Entropies, volumes, and Einstein metrics

We survey the definitions and some important properties of several asymptotic invariants of smooth manifolds, and discuss some open questions related to them. We prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms. We also formulate an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov--Hitchin--Thorpe inequality and Sambusetti's obstruction.Comment: This is a substantial revision and expansion of the 2004 preprint, which I prepared in spring of 2010 and which has since been published. The version here is essentially the published one, minus the problems introduced by Springer productio

Inverse problems for the connection Laplacian

We reconstruct a Riemannian manifold and a Hermitian vector bundle with compatible connection from the hyperbolic Dirichlet-to-Neumann operator associated with the wave equation of the connection Laplacian. The boundary data is local and the reconstruction is up to the natural gauge transformations of the problem. As a corollary we derive an elliptic analogue of the main result which solves a Calderón problem for connections on a cylinder

Linearization of Cohomology-free Vector Fields

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group

Energy transfer in a fast-slow Hamiltonian system

We consider a finite region of a lattice of weakly interacting geodesic flows on manifolds of negative curvature and we show that, when rescaling the interactions and the time appropriately, the energies of the flows evolve according to a non linear diffusion equation. This is a first step toward the derivation of macroscopic equations from a Hamiltonian microscopic dynamics in the case of weakly coupled systems

Methyl donor supplementation in rats reverses the deleterious effect of maternal separation on depression-like behaviour

Adverse early life events are associated with altered stress responsiveness and metabolic disturbances in the adult life. Dietary methyl donor supplementation could be able to reverse the negative effects of maternal separation by affecting DNA methylation in the brain. In this study, maternal separation during lactation reduced body weight gain in the female adult offspring without affecting food intake, and altered total and HDL-cholesterol levels. Also, maternal separation induced a cognitive deficit as measured by NORT and an increase in the immobility time in the Porsolt forced swimming test, consistent with increased depression-like behaviour. An 18-week dietary supplementation with methyl donors (choline, betaine, folate and vitamin B12) from postnatal day 60 also reduced body weight without affecting food intake. Some of the deleterious effects induced by maternal separation, such as the abnormal levels of total and HDL-cholesterol, but especially the depression-like behaviour as measured by the Porsolt test, were reversed by methyl donor supplementation. Also, the administration of methyl donors increased total DNA methylation (measured by immunohistochemistry) and affected the expression of insulin receptor in the hippocampus of the adult offspring. However, no changes were observed in the DNA methylation status of insulin receptor and corticotropin-releasing hormone (CRH) promoter regions in the hypothalamus. In summary, methyl donor supplementation reversed some of the deleterious effects of an early life-induced model of depression in rats and altered the DNA methylation profile in the brain

Prenatal stress increases the obesogenic effects of a high-fat-sucrose diet in adult rats in a sex-specific manner

Stress during pregnancy can induce metabolic disorders in adult offspring. To analyze the possible differential response to a high-fat-sucrose (HFS) diet in offspring affected by prenatal stress (PNS) or not, pregnant Wistar rats (n = 11) were exposed to a chronic mild stress during the third week of gestation. The aim of this study was to model a chronic depressive-like state that develops over time in response to exposure of rats to a series of mild and unpredictable stressors. Control dams (n = 11) remained undisturbed. Adult offspring were fed chow or HFS diet (20% protein, 35% carbohydrate, 45% fat) for 10 weeks. Changes in adiposity, biochemical profile, and retroperitoneal adipose tissue gene expression by real-time polymerase chain reaction were analyzed. An interaction was observed between HFS and PNS concerning visceral adiposity, with higher fat mass in HFS-fed stressed rats, statistically significant only in females. HFS modified lipid profile and increased insulin resistance biomarkers, while PNS reduced insulin concentrations and the homeostasis model assessment index. HFS diet increased gene (mRNA) expression for leptin and apelin and decreased cyclin-dependent kinase inhibitor 1A and fatty acid synthase (Fasn), whereas PNS increased Fasn and stearoyl-CoA desaturase1. An interaction between diet and PNS was observed for adiponutrin (Adpn) and peroxisome proliferator-activated receptor-gamma coactivator1-alpha (Ppargc1a) gene expression: Adpn was increased by the PNS only in HFS-fed rats, whereas Ppargc1a was increased by the PNS only in chow-fed rats. From these results, it can be concluded that experience of maternal stress during intrauterine development can enhance predisposition to obesity induced by a HFS diet intak

Metals detected by ICP/MS in wound tissue of war injuries without fragments in Gaza

<p>Abstract</p> <p>Background</p> <p>The amount and identity of metals incorporated into "weapons without fragments" remain undisclosed to health personnel. This poses a long-term risk of assumption and contributes to additional hazards for victims because of increased difficulties with clinical management. We assessed if there was evidence that metals are embedded in "wounds without fragments" of victims of the Israeli military operations in Gaza in 2006 and 2009.</p> <p>Methods</p> <p>Biopsies of "wounds without fragments" from clinically classified injuries, amputation (A), charred (C), burns (B), multiple piercing wounds by White Phosphorus (WP) (M), were analyzed by ICP/MS for content in 32 metals.</p> <p>Results</p> <p>Toxic and carcinogenic metals were detected in folds over control tissues in wound tissues from all injuries: in A and C wounds (Al, Ti, Cu, Sr, Ba, Co, Hg, V, Cs and Sn), in M wounds (Al, Ti, Cu, Sr, Ba, Co and Hg) and in B wounds (Co, Hg, Cs, and Sn); Pb and U in wounds of all classes; B, As, Mn, Rb, Cd, Cr, Zn in wounds of all classes, but M; Ni was in wounds of class A. Kind and amounts of metals correlate with clinical classification of injuries, exposing a specific metal signature, similar for 2006 and 2009 samples.</p> <p>Conclusions</p> <p>The presence of toxic and carcinogenic metals in wound tissue is indicative of the presence in weapon inducing the injury. Metal contamination of wounds carries unknown long term risks for survivors, and can imply effects on populations from environmental contamination. We discuss remediation strategies, and believe that these data suggest the need for epidemiological and environmental surveys.</p