Topological and differentiable rigidity of submanifolds in space forms

Let $F^{n+p}(c)$ be an $(n+p)$-dimensional simply connected space form with nonnegative constant curvature $c$. We prove that if $M^n(n\geq4)$ is a compact submanifold in $F^{n+p}(c)$, and if $Ric_M>(n-2)(c+H^2),$ where $H$ is the mean curvature of $M$, then $M$ is homeomorphic to a sphere. We also show that the pinching condition above is sharp. Moreover, we obtain a new differentiable sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page

The sphere theorems for manifolds with positive scalar curvature

Some new differentiable sphere theorems are obtained via the Ricci flow and stable currents. We prove that if $M^n$ is a compact manifold whose normalized scalar curvature and sectional curvature satisfy the pointwise pinching condition $R_0>\sigma_{n}K_{\max}$, where $\sigma_n\in (\frac{1}{4},1)$ is an explicit positive constant, then $M$ is diffeomorphic to a spherical space form. This gives a partial answer to Yau's conjecture on pinching theorem. Moreover, we prove that if $M^n(n\geq3)$ is a compact manifold whose $(n-2)$-th Ricci curvature and normalized scalar curvature satisfy the pointwise condition $Ric^{(n-2)}_{\min}>\tau_n(n-2)R_0,$ where $\tau_n\in (\frac{1}{4},1)$ is an explicit positive constant, then $M$ is diffeomorphic to a spherical space form. We then extend the sphere theorems above to submanifolds in a Riemannian manifold. Finally we give a classification of submanifolds with weakly pinched curvatures, which improves the differentiable pinching theorems due to Andrews, Baker and the authors.Comment: 35 page

On-demand plerixafor added to high-dose cyclophosphamide and pegylated recombinant human granulocyte colony-stimulating factor in the mobilization of patients with multiple myeloma: a treatment with high effectiveness, convenient, and affordable cost

ObjectiveThe combination of high-dose cyclophosphamide (HD-Cy) (3g/m2) plus granulocyte colony-stimulating factor (G-CSF) and on-demand plerixafor (PXF) has been considered an effective mobilization regimen of patients with multiple myeloma(MM). However, the daily multi-injection regimen of G-CSF poses challenges. This study delves into the efficiency and cost implications of a novel approach, using HD-Cy alongside pegylated G-CSF (PEG G-CSF) and on-demand PXF. Unlike G-CSF, which necessitates daily injections, the half-life of PEG G-CSF extended allows for a single injection.MethodsA retrospective analysis was conducted on 350 MM patients, which were categorized based on their mobilization regimens: Cy+PEG G-CSF+/-PXF (n=66), Cy+PEG G-CSF (n=91), Cy+ G-CSF (n=169), and G-CSF+PXF (n=24).ResultsMobilization with Cy+PEG G-CSF+/-PXF(8.79)yielded a notably higher median CD34+ cell count compared to the other regimens: Cy+PEG G-CSF(4.96), Cy+G-CSF (4.65), and G-CSF+PXF (2.99) (P<0.001). The percentage of patients who achieved >6×106/kg CD34+ cells was significantly higher in the Cy+PEG G-CSF+/-PXF group (77.3%) than in the other mobilization regimens: Cy+PEG G-CSF (41.8%), Cy+ G-CSF (37.3%), and G-CSF+PXF (8.3%) (P<0.001). From a cost perspective, the Cy+PEG G-CSF+/-PXF approach was more economical than the G-CSF+PXF strategy but was marginally costlier than the other two methods. A multivariate assessment highlighted that the combination of Cy+PEG G-CSF with on-demand PXF had a superior potential to achieve the desired harvest (6×106/kg) compared to the Cy+PEG G-CSF protocol without PXF. The incremental cost-effectiveness ratio for each 1% increase in the probability of achieving a successful optimal harvest was $ 97.02 per patient. The incidence of neutropenic fever was 3.0% in the Cy+PEG G-CSF+/-PXF group.ConclusionThe combination of on-demand PXF with HD-Cy and PEG G-CSF offers a cost-effective approach with a high mobilization success rate, manageable side effects, and the convenience of fewer injections. It stands as a promising mobilization strategy for MM patients

