Fourth order quasi-compact difference schemes for (tempered) space fractional diffusion equations

The continuous time random walk (CTRW) underlies many fundamental processes in non-equilibrium statistical physics. When the jump length of CTRW obeys a power-law distribution, its corresponding Fokker-Planck equation has space fractional derivative, which characterizes L\'{e}vy flights. Sometimes the infinite variance of L\'{e}vy flight discourages it as a physical approach; exponentially tempering the power-law jump length of CTRW makes it more `physical' and the tempered space fractional diffusion equation appears. This paper provides the basic strategy of deriving the high order quasi-compact discretizations for space fractional derivative and tempered space fractional derivative. The fourth order quasi-compact discretization for space fractional derivative is applied to solve space fractional diffusion equation and the unconditional stability and convergence of the scheme are theoretically proved and numerically verified. Furthermore, the tempered space fractional diffusion equation is effectively solved by its counterpart of the fourth order quasi-compact scheme; and the convergence orders are verified numerically.Comment: 27 pages, 1 figur

Maximal Quantum Fisher Information in a Mach-Zehnder Interferometer without initial parity

Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interferometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.Comment: 10 pages, 3 figure

TRIM47 promotes ovarian cancer cell proliferation, migration, and invasion by activating STAT3 signaling

Objectives: Tripartite Motif 47 (TRIM47) protein plays a prominent role in many cancers. This study aimed to investigate the biological roles of TRIM47 in ovarian cancer. Methods: TRIM47 was knocked down and overexpressed in ovarian cancer cell lines SKOV3 and OVCAR3, and the effects on proliferation, clone formation, apoptosis, invasion, and growth of xenograft tumors in nude mice were determined. The expression levels of the selected candidates were tested by western blotting and quantitative real-time PCR. Results: TRIM47 knockdown suppressed proliferation and encourages apoptosis of ovarian cancer cells. Similarly, TRIM47 knockdown suppressed ovarian cancer cell invasion, migration, and epithelial-mesenchymal transition. Ovarian cancer cell xenograft assays demonstrated that TRIM47 knockdown significantly inhibited tumor growth. Mechanistically, TRIM47 knockdown suppressed STAT3 phosphorylation and the expression of several downstream genes, including MCL-1, MMP2, and c-MYC. Silencing of STAT3 partially prevented TRIM47–induced tumor cell proliferation and invasion. Conclusion: The present study's findings demonstrate that by activating STAT3 signaling, TRIM47 functions as an oncogene in ovarian cancer. TRIM47, therefore, appears to be a potential target for ovarian cancer prevention and/or therapy

The effects of skewness on hedging decisions: an application of the skew-normal distribution in WTI and Brent futures

Skewness, as a proxy for extreme risks or losses, deserves more attention from risk management work of portfolio selection and futures hedging. We evaluate the hedging performance of strategies considering the skewness for two major benchmark international crude oil markets, Brent and WTI, with sample period ranging from June 11, 2018, to May 19, 2021. This paper contributes to the literature by accounting for futures basis and the skewness of the hedged portfolio return. Specifically, we first extend the existing literature of Lien (2010), whose study investigated the effect of skewness on optimal production and hedging decisions, to the case of a futures bias existing. Then, we propose minimum-risk hedging models wherein the return of the hedged portfolio return is assumed to follow a skew-normal distribution, which is a generalization of normality assumption. From the empirical results, we find that skewness cannot be ignored, otherwise it will lead to wrong hedging decision. Furthermore, hedging strategies under skew-normal distribution are outperformed than that under the normal distribution assumption. The research results of this paper have important implications for investors and decision makers to hedge the price risk of crude oil in extreme market conditions