Combinatorial Aspects of the Splitting Number

We define the strong splitting number, prove that it equals s when exists, and put some restrictions on the possibility that s is a singular carcinal

Analysis of a General Family of Regularized Navier-Stokes and MHD Models

We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n greater than or equal to 2. This family captures most of the specific regularized models that have been proposed and analyzed in the literature, including the Navier-Stokes equations, the Navier-Stokes-alpha model, the Leray-alpha model, the Modified Leray-alpha model, the Simplified Bardina model, the Navier-Stokes-Voight model, the Navier-Stokes-alpha-like models, and certain MHD models, in addition to representing a larger 3-parameter family of models not previously analyzed. We give a unified analysis of the entire three-parameter family using only abstract mapping properties of the principle dissipation and smoothing operators, and then use specific parameterizations to obtain the sharpest results. We first establish existence and regularity results, and under appropriate assumptions show uniqueness and stability. We then establish results for singular perturbations, including the inviscid and alpha limits. Next we show existence of a global attractor for the general model, and give estimates for its dimension. We finish by establishing some results on determining operators for subfamilies of dissipative and non-dissipative models. In addition to establishing a number of results for all models in this general family, the framework recovers most of the previous results on existence, regularity, uniqueness, stability, attractor existence and dimension, and determining operators for well-known members of this family.Comment: 37 pages; references added, minor typos corrected, minor changes to revise for publicatio

Loss of function NFKB1 variants are the most common monogenic cause of CVID in Europeans.

BACKGROUND: The genetic etiology of primary immunodeficiency disease (PID) carries prognostic information. OBJECTIVE: We conducted a whole-genome sequencing study assessing a large proportion of the NIHR-BioResource - Rare Disease cohort. METHODS: In the predominantly European study population of principally sporadic unrelated PID cases (n=846), a novel Bayesian method identified NFKB1 as one most strongly associated with PID, and the association was explained by 16 novel heterozygous truncating, missense and gene deletion variants. This accounted for 4% of common variable immunodeficiency (CVID) cases (n=390) in the cohort. Amino-acid substitutions predicted to be pathogenic were assessed by analysis of structural protein data. Immunophenotyping, immunoblotting and ex vivo stimulation of lymphocytes determined the functional effects of these variants. Detailed clinical and pedigree information was collected for genotype-phenotype co-segregation analyses. RESULTS: Both sporadic and familial cases demonstrated evidence of the non-infective complications of CVID, including massive lymphadenopathy (24%), unexplained splenomegaly (48%) and autoimmune disease (48%), features prior studies correlate with worse clinical prognosis. Although partial penetrance of clinical symptoms was noted in certain pedigrees, all carriers have a deficiency in B lymphocyte differentiation. Detailed assessment of B lymphocyte numbers, phenotype and function identifies the presence of a raised CD21lowB cell population: combined with identification of the disease-causing variant, this distinguishes between healthy individuals, asymptomatic carriers and clinically affected cases. CONCLUSION: We show that heterozygous loss-of-function variants in NFKB1 are the most common known monogenic cause of CVID that results in a temporally progressive defect in the formation of immunoglobulin-producing B cells.This study was supported by The National Institute for Health Research England (grant number RG65966), and by the Center of Immunodeficiencies Amsterdam (CIDA). JET is supported by an MRC Clinician Scientist Fellowship (MR/L006197/1). AJT is supported by both the Wellcome Trust (104807/Z/14/Z) and by the National Institute for Health Research Biomedical Research Centre at Great Ormond Street Hospital for Children NHS Foundation Trust and University College London. EO receives personal fees from CSL Behring and MSD

Indescribable cardinals without diamonds

We show that for m, n ≧1 the existence of a ∏ n m indescribable cardinal is equiconsistent with the failure of the combinatorial principle at a ∏ n m indescribable cardinal κ together with the Generalized Continuum Hypothesis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46066/1/153_2005_Article_BF01627508.pd

Templates of expected measurement uncertainties for average prompt and total fission neutron multiplicities

In this paper, we provide templates of measurement uncertainty sources expected to appear for average prompt- and total-fission neutron multiplicities, and , for the following measurement types: absolute manganese-bath experiments for , absolute and ratio liquid-scintillator measurements for . These templates also suggest a typical range of these uncertainties and their correlations based on a survey of available experimental data, associated literature, and feedback from experimentalists. In addition, the information needed to faithfully include the associated experimental data into the nuclear-data evaluation process is provided