On γ\gamma-vectors satisfying the Kruskal-Katona inequalities

We present examples of flag homology spheres whose $\gamma$-vectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit simplicial complexes whose $f$-vectors are the $\gamma$-vectors in question. In another direction, we show that if a flag $(d-1)$-sphere has at most $2d+2$ vertices its $\gamma$-vector satisfies the Kruskal-Katona inequalities. We conjecture that if $\Delta$ is a flag homology sphere then $\gamma(\Delta)$ satisfies the Kruskal-Katona inequalities. This conjecture is a significant refinement of Gal's conjecture, which asserts that such $\gamma$-vectors are nonnegative.Comment: 18 pages; Our main result and conjectures have been strengthened. Also we now have explicit constructions of simplicial complexes whose $f$-vectors are the $\gamma$-vectors in questio

'Education, education, education' : legal, moral and clinical

This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students

Contributions of the Women's Health Initiative to Cardiovascular Research: JACC State-of-the-Art Review

The WHI (Women's Health Initiative) enrolled 161,808 racially and ethnically diverse postmenopausal women, ages 50-79 years, from 1993 to 1998 at 40 clinical centers across the United States. In its clinical trial component, WHI evaluated 3 randomized interventions (menopausal hormone therapy; diet modification; and calcium/vitamin D supplementation) for the primary prevention of major chronic diseases, including cardiovascular disease, in older women. In the WHI observational study, numerous clinical, behavioral, and social factors have been evaluated as predictors of incident chronic disease and mortality. Although the original interventions have been completed, the WHI data and biomarker resources continue to be leveraged and expanded through ancillary studies to yield novel insights regarding cardiovascular disease prevention and healthy aging in women

Premature Menopause, Clonal Hematopoiesis, and Coronary Artery Disease in Postmenopausal Women

Background: Premature menopause is an independent risk factor for cardiovascular disease in women, but mechanisms underlying this association remain unclear. Clonal hematopoiesis of indeterminate potential (CHIP), the age-related expansion of hematopoietic cells with leukemogenic mutations without detectable malignancy, is associated with accelerated atherosclerosis. Whether premature menopause is associated with CHIP is unknown. Methods: We included postmenopausal women from the UK Biobank (n=11 495) aged 40 to 70 years with whole exome sequences and from the Women's Health Initiative (n=8111) aged 50 to 79 years with whole genome sequences. Premature menopause was defined as natural or surgical menopause occurring before age 40 years. Co-primary outcomes were the presence of any CHIP and CHIP with variant allele frequency >0.1. Logistic regression tested the association of premature menopause with CHIP, adjusted for age, race, the first 10 principal components of ancestry, smoking, diabetes, and hormone therapy use. Secondary analyses considered natural versus surgical premature menopause and gene-specific CHIP subtypes. Multivariable-adjusted Cox models tested the association between CHIP and incident coronary artery disease. Results: The sample included 19 606 women, including 418 (2.1%) with natural premature menopause and 887 (4.5%) with surgical premature menopause. Across cohorts, CHIP prevalence in postmenopausal women with versus without a history of premature menopause was 8.8% versus 5.5% (P0.1: odds ratio, 1.40 [95% CI, 1.10-1.79]; P=0.007). Associations were larger for natural premature menopause (all CHIP: odds ratio, 1.73 [95% CI, 1.23-2.44]; P=0.001; CHIP with variant allele frequency >0.1: odds ratio, 1.91 [95% CI, 1.30-2.80]; P0.1: 1.48 [95% CI, 1.13-1.94]; P=0.005). Conclusions: Premature menopause, especially natural premature menopause, is independently associated with CHIP among postmenopausal women. Natural premature menopause may serve as a risk signal for predilection to develop CHIP and CHIP-associated cardiovascular disease

Prospective associations of coronary heart disease loci in African Americans using the MetaboChip

Background: Coronary heart disease (CHD) is a leading cause of morbidity and mortality in African Americans. However, there is a paucity of studies assessing genetic determinants of CHD in African Americans. We examined the association of publishe

Subword complexes, cluster complexes, and generalized multi-associahedra

In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called multi-cluster complex. For k=1, we show that this subword complex is isomorphic to the cluster complex of the given type. We show that multi-cluster complexes of types A and B coincide with known simplicial complexes, namely with the simplicial complexes of multi-triangulations and centrally symmetric multi-triangulations respectively. Furthermore, we show that the multi-cluster complex is universal in the sense that every spherical subword complex can be realized as a link of a face of the multi-cluster complex.Comment: 26 pages, 3 Tables, 2 Figures; final versio

