Stefan Müller

Stefan Müller, Florian Schweiger

We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the square and the edges and corners of the cube. The main idea is to transfer estimates for the continuous bilaplacian using a new discrete compactness argument and a discrete version of the Cacciopoli (or reverse Poincaré) inequality. One application that we have in mind is the study of entropic repulsion for the membrane model from statistical physics.

Anna Severin, Michaela Strinzel, Matthias Egger et al.

The journal impact factor (JIF) is often equated with journal quality and the quality of the peer review of the papers submitted to the journal. We examined the association between the content of peer review and JIF by analysing 10,000 peer review reports submitted to 1,644 medical and life sciences journals. Two researchers hand-coded a random sample of 2,000 sentences. We then trained machine learning models to classify all 187,240 sentences as contributing or not contributing to content categories. We examined the association between ten groups of journals defined by JIF deciles and the content of peer reviews using linear mixed-effects models, adjusting for the length of the review. The JIF ranged from 0.21 to 74.70. The length of peer reviews increased from the lowest (median number of words 185) to the JIF group (387 words). The proportion of sentences allocated to different content categories varied widely, even within JIF groups. For thoroughness, sentences on 'Materials and Methods' were more common in the highest JIF journals than in the lowest JIF group (difference of 7.8 percentage points; 95% CI 4.9 to 10.7%). The trend for 'Presentation and Reporting' went in the opposite direction, with the highest JIF journals giving less emphasis to such content (difference -8.9%; 95% CI -11.3 to -6.5%). For helpfulness, reviews for higher JIF journals devoted less attention to 'Suggestion and Solution' and provided fewer Examples than lower impact factor journals. No, or only small differences were evident for other content categories. In conclusion, peer review in journals with higher JIF tends to be more thorough in discussing the methods used but less helpful in terms of suggesting solutions and providing examples. Differences were modest and variability high, indicating that the JIF is a bad predictor for the quality of peer review of an individual manuscript.

Lukas Stappen, Xinchen Du, Vincent Karas et al.

Systems for the automatic recognition and detection of automotive parts are crucial in several emerging research areas in the development of intelligent vehicles. They enable, for example, the detection and modelling of interactions between human and the vehicle. In this paper, we quantitatively and qualitatively explore the efficacy of deep learning architectures for the classification and localisation of 29 interior and exterior vehicle regions on three novel datasets. Furthermore, we experiment with joint and transfer learning approaches across datasets and point out potential applications of our systems. Our best network architecture achieves an F1 score of 93.67 % for recognition, while our best localisation approach utilising state-of-the-art backbone networks achieve a mAP of 63.01 % for detection. The MuSe-CAR-Part dataset, which is based on a large variety of human-car interactions in videos, the weights of the best models, and the code is publicly available to academic parties for benchmarking and future research.

Stefan Müller, Florian Schweiger, Endre Süli

We prove an optimal order error bound in the discrete $H^2(Ω)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n \in \{2,\dots,7\}$, whose generalized solution belongs to the Sobolev space $H^s(Ω) \cap H^2_0(Ω)$, for $\frac{1}{2} \max(5,n) < s \leq 4$, where $Ω= (0,1)^n$. The result extends the range of the Sobolev index $s$ in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of $H^s(Ω)$ into $C(\overlineΩ)$ in $n$ space dimensions.