Solution. Since (ab)(abc) = (bc) and (abc)(ab) = (ac), it is easy to see that the center of S3 is the trivial subgroup. Therefore, the group of inner automorphisms of S3 is isomorphic to S3 and has size 6. On the other hand, S3 has 3 transpositions. These must be permuted by an automorphism of S3, and a nontrivial automorphism induces a nontrivial permutation. This gives an injective homomorphi...

We sought to characterize WPEC by quantifying per-hour log-fold change. To do so, we regressed the log gene expression on time (hour) and extracted the linear slope. For genes with monotonically increasing or decreasing expression trajectories, the utility of our WPEC measure to discriminate is obvious. Our WPEC measure can also discriminate with more complex trajectories which may be reflectiv...

study design, analysis and interpretation The following table summarizes several key concepts relating to sample preparation and library construction that may influence analysis and interpretation of RNA-seq data. Several initiatives are underway to develop standards and best practices that cover many of these concepts. These include: the Sequencing Quality Control (SEQC) consortium [2], the En...

[S1,Q15=MAC15(S1), P13=MAC13(S1,Q15)] [S2,Q25=MAC25(S2),P23=MAC23(S2,Q25)] [S4,Q46=MAC46(S4),P45=MAC45(S4,Q46)] Q36=MAC36(S1|S2|S3) P35=MAC35(S3, S1|S2, Q15, Q25, Q36) [S3, (S1|S2), Q15, Q25, Q36, P35] Q5B= MAC5B(S1|S2|S3|S4|S5) P56=MAC56(S5, (S1|S2|S3|S4),Q36,Q46,Q5B) [S5, (S1|S2|S3|S4),Q36, Q46, Q5B, P56] P6B=MAC6B(S6, ((S1|S2|S3|S4 |S5)| S7|S8),Q5B,Q7B,Q8B) [S6, ((S1|S2|S3|S4 |S5)| S7|S8),Q5...

We estimated clinic-averaged co-ancestries from WGS data assuming SNPs were both linked and unlinked. Linked analyses require a recombination file specifying distances between SNPs. We used a uniform recombination rate equal to 7.4 × 10−7 Morgans per base pair (Miles et al. 2016), the same as that specified in hmmIBD (Schaffner et al., n.d.). ChromoPainter essentially treats each unlinked SNP a...