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