Abstract. There is strong evidence that the angiopoietin family is involved in the regulation of tumour progression, cellular growth and differentiation. Recently, it has been reported that angiopoietin-like 4 (ANGPTL4) in cancer cell promotes the metastatic process by increasing vascular permeability. To elucidate ANGPTL4 expression and its association with clinicopathological factors and prognosis in human gastric adenocarcinomas, we examined 103 cases of surgicallyresected human gastric adenocarcinoma by immunohistochemistry. Among 103 cases of adenocarcinoma, 38 cases (36.9%) showed positive staining in the cytoplasm of the carcinoma cells for ANGPTL4. Histologically, papillary and mucinous adenocarcinomas showed relatively high expression of ANGPTL4 (60 and 60%, respectively). The expression of ANGPTL4 was correlated with the depth of tumour invasion (p<0.005), lymph node metastasis (p<0.001), venous invasion (p<0.00005) and TNM stage (p<0.001) in the total carcinoma. In univariate survival analysis, ANGPTL4 expression was not associated with the overall survival. RT-PCR or Western blot analysis showed the expression of mRNA or protein of ANGPTL4 in all four surgically-resected samples and all four cell lines of human gastric adenocarcinoma. ANGPTL4 expression was correlated with several clinicopathological factors, especially venous invasion. These findings suggest that the ANGPTL4 is one of the factors involved in the progression of human gastric cancer. IntroductionGastric cancer is one of the most common cancer types in the world today, in spite of the fact that its incidence has shown a gradual decline in many countries (1). The occurrence and progression of cancer are considered to be a series of genetic events affecting the structure and/or expression of a number of oncogenes, tumour suppressors and growth factors (2,3). The deep invasive carcinomas, such as gastric cancer, have higher rates of lymph duct and venous invasions and lymph node metastasis (4). However, the mechanisms of invasion and metastasis of gastric carcinoma are not fully understood.The molecular mechanisms in tumour progression, local invasion and the formation of tumour metastases represent a major challenge in cancer research. Metastasis of tumour cells is the primary cause of death in patients with cancer (5). To metastasize, tumour cells undergo a multistep progression through a series of sequential and selective events (6). The metastatic process consists of tumour cell detachment, local invasion, motility, angiogenesis, vessel invasion, survival in the circulation, adhesion to endothelial cells, extravasation and regrowth in different organs (7). In each step, causative molecules have been identified; these include cell-adhesion molecules, various growth factors, matrix degradation enzymes and motility factors, of which most of these can be regarded as prognostic factors (7).There is strong evidence that the angiopoietin family is involved in the regulation of tumour progression, cellular growth and differentiation (8-10). A...

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We study asymptotic properties of kernel estimators of an unknown density when applying importance sampling (IS). In particular, we provide conditions under which the estimators are consistent, both pointwise and uniformly, and are asymptotically normal. We also study the optimal bandwidth for minimizing the asymptotic mean square error (MSE) at a single point and the asymptotic mean integrated square error (MISE). We show that IS can improve the asymptotic MSE at a single point, but IS always increases the asymptotic MISE. We also give conditions ensuring the consistency of an IS kernel estimator of the sparsity function, which is the inverse of the density evaluated at a quantile. This is useful for constructing a confidence interval for a quantile when applying IS. We also provide conditions under which the IS kernel estimator of the sparsity function is asymptotically normal. We provide some empirical results from experiments with a small model.

We consider a model of an irreducible network in which each node is subjected to a random demand, where the demands are jointly normally distributed. Each node has a given supply that it uses to try to meet its demand; if it cannot, the node distributes its unserved demand equally to its neighbors, which in turn do the same. The equilibrium is determined by solving a linear program (LP) to minimize the sum of the unserved demands across the nodes in the network. One possible application of the model might be the distribution of electricity in an electric power grid. This paper considers estimating the probability that the optimal objective function value of the LP exceeds a large threshold, which is a rare event. We develop a conditional Monte Carlo algorithm for estimating this probability, and we provide simulation results indicating that our method can significantly improve statistical efficiency.

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