TY - PAT A1 - Graf, Günter A1 - Groß, Heinz A1 - Sponagel, Stefan T1 - Verfahren zur Herstellung eines Dichtringes mit einer Dichtlippe : Patentschrift DE3621241C1 ; Veröffentlichungstag der Patenterteilung : 25.06.1987 Y1 - 1987 N1 - Volltext über Datenbank DEPATISnet PB - Deutsches Patent- und Markenamt CY - München ER - TY - BOOK A1 - Graf, Günter A1 - Groß, Heinz A1 - Sponagel, Stefan T1 - Verfahren zur Herstellung eines Dichtringes : Europäische Patentschrift EP0250642B1 ; Veröffentlichungstag der Patentschrift: 11.02.1988 Y1 - 1988 N1 - Volltext über Datenbank DEPATISnet PB - Europäisches Patentamt CY - [München u.a.] ER - TY - JOUR A1 - Grajewski, Matthias A1 - Hron, Jaroslav A1 - Turek, Stefan T1 - Numerical analysis for a new non-conforming linear finite element on quadrilaterals JF - Journal of Computational and Applied Mathematics Y1 - 2006 U6 - http://dx.doi.org/10.1016/j.cam.2005.05.024 SN - 0377-0427 VL - 193 IS - 1 SP - 38 EP - 50 ER - TY - JOUR A1 - Grajewski, Matthias A1 - Hron, Jaroslav A1 - Turek, Stefan T1 - Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals JF - Applied Numerical Mathematics N2 - 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. Y1 - 2005 U6 - http://dx.doi.org/10.1016/j.apnum.2004.09.016 SN - 0168-9274 VL - 54 IS - 3-4 SP - 504 EP - 518 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Grajewski, Matthias A1 - Kleefeld, Andreas T1 - Detecting and approximating decision boundaries in low-dimensional spaces JF - Numerical Algorithms N2 - 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. KW - MCDA KW - Inverse scattering problem KW - Fault approximation KW - Fault detection Y1 - 2023 SN - 1572-9265 N1 - Corresponding author: Matthias Grajewski VL - 93 IS - 4 PB - Springer Science+Business Media CY - Dordrecht ER - TY - JOUR A1 - Grajewski, Matthias A1 - Köster, Michael A1 - Turek, Stefam T1 - Numerical analysis and implementational aspects of a new multilevel grid deformation method JF - Applied Numerical Mathematics N2 - 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. Y1 - 2010 U6 - http://dx.doi.org/10.1016/j.apnum.2010.03.017 SN - 0168-9274 VL - 60 IS - 8 SP - 767 EP - 781 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Grajewski, Matthias A1 - Köster, Michael A1 - Turek, Stefan T1 - Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context JF - SIAM Journal on Scientific Computing Y1 - 2009 U6 - http://dx.doi.org/10.1137/050639387 VL - 31 IS - 2 SP - 1539 EP - 1557 PB - Society for Industrial and Applied Mathematics CY - Philadelphia, Pa. ER - TY - INPR A1 - Grieger, Niklas A1 - Mehrkanoon, Siamak A1 - Bialonski, Stephan T1 - Preprint: Data-efficient sleep staging with synthetic time series pretraining T2 - arXiv N2 - 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. Y1 - 2024 ER - TY - JOUR A1 - Grieger, Niklas A1 - Schwabedal, Justus T. C. A1 - Wendel, Stefanie A1 - Ritze, Yvonne A1 - Bialonski, Stephan T1 - Automated scoring of pre-REM sleep in mice with deep learning JF - Scientific Reports N2 - 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. Y1 - 2021 U6 - http://dx.doi.org/10.1038/s41598-021-91286-0 SN - 2045-2322 N1 - Corresponding author: Stephan Bialonski VL - 11 IS - Art. 12245 PB - Springer Nature CY - London ER - TY - JOUR A1 - Grießmeier, M. A1 - Sonnenberg, F. A1 - Weckesser, M. A1 - Ziemons, Karl A1 - Langen, K.-J. A1 - Müller-Gärtner, H. W. T1 - Improvement of SPECT quantification in small brain structures by using experiment based recovery-coefficient corrections JF - European Journal of Nuclear Medicine Y1 - 1996 SN - 1619-7089 N1 - Abstracts ; PSu827 VL - 23 IS - 9 SP - 1238 EP - 1238 ER -