Modeling software design diversity

Design diversity has been used for many years now as a means of achieving a degree of fault tolerance in software-based systems. Whilst there is clear evidence that the approach can be expected to deliver some increase in reliability compared with a single version, there is not agreement about the extent of this. More importantly, it remains difficult to evaluate exactly how reliable a particular diverse fault-tolerant system is. This difficulty arises because assumptions of independence of failures between different versions have been shown not to be tenable: assessment of the actual level of dependence present is therefore needed, and this is hard. In this tutorial we survey the modelling issues here, with an emphasis upon the impact these have upon the problem of assessing the reliability of fault tolerant systems. The intended audience is one of designers, assessors and project managers with only a basic knowledge of probabilities, as well as reliability experts without detailed knowledge of software, who seek an introduction to the probabilistic issues in decisions about design diversity

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

On a functional equation involving iterates and powers

We present a complete list of all continuous solutions f : (0,+∞)→(0,+∞) of the equation f 2(x) = γ [f (x)]αxβ, where α, β and γ > 0 are given real numbers

DNA deaminases: AIDing hormones in immunity and cancer

It is well established that hormones can cause cancer, much less known is how they induce this change in our somatic cells. This review highlights the recent finding that estrogen can exert its DNA-damaging potential by directly activating DNA deaminases. This recently discovered class of proteins deaminate cytosine to uracil in DNA, and are essential enzymes in the immune system. The enhanced production of a given DNA deaminase, induced by estrogen, can lead not only to a more active immune response, but also to an increase in mutations and oncogenic translocations. Identifying the direct molecular link between estrogen and a mutation event provides us with new targets for studying and possibly inhibiting the pathological side-effects of estrogen

Safety and immunogenicity of seven COVID-19 vaccines as a third dose (booster) following two doses of ChAdOx1 nCov-19 or BNT162b2 in the UK (COV-BOOST): a blinded, multicentre, randomised, controlled, phase 2 trial

