In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin scheme involving a Domain of Dependence (DoD) stabilization to correct the update in the neighborhood of small cut cells. Thereby, it is possible to employ explicit time stepping schemes with a time step length that is independent of the size of the very small cut cells. Our error analysis is based on a general framework for error estimates for first-order linear partial differential equations that relies on consistency, boundedness, and discrete dissipation of the discrete bilinear form. We prove these properties for the space discretization involving DoD stabilization. This allows us to prove, for the fully discrete scheme, a quasi-optimal error estimate of order one half in a norm that combines the L^∞-in-time L^2-in-space norm and a seminorm that contains velocity weighted jumps. We also provide corresponding numerical results.

Despite extensive global research into genetic predisposition for severe COVID-19, knowledge on the role of rare host genetic variants and their relation to other risk factors remains limited. Here, 52 genes with prior etiological evidence were sequenced in 1,772 severe COVID-19 cases and 5,347 population-based controls from Spain/Italy. Rare deleterious TLR7 variants were present in 2.4% of young (<60 years) cases with no reported clinical risk factors (n = 378), compared to 0.24% of controls (odds ratio [OR] = 12.3, p = 1.27 x 10(-10)). Incorporation of the results of either functional assays or protein modeling led to a pronounced increase in effect size (ORmax = 46.5, p = 1.74 x 10(-15)). Association signals for the X-chromosomal gene TLR7 were also detected in the female-only subgroup, suggesting the existence of additional mechanisms beyond X-linked recessive inheritance in males. Additionally, supporting evidence was generated for a contribution to severe COVID-19 of the previously implicated genes IFNAR2, IFIH1, and TBK1. Our results refine the genetic contribution of rare TLR7 variants to severe COVID-19 and strengthen evidence for the etiological relevance of genes in the interferon signaling pathway.

The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem: standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step size is chosen based on the size of the background cells. In May and Berger (J Sci Comput 71: 919–943, 2017), the mixed explicit-implicit approach in general and MUSCL-Trap (monotonic upwind scheme for conservation laws and trapezoidal scheme) in particular have been introduced to solve this problem by using implicit time stepping on the cut cells. Theoretical and numerical results have indicated that this might lead to a loss in accuracy when switching between the explicit and implicit time stepping. In this contribution, we examine this in more detail and will prove in one dimension that the specific combination MUSCL-Trap of an explicit second-order and an implicit second-order scheme results in a fully second-order mixed scheme. As this result is unlikely to hold in two dimensions, we also introduce two new versions of mixed explicit-implicit schemes based on exchanging the explicit scheme. We present numerical tests in two dimensions where we compare the new versions with the original MUSCL-Trap scheme.

Standard numerical methods for hyperbolic PDEs require for stability a CFL-condition which implies that the time step size depends on the size of the elements of the mesh. On cut-cell meshes, elements can become arbitrarily small and thus the time step size cannot take the size of small cut-cells into account but has to be chosen based on the background mesh elements. A remedy for this is the so called DoD (domain of dependence) stabilization for which several favorable theoretical and numerical properties have been shown in one and two space dimensions. Up to now the method is restricted to stabilization of cut-cells with exactly one inflow and one outflow face, i.e. triangular cut-cells with a no-flow face. We extend the DoD stabilization to cut-cells with multiple in- and out-flow faces by properly considering the flow distribution inside the cut-cell. We further prove L2-stability for the semi-discrete formulation in space and present numerical results to validate the proposed extension.

Objective Oesophageal cancer (EC) is the sixth leading cause of cancer-related deaths. Oesophageal adenocarcinoma (EA), with Barrett's oesophagus (BE) as a precursor lesion, is the most prevalent EC subtype in the Western world. This study aims to contribute to better understand the genetic causes of BE/EA by leveraging genome wide association studies (GWAS), genetic correlation analyses and polygenic risk modelling. Design We combined data from previous GWAS with new cohorts, increasing the sample size to 16 790 BE/EA cases and 32 476 controls. We also carried out a transcriptome wide association study (TWAS) using expression data from disease-relevant tissues to identify BE/EA candidate genes. To investigate the relationship with reported BE/EA risk factors, a linkage disequilibrium score regression (LDSR) analysis was performed. BE/EA risk models were developed combining clinical/lifestyle risk factors with polygenic risk scores (PRS) derived from the GWAS meta-analysis. Results The GWAS meta-analysis identified 27 BE and/or EA risk loci, 11 of which were novel. The TWAS identified promising BE/EA candidate genes at seven GWAS loci and at five additional risk loci. The LDSR analysis led to the identification of novel genetic correlations and pointed to differences in BE and EA aetiology. Gastro-oesophageal reflux disease appeared to contribute stronger to the metaplastic BE transformation than to EA development. Finally, combining PRS with BE/EA risk factors improved the performance of the risk models. Conclusion Our findings provide further insights into BE/EA aetiology and its relationship to risk factors. The results lay the foundation for future follow-up studies to identify underlying disease mechanisms and improving risk prediction.

Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The phase interface is modeled as a sharp interface and the mass transfer across the phase boundary is modeled by a kinetic relation. Existence and uniqueness results were proven in the work by Hantke and Thein [“A general existence result for isothermal two-phase flows with phase transition,” J. Hyperbolic Differ. Equations 16, 595–637 (2019)]. Using sharp interfaces for simulating nucleation and cavitation results in the grid containing tiny cells that are several orders of magnitude smaller than the remaining grid cells. This forces explicit time stepping schemes to take tiny time steps on these cells. As a remedy, we suggest an explicit implicit domain splitting where the majority of the grid cells is treated explicitly and only the neighborhood of the tiny cells is treated implicitly. We use dual time stepping to solve the resulting small implicit systems. Our numerical results indicate that the new scheme is robust and provides significant speed-up compared to a fully explicit treatment.

Cut-cell meshes are an attractive alternative to avoid common mesh generation problems. For hyperbolic problems they pose additional challenges, as elements can become arbitrarily small, leading to prohibitive time step restrictions for explicit time stepping methods. To alleviate this small cell problem we consider a particular stabilization method, the Domain of Dependence (DoD) method. So far, while posessing many favorable theoretical properties, in two dimensions the DoD method was essentially restricted to the transport equation. In this work we extend the DoD method to the acoustic wave equation in two dimensions and provide numerical results for validation.

We investigate the spatio-temporal structure of the most likely configurations realizing extremely high vorticity or strain in the stochastically forced three-dimensional incompressible Navier-Stokes equations. Most likely configurations are computed by numerically finding the highest probability velocity field realizing an extreme constraint as solution of a large optimization problem. High-vorticity configurations are identified as pinched vortex filaments with swirl, while high-strain configurations correspond to counter-rotating vortex rings. We additionally observe that the most likely configurations for vorticity and strain spontaneously break their rotational symmetry for extremely high observable values. Instanton calculus and large deviation theory allow us to show that these maximum likelihood realizations determine the tail probabilities of the observed quantities. In particular, we are able to demonstrate that artificially enforcing rotational symmetry for large strain configurations leads to a severe underestimate of their probability, as it is dominated in likelihood by an exponentially more likely symmetry-broken vortex-sheet configuration. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

When solving time-dependent hyperbolic conservation laws on cut cell meshes one has to overcome the small cell problem: standard explicit time stepping is not stable on small cut cells if the time step is chosen with respect to larger background cells. The domain of dependence (DoD) stabilization is designed to solve this problem in a discontinuous Galerkin framework. It adds a penalty term to the space discretization that restores proper domains of dependence. In this contribution we introduce the DoD stabilization for solving the advection equation in 2d with higher order. We show an L2 stability result for the stabilized semi-discrete scheme for arbitrary polynomial degrees p and provide numerical results for convergence tests indicating orders of p + 1 in the L1 norm and between $$p+\frac 1 2$$ and p + 1 in the L∞ norm.

In this work, we present the Domain of Dependence (DoD) stabilization for systems of hyperbolic conservation laws in one space dimension. The base scheme uses a method of lines approach consisting of a discontinuous Galerkin scheme in space and an explicit strong stability preserving Runge-Kutta scheme in time. When applied on a cut cell mesh with a time step length that is appropriate for the size of the larger background cells, one encounters stability issues. The DoD stabilization consists of penalty terms that are designed to address these problems by redistributing mass between the inflow and outflow neighbors of small cut cells in a physical way. For piecewise constant polynomials in space and explicit Euler in time, the stabilized scheme is monotone for scalar problems. For higher polynomial degrees $p$, our numerical experiments show convergence orders of $p+1$ for smooth flow and robust behavior in the presence of shocks.

