@unpublished{GriegerMehrkanoonBialonski2024, author = {Grieger, Niklas and Mehrkanoon, Siamak and Bialonski, Stephan}, title = {Preprint: Data-efficient sleep staging with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} } @book{ElsaesserKlebinggatKuhnetal.2024, author = {Elsaesser, Evelyn and Klebinggat, Michael and Kuhn, Wilfried and Michielsens, Constant and Pauels, Willibert and Popkes, Enno E. and Schneider, Elke and Laack, Walter van and Warven, Rinus van}, title = {Schnittstelle Tod - Ist die Menschheit zu retten ohne Vertrauen auf ein Danach}, editor = {Laack, Walter van}, publisher = {van Laack Buchverlag}, address = {Aachen}, isbn = {978-3-936624-58-8}, pages = {156 Seiten}, year = {2024}, language = {de} } @article{PieronekKleefeld2024, author = {Pieronek, Lukas and Kleefeld, Andreas}, title = {On trajectories of complex-valued interior transmission eigenvalues}, series = {Inverse problems and imaging : IPI}, volume = {18}, journal = {Inverse problems and imaging : IPI}, number = {2}, publisher = {AIMS}, address = {Springfield, Mo}, issn = {1930-8337 (Print)}, doi = {10.3934/ipi.2023041}, pages = {480 -- 516}, year = {2024}, abstract = {This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.}, language = {en} } @techreport{BarnatArntzBerneckeretal.2024, type = {Working Paper}, author = {Barnat, Miriam and Arntz, Kristian and Bernecker, Andreas and Fissabre, Anke and Franken, Norbert and Goldbach, Daniel and H{\"u}ning, Felix and J{\"o}rissen, J{\"o}rg and Kirsch, Ansgar and Pettrak, J{\"u}rgen and Rexforth, Matthias and Josef, Rosenkranz and Terstegge, Andreas}, title = {Strategische Gestaltung von Studieng{\"a}ngen f{\"u}r die Zukunft: Ein kollaborativ entwickeltes Self-Assessment}, series = {Hochschulforum Digitalisierung - Diskussionspapier}, journal = {Hochschulforum Digitalisierung - Diskussionspapier}, publisher = {Stifterverband f{\"u}r die Deutsche Wissenschaft}, address = {Berlin}, issn = {2365-7081}, pages = {16 Seiten}, year = {2024}, abstract = {Das Diskussionspapier beschreibt einen Prozess an der FH Aachen zur Entwicklung und Implementierung eines Self-Assessment-Tools f{\"u}r Studieng{\"a}nge. Dieser Prozess zielte darauf ab, die Relevanz der Themen Digitalisierung, Internationalisierung und Nachhaltigkeit in Studieng{\"a}ngen zu st{\"a}rken. Durch Workshops und kollaborative Entwicklung mit Studiendekan:innen entstand ein Fragebogen, der zur Reflexion und strategischen Weiterentwicklung der Studieng{\"a}nge dient.}, language = {de} } @article{AliaziziOezsoyluBakhshiSichanietal.2024, author = {Aliazizi, Fereshteh and {\"O}zsoylu, Dua and Bakhshi Sichani, Soroush and Khorshid, Mehran and Glorieux, Christ and Robbens, Johan and Sch{\"o}ning, Michael J. and Wagner, Patrick}, title = {Development and Calibration of a Microfluidic, Chip-Based Sensor System for Monitoring the Physical Properties of Water Samples in Aquacultures}, series = {Micromachines}, volume = {15}, journal = {Micromachines}, number = {6}, publisher = {MDPI}, address = {Basel}, issn = {2072-666X}, doi = {10.3390/mi15060755}, year = {2024}, abstract = {In this work, we present a compact, bifunctional chip-based sensor setup that measures the temperature and electrical conductivity of water samples, including specimens from rivers and channels, aquaculture, and the Atlantic Ocean. For conductivity measurements, we utilize the impedance amplitude recorded via interdigitated electrode structures at a single triggering frequency. The results are well in line with data obtained using a calibrated reference instrument. The new setup holds for conductivity values spanning almost two orders of magnitude (river versus ocean water) without the need for equivalent circuit modelling. Temperature measurements were performed in four-point geometry with an on-chip platinum RTD (resistance temperature detector) in the temperature range between 2 °C and 40 °C, showing no hysteresis effects between warming and cooling cycles. Although the meander was not shielded against the liquid, the temperature calibration provided equivalent results to low conductive Milli-Q and highly conductive ocean water. The sensor is therefore suitable for inline and online monitoring purposes in recirculating aquaculture systems.}, language = {en} } @article{HarrisKleefeld2018, author = {Harris, Isaac and Kleefeld, Andreas}, title = {The inverse scattering problem for a conductive boundary condition and transmission eigenvalues}, series = {Applicable Analysis}, volume = {99}, journal = {Applicable Analysis}, number = {3}, publisher = {Taylor \& Francis}, address = {London}, issn = {1563-504X}, doi = {10.1080/00036811.2018.1504028}, pages = {508 -- 529}, year = {2018}, abstract = {In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside-outside duality method can be used to reconstruct the interior conductive eigenvalues.}, language = {en} } @article{KleefeldPieronek2020, author = {Kleefeld, Andreas and Pieronek, J.}, title = {Elastic transmission eigenvalues and their computation via the method of fundamental solutions}, series = {Applicable Analysis}, volume = {100}, journal = {Applicable Analysis}, number = {16}, publisher = {Taylore \& Francis}, address = {London}, issn = {1563-504X}, doi = {10.1080/00036811.2020.1721473}, pages = {3445 -- 3462}, year = {2020}, abstract = {A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.}, language = {en} } @article{BreussKleefeld2020, author = {Breuß, Michael and Kleefeld, Andreas}, title = {Implicit monotone difference methods for scalar conservation laws with source terms}, series = {Acta Mathematica Vietnamica}, volume = {45}, journal = {Acta Mathematica Vietnamica}, publisher = {Springer Singapore}, address = {Singapore}, issn = {2315-4144}, doi = {10.1007/s40306-019-00354-1}, pages = {709 -- 738}, year = {2020}, abstract = {In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970-986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.}, language = {en} } @article{AsanteAsamaniKleefeldWade2020, author = {Asante-Asamani, E.O. and Kleefeld, Andreas and Wade, B.A.}, title = {A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting}, series = {Journal of Computational Physics}, volume = {415}, journal = {Journal of Computational Physics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0021-9991}, doi = {10.1016/j.jcp.2020.109490}, year = {2020}, abstract = {A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.}, language = {en} } @incollection{Kleefeld2020, author = {Kleefeld, Andreas}, title = {Numerical calculation of interior transmission eigenvalues with mixed boundary conditions}, series = {Computational and Analytic Methods in Science and Engineering}, booktitle = {Computational and Analytic Methods in Science and Engineering}, editor = {Constanda, Christian}, publisher = {Birkh{\"a}user}, address = {Cham}, isbn = {978-3-030-48185-8 (Hardcover)}, doi = {10.1007/978-3-030-48186-5_9}, pages = {173 -- 195}, year = {2020}, abstract = {Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.}, language = {en} }