BACKGROUND: Few data exist on the comparative safety and immunogenicity of different COVID-19 vaccines given as a third (booster) dose. To generate data to optimise selection of booster vaccines, we investigated the reactogenicity and immunogenicity of seven different COVID-19 vaccines as a third dose after two doses of ChAdOx1 nCov-19 (Oxford-AstraZeneca; hereafter referred to as ChAd) or BNT162b2 (Pfizer-BioNtech, hearafter referred to as BNT). METHODS: COV-BOOST is a multicentre, randomised, controlled, phase 2 trial of third dose booster vaccination against COVID-19. Participants were aged older than 30 years, and were at least 70 days post two doses of ChAd or at least 84 days post two doses of BNT primary COVID-19 immunisation course, with no history of laboratory-confirmed SARS-CoV-2 infection. 18 sites were split into three groups (A, B, and C). Within each site group (A, B, or C), participants were randomly assigned to an experimental vaccine or control. Group A received NVX-CoV2373 (Novavax; hereafter referred to as NVX), a half dose of NVX, ChAd, or quadrivalent meningococcal conjugate vaccine (MenACWY) control (1:1:1:1). Group B received BNT, VLA2001 (Valneva; hereafter referred to as VLA), a half dose of VLA, Ad26.COV2.S (Janssen; hereafter referred to as Ad26) or MenACWY (1:1:1:1:1). Group C received mRNA1273 (Moderna; hereafter referred to as m1273), CVnCov (CureVac; hereafter referred to as CVn), a half dose of BNT, or MenACWY (1:1:1:1). Participants and all investigatory staff were blinded to treatment allocation. Coprimary outcomes were safety and reactogenicity and immunogenicity of anti-spike IgG measured by ELISA. The primary analysis for immunogenicity was on a modified intention-to-treat basis; safety and reactogenicity were assessed in the intention-to-treat population. Secondary outcomes included assessment of viral neutralisation and cellular responses. This trial is registered with ISRCTN, number 73765130. FINDINGS: Between June 1 and June 30, 2021, 3498 people were screened. 2878 participants met eligibility criteria and received COVID-19 vaccine or control. The median ages of ChAd/ChAd-primed participants were 53 years (IQR 44-61) in the younger age group and 76 years (73-78) in the older age group. In the BNT/BNT-primed participants, the median ages were 51 years (41-59) in the younger age group and 78 years (75-82) in the older age group. In the ChAd/ChAD-primed group, 676 (46·7%) participants were female and 1380 (95·4%) were White, and in the BNT/BNT-primed group 770 (53·6%) participants were female and 1321 (91·9%) were White. Three vaccines showed overall increased reactogenicity: m1273 after ChAd/ChAd or BNT/BNT; and ChAd and Ad26 after BNT/BNT. For ChAd/ChAd-primed individuals, spike IgG geometric mean ratios (GMRs) between study vaccines and controls ranged from 1·8 (99% CI 1·5-2·3) in the half VLA group to 32·3 (24·8-42·0) in the m1273 group. GMRs for wild-type cellular responses compared with controls ranged from 1·1 (95% CI 0·7-1·6) for ChAd to 3·6 (2·4-5·5) for m1273. For BNT/BNT-primed individuals, spike IgG GMRs ranged from 1·3 (99% CI 1·0-1·5) in the half VLA group to 11·5 (9·4-14·1) in the m1273 group. GMRs for wild-type cellular responses compared with controls ranged from 1·0 (95% CI 0·7-1·6) for half VLA to 4·7 (3·1-7·1) for m1273. The results were similar between those aged 30-69 years and those aged 70 years and older. Fatigue and pain were the most common solicited local and systemic adverse events, experienced more in people aged 30-69 years than those aged 70 years or older. Serious adverse events were uncommon, similar in active vaccine and control groups. In total, there were 24 serious adverse events: five in the control group (two in control group A, three in control group B, and zero in control group C), two in Ad26, five in VLA, one in VLA-half, one in BNT, two in BNT-half, two in ChAd, one in CVn, two in NVX, two in NVX-half, and one in m1273. INTERPRETATION: All study vaccines boosted antibody and neutralising responses after ChAd/ChAd initial course and all except one after BNT/BNT, with no safety concerns. Substantial differences in humoral and cellular responses, and vaccine availability will influence policy choices for booster vaccination. FUNDING: UK Vaccine Taskforce and National Institute for Health Research

Persistence of immune responses after heterologous and homologous third COVID-19 vaccine dose schedules in the UK: eight-month analyses of the COV-BOOST trial

Background: COV-BOOST is a multicentre, randomised, controlled, phase 2 trial of seven COVID-19 vaccines used as a third booster dose in June 2021. Monovalent messenger RNA (mRNA) COVID-19 vaccines were subsequently widely used for the third and fourth-dose vaccination campaigns in high-income countries. Real-world vaccine effectiveness against symptomatic infections following third doses declined during the Omicron wave. This report compares the immunogenicity and kinetics of responses to third doses of vaccines from day (D) 28 to D242 following third doses in seven study arms. Methods: The trial initially included ten experimental vaccine arms (seven full-dose, three half-dose) delivered at three groups of six sites. Participants in each site group were randomised to three or four experimental vaccines, or MenACWY control. The trial was stratified such that half of participants had previously received two primary doses of ChAdOx1 nCov-19 (Oxford–AstraZeneca; hereafter referred to as ChAd) and half had received two doses of BNT162b2 (Pfizer–BioNtech, hereafter referred to as BNT). The D242 follow-up was done in seven arms (five full-dose, two half-dose). The BNT vaccine was used as the reference as it was the most commonly deployed third-dose vaccine in clinical practice in high-income countries. The primary analysis was conducted using all randomised and baseline seronegative participants who were SARS-CoV-2 naïve during the study and who had not received a further COVID-19 vaccine for any reason since third dose randomisation. Results: Among the 817 participants included in this report, the median age was 72 years (IQR: 55–78) with 50.7% being female. The decay rates of anti-spike IgG between vaccines are different among both populations who received initial doses of ChAd/ChAd and BNT/BNT. In the population that previously received ChAd/ChAd, mRNA vaccines had the highest titre at D242 following their vaccine dose although Ad26. COV2. S (Janssen; hereafter referred to as Ad26) showed slower decay. For people who received BNT/BNT as their initial doses, a slower decay was also seen in the Ad26 and ChAd arms. The anti-spike IgG became significantly higher in the Ad26 arm compared to the BNT arm as early as 3 months following vaccination. Similar decay rates were seen between BNT and half-BNT; the geometric mean ratios ranged from 0.76 to 0.94 at different time points. The difference in decay rates between vaccines was similar for wild-type live virus-neutralising antibodies and that seen for anti-spike IgG. For cellular responses, the persistence was similar between study arms. Conclusions: Heterologous third doses with viral vector vaccines following two doses of mRNA achieve more durable humoral responses compared with three doses of mRNA vaccines. Lower doses of mRNA vaccines could be considered for future booster campaigns

