Abstract. The identification of instability in large-scale dynamical systems caused by Hopf bifurcation is difficult because of the problem of identifying the rightmost pair of complex eigenvalues of large sparse generalized eigenvalue problems. A new method developed in [Meerbergen and Spence, SIAM J. Matrix Anal. Appl., 31 (2010Appl., 31 ( ), pp. 1982Appl., 31 ( -1999 avoids this computation, instead performing an inverse iteration for a certain set of real eigenvalues and that requires the solution of a large-scale Lyapunov equation at each iteration. In this study, we refine the Lyapunov inverse iteration method to make it more robust and efficient, and we examine its performance on challenging test problems arising from fluid dynamics. Various implementation issues are discussed, including the use of inexact inner iterations and the impact of the choice of iterative solution for the Lyapunov equations, and the effect of eigenvalue distribution on performance. Numerical experiments demonstrate the robustness of the algorithm.
miR-124 and miR-506 are reportedly down-regulated and associated with tumor progression in many cancers, but little is known about their intrinsic regulatory mechanisms in colorectal cancer (CRC). In this study, we found that the miR-124 and miR-506 levels were significantly lower in human CRC tissues than in controls, as indicated by qRT-PCR and in situ hybridization histochemistry. We also found that the overexpression of miR-124 or miR-506 inhibited tumor cell progression and increased sensitivity to chemotherapy in vitro. Increased miR-124 or miR-506 expression also inhibited tumor cell proliferation and invasion in vivo. Luciferase reporter assays and western blotting were used to determine the association between miR-124, miR-506 and their target genes, DNMTs. We further identified that miR-124 and miR-506 directly targeted DNMT3B and indirectly targeted DNMT1. The overexpression of miR-124 and miR-506 reduced global DNA methylation and restored the expression of E-cadherin, MGMT and P16. In conclusion, our data showed that miR-124 and miR-506 inhibit progression and increase sensitivity to chemotherapy by targeting DNMT3B and DNMT1 in CRC. These findings may provide novel avenues for the development of targeted therapies.
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