A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice

We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice. This semantics is an extension of the one used to show consistency of the intensional level of the Minimalist Foundation with the axiom of choice and formal Church's thesis in previous work. A main novelty here is that such a semantics is formalized in a constructive theory represented by Aczel's constructive set theory CZF extended with the regular extension axiom

Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice

Here we consider an extension MFcind of the Minimalist Foundation MF for predicative constructive mathematics with the addition of inductive and coinductive definitions sufficient to generate Sambin's Positive topologies, i.e. Martin-L\"of-Sambin formal topologies equipped with a Positivity relation (used to describe pointfree formal closed subsets). In particular the intensional level of MFcind, called mTTcind, is defined by extending with coinductive definitions another theory mTTind extending the intensional level mTT of MF with the sole addition of inductive definitions. In previous work we have shown that mTTind is consistent with Formal Church's Thesis CT and the Axiom of Choice AC via an interpretation in Aczel's CZF+REA. Our aim is to show the expectation that the addition of coinductive definitions to mTTind does not increase its consistency strength by reducing the consistency of mTTcind+CT+AC to the consistency of CZF+REA through various interpretations. We actually reach our goal in two ways. One way consists in first interpreting mTTcind+CT+AC in the theory extending CZF with the Union Regular Extension Axiom, REA_U, a strengthening of REA, and the Axiom of Relativized Dependent Choice, RDC. The theory CZF+REA_U+RDC is then interpreted in MLS*, a version of Martin-L\"of's type theory with Palmgren's superuniverse S. A last step consists in interpreting MLS* back into CZF+REA. The alternative way consists in first interpreting mTTcind+AC+CT directly in a version of Martin-L\"of's type theory with Palmgren's superuniverse extended with CT, which is then interpreted back to CZF+REA. A key benefit of the first way is that the theory CZF+REA_U+RDC also supports the intended set-theoretic interpretation of the extensional level of MFcind. Finally, all the theories considered, except mTTcind+AC+CT, are shown to be of the same proof-theoretic strength.Comment: arXiv admin note: text overlap with arXiv:1905.1196

A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice

We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice. This semantics is an extension of the one used to show consistency of the intensional level of the Minimalist Foundation with the axiom of choice and formal Church's thesis in previous work. A main novelty here is that such a semantics is formalized in a constructive theory represented by Aczel's constructive set theory CZF extended with the regular extension axiom

Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice

In this work we consider an extension MFcind of the Minimalist Foundation MF for predicative constructive mathematics with the addition of inductive and coinductive definitions sufficient to generate Sambin's Positive topologies, namely Martin-L\"of-Sambin formal topologies equipped with a Positivity relation (used to describe pointfree formal closed subsets). In particular the intensional level of MFcind, called mTTcind, is defined by extending with coinductive definitions another theory mTTind extending the intensional level mTT of MF with the sole addition of inductive definitions. In previous work we have shown that mTTind is consistent with Formal Church's Thesis CT and the Axiom of Choice AC via an interpretation in Aczel's CZF+REA. Our aim is to show the expectation that the addition of coinductive definitions to mTTind does not increase its consistency strength by reducing the consistency of mTTcind+CT+AC to the consistency of CZF+REA through various interpretations. We actually reach our goal in two ways. One way consists in first interpreting mTTcind+CT+AC in the theory extending CZF with the Union Regular Extension Axiom, REA_U, a strengthening of REA, and the Axiom of Relativized Dependent Choice, RDC. The theory CZF+REA_U+RDC is then interpreted in MLS*, a version of Martin-L\"of's type theory with Palmgren's superuniverse S. A last step consists in interpreting MLS* back into CZF+REA. The alternative way consists in first interpreting mTTcind+AC+CT directly in a version of Martin-L\"of's type theory with Palmgren's superuniverse extended with CT, which is then interpreted back to CZF+REA. A key benefit of the first way is that the theory CZF+REA_U+RDC also supports the intended set-theoretic interpretation of the extensional level of MFcind. Finally, all the theories considered, except mTTcind+AC+CT, are shown to be of the same proof-theoretic strength

The cost-effectiveness of an adjuvanted quadrivalent influenza vaccine in the United Kingdom

In the United Kingdom (UK), both the MF59-adjuvanted quadrivalent influenza vaccine (aQIV) and the high-dose QIV (QIV-HD) are preferred for persons aged 65 years and older but only aQIV is reimbursed by the National Health Service (NHS). The objective was to determine the potential cost-effectiveness of vaccinating adults aged 65 years and above with aQIV compared with QIV-HD in the UK. A dynamic transmission model, calibrated to match infection data from the UK, was used to estimate the impact of vaccination in 10 influenza seasons. Vaccine effectiveness was based on a meta-analysis that concluded the vaccines were not significantly different. Vaccine coverage, physician visits, hospitalizations, deaths, utility losses and NHS costs were estimated using published UK sources. The list price of aQIV was £11.88 while a range of prices were tested for QIV-HD. The price of the trivalent high-dose vaccine (TIV-HD) is £20.00 but a list price for QIV-HD is not yet available. The projected differences between the vaccines in terms of clinical cases and influenza treatment costs are minimal. Our analysis demonstrates that in order to be cost-effective, the price of QIV-HD must be similar to that of aQIV and may range from £7.57 to £12.94 depending on the relative effectiveness of the vaccines. The results of the analysis were most sensitive to variation in vaccine effectiveness and the rate of hospitalization due to influenza. Given the evidence, aQIV is cost-saving unless QIV-HD is priced lower than the existing list price of TIV-HD