ABSTRACT Given the highly variable clinical phenotype of Coronavirus disease 2019 (COVID-19), a deeper analysis of the host genetic contribution to severe COVID-19 is important to improve our understanding of underlying disease mechanisms. Here, we describe an extended GWAS meta-analysis of a well-characterized cohort of 3,260 COVID-19 patients with respiratory failure and 12,483 population controls from Italy, Spain, Norway and Germany/Austria, including stratified analyses based on age, sex and disease severity, as well as targeted analyses of chromosome Y haplotypes, the human leukocyte antigen (HLA) region and the SARS-CoV-2 peptidome. By inversion imputation, we traced a reported association at 17q21.31 to a highly pleiotropic ∼0.9-Mb inversion polymorphism and characterized the potential effects of the inversion in detail. Our data, together with the 5 th release of summary statistics from the COVID-19 Host Genetics Initiative, also identified a new locus at 19q13.33, including NAPSA , a gene which is expressed primarily in alveolar cells responsible for gas exchange in the lung.

Genome-wide association studies (GWASs) have identified hundreds of loci associated with Crohn’s disease (CD). However, as with all complex diseases, robust identification of the genes dysregulated by noncoding variants typically driving GWAS discoveries has been challenging. Here, to complement GWASs and better define actionable biological targets, we analyzed sequence data from more than 30,000 patients with CD and 80,000 population controls. We directly implicate ten genes in general onset CD for the first time to our knowledge via association to coding variation, four of which lie within established CD GWAS loci. In nine instances, a single coding variant is significantly associated, and in the tenth, ATG4C, we see additionally a significantly increased burden of very rare coding variants in CD cases. In addition to reiterating the central role of innate and adaptive immune cells as well as autophagy in CD pathogenesis, these newly associated genes highlight the emerging role of mesenchymal cells in the development and maintenance of intestinal inflammation. Large-scale sequence-based analyses identify novel risk variants and susceptibility genes for Crohn’s disease, and implicate mesenchymal cell-mediated intestinal homeostasis in disease etiology.

To elucidate cross-sectional patterns and longitudinal changes of oral and stool microbiota in multiple sclerosis (MS) patients and the effect of B-cell depletion. We conducted an observational, longitudinal clinical cohort study analysing four timepoints over 12 months in 36 MS patients, of whom 22 initiated B-cell depleting therapy with ocrelizumab and a healthy control group. For microbiota analysis of the oral cavity and the gut, provided stool and oral swab samples underwent 16S rDNA sequencing and subsequent bioinformatic analyses. Oral microbiota-patterns exhibited a reduced alpha-diversity and unique differential microbiota changes compared to stool such as increased levels of Proteobacteria and decreased abundance of Actinobacteria. Following B-cell depletion, we observed increased alpha-diversity in the gut and the oral cavity as well as a long-term sustained reduction of pro-inflammatory Gram-negative bacteria (e.g., Escherichia/Shigella). MS patients have altered stool and oral microbiota diversity patterns compared to healthy controls, which are most pronounced in patients with higher disease activity and disability. Therapeutic B-cell depletion is associated with persisting regression of these changes. Whether these microbial changes are unspecific side-effects of B-cell depletion or indirectly modulate MS disease activity and progression is currently unknown and necessitates further investigations.

Background Human well-being has been linked to the composition and functional capacity of the intestinal microbiota. As regular exercise is known to improve human health, it is not surprising that exercise was previously described to positively modulate the gut microbiota, too. However, most previous studies mainly focused on either elite athletes or animal models. Thus, we conducted a randomised intervention study that focused on the effects of different types of training (endurance and strength) in previously physically inactive, healthy adults in comparison to controls that did not perform regular exercise. Overall study duration was ten weeks including six weeks of intervention period. In addition to 16S rRNA gene amplicon sequencing of longitudinally sampled faecal material of participants (six time points), detailed body composition measurements and analysis of blood samples (at baseline and after the intervention) were performed to obtain overall physiological changes within the intervention period. Activity tracker devices (wrist-band wearables) provided activity status and sleeping patterns of participants as well as exercise intensity and heart measurements. Results Different biometric responses between endurance and strength activities were identified, such as a significant increase of lymphocytes and decrease of mean corpuscular haemoglobin concentration (MCHC) only within the strength intervention group. In the endurance group, we observed a significant reduction in hip circumference and an increase in physical working capacity (PWC). Though a large variation of microbiota changes were observed between individuals of the same group, we did not find specific collective alterations in the endurance nor the strength groups, arguing for microbiome variations specific to individuals, and therefore, were not captured in our analysis. Conclusions We could show that different types of exercise have distinct but moderate effects on the overall physiology of humans and very distinct microbial changes in the gut. The observed overall changes during the intervention highlight the importance of physical activity on well-being. Future studies should investigate the effect of exercise on a longer timescale, investigate different training intensities and consider high-resolution shotgun metagenomics technology. Trial registration DRKS, DRKS00015873 . Registered 12 December 2018; Retrospectively registered.

