The Seven-sphere and its Kac-Moody Algebra

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

Weakly Z symmetric manifolds

We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective- Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named "weakly Z symmetric" and denoted by (WZS)_n. If the Z tensor is singular we give conditions for the existence of a proper concircular vector. For non singular Z tensor, we study the closedness property of the associated covectors and give sufficient conditions for the existence of a proper concircular vector in the conformally harmonic case, and the general form of the Ricci tensor. For conformally flat (WZS)_n manifolds, we derive the local form of the metric tensor.Comment: 13 page

Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

The X-ray Correlation Spectroscopy instrument at the Linac Coherent Light Source

The X-ray Correlation Spectroscopy instrument is dedicated to the study of dynamics in condensed matter systems using the unique coherence properties of free-electron lasers. It covers a photon energy range of 4–25 keV. The intrinsic temporal characteristics of the Linac Coherent Light Source, in particular the 120 Hz repetition rate, allow for the investigation of slow dynamics (milli-seconds) by means of X-ray photon correlation spectroscopy. Double-pulse schemes could probe dynamics on the picosecond timescale. A description of theinstrument capabilities and recent achievements is presented

Risk loci involved in giant cell arteritis susceptibility: a genome-wide association study

Background: Giant cell arteritis is an age-related vasculitis that mainly affects the aorta and its branches in individuals aged 50 years and older. Current options for diagnosis and treatment are scarce, highlighting the need to better understand its underlying pathogenesis. Genome-wide association studies (GWAS) have emerged as a powerful tool for unravelling the pathogenic mechanisms involved in complex diseases. We aimed to characterise the genetic basis of giant cell arteritis by performing the largest GWAS of this vasculitis to date and to assess the functional consequences and clinical implications of identified risk loci. Methods: We collected and meta-analysed genomic data from patients with giant cell arteritis and healthy controls of European ancestry from ten cohorts across Europe and North America. Eligible patients required confirmation of giant cell arteritis diagnosis by positive temporal artery biopsy, positive temporal artery doppler ultrasonography, or imaging techniques confirming large-vessel vasculitis. We assessed the functional consequences of loci associated with giant cell arteritis using cell enrichment analysis, fine-mapping, and causal gene prioritisation. We also performed a drug repurposing analysis and developed a polygenic risk score to explore the clinical implications of our findings. Findings: We included a total of 3498 patients with giant cell arteritis and 15 550 controls. We identified three novel loci associated with risk of giant cell arteritis. Two loci, MFGE8 (rs8029053; p=4·96 × 10–8; OR 1·19 [95% CI 1·12–1·26]) and VTN (rs704; p=2·75 × 10–9; OR 0·84 [0·79–0·89]), were related to angiogenesis pathways and the third locus, CCDC25 (rs11782624; p=1·28 × 10–8; OR 1·18 [1·12–1·25]), was related to neutrophil extracellular traps (NETs). We also found an association between this vasculitis and HLA region and PLG. Variants associated with giant cell arteritis seemed to fulfil a specific regulatory role in crucial immune cell types. Furthermore, we identified several drugs that could represent promising candidates for treatment of this disease. The polygenic risk score model was able to identify individuals at increased risk of developing giant cell arteritis (90th percentile OR 2·87 [95% CI 2·15–3·82]; p=1·73 × 10–13). Interpretation: We have found several additional loci associated with giant cell arteritis, highlighting the crucial role of angiogenesis in disease susceptibility. Our study represents a step forward in the translation of genomic findings to clinical practice in giant cell arteritis, proposing new treatments and a method to measure genetic predisposition to this vasculitis. Funding: Institute of Health Carlos III, Spanish Ministry of Science and Innovation, UK Medical Research Council, and National Institute for Health and Care Researc

Age, anticoagulants, hypertension and cardiovascular genetic traits predict cranial ischaemic complications in patients with giant cell arteritis

\ua9 Author(s) (or their employer(s)) 2024. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ on behalf of EULAR.Objectives: This project aimed to determine whether cranial ischaemic complications at the presentation of giant cell arteritis (GCA) were associated with pre-existing cardiovascular (CV) risk factors, CV disease or genetic risk of CV-related traits. Methods: 1946 GCA patients with clinicodemographic data at GCA presentation were included. Associations between pre-existing CV-related traits (including Polygenic Risk Scores (PRS) for CV traits) and cranial ischaemic complications were tested. A model for cranial ischaemic complications was optimised using an elastic net approach. Positional gene mapping of associated PRS was performed to improve biological understanding. Results: In a sample of 1946 GCA patients (median age=71, 68.7% female), 17% had cranial ischaemic complications at presentation. In univariable analyses, 10 variables were associated with complications (likelihood-ratio test p≤0.05). In multivariable analysis, the two variables with the strongest effects, with or without PRS in the model, were anticoagulant therapy (adjusted OR (95% CI)=0.21 (0.05 to 0.62), p=4.95 710-3) and age (adjusted OR (95% CI)=1.60 (0.73 to 3.66), p=2.52 710-3, for ≥80 years versus <60 years). In sensitivity analyses omitting anticoagulant therapy from multivariable analysis, age and hypertension were associated with cranial ischaemic complications at presentation (hypertension: adjusted OR (95% CI)=1.35 (1.03 to 1.75), p=0.03). Positional gene mapping of an associated transient ischaemic attack PRS identified TEK, CD96 and MROH9 loci. Conclusion: Age and hypertension were risk factors for cranial ischaemic complications at GCA presentation, but in this dataset, anticoagulation appeared protective. Positional gene mapping suggested a role for immune and coagulation-related pathways in the pathogenesis of complications. Further studies are needed before implementation in clinical practice