A k-space method for nonlinear wave propagation

A k-space method for nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme [Mast et al., IEEE Tran. Ultrason. Ferroelectr. Freq. Control 48, 341-354 (2001)]. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to the finite element method. It is found that, in order to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant-Friedrichs-Lewy number can be as small as 0.4. As a result, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient than the conventional finite element method or finite-difference time-domain method for the conditions studied here. However, although the present method is highly accurate for weakly inhomogeneous media, it is found to be less accurate for strongly inhomogeneous media. A possible remedy to this limitation is discussed

A closer look at interacting dark energy with statefinder hierarchy and growth rate of structure

We investigate the interacting dark energy models by using the diagnostics of statefinder hierarchy and growth rate of structure. We wish to explore the deviations from $\Lambda$CDM and to differentiate possible degeneracies in the interacting dark energy models with the geometrical and structure growth diagnostics. We consider two interacting forms for the models, i.e., $Q_1=\beta H\rho_c$ and $Q_2=\beta H\rho_{de}$, with $\beta$ being the dimensionless coupling parameter. Our focus is the I$\Lambda$CDM model that is a one-parameter extension to $\Lambda$CDM by considering a direct coupling between the vacuum energy ($\Lambda$) and cold dark matter (CDM), with the only additional parameter $\beta$. But we begin with a more general case by considering the I$w$CDM model in which dark energy has a constant $w$ (equation-of-state parameter). For calculating the growth rate of structure, we employ the "parametrized post-Friedmann" theoretical framework for interacting dark energy to numerically obtain the $\epsilon(z)$ values for the models. We show that in both geometrical and structural diagnostics the impact of $w$ is much stronger than that of $\beta$ in the I$w$CDM model. We thus wish to have a closer look at the I$\Lambda$CDM model by combining the geometrical and structural diagnostics. We find that the evolutionary trajectories in the $S^{(1)}_3$--$\epsilon$ plane exhibit distinctive features and the departures from $\Lambda$CDM could be well evaluated, theoretically, indicating that the composite null diagnostic $\{S^{(1)}_3, \epsilon\}$ is a promising tool for investigating the interacting dark energy models.Comment: 17 pages, 4 figures; accepted for publication in JCA

HIF-1α Contributes to Hypoxia-induced Invasion and Metastasis of Esophageal Carcinoma via Inhibiting E-cadherin and Promoting MMP-2 Expression

Hypoxia-inducible factor-1α (HIF-1α) has been found to enhance tumor invasion and metastasis, but no study has reported its action in esophageal carcinoma. The goal of this study was to explore the probable mechanism of HIF-1α in the invasion and metastasis of esophageal carcinoma Eca109 cells in vitro and in vivo. mRNA and protein expression of HIF-1α, E-cadherin and matrix metalloproteinase-2 (MMP-2) under hypoxia were detected by RT-PCR and Western blotting. The effects of silencing HIF-1α on E-cadherin, MMP-2 mRNA and protein expression under hypoxia or normoxia were detected by RT-PCR and Western blotting, respectively. The invasive ability of Eca109 cells was tested using a transwell chambers. We established an Eca109-implanted tumor model and observed tumor growth and lymph node metastasis. The expression of HIF-1α, E-cadherin and MMP-2 in xenograft tumors was detected by Western blotting. After exposure to hypoxia, HIF-1α protein was up-regulated, both mRNA and protein levels of E-cadherin were down-regulated and MMP-2 was up-regulated, while HIF-1α mRNA showed no significant change. SiRNA could block HIF-1α effectively, increase E-cadherin expression and inhibit MMP-2 expression. The number of invading cells decreased after HIF-1α was silenced. Meanwhile, the tumor volume was much smaller, and the metastatic rate of lymph nodes and the positive rate were lower in vivo. Our observations suggest that HIF-1α inhibition might be an effective strategy to weaken invasion and metastasis in the esophageal carcinoma Eca109 cell line

Global and partitioned reconstructions of undirected complex networks

It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned reconstructions) are proposed to infer the structure of undirected networks from dynamics. These approaches are applied to evolutionary games occurring on both homogeneous and heterogeneous networks via compressed sensing, which can more efficiently achieve higher reconstruction accuracy with relatively small amounts of data. Our approaches provide different perspectives on effectively reconstructing complex networks.Comment: 6 pages, 2 figures, 1 table; revised version; added numerical results of the PR in Table 1 and expanded Section 4; added 7 reference