Supplemental Association of Clonal Hematopoiesis With Incident Heart Failure

Background: Age-related clonal hematopoiesis of indeterminate potential (CHIP), defined as clonally expanded leukemogenic sequence variations (particularly in DNMT3A, TET2, ASXL1, and JAK2) in asymptomatic individuals, is associated with cardiovascular events, including recurrent heart failure (HF). Objectives: This study sought to evaluate whether CHIP is associated with incident HF. Methods: CHIP status was obtained from whole exome or genome sequencing of blood DNA in participants without prevalent HF or hematological malignancy from 5 cohorts. Cox proportional hazards models were performed within each cohort, adjusting for demographic and clinical risk factors, followed by fixed-effect meta-analyses. Large CHIP clones (defined as variant allele frequency >10%), HF with or without baseline coronary heart disease, and left ventricular ejection fraction were evaluated in secondary analyses. Results: Of 56,597 individuals (59% women, mean age 58 years at baseline), 3,406 (6%) had CHIP, and 4,694 developed HF (8.3%) over up to 20 years of follow-up. CHIP was prospectively associated with a 25% increased risk of HF in meta-analysis (hazard ratio: 1.25; 95% confidence interval: 1.13-1.38) with consistent associations across cohorts. ASXL1, TET2, and JAK2 sequence variations were each associated with an increased risk of HF, whereas DNMT3A sequence variations were not associated with HF. Secondary analyses suggested large CHIP was associated with a greater risk of HF (hazard ratio: 1.29; 95% confidence interval: 1.15-1.44), and the associations for CHIP on HF with and without prior coronary heart disease were homogenous. ASXL1 sequence variations were associated with reduced left ventricular ejection fraction. Conclusions: CHIP, particularly sequence variations in ASXL1, TET2, and JAK2, represents a new risk factor for HF

Clonal Hematopoiesis Is Associated with Higher Risk of Stroke

Background and Purpose: Clonal hematopoiesis of indeterminate potential (CHIP) is a novel age-related risk factor for cardiovascular disease-related morbidity and mortality. The association of CHIP with risk of incident ischemic stroke was reported previously in an exploratory analysis including a small number of incident stroke cases without replication and lack of stroke subphenotyping. The purpose of this study was to discover whether CHIP is a risk factor for ischemic or hemorrhagic stroke. Methods: We utilized plasma genome sequence data of blood DNA to identify CHIP in 78 752 individuals from 8 prospective cohorts and biobanks. We then assessed the association of CHIP and commonly mutated individual CHIP driver genes (DNMT3A, TET2, and ASXL1) with any stroke, ischemic stroke, and hemorrhagic stroke. Results: CHIP was associated with an increased risk of total stroke (hazard ratio, 1.14 [95% CI, 1.03-1.27]; P=0.01) after adjustment for age, sex, and race. We observed associations with CHIP with risk of hemorrhagic stroke (hazard ratio, 1.24 [95% CI, 1.01-1.51]; P=0.04) and with small vessel ischemic stroke subtypes. In gene-specific association results, TET2 showed the strongest association with total stroke and ischemic stroke, whereas DMNT3A and TET2 were each associated with increased risk of hemorrhagic stroke. Conclusions: CHIP is associated with an increased risk of stroke, particularly with hemorrhagic and small vessel ischemic stroke. Future studies clarifying the relationship between CHIP and subtypes of stroke are needed

Identification and diagnosis of patients with familial chylomicronaemia syndrome (FCS)

Familial chylomicronaemia syndrome (FCS) is a rare, inherited disorder characterised by impaired clearance of triglyceride (TG)-rich lipoproteins from plasma, leading to severe hypertriglyceridaemia (HTG) and a markedly increased risk of acute pancreatitis. It is due to the lack of lipoprotein lipase (LPL) function, resulting from recessive loss of function mutations in the genes coding LPL or its modulators. A large overlap in the phenotype between FCS and multifactorial chylomicronaemia syndrome (MCS) contributes to the inconsistency in how patients are diagnosed and managed worldwide, whereas the incidence of acute hypertriglyceridaemic pancreatitis is more frequent in FCS. A panel of European experts provided guidance on the diagn

The Polygenic and Monogenic Basis of Blood Traits and Diseases

Blood cells play essential roles in human health, underpinning physiological processes such as immunity, oxygen transport, and clotting, which when perturbed cause a significant global health burden. Here we integrate data from UK Biobank and a large-scale international collaborative effort, including data for 563,085 European ancestry participants, and discover 5,106 new genetic variants independently associated with 29 blood cell phenotypes covering a range of variation impacting hematopoiesis. We holistically characterize the genetic architecture of hematopoiesis, assess the relevance of the omnigenic model to blood cell phenotypes, delineate relevant hematopoietic cell states influenced by regulatory genetic variants and gene networks, identify novel splice-altering variants mediating the associations, and assess the polygenic prediction potential for blood traits and clinical disorders at the interface of complex and Mendelian genetics. These results show the power of large-scale blood cell trait GWAS to interrogate clinically meaningful variants across a wide allelic spectrum of human variation. Analysis of blood cell traits in the UK Biobank and other cohorts illuminates the full genetic architecture of hematopoietic phenotypes, with evidence supporting the omnigenic model for complex traits and linking polygenic burden with monogenic blood diseases