Instability of bound states of a nonlinear Schr\"odinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing wave solution is stable in \hurad and unstable in \hu under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a {\em finite-width instability}). In the non-radial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability

Identification of marker genes distinguishing human periodontal ligament cells from human mesenchymal stem cells and human gingival fibroblasts

Background and Objective: Molecular gene markers, which can distinguish human bone marrow mesenchymal stem cells from human fibroblasts, have recently been reported. Messenger RNA levels of tissue factor pathway inhibitor-2, major histocompatibility complex-DR-α, major histocompatibility complex-DR-β, and neuroserpin are higher in human bone marrow mesenchymal stem cells than in human fibroblasts. However, human bone marrow mesenchymal stem cells express less apolipoprotein D mRNA than human fibroblasts. Periodontal ligament cells are a heterogeneous cell population including fibroblasts, mesenchymal stem cells, and progenitor cells of osteoblasts or cementoblasts. The use of molecular markers that distinguish human bone marrow mesenchymal stem cells from human fibroblasts may provide insight into the characteristics of human periodontal ligament cells. In this study, we compared the molecular markers of human periodontal ligament cells with those of human bone marrow mesenchymal stem cells and human gingival fibroblasts.Material and Methods: The mRNA expression of the molecular gene markers was analyzed using real-time polymerase chain reaction. Statistical differences were determined with the two-sided Mann–Whitney U-test.Results: Messenger RNA levels of major histocompatibility complex-DR-α and major histocompatibility complex-DR-β were lower and higher, respectively, in human periodontal ligament cells than in human bone marrow mesenchymal stem cells or human gingival fibroblasts. Human periodontal ligament cells showed the lowest apolipoprotein D mRNA levels among the three types of cells.Conclusion: Human periodontal ligament cells may be distinguished from human bone marrow mesenchymal stem cells and human gingival fibroblasts by the genes for apolipoprotein D, major histocompatibility complex-DR-α, and major histocompatibility complex-DR-β

Sorting of GPI-anchored proteins into ER exit sites by p24 proteins is dependent on remodeled GPI

Glycosylphosphatidylinositol (GPI) anchoring of proteins is a posttranslational modification occurring in the endoplasmic reticulum (ER). After GPI attachment, proteins are transported by coat protein complex II (COPII)-coated vesicles from the ER. Because GPI-anchored proteins (GPI-APs) are localized in the lumen, they cannot interact with cytosolic COPII components directly. Receptors that link GPI-APs to COPII are thought to be involved in efficient packaging of GPI-APs into vesicles; however, mechanisms of GPI-AP sorting are not well understood. Here we describe two remodeling reactions for GPI anchors, mediated by PGAP1 and PGAP5, which were required for sorting of GPI-APs to ER exit sites. The p24 family of proteins recognized the remodeled GPI-APs and sorted them into COPII vesicles. Association of p24 proteins with GPI-APs was pH dependent, which suggests that they bind in the ER and dissociate in post-ER acidic compartments. Our results indicate that p24 complexes act as cargo receptors for correctly remodeled GPI-APs to be sorted into COPII vesicles

Optical anomalous Hall effect enhanced by flat bands in ferromagnetic van der Waals semimetal

Abstract Geometrical aspects of electronic states in condensed matter have led to the experimental realization of enhanced electromagnetic phenomena, as exemplified by the giant anomalous Hall effect (AHE) in topological semimetals. However, the guideline to the large AHE is still immature due to lack of profound understanding of the sources of the Berry curvature in actual electronic structures; the main focus has concentrated only on the band crossings near the Fermi level. Here, we show that the band crossings and flat bands cooperatively produce the large intrinsic AHE in ferromagnetic nodal line semimetal candidate Fe3GeTe2. The terahertz and infrared magneto-optical spectroscopy reveals that two explicit resonance structures in the optical Hall conductivity spectra σ xy (ω) are closely related to the AHE. The first-principles calculation suggests that both the flat bands having large density of states (DOS) and the band crossings near the Fermi level are the main causes of these Hall resonances. Our findings unveil a mechanism to enhance the AHE based on the flat bands, which gives insights into the topological material design