Statistical inference and the replication crisis

The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the alternative—Bayesian statistics—that many have suggested as a replacement. The Frequentist approach and the Bayesian approach offer radically different perspectives on evidence and inference with the Frequentist approach prioritising error control and the Bayesian approach offering a formal method for quantifying the relative strength of evidence for hypotheses. We suggest that rather than mere statistical reform, what is needed is a better understanding of the different modes of statistical inference and a better understanding of how statistical inference relates to scientific inference

Persistence of immunogenicity after seven COVID-19 vaccines given as third dose boosters following two doses of ChAdOx1 nCov-19 or BNT162b2 in the UK: Three month analyses of the COV-BOOST trial

OBJECTIVES: To evaluate the persistence of immunogenicity three months after third dose boosters. METHODS: COV-BOOST is a multicentre, randomised, controlled, phase 2 trial of seven COVID-19 vaccines used as a third booster dose. The analysis was conducted using all randomised participants who were SARS-CoV-2 naïve during the study. RESULTS: Amongst the 2883 participants randomised, there were 2422 SARS-CoV-2 naïve participants until D84 visit included in the analysis with median age of 70 (IQR: 30-94) years. In the participants who had two initial doses of ChAdOx1 nCov-19 (Oxford-AstraZeneca; hereafter referred to as ChAd), schedules using mRNA vaccines as third dose have the highest anti-spike IgG at D84 (e.g. geometric mean concentration of 8674 ELU/ml (95% CI: 7461-10,085) following ChAd/ChAd/BNT162b2 (Pfizer-BioNtech, hearafter referred to as BNT)). However, in people who had two initial doses of BNT there was no significant difference at D84 in people given ChAd versus BNT (geometric mean ratio (GMR) of 0.95 (95%CI: 0.78, 1.15). Also, people given Ad26.COV2.S (Janssen; hereafter referred to as Ad26) as a third dose had significantly higher anti-spike IgG at D84 than BNT (GMR of 1.20, 95%CI: 1.01,1.43). Responses at D84 between people who received BNT (15 μg) or BNT (30 μg) after ChAd/ChAd or BNT/BNT were similar, with anti-spike IgG GMRs of half-BNT (15 μg) versus BNT (30 μg) ranging between 0.74-0.86. The decay rate of cellular responses were similar between all the vaccine schedules and doses. CONCLUSIONS: 84 days after a third dose of COVID-19 vaccine the decay rates of humoral response were different between vaccines. Adenoviral vector vaccine anti-spike IgG concentrations at D84 following BNT/BNT initial doses were similar to or even higher than for a three dose (BNT/BNT/BNT) schedule. Half dose BNT immune responses were similar to full dose responses. While high antibody tires are desirable in situations of high transmission of new variants of concern, the maintenance of immune responses that confer long-lasting protection against severe disease or death is also of critical importance. Policymakers may also consider adenoviral vector, fractional dose of mRNA, or other non-mRNA vaccines as third doses