@article{LeDucConrad2020, author = {Le Duc, Huy and Conrad, Tim}, title = {A light-weight and highly flexible software system for analyzing large bio-medical datasets}, journal = {Future Generation Computer Systems}, year = {2020}, language = {en} } @article{JudsSchmidtWelleretal.2020, author = {Juds, Carmen and Schmidt, Johannes and Weller, Michael and Lange, Thorid and Conrad, Tim and Boerner, Hans}, title = {Combining Phage Display and Next-generation Sequencing for Materials Sciences: A Case Study on Probing Polypropylene Surfaces}, volume = {142}, journal = {Journal of the American Chemical Society}, number = {24}, doi = {10.1021/jacs.0c03482}, pages = {10624 -- 10628}, year = {2020}, abstract = {Phage display biopanning with Illumina next-generation sequencing (NGS) is applied to reveal insights into peptide-based adhesion domains for polypropylene (PP). One biopanning round followed by NGS selects robust PP-binding peptides that are not evident by Sanger sequencing. NGS provides a significant statistical base that enables motif analysis, statistics on positional residue depletion/enrichment, and data analysis to suppress false-positive sequences from amplification bias. The selected sequences are employed as water-based primers for PP?metal adhesion to condition PP surfaces and increase adhesive strength by 100\\% relative to nonprimed PP.}, language = {en} } @article{CvetkovicConradLie2021, author = {Cvetkovic, Nada and Conrad, Tim and Lie, Han Cheng}, title = {A Convergent Discretisation Method for Transition Path Theory for Diffusion Processes}, volume = {19}, journal = {Multiscale Modeling \& Simulation}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, doi = {10.1137/20M1329354}, pages = {242 -- 266}, year = {2021}, language = {en} } @article{GreweLiuKahletal.2021, author = {Grewe, Carl Martin and Liu, Tuo and Kahl, Christoph and Andrea, Hildebrandt and Zachow, Stefan}, title = {Statistical Learning of Facial Expressions Improves Realism of Animated Avatar Faces}, volume = {2}, journal = {Frontiers in Virtual Reality}, publisher = {Frontiers}, doi = {10.3389/frvir.2021.619811}, pages = {1 -- 13}, year = {2021}, language = {en} } @article{GlatzederKomnikAmbellanetal.2022, author = {Glatzeder, Korbinian and Komnik, Igor and Ambellan, Felix and Zachow, Stefan and Potthast, Wolfgang}, title = {Dynamic pressure analysis of novel interpositional knee spacer implants in 3D-printed human knee models}, volume = {12}, journal = {Scientific Reports}, doi = {10.1038/s41598-022-20463-6}, year = {2022}, abstract = {Alternative treatment methods for knee osteoarthritis (OA) are in demand, to delay the young (< 50 Years) patient's need for osteotomy or knee replacement. Novel interpositional knee spacers shape based on statistical shape model (SSM) approach and made of polyurethane (PU) were developed to present a minimally invasive method to treat medial OA in the knee. The implant should be supposed to reduce peak strains and pain, restore the stability of the knee, correct the malalignment of a varus knee and improve joint function and gait. Firstly, the spacers were tested in artificial knee models. It is assumed that by application of a spacer, a significant reduction in stress values and a significant increase in the contact area in the medial compartment of the knee will be registered. Biomechanical analysis of the effect of novel interpositional knee spacer implants on pressure distribution in 3D-printed knee model replicas: the primary purpose was the medial joint contact stress-related biomechanics. A secondary purpose was a better understanding of medial/lateral redistribution of joint loading. Six 3D printed knee models were reproduced from cadaveric leg computed tomography. Each of four spacer implants was tested in each knee geometry under realistic arthrokinematic dynamic loading conditions, to examine the pressure distribution in the knee joint. All spacers showed reduced mean stress values by 84-88\% and peak stress values by 524-704\% in the medial knee joint compartment compared to the non-spacer test condition. The contact area was enlarged by 462-627\% as a result of the inserted spacers. Concerning the appreciable contact stress reduction and enlargement of the contact area in the medial knee joint compartment, the premises are in place for testing the implants directly on human knee cadavers to gain further insights into a possible tool for treating medial knee osteoarthritis.}, language = {en} } @article{BeckerTeepleCharlesetal.2022, author = {Becker, Kaitlyn P and Teeple, Clark and Charles, Nicholas and Jung, Yeonsu and Baum, Daniel and Weaver, James C and Mahadevan, L. and Wood, Robert J}, title = {Active entanglement enables stochastic, topological grasping}, volume = {119}, journal = {PNAS}, number = {42}, doi = {10.1073/pnas.2209819119}, pages = {e2209819119}, year = {2022}, abstract = {Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception and motion planning. Here we circumvent the need for feedback or precise planning by using an array of fluidically-actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performance of our strategy, and use a computational framework for the collective mechanics of flexible filaments in contact with complex objects to explain our findings. Overall, our study highlights how active collective entanglement of a filament array via an uncontrolled, spatially distributed scheme provides new options for soft, adaptable grasping.