Lattice fringe signatures of epitaxy on nanotubes

Carbon nanotubes are of potential interest as heterogeneous catalysis supports, in part because they offer a high surface area hexagonal array of carbon atoms for columnar or epitaxial attachment. Fringe visibility modeling of electron microscope lattice images allows one to investigate the relationship between individual nanoparticles and such nanotube supports. We show specifically how (111) columnar or epitaxial growth of FCC metal lattices, on carbon nanotubes viewed side-on, results in well-defined patterns of (111)-fringe orientations with respect to the tube axis. In the epitaxial case, the observations also provide information on chirality of the nanotube's outermost graphene sheet.Comment: 4 pages, 5 figures, 9 refs, cf. http://newton.umsl.edu/~run/nano/epitaxy.htm

Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS549 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org