A probabilistic method for gradient estimates of some geometric flows

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the Ricci flow, the mean curvature flow, the forced mean curvature flow and the Yamabe flow respectively. Our conclusion gives another example that probabilistic tools can be used to simplify proofs for some problems in geometric analysis.Comment: 22 pages. Minor revision to v1. Accepted for publication in Stochastic Processes and their Application

The catalogues and mid-infrared environment of Interstellar OH Masers

Data for a number of OH maser lines have been collected from surveys. The posi- tions are compared to recent mid-infrared (MIR) surveys such as Spitzer-GLIMPSE and WISE, restricting the comparison to point sources. The colors and intensities of the IR sources are compared. There are many 18 cm OH masers, but far fewer in lines arising from higher energy levels. We also make a comparison with the 5 cm Class II methanol masers. We have divided the results into 3 subsamples: those associated with OH masers only, those associated with OH masers and Class II methanol masers, and those only associated with Class II methanol masers. There are no obvious dif- ferences in the color-color or color-magnitude results for the GLIMPSE point sources. However, according to the results from the WISE 22 {\mu}m survey, the sources associ- ated with OH masers are brighter than those associated with methanol masers. We interpret the presence of OH and methanol masers mark the locations of regions where stars are forming. The OH masers are located on the borders of sharp features found in the IR. These are referred to as bubbles. If the OH masers mark the positions of protostars, the result provides indirect evidence for triggered star formation caused by the expansion of the bubbles.Comment: 23 pages (11 pages online only), 12 figures, Accepted. Monthly Notices of the Royal Astronomical Society,201

Self-organization and phase transition in financial markets with multiple choices

Market confidence is essential for successful investing. By incorporating multi-market into the evolutionary minority game, we investigate the effects of investor beliefs on the evolution of collective behaviors and asset prices. When there exists another investment opportunity, market confidence, including overconfidence and under-confidence, is not always good or bad for investment. The roles of market confidence is closely related to market impact. For low market impact, overconfidence in a particular asset makes an investor become insensitive to losses and a delayed strategy adjustment leads to a decline in wealth, and thereafter, one's runaway from the market. For high market impact, under-confidence in a particular asset makes an investor over-sensitive to losses and one's too frequent strategy adjustment leads to a large fluctuation in asset prices, and thereafter, a decrease in the number of agents. At an intermediate market impact, the phase transition occurs. No matter what the market impact is, an equilibrium between different markets exists, which is reflected in the occurrence of similar price fluctuations in different markets. A theoretical analysis indicates that such an equilibrium results from the coupled effects of strategy updating and shift in investment. The runaway of the agents trading a specific asset will lead to a decline in the asset price volatility and such a decline will be inhibited by the clustering of the strategies. A uniform strategy distribution will lead to a large fluctuation in asset prices and such a fluctuation will be suppressed by the decrease in the number of agents in the market. A functional relationship between the price fluctuations and the numbers of agents is found

CD44ICD promotes breast cancer stemness via PFKFB4-mediated glucose metabolism.

CD44 is a single-pass cell surface glycoprotein that is distinguished as the first molecule used to identify cancer stem cells in solid tumors based on its expression. In this regard, the CD44high cell population demonstrates not only the ability to regenerate a heterogeneous tumor, but also the ability to self-regenerate when transplanted into immune-deficient mice. However, the exact role of CD44 in cancer stem cells remains unclear in part because CD44 exists in various isoforms due to alternative splicing. Methods: Gain- and loss-of-function methods in different models were used to investigate the effects of CD44 on breast cancer stemness. Cancer stemness was analyzed by detecting SOX2, OCT4 and NANOG expression, ALDH activity, side population (SP) and sphere formation. Glucose consumption, lactate secretion and reactive oxygen species (ROS) levels were detected to assess glycolysis. Western blot, immunohistochemical staining, ELISA and TCGA dataset analysis were performed to determine the association of CD44ICD and PFKFB4 with clinical cases. A PFKFB4 inhibitor, 5MPN, was used in a xenograft model to inhibit breast cancer development. Results: In this report, we found that the shortest CD44 isoform (CD44s) inhibits breast cancer stemness, whereas the cleaved product of CD44 (CD44ICD) promotes breast cancer stemness. Furthermore, CD44ICD interacts with CREB and binds to the promoter region of PFKFB4, thereby regulating PFKFB4 transcription and expression. The resultant PFKFB4 expression facilitates the glycolysis pathway (vis-à-vis oxidative phosphorylation) and promotes stemness of breast cancer. In addition, we found that CD44ICD and PFKFB4 expressions are generally up-regulated in the tumor portion of breast cancer patient samples. Most importantly, we found that 5MPN (a selective inhibitor of PFKFB4) suppresses CD44ICD-induced tumor development. Conclusion: CD44ICD promotes breast cancer stemness via PFKFB4-mediated glycolysis, and therapies that target PFKFB4 (e.g., 5MPN therapy) may lead to improved outcomes for cancer patients

A spectral line survey of IRC +10216 between 13.3 and 18.5 GHz

A spectral line survey of IRC +10216 between 13.3 and 18.5 GHz is carried out using the Shanghai Tian Ma 65 m Radio Telescope (TMRT-65m) with a sensitivity of < 7 mK. Thirty-five spectral lines of 12 different molecules and radicals are detected in total. Except for SiS, the detected molecules are all carbon-chain molecules, including HC3N, HC5N, HC7N, HC9N, C6H, C6H-, C8H, SiC2, SiC4, c-C3H2 and l-C5H. The presence of rich carbon-bearing molecules is consistent with the identity of IRC +10216 as a carbon-rich AGB star. The excitation temperatures and column densities of the observed species are derived by assuming a local thermodynamic equilibrium and homogeneous conditions.Comment: This is the authors' version of the manuscript; 16 pages, 5 figures, 6 tables; Accepted for publication in A&A 8/17/201