}, language = {en} } @article{TuncayErdurConrad2023, author = {Tuncay, Erhun Giray and Erdur, R{\i}za Cenk and Conrad, Tim}, title = {Parallel Exchange of Randomized SubGraphs for Optimization of Network Alignment: PERSONA}, volume = {20}, journal = {IEEE/ACM Transactions on Computational Biology and Bioinformatics}, number = {3}, doi = {10.1109/TCBB.2022.3231489}, pages = {2064 -- 2077}, year = {2023}, abstract = {The aim of Network Alignment in Protein-Protein Interaction Networks is discovering functionally similar regions between compared organisms. One major compromise for solving a network alignment problem is the trade-off among multiple similarity objectives while applying an alignment strategy. An alignment may lose its biological relevance while favoring certain objectives upon others due to the actual relevance of unfavored objectives. One possible solution for solving this issue may be blending the stronger aspects of various alignment strategies until achieving mature solutions. This study proposes a parallel approach called PERSONA that allows aligners to share their partial solutions continuously while they progress. All these aligners pursue their particular heuristics as part of a particle swarm that searches for multi-objective solutions of the same alignment problem in a reactive actor environment. The actors use the stronger portion of a solution as a subgraph that they receive from leading or other actors and send their own stronger subgraphs back upon evaluation of those partial solutions. Moreover, the individual heuristics of each actor takes randomized parameter values at each cycle of parallel execution so that the problem search space can thoroughly be investigated. The results achieved with PERSONA are remarkably optimized and balanced for both topological and node similarity objectives.}, language = {de} } @article{LaguilloDiegoKiewiszMartiGomezetal.2022, author = {Laguillo-Diego, Alejandra and Kiewisz, Robert and Mart{\´i}-G{\´o}mez, Carlos and Baum, Daniel and M{\"u}ller-Reichert, Thomas and Vernos, Isabelle}, title = {MCRS1 modulates the heterogeneity of microtubule minus-end morphologies in mitotic spindles}, volume = {34}, journal = {Molecular Biology of the Cell}, number = {1}, doi = {10.1091/mbc.E22-08-0306-T}, year = {2022}, abstract = {Faithful chromosome segregation requires the assembly of a bipolar spindle, consisting of two antiparallel microtubule (MT) arrays having most of their minus ends focused at the spindle poles and their plus ends overlapping in the spindle midzone. Spindle assembly, chromosome alignment and segregation require highly dynamic MTs. The plus ends of MTs have been extensively investigated; instead, their minus end structure remains poorly characterized. Here, we used large-scale electron tomography to study the morphology of the MT minus ends in 3D-reconstructed metaphase spindles in HeLa cells. In contrast to the homogeneous open morphology of the MT plus ends at the kinetochores, we found that MT minus ends are heterogeneous showing either open or closed morphologies. Silencing the minus-end specific stabilizer, MCRS1 increased the proportion of open MT minus ends. Altogether, these data suggest a correlation between the morphology and the dynamic state of the MT ends. Taking this heterogeneity of the MT minus end morphologies into account, our work indicates an unsynchronized behavior of MTs at the spindle poles, thus laying the ground for further studies on the complexity of MT dynamics regulation.}, language = {en} } @article{MohammadzadehHNascimentoCdeLamareetal.2022, author = {Mohammadzadeh, Saeed and H. Nascimento, V{\´i}tor and C. de Lamare, Rodrigo and Hajarolasvadi, Noushin}, title = {Robust Beamforming Based on Complex-Valued Convolutional Neural Networks for Sensor Arrays}, volume = {29}, journal = {IEEE Signal Processing Letters}, doi = {10.1109/LSP.2022.3212637}, pages = {2018 -- 2021}, year = {2022}, abstract = {Robust adaptive beamforming (RAB) plays a vital role in modern communications by ensuring the reception of high-quality signals. This article proposes a deep learning approach to robust adaptive beamforming. In particular, we propose a novel RAB approach where the sample covariance matrix (SCM) is used as the input of a deep 1D Complex-Valued Convolutional Neural Network (CVCNN). The network employs complex convolutional and pooling layers, as well as a Cartesian Scaled Exponential Linear Unit activation function to directly compute the nearly-optimum weight vector through the training process and without prior knowledge about the direction of arrival of the desired signal. This means that reconstruction of the interference plus noise (IPN) covariance matrix is not required. The trained CVCNN accurately computes the nearly-optimum weight vector for data not used during training. The computed weight vector is employed to estimate the signal-to-interference plus noise ratio. Simulations show that the proposed RAB can provide performance close to that of the optimal beamformer.