Publications

In any spacecraft mission it is vital to have knowledge about the attitude. In this context, multiple ways can be employed to estimate the current attitude of the spacecraft. As temperature sensors are cheap and lightweight they appear to be a viable alternative. A method is investigated to estimate the attitude of a spacecraft based on twelve temperature sensors in a cuboid configuration. The method relies on a proposed mathematical model governing the temperature and attitude dynamics and employs non-linear observer design. Further, it is investigated if the attitude estimation is still possible if some of the sensors are malfunctioning. The proposed algorithms are validated using real mission data.

Purpose: Image-based blood flow simulations are increasingly used to investigate the hemodynamics in intracranial aneurysms (IAs). However, a strong variability in segmentation approaches as well as the absence of individualized boundary conditions (BCs) influence the quality of these simulation results leading to imprecision and decreased reliability. This study aims to analyze these influences on relevant hemodynamic parameters within IAs. Methods: As a follow-up study of an international multiple aneurysms challenge, the segmentation results of five IAs differing in size and location were investigated. Specifically, five possible outlet BCs were considered in each of the IAs. These are comprised of the zero-pressure condition (BC1), a flow distribution based on Murray’s law with the exponents n = 2 (BC2) and n = 3 (BC3) as well as two advanced flow-splitting models considering the real vessels by including circular cross sections (BC4) or anatomical cross sections (BC5), respectively. In total, 120 time-dependent blood flow simulations were analyzed qualitatively and quantitatively, focusing on five representative intra-aneurysmal flow and five shear parameters such as vorticity and wall shear stress. Results: The outlet BC variation revealed substantial differences. Higher shear stresses (up to Δ9.69 Pa), intrasaccular velocities (up to Δ0.15 m/s) and vorticities (up to Δ629.22 1/s) were detected when advanced flow-splitting was applied compared to the widely used zero-pressure BC. The tendency of outlets BCs to over- or underestimate hemodynamic parameters is consistent across different segmentations of a single aneurysm model. Segmentation-induced variability reaches Δ19.58 Pa, Δ0.42 m/s and Δ957.27 1/s, respectively. Excluding low fidelity segmentations, however, (a) reduces the deviation drastically (>43%) and (b) leads to a lower impact of the outlet BC on hemodynamic predictions. Conclusion: With a more realistic lumen segmentation, the influence of the BC on the resulting hemodynamics is decreased. A realistic lumen segmentation can be ensured, e.g., by using high-resolved 2D images. Furthermore, the selection of an advanced outflow-splitting model is advised and the use of a zero-pressure BC and BC based on Murray’s law with exponent n = 3 should be avoided.

Deep learning is increasingly being proposed for detecting neurological and psychiatric diseases from electroencephalogram (EEG) data but the method is prone to inadvertently incorporate biases from training data and exploit illegitimate patterns. The recent demonstration that deep learning can detect the sex from EEG implies potential sex-related biases in deep learning-based disease detectors for the many diseases with unequal prevalence between males and females. In this work, we present the male- and female-typical patterns used by a convolutional neural network that detects the sex from clinical EEG (81% accuracy in a separate test set with 142 patients). We considered neural sources, anatomical differences, and non-neural artifacts as sources of differences in the EEG curves. Using EEGs from 1140 patients, we found electrocardiac artifacts to be leaking into the supposedly brain activity-based classifiers. Nevertheless, the sex remained detectable after rejecting heart-related and other artifacts. In the cleaned data, EEG topographies were critical to detect the sex, but waveforms and frequencies were not. None of the traditional frequency bands was particularly important for sex detection. We were able to determine the sex even from EEGs with shuffled time points and therewith completely destroyed waveforms. Researchers should consider neural and non-neural sources as potential origins of sex differences in their data, they should maintain best practices of artifact rejection, even when datasets are large, and they should test their classifiers for sex biases.

In this paper, an extension of an algorithm for the implicit discretization of a super-twisting sliding mode observer is presented. Implicit and explicit discretization algorithms for homogeneous differentiators, where no physical model information is considered, are investigated in literature. This article studies the behavior when considering models of a rather general class of nonlinear systems. The discrete equations of the super-twisting observer are reformulated as generalized equation and an algorithm for the step-by-step solution is given. The uniqueness of the derived algorithm is investigated with an equivalent variational inequality formulation which is derived for a class of nonlinear systems. Furthermore, a semi-implicit predictor-corrector discretization is presented which is an approximation method for the presented algorithms and allows an explicit implementation in practical applications. Accuracy properties under noise and sampling are given. The algorithm is applied on two mechanical example systems taken from practice.

We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are given as terms while moduli and thresholds are given explicitly). Our main result shows that satisfaction for this logic is decidable in two-fold exponential space. If only threshold- and exact-counting quantifiers are allowed, we prove an upper bound of alternating two-fold exponential time with linearly many alternations. This latter result almost matches Berman's exact complexity of first-order logic without counting quantifiers. To obtain these results, we first translate threshold- and exact-counting quantifiers into classical first-order logic in polynomial time (which already proves the second result). To handle the remaining modulo-counting quantifiers for tuples, we first reduce them in doubly exponential time to modulo-counting quantifiers for single elements. For these quantifiers, we provide a quantifier elimination procedure similar to Reddy and Loveland's procedure for first-order logic and analyse the growth of coefficients, constants, and moduli appearing in this process. The bounds obtained this way allow to restrict quantification in the original formula to integers of bounded size which then implies the first result mentioned above. Our logic is incomparable with the logic considered by Chistikov et al. in 2022. They allow more general counting operations in quantifiers, but only unary quantifiers. The move from unary to non-unary quantifiers is non-trivial, since, e.g., the non-unary version of the Härtig quantifier results in an undecidable theory.