Multiple Conclusion Rules in Logics with the Disjunction Property

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics

∗\ast-SDYM Fields and Heavenly Spaces. I. ∗\ast-SDYM equations as an integrable system

It is shown that the self-dual Yang-Mills (SDYM) equations for the $\ast$-bracket Lie algebra on a heavenly space can be reduced to one equation (the \it master equation\rm). Two hierarchies of conservation laws for this equation are constructed. Then the twistor transform and a solution to the Riemann-Hilbert problem are given.Comment: 25 page

Mutations in NLRP5 are associated with reproductive wastage and multilocus imprinting disorders in humans

This is the final version. It first appeared at http://www.nature.com/ncomms/2015/150901/ncomms9086/full/ncomms9086.html.Human-imprinting disorders are congenital disorders of growth, development and metabolism, associated with disturbance of parent of origin-specific DNA methylation at imprinted loci across the genome. Some imprinting disorders have higher than expected prevalence of monozygotic twinning, of assisted reproductive technology among parents, and of disturbance of multiple imprinted loci, for which few causative trans-acting mutations have been found. Here we report mutations in NLRP5 in five mothers of individuals affected by multilocus imprinting disturbance. Maternal-effect mutations of other human NLRP genes, NLRP7 and NLRP2, cause familial biparental hydatidiform mole and multilocus imprinting disturbance, respectively. Offspring of mothers with NLRP5 mutations have heterogenous clinical and epigenetic features, but cases include a discordant monozygotic twin pair, individuals with idiopathic developmental delay and autism, and families affected by infertility and reproductive wastage. NLRP5 mutations suggest connections between maternal reproductive fitness, early zygotic development and genomic imprinting.L.E.D. and F.I.R. were supported by the Medical Research Council (MR/J000329/1). J.B., K.B., B.H., L.S. M.B. and T.E. were supported by Bundesministerium fu?r Bildung und Forschung (grant number 01GM1513A and 01GM1513C) and C.T. was supported by an Ipsen Fellowship Grant. The cohort ?Imprinting Disorders-Finding out Why? was accrued through the support of the Newlife Foundation for Disabled Children and through support from the Wessex NIHR clinical research network and NIHR Wellcome Southampton clinical research facility. Funding for DNA collection and methylation analysis of normal control samples was provided in part by the National Institutes of Health R01 AI091905-01, R01 AI061471 and R01 HL082925. ERM thanks Action Medical Research for support