p21 expression was shown to be an independent prognostic factor in NSCLC.

Abstract-This paper proposes a general framework for structure-preserving model reduction of a second-order network system based on graph clustering. In this approach, vertex dynamics are captured by the transfer functions from inputs to individual states, and the dissimilarities of vertices are quantified by the H2-norms of the transfer function discrepancies. A greedy hierarchical clustering algorithm is proposed to place those vertices with similar dynamics into same clusters. Then, the reduced-order model is generated by the Petrov-Galerkin method, where the projection is formed by the characteristic matrix of the resulting network clustering. It is shown that the simplified system preserves an interconnection structure, i.e., it can be again interpreted as a second-order system evolving over a reduced graph. Furthermore, this paper generalizes the definition of network controllability Gramian to second-order network systems. Based on it, we develop an efficient method to compute H2-norms and derive the approximation error between the full-order and reduced-order models. Finally, the approach is illustrated by the example of a small-world network.

AI proved to be an independent prognostic factor in NSCLC.

Purpose:The purpose is to assess clinical significance of matrix metalloproteinase (MMP)-2 and MMP-9 status, especially MMP-2 status, in stromal cells in non-small-cell lung cancer (NSCLC) because experimental studies have revealed that stromal MMP-2 plays important roles in progression of malignant tumors, but most clinical studies focused on tumoral MMP-2 expression, not stromal MMP-2 expression.Experimental Design: We conducted a retrospective study on MMP-2 and MMP-9 expression as evaluated immunohistochemically in a total of 218 consecutive patients with completely resected pathological stage I-IIIA, NSCLC.Results: Strong MMP-2 expression in tumor cells and stromal fibroblasts were documented in 54 (24.8%) and 132 (60.6%) patients, respectively. Strong MMP-2 expression in stromal fibroblasts was more frequently seen in squamous cell carcinoma (72.7%) than in adenocarcinoma (54.9%; P ‫؍‬ 0.016). Tumors showing strong MMP-2 expression in stromal fibroblasts showed a significantly higher intratumoral microvessel density (IMVD) than weak stromal MMP-2 tumors (mean intratumoral microvessel density, 50.9 versus 32.4, P ‫؍‬ 0.003). In addition, postoperative prognosis of strong stromal MMP-2 patients was significantly poorer than that of weak stromal MMP-2 patients (5-year survival rate, 77.5 versus 60.2%, P ‫؍‬ 0.032), and the prognostic significance was enhanced in squamous cell carcinoma patients but disappeared in adenocarcinoma patients. Multivariate analyses confirmed that strong stromal MMP-2 expression was a significant factor to predict a poor prognosis in squamous cell carcinoma patients, not in adenocarcinoma patients. In contrast, MMP-2 or MMP-9 status in tumor cells was not a significant prognostic factor.Conclusions: MMP-2 status in stromal fibroblasts, not in tumor cells, was a significant prognostic factor associated with angiogenesis in NSCLC.

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