Critical set of eigenfunctions of the Laplacian

We give an upper bound for the $(n-1)$-dimensional Hausdorff measure of the critical set of eigenfunctions of the Laplacian on compact analytic Riemannian manifolds. This is the analog of H. Donnely and C. Fefferman result on nodal set of eigenfunctions.Comment: 21 page

Carleman Estimates for the Schrödinger Operator. Applications to Quantitative Uniqueness

International audienceOn a closed manifold, we give a quantitative Carleman estimate on the Schrödinger operator. We then deduce quantitative uniqueness results for solutions to the Schrödinger equation using doubling estimates. Finally we investigate the sharpness of this results with respect to the electric potential

Quantitative uniqueness for Schrödinger operator

International audienceWe give an upper bound on the vanishing order of solutions to Schrödinger equation on a compact smooth manifold. Our method is based on Carleman type inequalities, and gives a generalisation to a result of H. Donnely and C. Fefferman [DF88] on eigenfunctions. It also sharpens previous results of I. Kukavica [Kuk98]

Development of Macrophages with Altered Actin Organization in the Absence of MafB

In the hematopoietic system the bZip transcription factor MafB is selectively expressed at high levels in monocytes and macrophages and promotes macrophage differentiation in myeloid progenitors, whereas a dominant-negative allele can inhibit this process. To analyze the requirement of MafB for macrophage development, we generated MafB-deficient mice and, due to their neonatal lethal phenotype, analyzed macrophage differentiation in vitro, in the embryo, and in reconstituted mice. Surprisingly we observed in vitro differentiation of macrophages from E14.5 fetal liver (FL) cells and E18.5 splenocytes. Furthermore we found normal numbers of F4/80(+)/Mac-1(+) macrophages and monocytes in fetal liver, spleen, and blood as well as in bone marrow, spleen, and peritoneum of adult MafB(−/−) FL reconstituted mice. MafB(−/−) macrophages showed intact basic macrophage functions such as phagocytosis of latex beads or Listeria monocytogenes and nitric oxide production in response to lipopolysaccharide. By contrast, MafB(−/−) macrophages expressed increased levels of multiple genes involved in actin organization. Consistent with this, phalloidin staining revealed an altered morphology involving increased numbers of branched protrusions of MafB(−/−) macrophages in response to macrophage colony-stimulating factor. Together these data point to an unexpected redundancy of MafB function in macrophage differentiation and a previously unknown role in actin-dependent macrophage morphology

SUMO Modification Regulates MafB-Driven Macrophage Differentiation by Enabling Myb-Dependent Transcriptional Repression.

During the execution of differentiation programs, lineage-specific transcription factors are in competition with antagonistic factors that drive progenitor proliferation. Thus, the myeloid transcription factor MafB promotes macrophage differentiation of myeloid progenitors, but a constitutively active Myb transcription factor (v-Myb) can maintain proliferation and block differentiation. Little is known, however, about the regulatory mechanisms that control such competing activities. Here we report that the small ubiquitin-like protein SUMO-1 can modify MafB in vitro and in vivo on lysines 32 and 297. The absence of MafB SUMO modification increased MafB-driven transactivation and macrophage differentiation potential but inhibited cell cycle progression and myeloid progenitor growth. Furthermore, we observed that direct repression of MafB transactivation by v-Myb was strictly dependent on MafB SUMO modification. Consequently, a SUMOylation-deficient MafB K32R K297R (K32,297R) mutant could specify macrophage fate even after activation of inducible Myb alleles and resist their differentiation-inhibiting activity. Our findings suggest that SUMO modification of MafB affects the balance between myeloid progenitor expansion and terminal macrophage differentiation by controlling MafB transactivation capacity and susceptibility to Myb repression. SUMO modification of lineage-specific transcription factors may thus modulate transcription factor antagonism to control tissue homeostasis in the hematopoietic system

New high-resolution analysis of the ν7 and ν9 fundamental bands of trans-formic acid by IR Fourier transform and millimeterwave spectroscopies

info:eu-repo/semantics/publishe

Some non-stability results for geometric Paneitz–Branson type equations

International audienceLet (M, g) be a compact riemannian manifold of dimension n ≥ 5. We consider two Paneitz-Branson type equations with general coefficients ∆ 2 g u − div g (A g du) + hu = |u| 2 * −2−ε u on M, (E1) and ∆ 2 g u − div g ((A g + εB g)du) + hu = |u| 2 * −2 u on M, (E2) where A g and B g are smooth symmetric (2, 0)-tensors, h ∈ C ∞ (M), 2 * = 2n n − 4 and ε is a small positive parameter. Under suitable assumptions , we construct solutions u ε to (??) and (??) which blow up at one point of the manifold when ε tends to 0. In particular, we extend the result of Deng and Pistoia 2011 (to the case where A g is the one defined in the Paneitz operator) and the result of Pistoia and Vaira 2013 (to the case n = 8 and (M, g) locally conformally flat)