The Cost-Effectiveness of Expanding Vaccination with a Cell-Based Influenza Vaccine to Low Risk Adults Aged 50 to 64 Years in the United Kingdom

Background: In response to COVID-19, the UK National Health Service (NHS) extended influenza vaccination in 50- to 64-year-olds from at-risk only to all in this age group for the 2020/21 season. The objective of this research is to determine the cost-effectiveness of continuing to vaccinate all with a quadrivalent cell-based vaccine (QIVc) compared to returning to an at-risk only policy after the pandemic resolves. Methods: A dynamic transmission model, calibrated to match infection data from the UK, was used to estimate the clinical and economic impact of vaccination across 10 influenza seasons. The base case effectiveness of QIVc was 63.9% and the list price was GBP 9.94. Results: Vaccinating 50% of all 50- to 64-year-olds with QIVc reduced the average annual number of clinical infections (−682,000), hospitalizations (−5800) and deaths (−740) in the UK. The base case incremental cost per quality-adjusted life-year gained (ICER) of all compared to at-risk only was GBP6000 (NHS perspective). When the cost of lost productivity was considered, vaccinating all 50-to 64-year-olds with QIVc became cost-saving. Conclusion: Vaccinating all 50- to 64-year-olds with QIVc is likely to be cost-effective. The NHS should consider continuing this policy in future seasons

Hundreds of variants clustered in genomic loci and biological pathways affect human height

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.

A Genome-Wide Association Scan on the Levels of Markers of Inflammation in Sardinians Reveals Associations That Underpin Its Complex Regulation

Identifying the genes that influence levels of pro-inflammatory molecules can help to elucidate the mechanisms underlying this process. We first conducted a two-stage genome-wide association scan (GWAS) for the key inflammatory biomarkers Interleukin-6 (IL-6), the general measure of inflammation erythrocyte sedimentation rate (ESR), monocyte chemotactic protein-1 (MCP-1), and high-sensitivity C-reactive protein (hsCRP) in a large cohort of individuals from the founder population of Sardinia. By analysing 731,213 autosomal or X chromosome SNPs and an additional ∼1.9 million imputed variants in 4,694 individuals, we identified several SNPs associated with the selected quantitative trait loci (QTLs) and replicated all the top signals in an independent sample of 1,392 individuals from the same population. Next, to increase power to detect and resolve associations, we further genotyped the whole cohort (6,145 individuals) for 293,875 variants included on the ImmunoChip and MetaboChip custom arrays. Overall, our combined approach led to the identification of 9 genome-wide significant novel independent signals—5 of which were identified only with the custom arrays—and provided confirmatory evidence for an additional 7. Novel signals include: for IL-6, in the ABO gene (rs657152, p = 2.13×10−29); for ESR, at the HBB (rs4910472, p = 2.31×10−11) and UCN119B/SPPL3 (rs11829037, p = 8.91×10−10) loci; for MCP-1, near its receptor CCR2 (rs17141006, p = 7.53×10−13) and in CADM3 (rs3026968, p = 7.63×10−13); for hsCRP, within the CRP gene (rs3093077, p = 5.73×10−21), near DARC (rs3845624, p = 1.43×10−10), UNC119B/SPPL3 (rs11829037, p = 1.50×10−14), and ICOSLG/AIRE (rs113459440, p = 1.54×10−08) loci. Confirmatory evidence was found for IL-6 in the IL-6R gene (rs4129267); for ESR at CR1 (rs12567990) and TMEM57 (rs10903129); for MCP-1 at DARC (rs12075); and for hsCRP at CRP (rs1205), HNF1A (rs225918), and APOC-I (rs4420638). Our results improve the current knowledge of genetic variants underlying inflammation and provide novel clues for the understanding of the molecular mechanisms regulating this complex process

Variants within the immunoregulatory CBLB gene are associated with multiple sclerosis

A genome wide association scan of ~6.6 million genotyped or imputed variants in 882 Sardinian Multiple Sclerosis (MS) cases and 872 controls suggested association of CBLB gene variants with disease, which was confirmed in 1,775 cases and 2,005 controls (overall P =1.60 × 10-10). CBLB encodes a negative regulator of adaptive immune responses and mice lacking the orthologue are prone to experimental autoimmune encephalomyelitis, the animal model of MS