Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

Completeness and Decidability Results for First-order Clauses with Indices

Session: Inference systems (www.cl.cam.ac.uk/~gp351/cade24)International audienceWe define a proof procedure that allows for a limited form of inductive reasoning. The first argument of a function symbol is allowed to belong to an inductive type. We will call such an argument an index. We enhance the standard superposition calculus with a loop detection rule, in order to encode a particular form of mathematical induction. The satisfiability problem is not semi-decidable, but some classes of clause sets are identified for which the proposed procedure is complete and/or terminating

Polygenic risk modeling for prediction of epithelial ovarian cancer risk

Polygenic risk scores (PRS) for epithelial ovarian cancer (EOC) have the potential to improve risk stratification. Joint estimation of Single Nucleotide Polymorphism (SNP) effects in models could improve predictive performance over standard approaches of PRS construction. Here, we implemented computationally efficient, penalized, logistic regression models (lasso, elastic net, stepwise) to individual level genotype data and a Bayesian framework with continuous shrinkage, "select and shrink for summary statistics" (S4), to summary level data for epithelial non-mucinous ovarian cancer risk prediction. We developed the models in a dataset consisting of 23,564 non-mucinous EOC cases and 40,138 controls participating in the Ovarian Cancer Association Consortium (OCAC) and validated the best models in three populations of different ancestries: prospective data from 198,101 women of European ancestries; 7,669 women of East Asian ancestries; 1,072 women of African ancestries, and in 18,915 BRCA1 and 12,337 BRCA2 pathogenic variant carriers of European ancestries. In the external validation data, the model with the strongest association for non-mucinous EOC risk derived from the OCAC model development data was the S4 model (27,240 SNPs) with odds ratios (OR) of 1.38 (95% CI: 1.28-1.48, AUC: 0.588) per unit standard deviation, in women of European ancestries; 1.14 (95% CI: 1.08-1.19, AUC: 0.538) in women of East Asian ancestries; 1.38 (95% CI: 1.21-1.58, AUC: 0.593) in women of African ancestries; hazard ratios of 1.36 (95% CI: 1.29-1.43, AUC: 0.592) in BRCA1 pathogenic variant carriers and 1.49 (95% CI: 1.35-1.64, AUC: 0.624) in BRCA2 pathogenic variant carriers. Incorporation of the S4 PRS in risk prediction models for ovarian cancer may have clinical utility in ovarian cancer prevention programs

Association between adolescent idiopathic scoliosis prevalence and age at menarche in different geographic latitudes

BACKGROUND: Age at menarche is considered a reliable prognostic factor for idiopathic scoliosis and varies in different geographic latitudes. Adolescent idiopathic scoliosis prevalence has also been reported to be different in various latitudes and demonstrates higher values in northern countries. A study on epidemiological reports from the literature was conducted to investigate a possible association between prevalence of adolescent idiopathic scoliosis and age at menarche among normal girls in various geographic latitudes. An attempt is also made to implicate a possible role of melatonin in the above association. MATERIAL-METHODS: 20 peer-reviewed published papers reporting adolescent idiopathic scoliosis prevalence and 33 peer-reviewed papers reporting age at menarche in normal girls from most geographic areas of the northern hemisphere were retrieved from the literature. The geographic latitude of each centre where a particular study was originated was documented. The statistical analysis included regression of the adolescent idiopathic scoliosis prevalence and age at menarche by latitude. RESULTS: The regression of prevalence of adolescent idiopathic scoliosis and age at menarche by latitude is statistically significant (p < 0.001) and are following a parallel declining course of their regression curves, especially in latitudes northern than 25 degrees. CONCLUSION: Late age at menarche is parallel with higher prevalence of adolescent idiopathic scoliosis. Pubarche appears later in girls that live in northern latitudes and thus prolongs the period of spine vulnerability while other pre-existing or aetiological factors are contributing to the development of adolescent idiopathic scoliosis. A possible role of geography in the pathogenesis of idiopathic scoliosis is discussed, as it appears that latitude which differentiates the sunlight influences melatonin secretion and modifies age at menarche, which is associated to the prevalence of idiopathic scoliosis

Design concepts for the Cherenkov Telescope Array CTA: an advanced facility for ground-based high-energy gamma-ray astronomy

Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA

Polygenic risk modeling for prediction of epithelial ovarian cancer risk

Polygenic risk scores (PRS) for epithelial ovarian cancer (EOC) have the potential to improve risk stratification. Joint estimation of Single Nucleotide Polymorphism (SNP) effects in models could improve predictive performance over standard approaches of PRS construction. Here, we implemented computationally efficient, penalized, logistic regression models (lasso, elastic net, stepwise) to individual level genotype data and a Bayesian framework with continuous shrinkage, "select and shrink for summary statistics" (S4), to summary level data for epithelial non-mucinous ovarian cancer risk prediction. We developed the models in a dataset consisting of 23,564 non-mucinous EOC cases and 40,138 controls participating in the Ovarian Cancer Association Consortium (OCAC) and validated the best models in three populations of different ancestries: prospective data from 198,101 women of European ancestries; 7,669 women of East Asian ancestries; 1,072 women of African ancestries, and in 18,915 BRCA1 and 12,337 BRCA2 pathogenic variant carriers of European ancestries. In the external validation data, the model with the strongest association for non-mucinous EOC risk derived from the OCAC model development data was the S4 model (27,240 SNPs) with odds ratios (OR) of 1.38 (95% CI: 1.28-1.48, AUC: 0.588) per unit standard deviation, in women of European ancestries; 1.14 (95% CI: 1.08-1.19, AUC: 0.538) in women of East Asian ancestries; 1.38 (95% CI: 1.21-1.58, AUC: 0.593) in women of African ancestries; hazard ratios of 1.36 (95% CI: 1.29-1.43, AUC: 0.592) in BRCA1 pathogenic variant carriers and 1.49 (95% CI: 1.35-1.64, AUC: 0.624) in BRCA2 pathogenic variant carriers. Incorporation of the S4 PRS in risk prediction models for ovarian cancer may have clinical utility in ovarian cancer prevention programs

Identification of 12 new susceptibility loci for different histotypes of epithelial ovarian cancer.

To identify common alleles associated with different histotypes of epithelial ovarian cancer (EOC), we pooled data from multiple genome-wide genotyping projects totaling 25,509 EOC cases and 40,941 controls. We identified nine new susceptibility loci for different EOC histotypes: six for serous EOC histotypes (3q28, 4q32.3, 8q21.11, 10q24.33, 18q11.2 and 22q12.1), two for mucinous EOC (3q22.3 and 9q31.1) and one for endometrioid EOC (5q12.3). We then performed meta-analysis on the results for high-grade serous ovarian cancer with the results from analysis of 31,448 BRCA1 and BRCA2 mutation carriers, including 3,887 mutation carriers with EOC. This identified three additional susceptibility loci at 2q13, 8q24.1 and 12q24.31. Integrated analyses of genes and regulatory biofeatures at each locus predicted candidate susceptibility genes, including OBFC1, a new candidate susceptibility gene for low-grade and borderline serous EOC