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Density of mitotic figures in histologic sections is a prognostically relevant characteristic for many tumours. Due to high inter-pathologist variability, deep learning-based algorithms are a promising solution to improve tumour prognostication. Pathologists are the gold standard for database development, however, labelling errors may hamper development of accurate algorithms. In the present work we evaluated the benefit of multi-expert consensus (n = 3, 5, 7, 9, 11) on algorithmic performance. While training with individual databases resulted in highly variable F$_1$ scores, performance was notably increased and more consistent when using the consensus of three annotators. Adding more annotators only resulted in minor improvements. We conclude that databases by few pathologists and high label accuracy may be the best compromise between high algorithmic performance and time investment., Comment: Due to data inconsistencies experiments had to be repeated with a reduced number of annotators (17 in version 1). All findings of the previous version were reproducible. 7 pages, 2 figures, accepted at BVM workshop 2021

Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement strategies for triangular and quadrilateral meshes implemented in the ameshref package (Funken and Schmidt 2018, 2019). The ameshref package is a MATLAB-toolbox for research and teaching purposes which offers the user a certain flexibility in the REFINE step of an adaptive finite element method but can also be used in other contexts like computer graphics. This toolbox is now be extended by the coarsening option. In ameshref, no explicit information about the refinement process is stored, but is instead implicit in the data structure. In this work, we present coarsening algorithms that use easy-to-verify criteria to coarsen adaptively generated meshes by exploiting the data structure. Thereby, the desired properties are guaranteed and computational efficiency is maintained. A MATLAB implementation and some numerical examples are discussed in this work and are included in full in the toolbox ameshcoars (Funken and Schmidt 2020)., Comment: 29 pages, 15 figures, 8 algorithms, 8 listings

Current In-Vehicle Networks (IVNs) connect Electronic Control Units (ECUs) via domain busses. A gateway forwards messages between these domains. Automotive Ethernet emerges as a flat, high-speed backbone technology for IVNs that carries the various control flows within Ethernet frames. Recently, Software-Defined-Networking (SDN) has been identified as a useful building block of the vehicular domain, as it allows the differentiation of packets based on all header fields and thus can isolate unrelated control flows. In this work, we systematically explore the different strategies for integrating automotive control flows in switched Ether-networks and analyze their security impact for a software-defined IVN. We discuss how control flow identifiers can be embedded on different layers resulting in a range of solutions from fully exposed embedding to deep encapsulation. We evaluate these strategies in a realistic IVN based on the communication matrix of a production grade vehicle, which we map into a modern Ethernet topology. We find that visibility of automotive control flows within packet headers is essential for the network infrastructure to enable isolation and access control. With an exposed embedding, the SDN backbone can establish and survey trust zones within the IVN and largely reduce the attack surface of connected cars. An exposed embedding strategy also minimizes communication expenses.

The $L^2$-orthogonal projection $\Pi_h:L^2(\Omega)\rightarrow\mathbb{V}_h$ onto a finite element (FE) space $\mathbb{V}_h$ is called $H^1$-stable iff $\|\nabla\Pi_h u\|_{L^2(\Omega)}\leq C\|u\|_{H^1(\Omega)}$, for any $u\in H^1(\Omega)$ with a positive constant $C\neq C(h)$ independent of the mesh size $h>0$. In this work, we discuss local criteria for the $H^1$-stability of adaptively refined meshes. We show that adaptive refinement strategies for quadrilateral meshes in 2D (Q-RG and Q-RB), introduced originally in Bank et al. 1982 and Kobbelt 1996, are $H^1$-stable for FE spaces of polynomial degree $p=2,\ldots,9$., Comment: 19 pages, 4 figures, 6 tables

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its counterpart - coarsening. In general, coarsening algorithms are mostly based on an explicitly given refinement history. In this work, we present a coarsening algorithm on adaptive red-green-blue meshes in two dimensions without explicitly knowing the refinement history. To this end, we examine the local structure of these meshes, find an easy-to-verify criterion to adaptively coarsen red-green-blue meshes and prove that this criterion generates meshes with the desired properties. We present a MATLAB implementation built on the red-green-blue refinement routine of the ameshref-package., Comment: 22 pages, 25 figures, 3 tables, 2 listings

Manual count of mitotic figures, which is determined in the tumor region with the highest mitotic activity, is a key parameter of most tumor grading schemes. It can be, however, strongly dependent on the area selection due to uneven mitotic figure distribution in the tumor section.We aimed to assess the question, how significantly the area selection could impact the mitotic count, which has a known high inter-rater disagreement. On a data set of 32 whole slide images of H&E-stained canine cutaneous mast cell tumor, fully annotated for mitotic figures, we asked eight veterinary pathologists (five board-certified, three in training) to select a field of interest for the mitotic count. To assess the potential difference on the mitotic count, we compared the mitotic count of the selected regions to the overall distribution on the slide.Additionally, we evaluated three deep learning-based methods for the assessment of highest mitotic density: In one approach, the model would directly try to predict the mitotic count for the presented image patches as a regression task. The second method aims at deriving a segmentation mask for mitotic figures, which is then used to obtain a mitotic density. Finally, we evaluated a two-stage object-detection pipeline based on state-of-the-art architectures to identify individual mitotic figures. We found that the predictions by all models were, on average, better than those of the experts. The two-stage object detector performed best and outperformed most of the human pathologists on the majority of tumor cases. The correlation between the predicted and the ground truth mitotic count was also best for this approach (0.963 to 0.979). Further, we found considerable differences in position selection between pathologists, which could partially explain the high variance that has been reported for the manual mitotic count., Comment: 13 pages, 7 figures