The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

Postoperative complications after procedure for prolapsed hemorrhoids (PPH) and stapled transanal rectal resection (STARR) procedures

Procedure for prolapsing hemorrhoids (PPH) and stapled transanal rectal resection for obstructed defecation (STARR) carry low postoperative pain, but may be followed by unusual and severe postoperative complications. This review deals with the pathogenesis, prevention and treatment of adverse events that may occasionally be life threatening. PPH and STARR carry the expected morbidity following anorectal surgery, such as bleeding, strictures and fecal incontinence. Complications that are particular to these stapled procedures are rectovaginal fistula, chronic proctalgia, total rectal obliteration, rectal wall hematoma and perforation with pelvic sepsis often requiring a diverting stoma. A higher complication rate and worse results are expected after PPH for fourth-degree piles. Enterocele and anismus are contraindications to PPH and STARR and both operations should be used with caution in patients with weak sphincters. In conclusion, complications after PPH and STARR are not infrequent and may be difficult to manage. However, if performed in selected cases by skilled specialists aware of the risks and associated diseases, some complications may be prevented

Simvastatin inhibits lymphocyte function in normal subjects and patients with cardiovascular disease

HMG-CoA reductase inhibitors (statins) block the mevalonate pathway, preventing biosynthesis of cholesterol and isoprenoids. We investigated the effect of simvastatin on lymphocytes from normal human subjects and cardiovascular disease patients in order to provide a model for the in vivo actions of statins. Thirteen healthy volunteers were treated with 40 mg per day of simvastatin following which mean total cholesterol was reduced by 23% (S.D.±11.7%) and mean LDL-cholesterol by 36% (S.D.±16.3%). Lymphocyte lipid raft levels, represented by Lyn and Fyn, were also reduced by simvastatin. Treatment with simvastatin did not alter ex vivo T-lymphocyte proliferation. However, the in vitro addition of 1 μM simvastatin reduced T-lymphocyte proliferation by 39% (S.D.±18.1%) and a combination of prenyl transferase inhibitors reduced proliferation by 19% (S.D.±22.7%). We also assessed the cytotoxicity of natural killer (NK) cells—a T-lymphocyte subset. NK cell cytotoxicity ex vivo was reduced by 30% (S.D.±33.6%) following oral simvastatin treatment and by 56% (S.D.±24.68%) after the in vitro addition of 1 μM simvastatin. Significant ex vivo reductions in T-cell proliferation and NK cell cytotoxicity were observed in patients with cardiovascular disease on treatment with statins. NK cells have been implicated in the pathogenesis of atherosclerosis, so the effect of statin therapy on NK cell cytotoxicity may contribute to the benefits of statins in cardiovascular disease

Genetic contributions to variation in general cognitive function: a meta-analysis of genome-wide association studies in the CHARGE consortium (N=53 949)

General cognitive function is substantially heritable across the human life course from adolescence to old age. We investigated the genetic contribution to variation in this important, health- and well-being-related trait in middle-aged and older adults. We conducted a meta-analysis of genome-wide association studies of 31 cohorts (N=53,949) in which the participants had undertaken multiple, diverse cognitive tests. A general cognitive function phenotype was tested for, and created in each cohort by principal component analysis. We report 13 genome-wide significant single-nucleotide polymorphism (SNP) associations in three genomic regions, 6q16.1, 14q12 and 19q13.32 (best SNP and closest gene, respectively: rs10457441, P=3.93 × 10(-9), MIR2113; rs17522122, P=2.55 × 10(-8), AKAP6; rs10119, P=5.67 × 10(-9), APOE/TOMM40). We report one gene-based significant association with the HMGN1 gene located on chromosome 21 (P=1 × 10(-6)). These genes have previously been associated with neuropsychiatric phenotypes. Meta-analysis results are consistent with a polygenic model of inheritance. To estimate SNP-based heritability, the genome-wide complex trait analysis procedure was applied to two large cohorts, the Atherosclerosis Risk in Communities Study (N=6617) and the Health and Retirement Study (N=5976). The proportion of phenotypic variation accounted for by all genotyped common SNPs was 29% (s.e.=5%) and 28% (s.e.=7%), respectively. Using polygenic prediction analysis, ~1.2% of the variance in general cognitive function was predicted in the Generation Scotland cohort (N=5487; P=1.5 × 10(-17)). In hypothesis-driven tests, there was significant association between general cognitive function and four genes previously associated with Alzheimer's disease: TOMM40, APOE, ABCG1 and MEF2C