Decaying Superheavy Dark Matter and Subgalactic Structure of the Universe

The collisionless cold dark matter (CCDM) model predicts overly dense cores in dark matter halos and overly abundant subhalos. We show that the idea that CDM are decaying superheavy particles which produce ultra-high energy cosmic rays with energies beyond the Greisen-Zatsepin-Kuzmin cutoff may simultaneously solve the problem of subgalactic structure formation in CCDM model. In particular, the Kuzmin-Rubakov's decaying superheavy CDM model may give an explanation to the smallness of the cosmological constant and a new thought to the CDM experimental search.Comment: 5 pages, 1 figure. Add a new paragraph on the production of UHECR. References added. Final version which is to appear in Phys.Lett.

On summary measures analysis of the linear mixed effects model for repeated measures when data are not missing completely at random

Subjects often drop out of longitudinal studies prematurely, yielding unbalanced data with unequal numbers of measures for each subject. A simple and convenient approach to analysis is to develop summary measures for each individual and then regress the summary measures on between-subject covariates. We examine properties of this approach in the context of the linear mixed effects model when the data are not missing completely at random, in the sense that drop-out depends on the values of the repeated measures after conditioning on fixed covariates. The approach is compared with likelihood-based approaches that model the vector of repeated measures for each individual. Methods are compared by simulation for the case where repeated measures over time are linear and can be summarized by a slope and intercept for each individual. Our simulations suggest that summary measures analysis based on the slopes alone is comparable to full maximum likelihood when the data are missing completely at random but is markedly inferior when the data are not missing completely at random. Analysis discarding the incomplete cases is even worse, with large biases and very poor confidence coverage. Copyright © 1999 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34853/1/269_ftp.pd