Fermat hypersurfaces and Subcanonical curves

We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectively normal curve, and vice versa.Comment: 18 pages; AMS-LaTe

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

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, immunogenicity, and reactogenicity of BNT162b2 and mRNA-1273 COVID-19 vaccines given as fourth-dose boosters following two doses of ChAdOx1 nCoV-19 or BNT162b2 and a third dose of BNT162b2 (COV-BOOST): a multicentre, blinded, phase 2, randomised trial

BACKGROUND: Some high-income countries have deployed fourth doses of COVID-19 vaccines, but the clinical need, effectiveness, timing, and dose of a fourth dose remain uncertain. We aimed to investigate the safety, reactogenicity, and immunogenicity of fourth-dose boosters against COVID-19. METHODS: The COV-BOOST trial is a multicentre, blinded, phase 2, randomised controlled trial of seven COVID-19 vaccines given as third-dose boosters at 18 sites in the UK. This sub-study enrolled participants who had received BNT162b2 (Pfizer-BioNTech) as their third dose in COV-BOOST and randomly assigned them (1:1) to receive a fourth dose of either BNT162b2 (30 μg in 0·30 mL; full dose) or mRNA-1273 (Moderna; 50 μg in 0·25 mL; half dose) via intramuscular injection into the upper arm. The computer-generated randomisation list was created by the study statisticians with random block sizes of two or four. Participants and all study staff not delivering the vaccines were masked to treatment allocation. The coprimary outcomes were safety and reactogenicity, and immunogenicity (anti-spike protein IgG titres by ELISA and cellular immune response by ELISpot). We compared immunogenicity at 28 days after the third dose versus 14 days after the fourth dose and at day 0 versus day 14 relative to the fourth dose. Safety and reactogenicity were assessed in the per-protocol population, which comprised all participants who received a fourth-dose booster regardless of their SARS-CoV-2 serostatus. Immunogenicity was primarily analysed in a modified intention-to-treat population comprising seronegative participants who had received a fourth-dose booster and had available endpoint data. This trial is registered with ISRCTN, 73765130, and is ongoing. FINDINGS: Between Jan 11 and Jan 25, 2022, 166 participants were screened, randomly assigned, and received either full-dose BNT162b2 (n=83) or half-dose mRNA-1273 (n=83) as a fourth dose. The median age of these participants was 70·1 years (IQR 51·6-77·5) and 86 (52%) of 166 participants were female and 80 (48%) were male. The median interval between the third and fourth doses was 208·5 days (IQR 203·3-214·8). Pain was the most common local solicited adverse event and fatigue was the most common systemic solicited adverse event after BNT162b2 or mRNA-1273 booster doses. None of three serious adverse events reported after a fourth dose with BNT162b2 were related to the study vaccine. In the BNT162b2 group, geometric mean anti-spike protein IgG concentration at day 28 after the third dose was 23 325 ELISA laboratory units (ELU)/mL (95% CI 20 030-27 162), which increased to 37 460 ELU/mL (31 996-43 857) at day 14 after the fourth dose, representing a significant fold change (geometric mean 1·59, 95% CI 1·41-1·78). There was a significant increase in geometric mean anti-spike protein IgG concentration from 28 days after the third dose (25 317 ELU/mL, 95% CI 20 996-30 528) to 14 days after a fourth dose of mRNA-1273 (54 936 ELU/mL, 46 826-64 452), with a geometric mean fold change of 2·19 (1·90-2·52). The fold changes in anti-spike protein IgG titres from before (day 0) to after (day 14) the fourth dose were 12·19 (95% CI 10·37-14·32) and 15·90 (12·92-19·58) in the BNT162b2 and mRNA-1273 groups, respectively. T-cell responses were also boosted after the fourth dose (eg, the fold changes for the wild-type variant from before to after the fourth dose were 7·32 [95% CI 3·24-16·54] in the BNT162b2 group and 6·22 [3·90-9·92] in the mRNA-1273 group). INTERPRETATION: Fourth-dose COVID-19 mRNA booster vaccines are well tolerated and boost cellular and humoral immunity. Peak responses after the fourth dose were similar to, and possibly better than, peak responses after the third dose. FUNDING: UK Vaccine Task Force and National Institute for Health Research

First measurement of the BSB_S meson mass

If simplified, every information retrieval problem can be solved when the information need implied by its expression has been identified. We are interested in the criteria used in realising a good information retrieval problem expression. We have listed these criteria through some principles and maxims which first characterized the communication between two persons are applied. We choose to use the gricean maxims because they are the most favoured for this type of situation. Secondly, we have tried to identify some others principles that can be used to realise a good information retrieval problem expression. The principles by Grice can not resolve all forms of error associated with this particular form of communication. In our work, we defined three other principles namely: adhesion principle, reformulation principle, memorization principle. We give some examples of situations where the principles we have formulated are not applicable and the consequences. We present the possible applications of our new model: MIRABEL, which can help in the description of information retrieval problem from. It also compels its user to use essential good expression principle implicitly

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: Among 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 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: 7461-10085) following ChAd/ChAd/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 concentration at D84 following BNT/BNT initial doses were 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