Millimeter line observations toward four local galaxies

We present results of millimeter line observations toward four local gas-rich galaxies (NGC 3079, NGC 4258, NGC 6240 and VII Zw 31) with the IRAM 30 meter millimeter telescope. More than 33 lines in these four sources were detected, including normal dense gas tracers (HCN 1-0, HCO$^+$ 1-0, and C$_2$H 1-0, etc) and their isotopic species. H$^{13}$CN (1-0) and H$^{13}$CO$^+$ (1-0) are detected for the first time in NGC 4258. Optical depths of HCN 1-0 and HCO$^{+}$ 1-0 were estimated with detected isotopic lines in NGC 4258, which were 4.1 and 2.6, respectively. HC$_3$N $J=29-28$, which requires high volume density and high temperature to excite, was detected in NGC 6240. High ratios of HCO$^+$/HCN in NGC 4258 and NGC 6240 imply that this ratio might not be a perfect diagnostic tool between AGN and starburst environments, due to contamination/combination of both processes. The low HC$_3$N/HCN line ratios with less than 0.15 in NGC 4258, NGC 6240 and the non-detection of HC$_3$N line in NGC 3079 and VII Zw 31 indicates that these four galaxies are HC$_3$N-poor galaxies. The variation of fractional abundance of CN in different types of galaxies is large.Comment: 15pages, 13 figures; accepted for publication in MNRA

Multivariate varying coefficient model for functional responses

Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate. We establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions. We propose a global test for linear hypotheses of varying coefficient functions, and derive its asymptotic distribution under the null hypothesis. We also propose a simultaneous confidence band for each individual effect curve. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply MVCM to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1045 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org