}, language = {en} } @article{SunkaraLewisNguyenetal.2022, author = {Sunkara, Vikram and Lewis, Angus and Nguyen, Giang T. and O'Reilly, Malgorzata M. and Bean, Nigel}, title = {A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes}, journal = {Methodology and Computing in Applied Probability}, doi = {10.1007/s11009-022-09945-2}, year = {2022}, language = {en} } @article{LangVesterFerreiraGomesetal.2022, author = {Lang, Annemarie and Vester, Antja and Ferreira-Gomes, M. and Guerra, G.M. and Heinrich, Fredrich R. and G{\"o}tzke, C.C. and Kurmies, Sebastian and Sunkara, Vikram and Durek, Pawel and Boerckel, Joel D. and Mashreghi, Mir-Farzin}, title = {PIPELINE FOR SINGLE CELL SEQUENCING OF HUMAN CHONDROCYTE PELLET CULTURES TO DELINEATE IL-1β MODULATED CHANGES IN CELL HETEROGENEITY}, volume = {30}, journal = {Osteoarthritis and Cartilage}, number = {Supplement 1}, doi = {10.1016/j.joca.2022.02.112}, pages = {S90}, year = {2022}, language = {en} } @article{SchulzePeppertSchuetteetal.2025, author = {Schulze, Kenrick and Peppert, Felix and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Chimeric U-Net - Modifying the standard U-Net towards Explainability}, volume = {338}, journal = {Artificial Intelligence}, doi = {10.1016/j.artint.2024.104240}, year = {2025}, abstract = {Healthcare guided by semantic segmentation has the potential to improve our quality of life through early and accurate disease detection. Convolutional Neural Networks, especially the U-Net-based architectures, are currently the state-of-the-art learning-based segmentation methods and have given unprecedented performances. However, their decision-making processes are still an active field of research. In order to reliably utilize such methods in healthcare, explainability of how the segmentation was performed is mandated. To date, explainability is studied and applied heavily in classification tasks. In this work, we propose the Chimeric U-Net, a U-Net architecture with an invertible decoder unit, that inherently brings explainability into semantic segmentation tasks. We find that having the restriction of an invertible decoder does not hinder the performance of the segmentation task. However, the invertible decoder helps to disentangle the class information in the latent space embedding and to construct meaningful saliency maps. Furthermore, we found that with a simple k-Nearest-Neighbours classifier, we could predict the Intersection over Union scores of unseen data, demonstrating that the latent space, constructed by the Chimeric U-Net , encodes an interpretable representation of the segmentation quality. Explainability is an emerging field, and in this work, we propose an alternative approach, that is, rather than building tools for explaining a generic architecture, we propose constraints on the architecture which induce explainability. With this approach, we could peer into the architecture to reveal its class correlations and local contextual dependencies, taking an insightful step towards trustworthy and reliable AI. Code to build and utilize the Chimeric U-Net is made available under: https://github.com/kenrickschulze/Chimeric-UNet---Half-invertible-UNet-in-Pytorch}, language = {en} } @article{AlchikhConradObermeieretal.2024, author = {Alchikh, Maren and Conrad, Tim and Obermeier, Patrick and Ma, Xiaolin and Schweiger, Brunhilde and Opota, Onya and Rath, Barbara}, title = {Disease Burden and Inpatient Management of Children with Acute Respiratory Viral Infections during the Pre-COVID Era in Germany: A Cost-of-Illness Study}, volume = {16}, journal = {Viruses}, number = {4}, doi = {10.3390/v16040507}, year = {2024}, abstract = {Respiratory viral infections (RVIs) are common reasons for healthcare consultations. The inpatient management of RVIs consumes significant resources. From 2009 to 2014, we assessed the costs of RVI management in 4776 hospitalized children aged 0-18 years participating in a quality improvement program, where all ILI patients underwent virologic testing at the National Reference Centre followed by detailed recording of their clinical course. The direct (medical or non-medical) and indirect costs of inpatient management outside the ICU ('non-ICU') versus management requiring ICU care ('ICU') added up to EUR 2767.14 (non-ICU) vs. EUR 29,941.71 (ICU) for influenza, EUR 2713.14 (non-ICU) vs. EUR 16,951.06 (ICU) for RSV infections, and EUR 2767.33 (non-ICU) vs. EUR 14,394.02 (ICU) for human rhinovirus (hRV) infections, respectively. Non-ICU inpatient costs were similar for all eight RVIs studied: influenza, RSV, hRV, adenovirus (hAdV), metapneumovirus (hMPV), parainfluenza virus (hPIV), bocavirus (hBoV), and seasonal coronavirus (hCoV) infections. ICU costs for influenza, however, exceeded all other RVIs. At the time of the study, influenza was the only RVI with antiviral treatment options available for children, but only 9.8\% of influenza patients (non-ICU) and 1.5\% of ICU patients with influenza received antivirals; only 2.9\% were vaccinated. Future studies should investigate the economic impact of treatment and prevention of influenza, COVID-19, and RSV post vaccine introduction.