Semiclassical analysis for a Schr\"odinger operator with a U(2) artificial gauge: the periodic case

We consider a Schr\"odinger operator with a Hermitian 2x2 matrix-valued potential which is lattice periodic and can be diagonalized smoothly on the whole $R^n.$ In the case of potential taking its minimum only on the lattice, we prove that the well-known semiclassical asymptotic of first band spectrum for a scalar potential remains valid for our model

Magnetic bottles on the Poincar\'e half-plane: spectral asymptotics

We consider a magnetic laplacian P(A) on the Poincar\'e half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues

Accuracy on eigenvalues for a Schrodinger operator with a degenerate potential in the semi-classical limit

We consider a semi-classical Schrodinger operator with a degenerate potential V(x,y) =f(x) g(y) . g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum. We give sharp asymptotic behaviour of low eigenvalues bounded by some power of the parameter h, by improving Born-Oppenheimer approximation

Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian

We consider a non compact, complete manifold {\bf{M}} of finite area with cuspidal ends. The generic cusp is isomorphic to ${\bf{X}}\times ]1,+\infty [$ with metric $ds^2=(h+dy^2)/y^{2\delta}.$ {\bf{X}} is a compact manifold with nonzero first Betti number equipped with the metric $h.$ For a one-form $A$ on {\bf{M}} such that in each cusp $A$ is a non exact one-form on the boundary at infinity, we prove that the magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ satisfies the Weyl asymptotic formula with sharp remainder. We deduce an upper bound for the counting function of the embedded eigenvalues of the Laplace-Beltrami operator $-\Delta =-\Delta_0.

Updated results on atypical human trypanosomoses caused by animal trypanosomes

There are only two classical human forms of trypanosomoses, they are sleeping sickness in Africa (Trypanosoma brucei spp.) and Chagas' disease (T. cruzi) mainly in South America respectively. Other trypanosomes can infect a wide range of wild and domestic animals (fish, reptile, amphibians, mammals including cattle), but they are not supposed to be infective to human beings. However, several human cases infected by animal trypanosomes have been recently reported, in particular Trypanosoma lewisi (a Rattus trypanosome usually transmitted by fleas), and T. evansi (found for instance in cattle, camels, and mechanically transmitted by blood sucking insects such as tabanids or stomoxes). High density lipoprotein (HDL) in normal human serum (NHS) contains several compounds (e.g. ApoL-1) which protect us against African trypanosomes. The Indian patient infected with T. evansi reported in 2005 because of a genetic deletion was confirmed in the ApoL-1 gene in this patient, while another naturally T. evansi infected patient reported in Viet Nam in 2015 had a normal ApoL-1. The mode of transmission suspected in both cases was direct contamination via a wound while butchering raw beef. Both patients were cured successfully by using suramine, a drug for the acute form of sleeping sickness. Human infected with T. lewisi was mainly reported in babies. Although most of cases were transient infections, other required treatment or died. A recent case died from T. lewisi infection in India in 2015. It has been demonstrated that this parasite is resistant to NHS. Thus, T. lewisi is potentially a human pathogen or zoonotic pathogen. We present the new cases either described or suspected since the 2012, and previous cases as well (including infection by T. b. brucei, T. congolense). The problem of diagnosis and treatment will be considered, and the potential risk of emergence of a new zoonotic disease will be discussed

Lipid droplets and lipotoxicity during autophagy.

Lipid droplets (LDs) are neutral lipid storage organelles that provide a rapidly accessible source of fatty acids (FAs) for energy during periods of nutrient deprivation. Surprisingly, lipids released by the macroautophagic/autophagic breakdown of membranous organelles are packaged and stored in new LDs during periods of prolonged starvation. Why cells would store FAs during an energy crisis was unknown. In our recent study, we demonstrated that FAs released during MTORC1-regulated autophagy are selectively channeled by DGAT1 (diacylglycerol O-acyltransferase 1) into triacylglycerol (TAG)-rich LDs. These DGAT1-dependent LDs sequester FAs and prevent the accumulation of acylcarnitines, which otherwise directly disrupt mitochondrial integrity. Our findings establish LD biogenesis as a general cellular response to periods of high autophagic flux that provide a lipid buffering system to mitigate lipotoxic cellular damage