On occurrence of spectral edges for periodic operators inside the Brillouin zone

The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the (reduced) Brillouin zone only, rather than the whole zone? Or, do the edges of the spectrum occur necessarily at the set of ``corner'' high symmetry points? This is known to be true in 1D, while no apparent reasons exist for this to be happening in higher dimensions. In many practical cases, though, this appears to be correct, which sometimes leads to the claims that this is always true. There seems to be no definite answer in the literature, and one encounters different opinions about this problem in the community. In this paper, starting with simple discrete graph operators, we construct a variety of convincing multiply-periodic examples showing that the spectral edges might occur deeply inside the Brillouin zone. On the other hand, it is also shown that in a ``generic'' case, the situation of spectral edges appearing at high symmetry points is stable under small perturbations. This explains to some degree why in many (maybe even most) practical cases the statement still holds.Comment: 25 pages, 10 EPS figures. Typos corrected and a reference added in the new versio

Genome-wide association study of REM sleep behavior disorder identifies polygenic risk and brain expression effects

Rapid-eye movement (REM) sleep behavior disorder (RBD), enactment of dreams during REM sleep, is an early clinical symptom of alpha-synucleinopathies and defines a more severe subtype. The genetic background of RBD and its underlying mechanisms are not well understood. Here, we perform a genome-wide association study of RBD, identifying five RBD risk loci near SNCA, GBA, TMEM175, INPP5F, and SCARB2. Expression analyses highlight SNCA-AS1 and potentially SCARB2 differential expression in different brain regions in RBD, with SNCA-AS1 further supported by colocalization analyses. Polygenic risk score, pathway analysis, and genetic correlations provide further insights into RBD genetics, highlighting RBD as a unique alpha-synucleinopathy subpopulation that will allow future early intervention

Implantation of Mouse Embryonic Stem Cell-Derived Cardiac Progenitor Cells Preserves Function of Infarcted Murine Hearts

Stem cell transplantation holds great promise for the treatment of myocardial infarction injury. We recently described the embryonic stem cell-derived cardiac progenitor cells (CPCs) capable of differentiating into cardiomyocytes, vascular endothelium, and smooth muscle. In this study, we hypothesized that transplanted CPCs will preserve function of the infarcted heart by participating in both muscle replacement and neovascularization. Differentiated CPCs formed functional electromechanical junctions with cardiomyocytes in vitro and conducted action potentials over cm-scale distances. When transplanted into infarcted mouse hearts, CPCs engrafted long-term in the infarct zone and surrounding myocardium without causing teratomas or arrhythmias. The grafted cells differentiated into cross-striated cardiomyocytes forming gap junctions with the host cells, while also contributing to neovascularization. Serial echocardiography and pressure-volume catheterization demonstrated attenuated ventricular dilatation and preserved left ventricular fractional shortening, systolic and diastolic function. Our results demonstrate that CPCs can engraft, differentiate, and preserve the functional output of the infarcted heart

Imaging Long-Term Fate of Intramyocardially Implanted Mesenchymal Stem Cells in a Porcine Myocardial Infarction Model

The long-term fate of stem cells after intramyocardial delivery is unknown. We used noninvasive, repetitive PET/CT imaging with [18F]FEAU to monitor the long-term (up to 5 months) spatial-temporal dynamics of MSCs retrovirally transduced with the sr39HSV1-tk gene (sr39HSV1-tk-MSC) and implanted intramyocardially in pigs with induced acute myocardial infarction. Repetitive [18F]FEAU PET/CT revealed a biphasic pattern of sr39HSV1-tk-MSC dynamics; cell proliferation peaked at 33–35 days after injection, in periinfarct regions and the major cardiac lymphatic vessels and lymph nodes. The sr39HSV1-tk-MSC–associated [18F]FEAU signals gradually decreased thereafter. Cardiac lymphography studies using PG-Gd-NIRF813 contrast for MRI and near-infrared fluorescence imaging showed rapid clearance of the contrast from the site of intramyocardial injection through the subepicardial lymphatic network into the lymphatic vessels and periaortic lymph nodes. Immunohistochemical analysis of cardiac tissue obtained at 35 and 150 days demonstrated several types of sr39HSV1-tk expressing cells, including fibro-myoblasts, lymphovascular cells, and microvascular and arterial endothelium. In summary, this study demonstrated the feasibility and sensitivity of [18F]FEAU PET/CT imaging for long-term, in-vivo monitoring (up to 5 months) of the fate of intramyocardially injected sr39HSV1-tk-MSC cells. Intramyocardially transplanted MSCs appear to integrate into the lymphatic endothelium and may help improve myocardial lymphatic system function after MI