricted, the network showed lower F1 scores on pre-REM (0.5) compared to the classical stages. The result is comparable to previous attempts to score transitional stages in other species such as transition sleep in rats or N1 sleep in humans. Nevertheless, we observed that the sequence of predictions including pre-REM typically transitioned from Non-REM to REM reflecting sleep dynamics observed by human scorers. Our findings provide further evidence for the difficulty of scoring transitional sleep stages, likely because such stages of sleep are under-represented in typical data sets or show large inter-scorer variability. We further provide our source code and an online platform to run predictions with our trained network.}, language = {en} } @article{GriessmeierSonnenbergWeckesseretal.1996, author = {Grießmeier, M. and Sonnenberg, F. and Weckesser, M. and Ziemons, Karl and Langen, K.-J. and M{\"u}ller-G{\"a}rtner, H. W.}, title = {Improvement of SPECT quantification in small brain structures by using experiment based recovery-coefficient corrections}, series = {European Journal of Nuclear Medicine}, volume = {23}, journal = {European Journal of Nuclear Medicine}, number = {9}, issn = {1619-7089}, pages = {1238 -- 1238}, year = {1996}, language = {en} }