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

Mutations in Radial Spoke Head Genes and Ultrastructural Cilia Defects in East-European Cohort of Primary Ciliary Dyskinesia Patients

Primary ciliary dyskinesia (PCD) is a rare (1/20,000), multisystem disease with a complex phenotype caused by the impaired motility of cilia/flagella, usually related to ultrastructural defects of these organelles. Mutations in genes encoding radial spoke head (RSPH) proteins, elements of the ciliary ultrastructure, have been recently described. However, the relative involvement of RSPH genes in PCD pathogenesis remained unknown, due to a small number of PCD families examined for mutations in these genes. The purpose of this study was to estimate the involvement of RSPH4A and RSPH9 in PCD pathogenesis among East Europeans (West Slavs), and to shed more light on ultrastructural ciliary defects caused by mutations in these genes. The coding sequences of RSPH4A and RSPH9 were screened in PCD patients from 184 families, using single strand conformational polymorphism analysis and sequencing. Two previously described (Q109X; R490X) and two new RSPH4A mutations (W356X; IVS3_2–5del), in/around exons 1 and 3, were identified; no mutations were found in RSPH9. We estimate that mutations in RSPH4A, but not in RSPH9, are responsible for 2–3% of cases in the East European PCD population (4% in PCD families without situs inversus; 11% in families preselected for microtubular defects). Analysis of the SNP-haplotype background provided insight into the ancestry of repetitively found mutations (Q109X; R490X; IVS3_2–5del), but further studies involving other PCD cohorts are required to elucidate whether these mutations are specific for Slavic people or spread among other European populations. Ultrastructural defects associated with the mutations were analyzed in the transmission electron microscope images; almost half of the ciliary cross-sections examined in patients with RSPH4A mutations had the microtubule transposition phenotype (9+0 and 8+1 pattern). While microtubule transposition was a prevalent ultrastructural defect in cilia from patients with RSPH4A mutations, similar defects were also observed in PCD patients with mutations in other genes