Tips for implementing multigrid methods on domains containing holes

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised regions), via the multigrid method. We consider as a test case the Poisson equation with a nonlinear term added, as a means of illustrating the principles involved, and move to a "real world" 3-dimensional problem which is the solution of the conformally flat Hamiltonian constraint with Dirichlet and Robin boundary conditions. Using our vertex-centered multigrid code, we demonstrate globally second-order-accurate solutions of elliptic equations over domains containing holes, in two and three spatial dimensions. Keys to the success of this method are the choice of the restriction operator near the holes and definition of the location of the inner boundary. In some cases (e.g. two holes in two dimensions), more and more smoothing may be required as the mesh spacing decreases to zero; however for the resolutions currently of interest to many numerical relativists, it is feasible to maintain second order convergence by concentrating smoothing (spatially) where it is needed most. This paper, and our publicly available source code, are intended to serve as semi-pedagogical guides for those who may wish to implement similar schemes.Comment: 18 pages, 11 figures, LaTeX. Added clarifications and references re. scope of paper, mathematical foundations, relevance of work. Accepted for publication in Classical & Quantum Gravit

[Comment] Redefine statistical significance

The lack of reproducibility of scientific studies has caused growing concern over the credibility of claims of new discoveries based on “statistically significant” findings. There has been much progress toward documenting and addressing several causes of this lack of reproducibility (e.g., multiple testing, P-hacking, publication bias, and under-powered studies). However, we believe that a leading cause of non-reproducibility has not yet been adequately addressed: Statistical standards of evidence for claiming discoveries in many fields of science are simply too low. Associating “statistically significant” findings with P < 0.05 results in a high rate of false positives even in the absence of other experimental, procedural and reporting problems. For fields where the threshold for defining statistical significance is P<0.05, we propose a change to P<0.005. This simple step would immediately improve the reproducibility of scientific research in many fields. Results that would currently be called “significant” but do not meet the new threshold should instead be called “suggestive.” While statisticians have known the relative weakness of using P≈0.05 as a threshold for discovery and the proposal to lower it to 0.005 is not new (1, 2), a critical mass of researchers now endorse this change. We restrict our recommendation to claims of discovery of new effects. We do not address the appropriate threshold for confirmatory or contradictory replications of existing claims. We also do not advocate changes to discovery thresholds in fields that have already adopted more stringent standards (e.g., genomics and high-energy physics research; see Potential Objections below). We also restrict our recommendation to studies that conduct null hypothesis significance tests. We have diverse views about how best to improve reproducibility, and many of us believe that other ways of summarizing the data, such as Bayes factors or other posterior summaries based on clearly articulated model assumptions, are preferable to P-values. However, changing the P-value threshold is simple and might quickly achieve broad acceptance

Understanding complexity in the HIF signaling pathway using systems biology and mathematical modeling

Hypoxia is a common micro-environmental stress which is experienced by cells during a range of physiologic and pathophysiologic processes. The identification of the hypoxia-inducible factor (HIF) as the master regulator of the transcriptional response to hypoxia transformed our understanding of the mechanism underpinning the hypoxic response at the molecular level and identified HIF as a potentially important new therapeutic target. It has recently become clear that multiple levels of regulatory control exert influence on the HIF pathway giving the response a complex and dynamic activity profile. These include positive and negative feedback loops within the HIF pathway as well as multiple levels of crosstalk with other signaling pathways. The emerging model reflects a multi-level regulatory network that affects multiple aspects of the physiologic response to hypoxia including proliferation, apoptosis, and differentiation. Understanding the interplay between the molecular mechanisms involved in the dynamic regulation of the HIF pathway at a systems level is critically important in defining new appropriate therapeutic targets for human diseases including ischemia, cancer, and chronic inflammation. Here, we review our current knowledge of the regulatory circuits which exert influence over the HIF response and give examples of in silico model-based predictions of the dynamic behaviour of this system

HER2-enriched subtype and novel molecular subgroups drive aromatase inhibitor resistance and an increased risk of relapse in early ER+/HER2+ breast cancer

