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Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes(Communications on Applied Mathematics and Computation, Springer Science and Business Media LLC, 2021-07-31) [Article]Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible Euler equations. The issue is related to missing local linear stability, i.e., the stability of the discretization towards perturbations added to a stable base flow. This is strongly related to an anti-diffusion mechanism, that is inherent in entropy-conserving two-point fluxes, which are a key ingredient for the high-order discontinuous Galerkin extension. In this paper, we investigate if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations. Pressure equilibrium preservation describes the property of a discretization to keep pressure and velocity constant for pure density wave propagation. We present the full theoretical derivation, analysis, and show corresponding numerical results to underline our findings. In addition, we characterize numerical fluxes for the Euler equations that are entropy-conservative, kinetic-energy-preserving, pressure-equilibrium-preserving, and have a density flux that does not depend on the pressure. The source code to reproduce all numerical experiments presented in this article is available online (10.5281/zenodo.4054366).
The emergence and transmission of COVID-19 in European countries, 2019–2020: a comprehensive review of timelines, cases and containment(International Health, Oxford University Press (OUP), 2021-07-31) [Article]When it emerged in late 2019, COVID-19 was carried via travelers to Germany, France and Italy, where freedom of movement accelerated its transmission throughout Europe. However, effective non-pharmaceutical interventions introduced by European governments led to containment of the rapid increase in cases within European nations. Electronic searches were performed to obtain the number of confirmed cases, incident rates and non-pharmaceutical government measures for each European country. The spread and impact of non-pharmaceutical interventions throughout Europe were assessed and visualized. Specifically, heatmaps were used to represent the number of confirmed cases and incident rates for each of the countries over time. In addition, maps were created showing the number of confirmed cases and incident rates in Europe on three different dates (15 March, 15 April and 15 May 2020), which allowed us to assess the geographic and temporal patterns of the disease.
Enhancing Adversarial Robustness via Test-time Transformation Ensembling(arXiv, 2021-07-29) [Preprint]Deep learning models are prone to being fooled by imperceptible perturbations known as adversarial attacks. In this work, we study how equipping models with Test-time Transformation Ensembling (TTE) can work as a reliable defense against such attacks. While transforming the input data, both at train and test times, is known to enhance model performance, its effects on adversarial robustness have not been studied. Here, we present a comprehensive empirical study of the impact of TTE, in the form of widely-used image transforms, on adversarial robustness. We show that TTE consistently improves model robustness against a variety of powerful attacks without any need for re-training, and that this improvement comes at virtually no trade-off with accuracy on clean samples. Finally, we show that the benefits of TTE transfer even to the certified robustness domain, in which TTE provides sizable and consistent improvements.
Shape Matching and Map Space Exploration via Functional Maps(2021-07-29) [Dissertation]
Advisor: Wonka, Peter
Committee members: Ovsjanikov, Maks; Ghanem, Bernard; Pottmann, Helmut; Solomon, JustinComputing correspondences or maps between shapes is one of the oldest problems in Computer Graphics and Geometry Processing with a wide range of applications from deformation transfer, statistical shape analysis, to co-segmentation and exploration among a myriad others. A good map is supposed to be continuous, as-bijective-as-possible, accurate if there are ground-truth corresponding landmarks given, and lowdistortionw.r.t. different measures, for example as-conformal-as-possible to preserve the angles. This thesis contributes to the area of non-rigid shape matching and map space exploration in Geometry Processing. Specifically, we consider the discrete setting, where the shapes are discretized as amesh structure consisting of vertices, edges, and polygonal faces. In the simplest case, we only consider the graph structure with vertices and edges only. In this thesis, we design algorithms to compute soft correspondences between discrete shapes. Specifically, (1)we propose different regularizers, including orientation-preserving operator and the Resolvent Laplacian Commutativity operator, to promote the shape correspondences in the functional map framework. (2) We propose two refinement methods, namely BCICP and ZoomOut, to improve the accuracy, continuity, bijectivity and the coverage of given point-wisemaps. (3)We propose a tree structure and an enumeration algorithm to explore the map space between a pair of shapes that can update multiple high-quality dense correspondences.
Predicting the environmental suitability for onchocerciasis in Africa as an aid to elimination planning.(PLoS neglected tropical diseases, Public Library of Science (PLoS), 2021-07-28) [Article]Recent evidence suggests that, in some foci, elimination of onchocerciasis from Africa may be feasible with mass drug administration (MDA) of ivermectin. To achieve continental elimination of transmission, mapping surveys will need to be conducted across all implementation units (IUs) for which endemicity status is currently unknown. Using boosted regression tree models with optimised hyperparameter selection, we estimated environmental suitability for onchocerciasis at the 5 × 5-km resolution across Africa. In order to classify IUs that include locations that are environmentally suitable, we used receiver operating characteristic (ROC) analysis to identify an optimal threshold for suitability concordant with locations where onchocerciasis has been previously detected. This threshold value was then used to classify IUs (more suitable or less suitable) based on the location within the IU with the largest mean prediction. Mean estimates of environmental suitability suggest large areas across West and Central Africa, as well as focal areas of East Africa, are suitable for onchocerciasis transmission, consistent with the presence of current control and elimination of transmission efforts. The ROC analysis identified a mean environmental suitability index of 0·71 as a threshold to classify based on the location with the largest mean prediction within the IU. Of the IUs considered for mapping surveys, 50·2% exceed this threshold for suitability in at least one 5 × 5-km location. The formidable scale of data collection required to map onchocerciasis endemicity across the African continent presents an opportunity to use spatial data to identify areas likely to be suitable for onchocerciasis transmission. National onchocerciasis elimination programmes may wish to consider prioritising these IUs for mapping surveys as human resources, laboratory capacity, and programmatic schedules may constrain survey implementation, and possibly delaying MDA initiation in areas that would ultimately qualify.