Strictly Toral Dynamics

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points $ine(f)$ is shown to be a disjoint union of periodic topological disks ("elliptic islands"), while the set of essential points $ess(f)$ is an essential continuum, with typically rich dynamics (the "chaotic region"). This generalizes and improves a similar description by J\"ager. The key result is boundedness of these "elliptic islands", which allows, among other things, to obtain sharp (uniform) bounds of the diffusion rates. We also show that the dynamics in $ess(f)$ is as rich as in $\mathbb{T}^2$ from the rotational viewpoint, and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points.Comment: Incorporates suggestions and corrections by the referees. To appear in Inv. Mat

Global surfaces of section in the planar restricted 3-body problem

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.Comment: 11 pages, 1 figur

Specific trends in phosphate glass crystallization

This paper focusses on investigating and comparing the congruent crystallization of phosphate glasses with different degrees of polymerization. The study was performed both on powders, with different size fractions, and coarse particles which can be assimilated to bulk. From DSC experiments, corroborated by SEM analysis, it was demonstrated that LiPO3 crystallizes from surface whereas LiGe2(PO4)3 crystallizes in the whole volume. Sn2P2O7 presented both phenomena, the nucleation time lag being short enough to observe internal crystallization at the laboratory time scale. Using the non-isothermal Ozawa method, the kinetic parameters of the overall devitrification process were determined in terms of the Avrami exponent and of the activation energy for crystallization. The temperature of the maximum nucleation rate was calculated by using the nucleation adiabatic theory. For the achievement of this calculation, the heat capacity temperature dependence up to melting was determined from DSC experiments. The results were found in a good agreement with the SEM observation and the results of the non-isothermal crystallization study.acceptedVersionPeer reviewe

PGL-III, a Rare Intermediate of <i>Mycobacterium leprae</i> Phenolic Glycolipid Biosynthesis, Is a Potent Mincle Ligand

Although leprosy (Hansen's disease) is one of the oldest known diseases, the pathogenicity of Mycobacterium leprae (M. leprae) remains enigmatic. Indeed, the cell wall components responsible for the immune response against M. leprae are as yet largely unidentified. We reveal here phenolic glycolipid-III (PGL-III) as an M. leprae-specific ligand for the immune receptor Mincle. PGL-III is a scarcely present trisaccharide intermediate in the biosynthetic pathway to PGL-I, an abundant and characteristic M. leprae glycolipid. Using activity-based purification, we identified PGL-III as a Mincle ligand that is more potent than the well-known M. tuberculosis trehalose dimycolate. The cocrystal structure of Mincle and a synthetic PGL-III analogue revealed a unique recognition mode, implying that it can engage multiple Mincle molecules. In Mincle-deficient mice infected with M. leprae, increased bacterial burden with gross pathologies were observed. These results show that PGL-III is a noncanonical ligand recognized by Mincle, triggering protective immunity. </p

Symplectically degenerate maxima via generating functions

We provide a simple proof of a theorem due to Nancy Hingston, asserting that symplectically degenerate maxima of any Hamiltonian diffeomorphism of the standard symplectic 2d-torus are non-isolated contractible periodic points or their action is a non-isolated point of the average-action spectrum. Our argument is based on generating functions.Comment: 25 pages, thoroughly revised version, new titl

Exposure to aflatoxin B1in uterois associated with DNA methylation in white blood cells of infants in The Gambia

Background Exposure to environmental toxins during embryonic development may lead to epigenetic changes that influence disease risk in later life. Aflatoxin is a contaminant of staple foods in sub-Saharan Africa, is a known human liver carcinogen and has been associated with stunting in infants. Methods We have measured aflatoxin exposure in 115 pregnant women in The Gambia and examined the DNA methylation status of white blood cells from their infants at 2-8 months old (mean 3.6 ± 0.9). Aflatoxin exposure in women was assessed using an ELISA method to measure aflatoxin albumin (AF-alb) adducts in plasma taken at 1-16 weeks of pregnancy. Genome-wide DNA methylation of infant white blood cells was measured using the Illumina Infinium HumanMethylation450beadchip. Results AF-alb levels ranged from 3.9 to 458.4 pg/mg albumin. We found that aflatoxin exposure in the mothers was associated to DNA methylation in their infants for 71 CpG sites (false discovery rate < 0.05), with an average effect size of 1.7% change in methylation. Aflatoxin-associated differential methylation was observed in growth factor genes such as FGF12 and IGF1, and immune-related genes such as CCL28, TLR2 and TGFBI. Moreover, one aflatoxin-associated methylation region (corresponding to the miR-4520b locus) was identified. Conclusions This study shows that maternal exposure to aflatoxin during the early stages of pregnancy is associated with differential DNA methylation patterns of infants, including in genes related to growth and immune function. This reinforces the need for interventions to reduce aflatoxin exposure, especially during critical periods of fetal and infant development