On certain modules of covariants in exterior algebras

We study the structure of the space of covariants $B:=\left(\bigwedge (\mathfrak g/\mathfrak k)^*\otimes \mathfrak g\right)^{\mathfrak k},$ for a certain class of infinitesimal symmetric spaces $(\mathfrak g,\mathfrak k)$ such that the space of invariants $A:=\left(\bigwedge (\mathfrak g/\mathfrak k)^*\right)^{\mathfrak k}$ is an exterior algebra $\wedge (x_1,...,x_r),$ with $r=rk(\mathfrak g)-rk(\mathfrak k)$. We prove that they are free modules over the subalgebra $A_{r-1}=\wedge (x_1,...,x_{r-1})$ of rank $4r$. In addition we will give an explicit basis of $B$. As particular cases we will recover same classical results. In fact we will describe the structure of $\left(\bigwedge (M_n^{\pm})^*\otimes M_n\right)^G$, the space of the $G-$equivariant matrix valued alternating multilinear maps on the space of (skew-symmetric or symmetric with respect to a specific involution) matrices, where $G$ is the symplectic group or the odd orthogonal group. Furthermore we prove new polynomial trace identities.Comment: Title changed. Results have been generalised to other infinitesimal symmetric space

Network segregation in a model of misinformation and fact checking

Misinformation under the form of rumor, hoaxes, and conspiracy theories spreads on social media at alarming rates. One hypothesis is that, since social media are shaped by homophily, belief in misinformation may be more likely to thrive on those social circles that are segregated from the rest of the network. One possible antidote is fact checking which, in some cases, is known to stop rumors from spreading further. However, fact checking may also backfire and reinforce the belief in a hoax. Here we take into account the combination of network segregation, finite memory and attention, and fact-checking efforts. We consider a compartmental model of two interacting epidemic processes over a network that is segregated between gullible and skeptic users. Extensive simulation and mean-field analysis show that a more segregated network facilitates the spread of a hoax only at low forgetting rates, but has no effect when agents forget at faster rates. This finding may inform the development of mitigation techniques and overall inform on the risks of uncontrolled misinformation online

Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H of G. Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be time-dependent to yield a form of quantum mechanics on the co-adjoint orbit. The quantum states correspond to symmetric tensor representations of the symmetry group H and have the interpretation of a fuzzy geometric version of the co-adjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final journal versio

Derivations and automorphisms of free nilpotent Lie algebras and their quotiens

Let \n_{d,t} be the free nilpotent Lie algebra of type $d$ and nilindex $t$. Starting out with the derivation algebra and the automorphism group of \n_{d,t}, we get a natural description of derivations and automorphisms of any generic nilpotent Lie algebra of the same type and nilindex. Moreover, along the paper we discuss several examples to illustrate the obtained results.Comment: 13 page

Early endostatin treatment inhibits metastatic seeding of murine colorectal cancer cells in the liver and their adhesion to endothelial cells

Endostatin, a carboxy-terminal fragment of collagen XVIII, potently inhibits angiogenesis and tumour growth, presumably through induction of apoptosis in endothelial cells and/or inhibition of their migration. Here we have tested how the timing of recombinant human endostatin (rh-E) administration affects its antitumour activity in a liver metastasis model of mouse C26 colorectal carcinoma cells. The effects of rh-E treatment on hepatic tumour load and on early tumour cell seeding were evaluated. Recombinant human endostatin was most effective in reducing intrahepatic tumour growth when administered prior to tumour cell inoculation. Analysis of early tumour cell seeding by using [125I]iododeoxyuridine-labelled C26 cells or by in vivo microscopy showed that rh-E reduced tumour cell seeding in the liver sinusoids. Recombinant human endostatin did not inhibit tumour growth when administered later than 4 days after tumour injection. Pretreatment of human umbilical vein endothelial cells with rh-E in vitro reduced C26 tumour cell adhesion under flow conditions two-fold as assessed by video microscopy and multiphoton laser scanning microscopy. Our results show that rh-E, in addition to antiangiogenic effects, reduces tumour cell adhesion in the liver sinusoids during the very early phases of metastasis formation. These data point towards a previously unknown mode of action of endostatin, that is, its ability to interfere with tumour cell seeding. Such insights may be helpful in the design of trials to improve (surgical) treatment of colorectal carcinoma and liver metastases

rs5888 Variant of SCARB1 Gene Is a Possible Susceptibility Factor for Age-Related Macular Degeneration

