A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function $f(r)$. As an explicit example of our method, we show plots for vacuum polarization of a massless scalar field in the Schwarzschild-Tangherlini spacetime for even $d=4,...,10$. However, the method presented applies straightforwardly to massive fields or to nonvacuum spacetimes.Comment: arXiv admin note: text overlap with arXiv:1609.0816

Additional file 1: Table S1. of FOXA1 inhibits hepatocellular carcinoma progression by suppressing PIK3R1 expression in male patients

siRNA used in this study. Table S2 Primers used in qPCR. Table S3 Primers used in ChIP analysis. Table S4 Correlation between clinical pathological factors and expression of FOXA1, PI3Kp85 in HCC Table S5 Specimens exhibit low or high FOXA1 expression in relation to PI3Kp85 expression. (DOCX 25 kb

Increased Expression of Cathepsin L: A Novel Independent Prognostic Marker of Worse Outcome in Hepatocellular Carcinoma Patients

<div><p>Objectives</p><p>To investigate the expression and role of Cathepsin L (CTSL) in Hepatocellular carcinoma (HCC) tissue and cell line (MHCC-97H), and to evaluate the clinical and prognostic significance of CTSL protein in patients with HCC.</p><p>Methods</p><p>The expression of CTSL was examined in HCC tissue and MHCC-97H cells by Western-blotting, Real-time PCR and immunohistochemical staining. Cell growth curve assay and colony formation assay were used to verify the effect of CTSL on the proliferation and tumor progression ability of MHCC-97H cells. Tumor formation assay in nude mice was used to analyze the effect of CTSL on the tumorigenicity of MHCC-97H cells.</p><p>Results</p><p>The status of CTSL protein in carcinoma tissues is much higher than that in paracarcinoma tissues. The overall survival of the patients with high CTSL expression was significantly shorter than the low CTSL expression group. high CTSL expression was significantly correlated with advanced clinical staging, histological grade and tumor recurrence. In vitro experiments demonstrated that over-expression of CTSL in MHCC-97H cells promoted cell proliferation and tumor progression ability. Down-regulation of CTSL showed the opposite effects. Over-expression of CTSL increase the tumorigenicity of MHCC-97H cells by in vivo experiments. Moreover, multivariate analysis suggested that CTSL expression might be an independent prognostic indicator for the survival of HCC patients after curative surgery.</p><p>Conclusions</p><p>CTSL might involve in the development and progression of HCC as a oncogene, and thereby may be a valuable prognostic marker for HCC patients.</p></div

Univariate survival analysis of 82 patients with HCC.

<p>Δ: The largest dimension of the tumor specimen.</p><p>Univariate survival analysis of 82 patients with HCC.</p

Survival curves for patients with high CTSL expression versus low CTSL-expressing carcinoma.

<p>The 5-year overall survival rate was 22.7% in the high CTSL protein expression group (green line), but it was only 41.4% in the low expression group (blue line), P = 0.032.</p

The effect of CTSL on the proliferation and tumor progression ability of MHCC-97H cells.

<p>A. Western blotting analysis of CTSL protein expression in HCC cell line (MHCC-97H), colorectal carcinoma cell lines (CaCO2 and LoVo), stably CTSL-expressed MHCC-97H cell line, stably CTSL-expressed CaCO2 cell line, empty vector stable cell lines (MHCC-97H-Con or CaCO2-Con), and MHCC-97H cell line transfected by CTSL-shRNA or Con-shRNA. B. Colony formation assay and MTT assay of MHCC-97H cells and CaCO2 cells with over-expression of CTSL. (Colony formation assay: MHCC-97H-Con (vector) vs MHCC-97H-CTSL, P = 0.0042; CaCO2-Con (vector) vs CaCO2-CTSL, P = 0.0072. MTT: MHCC-97H-Con (vector) vs MHCC-97H-CTSL, P = 0.012; CaCO2-Con (vector) vs CaCO2-CTSL, P = 0.035). C. Colony formation assay and MTT assay of MHCC-97H cells with down-regulated CTSL. (Colony formation assay: MHCC-97H-Con-shRNA vs MHCC-97H-CTSL-shRNA, P = 0.003; MTT: MHCC-97H-Con-shRNA vs MHCC-97H-CTSL-shRNA, P = 0.001. (**P<0.01 as compared to parental groups, *P<0.05 as compared to parental groups).</p

Relationship between CTSL expression and clinicopathologic features of HCC patients.

<p>Δ: The largest dimension of the tumor specimen.</p><p>Relationship between CTSL expression and clinicopathologic features of HCC patients.</p

Effect of CTSL knockdown on subcutaneous tumorigencity of MHCC-97H.

<p>A. Tumor growth curve of after injection of nude mice with CTSL or control vector expressing MHCC-97H cells. (P<0.001) B. The picture of tumors from nude mice with CTSL or control vector expressing MHCC-97H cells. C. The weight of tumors from nude mice with CTSL or control vector expressing MHCC-97H cells (P = 0.005). (**P<0.01 as compared to control groups, *P<0.05 as compared to control groups).</p

Cox regression analysis of patients with HCC.

<p>Cox regression analysis of patients with HCC.</p

Analysis of CTSL protein in tissues by immunohistochemistry.

<p>A and B, CTSL expression is negative in normal liver cells. C and D, CTSL expression is weak in well-differentiated HCC cells. E and F, CTSL expression is moderate in moderately differentiated HCC cells. G and H, CTSL expression is strong in poorly differentiated HCC cells. (A, C, E, G ×200; B, D, F, H ×400).</p