p21 as a Transcriptional Co-Repressor of S-Phase and Mitotic Control Genes

It has been previously described that p21 functions not only as a CDK inhibitor but also as a transcriptional co-repressor in some systems. To investigate the roles of p21 in transcriptional control, we studied the gene expression changes in two human cell systems. Using a human leukemia cell line (K562) with inducible p21 expression and human primary keratinocytes with adenoviral-mediated p21 expression, we carried out microarray-based gene expression profiling. We found that p21 rapidly and strongly repressed the mRNA levels of a number of genes involved in cell cycle and mitosis. One of the most strongly down-regulated genes was CCNE2 (cyclin E2 gene). Mutational analysis in K562 cells showed that the N-terminal region of p21 is required for repression of gene expression of CCNE2 and other genes. Chromatin immunoprecipitation assays indicated that p21 was bound to human CCNE2 and other p21-repressed genes gene in the vicinity of the transcription start site. Moreover, p21 repressed human CCNE2 promoter-luciferase constructs in K562 cells. Bioinformatic analysis revealed that the CDE motif is present in most of the promoters of the p21-regulated genes. Altogether, the results suggest that p21 exerts a repressive effect on a relevant number of genes controlling S phase and mitosis. Thus, p21 activity as inhibitor of cell cycle progression would be mediated not only by the inhibition of CDKs but also by the transcriptional down-regulation of key genes

Prunella vulgaris: A comprehensive review of chemical constituents, pharmacological effects and clinical applications.

Prunella vulgaris (PV) is a perennial herb belonging to the Labiate family and is widely distributed in northeastern Asian countries such as Korea, Japan, and China. It is reported to display diverse biological activities including anti-microbial, anti-cancer, and anti-inflammation as determined by in vitro or in vivo studies. So far, about 200 compounds have been isolated from PV plant and majority of these have been characterized mainly as triterpenoids, sterols and flavonoids, followed by coumarins, phenylpropanoids, polysaccharides and volatile oils. This review summarizes and analyzes the current knowledge on the chemical constituents, pharmacological activities, mechanisms of action and clinical applications of the PV plant including its potential as a future medicinal plant. Although some of the chemical constituents of the PV plant and their mechanism of action have been investigated the biological activities of many of these remain unknown and further clinical trials are required to further enhance its reputation as a medicinal plant

A Search for Pulsars around Sgr A* in the First Event Horizon Telescope Data Set

In 2017 the Event Horizon Telescope (EHT) observed the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), at a frequency of 228.1 GHz (λ = 1.3 mm). The fundamental physics tests that even a single pulsar orbiting Sgr A* would enable motivate searching for pulsars in EHT data sets. The high observing frequency means that pulsars—which typically exhibit steep emission spectra—are expected to be very faint. However, it also negates pulse scattering, an effect that could hinder pulsar detections in the Galactic center. Additionally, magnetars or a secondary inverse Compton emission could be stronger at millimeter wavelengths than at lower frequencies. We present a search for pulsars close to Sgr A* using the data from the three most sensitive stations in the EHT 2017 campaign: the Atacama Large Millimeter/submillimeter Array, the Large Millimeter Telescope, and the IRAM 30 m Telescope. We apply three detection methods based on Fourier-domain analysis, the fast folding algorithm, and single-pulse searches targeting both pulsars and burst-like transient emission. We use the simultaneity of the observations to confirm potential candidates. No new pulsars or significant bursts were found. Being the first pulsar search ever carried out at such high radio frequencies, we detail our analysis methods and give a detailed estimation of the sensitivity of the search. We conclude that the EHT 2017 observations are only sensitive to a small fraction (≲2.2%) of the pulsars that may exist close to Sgr A*, motivating further searches for fainter pulsars in the region.</p