AbstractGenome-wide association studies (GWAS) have identified hundreds of loci associated with Crohns disease (CD), however, as with all complex diseases, deriving pathogenic mechanisms from these non-coding GWAS discoveries has been challenging. To complement GWAS and better define actionable biological targets, we analysed sequenced data from more than 30,000 CD patients and 80,000 population controls. We observe rare coding variants in established CD susceptibility genes as well as ten genes where coding variation directly implicates the gene in disease risk for the first time.

We consider one-dimensional distributed optimal control problems with the state equation being given by the viscous Burgers equation. We discretize using a space-time discontinuous Galerkin approach. We use upwind flux in time and the symmetric interior penalty approach for discretizing the viscous term. Our focus is on the discretization of the convection terms. We aim for using conservative discretizations for the convection terms in both the state and the adjoint equation, while ensuring that the approaches of discretize-then-optimize and optimize-then-discretize commute. We show that this is possible if the arising source term in the adjoint equation is discretized properly, following the ideas of well-balanced discretizations for balance laws. We support our findings by numerical results.

Objective Impaired lysosomal degradation of alpha-synuclein and other cellular constituents may play an important role in Parkinson's disease (PD). Rare genetic variants in the glucocerebrosidase (GBA) gene were consistently associated with PD. Here we examine the association between rare variants in lysosomal candidate genes and PD. Methods We investigated the association between PD and rare genetic variants in 23 lysosomal candidate genes in 4096 patients with PD and an equal number of controls using pooled targeted next-generation DNA sequencing. Genewise association of rare variants in cases or controls was analyzed using the optimized sequence kernel association test with Bonferroni correction for the 23 tested genes. Results We confirm the association of rare variants inGBAwith PD and report novel associations for rare variants inATP13A2,LAMP1,TMEM175, andVPS13C. Conclusion Rare variants in selected lysosomal genes, first and foremostGBA, are associated with PD. Rare variants inATP13A2andVPC13Cpreviously linked to monogenic PD and more common variants inTMEM175andVPS13Cpreviously linked to sporadic PD in genome-wide association studies are associated with PD. (c) 2020 International Parkinson and Movement Disorder Society

BACKGROUND:There is considerable variation in disease behavior among patients infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes coronavirus disease 2019 (Covid-19). Genomewide association analysis may allow for the identification of potential genetic factors involved in the development of Covid-19.METHODS:We conducted a genomewide association study involving 1980 patients with Covid-19 and severe disease (defined as respiratory failure) at seven hospitals in the Italian and Spanish epicenters of the SARS-CoV-2 pandemic in Europe. After quality control and the exclusion of population outliers, 835 patients and 1255 control participants from Italy and 775 patients and 950 control participants from Spain were included in the final analysis. In total, we analyzed 8,582,968 single-nucleotide polymorphisms and conducted a meta-analysis of the two case-control panels.RESULTS:We detected cross-replicating associations with rs11385942 at locus 3p21.31 and with rs657152 at locus 9q34.2, which were significant at the genomewide level (P<5×10-8) in the meta-analysis of the two case-control panels (odds ratio, 1.77; 95% confidence interval [CI], 1.48 to 2.11; P = 1.15×10-10; and odds ratio, 1.32; 95% CI, 1.20 to 1.47; P = 4.95×10-8, respectively). At locus 3p21.31, the association signal spanned the genes SLC6A20, LZTFL1, CCR9, FYCO1, CXCR6 and XCR1. The association signal at locus 9q34.2 coincided with the ABO blood group locus; in this cohort, a blood-group-specific analysis showed a higher risk in blood group A than in other blood groups (odds ratio, 1.45; 95% CI, 1.20 to 1.75; P = 1.48×10-4) and a protective effect in blood group O as compared with other blood groups (odds ratio, 0.65; 95% CI, 0.53 to 0.79; P = 1.06×10-5).CONCLUSIONS:We identified a 3p21.31 gene cluster as a genetic susceptibility locus in patients with Covid-19 with respiratory failure and confirmed a potential involvement of the ABO blood-group system. (Funded by Stein Erik Hagen and others.).