BACKGROUND: Oestrogen receptor positive/ human epidermal growth factor receptor positive (ER+/HER2+) breast cancers (BCs) are less responsive to endocrine therapy than ER+/HER2- tumours. Mechanisms underpinning the differential behaviour of ER+HER2+ tumours are poorly characterised. Our aim was to identify biomarkers of response to 2 weeks’ presurgical AI treatment in ER+/HER2+ BCs. METHODS: All available ER+/HER2+ BC baseline tumours (n=342) in the POETIC trial were gene expression profiled using BC360™ (NanoString) covering intrinsic subtypes and 46 key biological signatures. Early response to AI was assessed by changes in Ki67 expression and residual Ki67 at 2 weeks (Ki672wk). Time-To-Recurrence (TTR) was estimated using Kaplan-Meier methods and Cox models adjusted for standard clinicopathological variables. New molecular subgroups (MS) were identified using consensus clustering. FINDINGS: HER2-enriched (HER2-E) subtype BCs (44.7% of the total) showed poorer Ki67 response and higher Ki672wk (p<0.0001) than non-HER2-E BCs. High expression of ERBB2 expression, homologous recombination deficiency (HRD) and TP53 mutational score were associated with poor response and immune-related signatures with High Ki672wk. Five new MS that were associated with differential response to AI were identified. HER2-E had significantly poorer TTR compared to Luminal BCs (HR 2.55, 95% CI 1.14–5.69; p=0.0222). The new MS were independent predictors of TTR, adding significant value beyond intrinsic subtypes. INTERPRETATION: Our results show HER2-E as a standardised biomarker associated with poor response to AI and worse outcome in ER+/HER2+. HRD, TP53 mutational score and immune-tumour tolerance are predictive biomarkers for poor response to AI. Lastly, novel MS identify additional non-HER2-E tumours not responding to AI with an increased risk of relapse

Clinical Utility of Random Anti–Tumor Necrosis Factor Drug–Level Testing and Measurement of Antidrug Antibodies on the Long-Term Treatment Response in Rheumatoid Arthritis

Objective: To investigate whether antidrug antibodies and/or drug non-trough levels predict the long-term treatment response in a large cohort of patients with rheumatoid arthritis (RA) treated with adalimumab or etanercept and to identify factors influencing antidrug antibody and drug levels to optimize future treatment decisions.  Methods: A total of 331 patients from an observational prospective cohort were selected (160 patients treated with adalimumab and 171 treated with etanercept). Antidrug antibody levels were measured by radioimmunoassay, and drug levels were measured by enzyme-linked immunosorbent assay in 835 serial serum samples obtained 3, 6, and 12 months after initiation of therapy. The association between antidrug antibodies and drug non-trough levels and the treatment response (change in the Disease Activity Score in 28 joints) was evaluated.  Results: Among patients who completed 12 months of followup, antidrug antibodies were detected in 24.8% of those receiving adalimumab (31 of 125) and in none of those receiving etanercept. At 3 months, antidrug antibody formation and low adalimumab levels were significant predictors of no response according to the European League Against Rheumatism (EULAR) criteria at 12 months (area under the receiver operating characteristic curve 0.71 [95% confidence interval (95% CI) 0.57, 0.85]). Antidrug antibody–positive patients received lower median dosages of methotrexate compared with antidrug antibody–negative patients (15 mg/week versus 20 mg/week; P = 0.01) and had a longer disease duration (14.0 versus 7.7 years; P = 0.03). The adalimumab level was the best predictor of change in the DAS28 at 12 months, after adjustment for confounders (regression coefficient 0.060 [95% CI 0.015, 0.10], P = 0.009). Etanercept levels were associated with the EULAR response at 12 months (regression coefficient 0.088 [95% CI 0.019, 0.16], P = 0.012); however, this difference was not significant after adjustment. A body mass index of ≥30 kg/m2 and poor adherence were associated with lower drug levels.  Conclusion: Pharmacologic testing in anti–tumor necrosis factor–treated patients is clinically useful even in the absence of trough levels. At 3 months, antidrug antibodies and low adalimumab levels are significant predictors of no response according to the EULAR criteria at 12 months

Combined Forward-Backward Asymmetry Measurements in Top-Antitop Quark Production at the Tevatron

The CDF and D0 experiments at the Fermilab Tevatron have measured the asymmetry between yields of forward- and backward-produced top and antitop quarks based on their rapidity difference and the asymmetry between their decay leptons. These measurements use the full data sets collected in proton-antiproton collisions at a center-of-mass energy of $\sqrt s =1.96$ TeV. We report the results of combinations of the inclusive asymmetries and their differential dependencies on relevant kinematic quantities. The combined inclusive asymmetry is $A_{\mathrm{FB}}^{t\bar{t}} = 0.128 \pm 0.025$. The combined inclusive and differential asymmetries are consistent with recent standard model predictions

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio