A precise definition of reduction of partial differential equations

We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equation in (1+3) dimensions. The conditional symmetry approach when applied to the equation in question yields a number of non-Lie reductions which are far-reaching generalization of the well-known symmetry reductions of the nonlinear wave equations.Comment: LaTeX, 21 page

A CHecklist for statistical Assessment of Medical Papers (the CHAMP statement): explanation and elaboration

Misuse of statistics in medical and sports science research is common and may lead to detrimental consequences to healthcare. Many authors, editors and peer reviewers of medical papers will not have expert knowledge of statistics or may be unconvinced about the importance of applying correct statistics in medical research. Although there are guidelines on reporting statistics in medical papers, a checklist on the more general and commonly seen aspects of statistics to assess when peer-reviewing an article is needed. In this article, we propose a CHecklist for statistical Assessment of Medical Papers (CHAMP) comprising 30 items related to the design and conduct, data analysis, reporting and presentation, and interpretation of a research paper. While CHAMP is primarily aimed at editors and peer reviewers during the statistical assessment of a medical paper, we believe it will serve as a useful reference to improve authors’ and readers’ practice in their use of statistics in medical research. We strongly encourage editors and peer reviewers to consult CHAMP when assessing manuscripts for potential publication. Authors also may apply CHAMP to ensure the validity of their statistical approach and reporting of medical research, and readers may consider using CHAMP to enhance their statistical assessment of a paper

CHecklist for statistical Assessment of Medical Papers: the CHAMP statement

Misuse of statistics in medical and sports science research is common and may lead to detrimental consequences to healthcare. Many authors, editors and peer reviewers of medical papers will not have expert knowledge of statistics or may be unconvinced about the importance of applying correct statistics in medical research. Although there are guidelines on reporting statistics in medical papers, a checklist on the more general and commonly seen aspects of statistics to assess when peer-reviewing an article is needed. In this article, we propose a CHecklist for statistical Assessment of Medical Papers (CHAMP) comprising 30 items related to the design and conduct, data analysis, reporting and presentation, and interpretation of a research paper. While CHAMP is primarily aimed at editors and peer reviewers during the statistical assessment of a medical paper, we believe it will serve as a useful reference to improve authors’ and readers’ practice in their use of statistics in medical research. We strongly encourage editors and peer reviewers to consult CHAMP when assessing manuscripts for potential publication. Authors also may apply CHAMP to ensure the validity of their statistical approach and reporting of medical research, and readers may consider using CHAMP to enhance their statistical assessment of a paper

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

Observations have established that extremely compact, massive objects are common in the universe. It is generally accepted that these objects are black holes. As observations improve, it becomes possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or with gravitational-waves) and to test whether they have the characteristics of black hole orbits in general relativity. Such measurements can be used to map the spacetime of a massive compact object, testing whether the object's multipoles satisfy the strict constraints of the black hole hypothesis. Such a test requires that we compare against objects with the ``wrong'' multipole structure. In this paper, we present tools for constructing bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. The spacetimes which we present are good deep into the strong field of the object -- we do not use a large r expansion, except to make contact with weak field intuition. Also, our spacetimes reduce to the black hole spacetimes of general relativity when the ``bumpiness'' is set to zero. We propose bumpy black holes as the foundation for a null experiment: if black hole candidates are the black holes of general relativity, their bumpiness should be zero. By comparing orbits in a bumpy spacetime with those of an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are the black holes of general relativity. (Abridged)Comment: 16 pages + 2 appendices + 3 figures. Submitted to PR

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

Human leukocyte antigen alleles associate with COVID-19 vaccine immunogenicity and risk of breakthrough infection

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine immunogenicity varies between individuals, and immune responses correlate with vaccine efficacy. Using data from 1,076 participants enrolled in ChAdOx1 nCov-19 vaccine efficacy trials in the United Kingdom, we found that inter-individual variation in normalized antibody responses against SARS-CoV-2 spike and its receptor-binding domain (RBD) at 28 days after first vaccination shows genome-wide significant association with major histocompatibility complex (MHC) class II alleles. The most statistically significant association with higher levels of anti-RBD antibody was HLA-DQB1*06 (P = 3.2 × 10−9), which we replicated in 1,677 additional vaccinees. Individuals carrying HLA-DQB1*06 alleles were less likely to experience PCR-confirmed breakthrough infection during the ancestral SARS-CoV-2 virus and subsequent Alpha variant waves compared to non-carriers (hazard ratio = 0.63, 0.42–0.93, P = 0.02). We identified a distinct spike-derived peptide that is predicted to bind differentially to HLA-DQB1*06 compared to other similar alleles, and we found evidence of increased spike-specific memory B cell responses in HLA-DQB1*06 carriers at 84 days after first vaccination. Our results demonstrate association of HLA type with Coronavirus Disease 2019 (COVID-19) vaccine antibody response and risk of breakthrough infection, with implications for future vaccine design and implementation