Decomposed element-free Galerkin method compared with finite-difference method for elastic wave propagation

The decomposed element-free Galerkin (DEFG) method is a modified scheme to resolve shortcomings of memory use in element-free Galerkin (EFG) methods. DEFG solves elastic wave equation problems by alternately updating the stress-strain relations and the equations of motion as in the staggered-grid finite-difference (FD) method. DEFG requires at most twice the memory space, a size comparable to that used by the FD method. In addition, DEFG can adopt perfectly matched layer (PML) absorbing boundary conditions as in the FD case. To confirm that DEFG performs as well as FD, a 2D DEFG under PML boundary conditions was compared with an FD with fourth-order spatial accuracy (FD4) using an exact analytical solution of PS reflection waves. The DEFG results are as accurate as those obtained by FD4. In a comparison using Lamb's problem with eight nodal spaces for the shortest S-wavelength, DEFG provides a remarkably accurate Rayleigh waveform over a distance of at least 50 wavelengths compared with 10 wavelengths for FD4. In the Rayleigh-wave case, DEFG with 1-m grid spacing is more accurate than FD4 with 0.5-m grid spacing, and DEFG uses less CPU time. DEFG may be a suitable method for numerical simulations of elastic wavefields, especially where a free surface is considered

Functional analysis of Tcl1 using Tcl1-deficient mouse embryonic stem cells.

Tcl1 is highly expressed in embryonic stem (ES) cells, but its expression rapidly decreases following differentiation. To assess Tcl1's roles in ES cells, we generated Tcl1-deficient and -overexpressing mouse ES cell lines. We found that Tcl1 was neither essential nor sufficient for maintaining the undifferentiated state. Tcl1 is reported to activate Akt and to enhance cell proliferation. We found that Tcl1 expression levels correlated positively with the proliferation rate and negatively with the apoptosis of ES cells, but did not affect Akt phosphorylation. On the other hand, the phosphorylation level of β-catenin decreased in response to Tcl1 overexpression. We measured the β-catenin activity using the TOPflash reporter assay, and found that wild-type ES cells had low activity, which Tcl1 overexpression enhanced 1.8-fold. When the canonical Wnt signaling is activated by β-catenin stabilization, it reportedly helps maintain ES cells in the undifferentiated state. We then performed DNA microarray analyses between the Tcl1-deficient and -expressing ES cells. The results revealed that Tcl1 expression downregulated a distinct group of genes, including Ndp52, whose expression is very high in blastocysts but reduced in the primitive ectoderm. Based on these results, we discuss the possible roles of Tcl1 in ES cells

Analysis of Akt and Wnt/β-catenin signaling in <i>Tcl1-</i>deficient and -overexpressing ES cells.

<p>(A) Western blot analysis of GSK, Akt, and β-catenin in wild-type (WT), <i>Tcl1^−/−</i> (KO) #2 and #4, <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #1 and #3, and <i>Tcl1^−/−</i>(CAG-EGFP) #5 ES cells. (B) Western blot analysis of active β-catenin, Oct3/4, and HSP90 in the cytoplasmic (C) and nuclear (N) fractions of wild-type (WT), <i>Tcl1^−/−</i> (KO) #2 and #4, and <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #10 and #1 ES cells. <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #10 and #1 were derived from <i>Tcl1^−/−</i> (KO) #2 and #4, respectively. Proper fractionation was confirmed by western blotting of Oct3/4 and HSP90, which localize to the nucleus and cytoplasm, respectively. Be8cause active β-catenin levels in the nuclear fractions were much lower than those in the cytoplasmic fractions, active β-catenin in the nuclear fractions was detected by approximately two-fold longer exposure compared with that in the cytoplasmic fractions. (C) TOPflash assay. <i>P</i> values of wild-type ES cells (WT) compared with <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #1 and #3 ES cells were less than 0.01. <i>P</i> values of <i>Tcl1^−/−</i> (KO) #4 and #5 ES cells compared with <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #1 and #3 ES cells were less than 0.02.</p

Representative genes from microarray analysis.

*<p>Genes listed are those which showed more than 2.0-fold differences in Exp. 1 and 2 and more than 1.7-fold differences in Exp. 3 between <i>Tcl1</i>-expressing and -deficient ES cells.</p>**<p>Exp. 1: <i>Tcl1^−/−</i> #4 vs. <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #1.</p>***<p>Exp. 2: <i>Tcl1^−/−</i>(CAG-EGFP) #6 vs. <i>Tcl1^−/−</i>(CAG-<i>Tcl1</i>) #4.</p>****<p>Exp. 3: Mean values of relative gene expression in <i>Tcl1^−/−</i> #4 vs. wild-type and that in <i>Tcl1^−/−</i> #5 vs. wild-type.</p