}, language = {en} } @article{SherrattSrivastavaAinslieetal.2024, author = {Sherratt, Katharine and Srivastava, Ajitesh and Ainslie, Kylie and Singh, David E. and Cublier, Aymar and Marinescu, Maria Cristina and Carretero, Jesus and Garcia, Alberto Cascajo and Franco, Nicolas and Willem, Lander and Abrams, Steven and Faes, Christel and Beutels, Philippe and Hens, Niel and M{\"u}ller, Sebastian and Charlton, Billy and Ewert, Ricardo and Paltra, Sydney and Rakow, Christian and Rehmann, Jakob and Conrad, Tim and Sch{\"u}tte, Christof and Nagel, Kai and Abbott, Sam and Grah, Rok and Niehus, Rene and Prasse, Bastian and Sandmann, Frank and Funk, Sebastian}, title = {Characterising information gains and losses when collecting multiple epidemic model outputs}, volume = {47}, journal = {Epidemics}, publisher = {Elsevier BV}, issn = {1755-4365}, doi = {10.1016/j.epidem.2024.100765}, year = {2024}, abstract = {Collaborative comparisons and combinations of epidemic models are used as policy-relevant evidence during epidemic outbreaks. In the process of collecting multiple model projections, such collaborations may gain or lose relevant information. Typically, modellers contribute a probabilistic summary at each time-step. We compared this to directly collecting simulated trajectories. We aimed to explore information on key epidemic quantities; ensemble uncertainty; and performance against data, investigating potential to continuously gain information from a single cross-sectional collection of model results. Methods We compared July 2022 projections from the European COVID-19 Scenario Modelling Hub. Five modelling teams projected incidence in Belgium, the Netherlands, and Spain. We compared projections by incidence, peaks, and cumulative totals. We created a probabilistic ensemble drawn from all trajectories, and compared to ensembles from a median across each model's quantiles, or a linear opinion pool. We measured the predictive accuracy of individual trajectories against observations, using this in a weighted ensemble. We repeated this sequentially against increasing weeks of observed data. We evaluated these ensembles to reflect performance with varying observed data. Results. By collecting modelled trajectories, we showed policy-relevant epidemic characteristics. Trajectories contained a right-skewed distribution well represented by an ensemble of trajectories or a linear opinion pool, but not models' quantile intervals. Ensembles weighted by performance typically retained the range of plausible incidence over time, and in some cases narrowed this by excluding some epidemic shapes. Conclusions. We observed several information gains from collecting modelled trajectories rather than quantile distributions, including potential for continuously updated information from a single model collection. The value of information gains and losses may vary with each collaborative effort's aims, depending on the needs of projection users. Understanding the differing information potential of methods to collect model projections can support the accuracy, sustainability, and communication of collaborative infectious disease modelling efforts. Data availability All code and data available on Github: https://github.com/covid19-forecast-hub-europe/aggregation-info-loss}, language = {en} } @article{KoflerWaldKolbitschetal.2024, author = {Kofler, Andreas and Wald, Christian and Kolbitsch, Christoph and von Tycowicz, Christoph and Ambellan, Felix}, title = {Joint Reconstruction and Segmentation in Undersampled 3D Knee MRI combining Shape Knowledge and Deep Learning}, volume = {69}, journal = {Physics in Medicine and Biology}, number = {9}, doi = {10.1088/1361-6560/ad3797}, year = {2024}, abstract = {Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge. In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step. We compare the proposed method to a state-of-the-art (SOTA) simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS). Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors. In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude. Remarkably, even for undersampling factors of up to R=8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images.}, language = {en} } @article{GaskinConradPavliotisetal.2024, author = {Gaskin, Thomas and Conrad, Tim and Pavliotis, Grigorios A. and Sch{\"u}tte, Christof}, title = {Neural parameter calibration and uncertainty quantification for epidemic forecasting}, volume = {19}, journal = {PLOS ONE}, number = {10}, arxiv = {http://arxiv.org/abs/2312.03147}, doi = {10.1371/journal.pone.0306704}, year = {2024}, abstract = {The recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method's learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available.