The absolute continuity of the integrated density of states for magnetic Schr\"odinger operators with certain unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr{\"o}dinger operator with magnetic field and a random potential which may be unbounded from above and below. In case that the magnetic field is constant and the random potential is ergodic and admits a so-called one-parameter decomposition, we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative, the density of states. This local Lipschitz continuity of the integrated density of states is derived by establishing a Wegner estimate for finite-volume Schr\"odinger operators which holds for rather general magnetic fields and different boundary conditions. Examples of random potentials to which the results apply are certain alloy-type and Gaussian random potentials. Besides we show a diamagnetic inequality for Schr\"odinger operators with Neumann boundary conditions.Comment: This paper will appear in "Communications in Mathematical Physics". It is a revised version of the second part of the first version of math-ph/0010013, which in its second version only contains the (revised) first par

Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Herstellung von LATP für den Einsatz als Festkörperelektrolyt und dessen Eigenschaften

In dieser Arbeit wird das oxidische Material Li₁₊ₓAlₓTi₂₋ₓ(PO₄)₃ (LATP) im Detail auf seine Eignung als Festkörperelektrolyt untersucht. Ausgehend von der Rohmaterialherstellung von LATP mittels Sol-Gel-Methoden über die Pulveraufbereitung bis zur Sinterung vollkeramischer Proben wird der vollständige Herstellungsprozess von LATP abgebildet und analysiert

Stat6-Dependent Inhibition of Mincle Expression in Mouse and Human Antigen-Presenting Cells by the Th2 Cytokine IL-4

The C-type lectin receptors (CLR) Mincle, Mcl and Dectin-2 bind mycobacterial and fungal cell wall glycolipids and carbohydrates. Recently, we described that expression of these CLR is down-regulated during differentiation of human monocytes to dendritic cells (DC) in the presence of GM-CSF and IL-4. Here, we demonstrate that the Th2 cytokine IL-4 specifically inhibits expression of Mincle, Mcl and Dectin-2in human APC. This inhibitory effect of IL-4 was observed across species, as murine macrophages and DC treated with IL-4 also down-regulated these receptors. IL-4 blocked up-regulation of Mincle and Mcl mRNA expression and cell surface protein by murine macrophages in response to the Mincle ligand Trehalose-6,6-dibehenate (TDB), whereas the TLR4 ligand LPS overcame inhibition by IL-4. Functionally, down-regulation of Mincle expression by IL-4 was accompanied by reduced cytokine production upon stimulation with TDB. These inhibitory effects of IL-4 were dependent on the transcription factor Stat6. Together, our results show that the key Th2 cytokine IL-4 exerts a negative effect on the expression of Mincle and other Dectin-2 cluster CLR in mouse and human macrophages and DC, which may render these sentinel cells less vigilant for sensing mycobacterial and fungal ligands

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics

Autoimmunity and immunodeficiency associated with monoallelic LIG4 mutations via haploinsufficiency

BACKGROUND: Biallelic mutations in LIG4 encoding DNA-ligase 4 cause a rare immunodeficiency syndrome manifesting as infant-onset life-threatening and/or opportunistic infections, skeletal malformations, radiosensitivity and neoplasia. LIG4 is pivotal during DNA repair and during V(D)J recombination as it performs the final DNA-break sealing step. OBJECTIVE: We explored whether monoallelic LIG4 missense mutations may underlie immunodeficiency and autoimmunity with autosomal dominant inheritance. METHODS: Extensive flow-cytometric immune-phenotyping was performed. Rare variants of immune system genes were analyzed by whole exome sequencing. DNA repair functionality and T cell-intrinsic DNA damage tolerance was tested with an ensemble of in vitro and in silico tools. Antigen-receptor diversity and autoimmune features were characterized by high-throughput sequencing and autoantibody arrays. Reconstitution of wild-type vs. mutant LIG4 were performed in LIG4 knock-out Jurkat T cells and DNA damage tolerance was subsequently assessed. RESULTS: A novel heterozygous LIG4 loss-of-function mutation (p.R580Q), associated with a dominantly inherited familial immune-dysregulation consisting of autoimmune cytopenias, and in the index patient with lymphoproliferation, agammaglobulinemia and adaptive immune cell infiltration into nonlymphoid organs. Immunophenotyping revealed reduced naïve CD4$^{+}$ T cells and low TCR-Vα7.2$^{+}$ T cells, while T/B-cell receptor repertoires showed only mild alterations. Cohort screening identified two other non-related patients with the monoallelic LIG4 mutation p.A842D recapitulating clinical and immune-phenotypic dysregulations observed in the index family and displaying T cell-intrinsic DNA damage intolerance. Reconstitution experiments and molecular dynamics simulations categorize both missense mutations as loss-of-function and haploinsufficient. CONCLUSION: We provide evidence that certain monoallelic LIG4 mutations may cause human immune dysregulation via haploinsufficiency

An exceptional horizontal gene transfer in plastids: gene replacement by a distant bacterial paralog and evidence that haptophyte and cryptophyte plastids are sisters

BACKGROUND: Horizontal gene transfer (HGT) to the plant mitochondrial genome has recently been shown to occur at a surprisingly high rate; however, little evidence has been found for HGT to the plastid genome, despite extensive sequencing. In this study, we analyzed all genes from sequenced plastid genomes to unearth any neglected cases of HGT and to obtain a measure of the overall extent of HGT to the plastid. RESULTS: Although several genes gave strongly supported conflicting trees under certain conditions, we are confident of HGT in only a single case beyond the rubisco HGT already reported. Most of the conflicts involved near neighbors connected by long branches (e.g. red algae and their secondary hosts), where phylogenetic methods are prone to mislead. However, three genes – clpP, ycf2, and rpl36 – provided strong support for taxa moving far from their organismal position. Further taxon sampling of clpP and ycf2 resulted in rejection of HGT due to long-branch attraction and a serious error in the published plastid genome sequence of Oenothera elata, respectively. A single new case, a bacterial rpl36 gene transferred into the ancestor of the cryptophyte and haptophyte plastids, appears to be a true HGT event. Interestingly, this rpl36 gene is a distantly related paralog of the rpl36 type found in other plastids and most eubacteria. Moreover, the transferred gene has physically replaced the native rpl36 gene, yet flanking genes and intergenic regions show no sign of HGT. This suggests that gene replacement somehow occurred by recombination at the very ends of rpl36, without the level and length of similarity normally expected to support recombination. CONCLUSION: The rpl36 HGT discovered in this study is of considerable interest in terms of both molecular mechanism and phylogeny. The plastid acquisition of a bacterial rpl36 gene via HGT provides the first strong evidence for a sister-group relationship between haptophyte and cryptophyte plastids to the exclusion of heterokont and alveolate plastids. Moreover, the bacterial gene has replaced the native plastid rpl36 gene by an uncertain mechanism that appears inconsistent with existing models for the recombinational basis of gene conversion