Bayesian modeling longitudinal dyadic data with nonignorable dropout, with application to a breast cancer study

Dyadic data are common in the social and behavioral sciences, in which members of dyads are correlated due to the interdependence structure within dyads. The analysis of longitudinal dyadic data becomes complex when nonignorable dropouts occur. We propose a fully Bayesian selection-model-based approach to analyze longitudinal dyadic data with nonignorable dropouts. We model repeated measures on subjects by a transition model and account for within-dyad correlations by random effects. In the model, we allow subject's outcome to depend on his/her own characteristics and measure history, as well as those of the other member in the dyad. We further account for the nonignorable missing data mechanism using a selection model in which the probability of dropout depends on the missing outcome. We propose a Gibbs sampler algorithm to fit the model. Simulation studies show that the proposed method effectively addresses the problem of nonignorable dropouts. We illustrate our methodology using a longitudinal breast cancer study.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS515 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory

Spin liquids are novel states of matter with fractionalized excitations. A recent numerical study of Hubbard model on a honeycomb lattice\cite{Meng2010} indicates that a gapped spin liquid phase exists close to the Mott transition. Using Projective Symmetry Group, we classify all the possible spin liquid states by Schwinger fermion mean-field approach. We find there is only one fully gapped spin liquid candidate state: "Sublattice Pairing State" that can be realized up to the 3rd neighbor mean-field amplitudes, and is in the neighborhood of the Mott transition. We propose this state as the spin liquid phase discovered in the numerical work. To understand whether SPS can be realized in the Hubbard model, we study the mean-field phase diagram in the $J_1-J_2$ spin-1/2 model and find an s-wave pairing state. We argue that s-wave pairing state is not a stable phase and the true ground state may be SPS. A scenario of a continuous phase transition from SPS to the semimetal phase is proposed. This work also provides guideline for future variational studies of Gutzwiller projected wavefunctions.Comment: 13 pages, 4 figures, Revtex

Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Korteweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the complex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.Comment: 12 figure