Pathway Analysis for Genome-Wide Association Study of Basal Cell Carcinoma of the Skin

Recently, a pathway-based approach has been developed to evaluate the cumulative contribution of the functionally related genes for genome-wide association studies (GWASs), which may help utilize GWAS data to a greater extent.In this study, we applied this approach for the GWAS of basal cell carcinoma (BCC) of the skin. We first conducted the BCC GWAS among 1,797 BCC cases and 5,197 controls in Caucasians with 740,760 genotyped SNPs. 115,688 SNPs were grouped into gene transcripts within 20 kb in distance and then into 174 Kyoto Encyclopedia of Genes and Genomes pathways, 205 BioCarta pathways, as well as two positive control gene sets (pigmentation gene set and BCC risk gene set). The association of each pathway with BCC risk was evaluated using the weighted Kolmogorov-Smirnov test. One thousand permutations were conducted to assess the significance.Both of the positive control gene sets reached pathway p-values<0.05. Four other pathways were also significantly associated with BCC risk: the heparan sulfate biosynthesis pathway (p  =  0.007, false discovery rate, FDR  =  0.35), the mCalpain pathway (p  =  0.002, FDR  =  0.12), the Rho cell motility signaling pathway (p  =  0.011, FDR  =  0.30), and the nitric oxide pathway (p  =  0.022, FDR  =  0.42).We identified four pathways associated with BCC risk, which may offer new insights into the etiology of BCC upon further validation, and this approach may help identify potential biological pathways that might be missed by the standard GWAS approach

Convergence and hardness of strategic Schelling segregation

The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least $\tau$, for some $0<\tau<1$. Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in $\mathcal{O}(m)$ steps, where $m$ is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.Comment: 21 pages, 8 figure