}, language = {en} } @article{AmiranashviliLuedkeLietal.2024, author = {Amiranashvili, Tamaz and L{\"u}dke, David and Li, Hongwei Bran and Zachow, Stefan and Menze, Bjoern}, title = {Learning continuous shape priors from sparse data with neural implicit functions}, volume = {94}, journal = {Medical Image Analysis}, doi = {10.1016/j.media.2024.103099}, pages = {103099}, year = {2024}, abstract = {Statistical shape models are an essential tool for various tasks in medical image analysis, including shape generation, reconstruction and classification. Shape models are learned from a population of example shapes, which are typically obtained through segmentation of volumetric medical images. In clinical practice, highly anisotropic volumetric scans with large slice distances are prevalent, e.g., to reduce radiation exposure in CT or image acquisition time in MR imaging. For existing shape modeling approaches, the resolution of the emerging model is limited to the resolution of the training shapes. Therefore, any missing information between slices prohibits existing methods from learning a high-resolution shape prior. We propose a novel shape modeling approach that can be trained on sparse, binary segmentation masks with large slice distances. This is achieved through employing continuous shape representations based on neural implicit functions. After training, our model can reconstruct shapes from various sparse inputs at high target resolutions beyond the resolution of individual training examples. We successfully reconstruct high-resolution shapes from as few as three orthogonal slices. Furthermore, our shape model allows us to embed various sparse segmentation masks into a common, low-dimensional latent space — independent of the acquisition direction, resolution, spacing, and field of view. We show that the emerging latent representation discriminates between healthy and pathological shapes, even when provided with sparse segmentation masks. Lastly, we qualitatively demonstrate that the emerging latent space is smooth and captures characteristic modes of shape variation. We evaluate our shape model on two anatomical structures: the lumbar vertebra and the distal femur, both from publicly available datasets.}, language = {en} } @article{Navayazdani2024, author = {Navayazdani, Esfandiar}, title = {On Geodesics in the Spaces of Constrained Curves}, volume = {97}, journal = {Journal of Differential Geometry and its Applications}, arxiv = {http://arxiv.org/abs/2309.12883}, doi = {https://doi.org/10.1016/j.difgeo.2024.102209}, pages = {102209}, year = {2024}, abstract = {In this work, we study the geodesics of the space of certain geometrically and physically motivated subspaces of the space of immersed curves endowed with a first order Sobolev metric. This includes elastic curves and also an extension of some results on planar concentric circles to surfaces. The work focuses on intrinsic and constructive approaches.}, language = {en} } @article{HanikNavayazdanivonTycowicz2024, author = {Hanik, Martin and Navayazdani, Esfandiar and von Tycowicz, Christoph}, title = {De Casteljau's Algorithm in Geometric Data Analysis: Theory and Application}, volume = {110}, journal = {Computer Aided Geometric Design}, arxiv = {http://arxiv.org/abs/2402.07550}, doi = {10.1016/j.cagd.2024.102288}, pages = {102288}, year = {2024}, abstract = {For decades, de Casteljau's algorithm has been used as a fundamental building block in curve and surface design and has found a wide range of applications in fields such as scientific computing, and discrete geometry to name but a few. With increasing interest in nonlinear data science, its constructive approach has been shown to provide a principled way to generalize parametric smooth curves to manifolds. These curves have found remarkable new applications in the analysis of parameter-dependent, geometric data. This article provides a survey of the recent theoretical developments in this exciting area as well as its applications in fields such as geometric morphometrics and longitudinal data analysis in medicine, archaeology, and meteorology.}, language = {en} } @article{HanikSteidlvonTycowicz2024, author = {Hanik, Martin and Steidl, Gabriele and von Tycowicz, Christoph}, title = {Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs}, arxiv = {http://arxiv.org/abs/2401.14381}, year = {2024}, abstract = {We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and graph connectivity patterns. Second, we model a tangent multilayer perceptron by transferring ideas from the vector neuron framework to our general setting. Both layers are equivariant with respect to node permutations and isometries of the feature manifold. These properties have been shown to lead to a beneficial inductive bias in many deep learning tasks. Numerical examples on synthetic data as well as on triangle meshes of the right hippocampus to classify Alzheimer's disease demonstrate the very good performance of our layers.}, language = {en} }