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

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

The eight basic topological relations between two simple crisp regions [36]

<p>The eight basic topological relations between two simple crisp regions [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0117379#pone.0117379.ref036" target="_blank">36</a>]</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

Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions

<div><p>In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models.</p></div

(a) Fuzzy region <i>A1</i> for given <i>α</i>; (b) Fuzzy region <i>A2</i> for given <i>β</i>.

<p>(a) Fuzzy region <i>A1</i> for given <i>α</i>; (b) Fuzzy region <i>A2</i> for given <i>β</i>.</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

(a) The inner-outer boundary of simple fuzzy line segment <i>L</i> for given <i>α</i>; (b) the inner-outer boundary of simple fuzzy region <i>A</i> for given <i>α</i>.

<p>(a) The inner-outer boundary of simple fuzzy line segment <i>L</i> for given <i>α</i>; (b) the inner-outer boundary of simple fuzzy region <i>A</i> for given <i>α</i>.</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

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