Major genetic factors for age-related macular degeneration (AMD) have recently been identified as susceptibility risk factors, including variants in the CFH gene and the ARMS2 LOC387715/HTRA1locus. Our purpose was to perform a case-control study in two populations among individuals who did not carry risk variants for CFHY402H and LOC387715 A69S (ARMS2), called “study” individuals, in order to identify new genetic risk factors. Based on a candidate gene approach, we analyzed SNP rs5888 of the SCARB1 gene, coding for SRBI, which is involved in the lipid and lutein pathways. This study was conducted in a French series of 1241 AMD patients and 297 controls, and in a North American series of 1257 patients with advanced AMD and 1732 controls. Among these individuals, we identified 61 French patients, 77 French controls, 85 North American patients and 338 North American controls who did not carry the CFH nor ARMS2 polymorphisms. An association between AMD and the SCARB1 gene was seen among the study subjects. The genotypic distribution of the rs5888 polymorphism was significantly different between cases and controls in the French population (p<0.006). Heterozygosity at the rs5888 SNP increased risk of AMD compared to the CC genotypes in the French study population (odds ratio (OR) = 3.5, CI95%: 1.4–8.9, p<0.01) and after pooling the 2 populations (OR = 2.9, 95% CI: 1.6–5.3, p<0.002). Subgroup analysis in exudative forms of AMD revealed a pooled OR of 3.6 for individuals heterozygous for rs5888 (95% CI: 1.7–7.6, p<0.0015). These results suggest the possible contribution of SCARB1, a new genetic factor in AMD, and implicate a role for cholesterol and antioxidant micronutrient (lutein and vitamin E) metabolism in AMD

Neck circumference is associated with adipose tissue content in thigh skeletal muscle in overweight and obese premenopausal women

Neck circumference (NC) has been proposed as a simple and practical tool, independently associated with cardiometabolic risk factors. However, the association of NC with inter-muscular adipose tissue (IMAT) is still to be determined. We aimed to examine the association of NC with thigh IMAT, and visceral adipose tissue (VAT) measured with computed tomography (CT) in overweight/obese women. 142 premenopausal overweight and obese Caucasian women participated in this crosssectional study. NC was measured with an inextensible metallic tape above the thyroid cartilage according to International Society for Advancement of Kinanthropometry protocol. Thigh IMAT and VAT volumes were measured with a single cross-sectional CT. Regarding the covariates, fat mass (FM) was assessed with dual-energy x-ray absorptiometry and physical activity was objectively measured with accelerometry. NC was positively associated with thigh IMAT and VAT volumes (standardized β coefcient: β=0.45, P-value= ≤0.001, β=0.60, P=≤0.001; respectively), which persisted after adjusting for age, height, overall FM or moderate-to-vigorous physical activity. Our fndings show that NC is associated with thigh IMAT volume in overweight and obese premenopausal Caucasian women, regardless of the amount of lower-body fatness. These results suggest underscoring the relevance of NC as a marker of adipose tissue content in thigh skeletal muscle.Portuguese Foundation for Science and Technology Sapiens 358007/99Oeiras City CouncilBecel PortugalRoche Pharmaceuticals PortugalCompal PortugalUniversity of Granada Plan Propio de Investigacion 2016 -Excellence actions: Unit of Excellence on Exercise and Health (UCEES)Junta de AndaluciaEuropean Union (EU) SOMM17/6107/UGRFundacion Carolina C.201657496

PABPN1 gene therapy for oculopharyngeal muscular dystrophy

International audienceOculopharyngeal muscular dystrophy (OPMD) is an autosomal dominant, late-onset muscle disorder characterized by ptosis, swallowing difficulties, proximal limb weakness and nuclear aggregates in skeletal muscles. OPMD is caused by a trinucleotide repeat expansion in the PABPN1 gene that results in an N-terminal expanded polyalanine tract in polyA-binding protein nuclear 1 (PABPN1). Here we show that the treatment of a mouse model of OPMD with an adeno-associated virus-based gene therapy combining complete knockdown of endogenous PABPN1 and its replacement by a wild-type PABPN1 substantially reduces the amount of insoluble aggregates, decreases muscle fibrosis, reverts muscle strength to the level of healthy muscles and normalizes the muscle transcriptome. The efficacy of the combined treatment is further confirmed in cells derived from OPMD patients. These results pave the way towards a gene replacement approach for OPMD treatment

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur