We propose a novel, efficient approach for obtaining high-quality experimental designs for event-related functional magnetic resonance imaging (ER-fMRI), a popular brain mapping technique. Our proposed approach combines a greedy hill-climbing algorithm and a cyclic permutation method. When searching for optimal ER-fMRI designs, the proposed approach focuses only on a promising restricted class of designs with equal frequency of occurrence across stimulus types. The computational time is significantly reduced. We demonstrate that our proposed approach is very efficient compared with a recently proposed genetic algorithm approach. We also apply our approach in obtaining designs that are robust against misspecification of error correlations.

K-shuff is a new algorithm for comparing the similarity of gene sequence libraries, providing measures of the structural and compositional diversity as well as the significance of the differences between these measures. Inspired by Ripley’s K-function for spatial point pattern analysis, the Intra K-function or IKF measures the structural diversity, including both the richness and overall similarity of the sequences, within a library. The Cross K-function or CKF measures the compositional diversity between gene libraries, reflecting both the number of OTUs shared as well as the overall similarity in OTUs. A Monte Carlo testing procedure then enables statistical evaluation of both the structural and compositional diversity between gene libraries. For 16S rRNA gene libraries from complex bacterial communities such as those found in seawater, salt marsh sediments, and soils, K-shuff yields reproducible estimates of structural and compositional diversity with libraries greater than 50 sequences. Similarly, for pyrosequencing libraries generated from a glacial retreat chronosequence and Illumina^® libraries generated from US homes, K-shuff required >300 and 100 sequences per sample, respectively. Power analyses demonstrated that K-shuff is sensitive to small differences in Sanger or Illumina^® libraries. This extra sensitivity of K-shuff enabled examination of compositional differences at much deeper taxonomic levels, such as within abundant OTUs. This is especially useful when comparing communities that are compositionally very similar but functionally different. K-shuff will therefore prove beneficial for conventional microbiome analysis as well as specific hypothesis testing.