Generating Realistic Labelled, Weighted Random Graphs

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

The prognostic and therapeutic value of EpHA2 in early colorectal cancer (CRC).

Background: EpHA2 is a 130 kD transmembrane glycoprotein belonging to ephrin receptor subfamily and involved in angiogenesis/tumour neovascularisation. High EpHA2 mRNA level has recently been implicated in cetuximab resistance. Previously, we found high EpHA2 levels in a panel of invasive colorectal cancer (CRC) cells, which was associated with high levels of stem-cell marker CD44. Our aim was to investigate the prognostic value of EpHA2 and subsequently correlate expression levels to known clinico-pathological variables in early stage CRC. Methods: Tissue samples from 509 CRC patients were analysed. EpHA2 expression was measured using IHC. Kaplan-Meier graphs were used. Univariate and multivariate analyses employed Cox Proportional Hazards Ratio (HR) method. A backward selection method (Akaike’s information criterion) was used to determine a refined multivariate model. Results: EpHA2 was highly expressed in CRC adenocarcinoma compared to matched normal colon tissue. In support of our preclinical invasive models, strong correlation was found between EpHA2 expression and CD44 and Lgr5 staining (p<0.001). In addition, high EpHA2 expression significantly correlated with vascular invasion (p=0.03).HR for OS for stage II/III patients with high EpHA2 expression was 1.69 (95%CI: 1.164-2.439; p=0.003). When stage II/III was broken down into individual stages, there was significant correlation between high EpHA2 expression and poor 5-years OS in stage II patients (HR: 2.18; 95%CI: 1.28-3.71; p=0.005).HR in the stage III group showed a trend to statistical significance (HR: 1.48; 95%CI=0.87-2.51; p=0.05). In both univariate and multivariate analyses of stage II patients, high EpHA2 expression was the only significant factor and was retained in the final multivariate model. Higher levels of EpHA2 were noted in our RAS and BRAF mutant CRC cells, and silencing EpHA2 resulted in significant decreases in migration/invasion in parental and invasive CRC sublines. Correlation between KRAS/NRAS/BRAFmutational status and EpHA2 expression in clinical samples is ongoing. Conclusions: Taken together, our study is the first to indicate that EpHA2 expression is a predictor of poor clinical outcome and a potential novel target in early stage CRC.