We introduce the concept of pattern graphs–directed acyclic graphs representing how response patterns are associated. A graph represents an identifying restriction that is nonparametrically identified/saturated and often a missing not at random restriction. selection model mixture formulations using show they equivalent. leads to inverse probability weighting estimator as well imputation-based ...

concrete deformation due to temperature and moisture condition will always develop simultaneously and interactively. the environmentally (hygral and thermally) induced stress and deformation are essential to concrete durability. to simulate the deformation of concrete caused by the coupling effect of temperature and moisture, a numerical simulation approach is proposed comprising analytical pro...

In this work we discuss the calculation of spin-density matrix from fundamental spin principles as implemented in COLUMBUS Program System employing graphical unitary group approach (GUGA). First, a general equation for is derived terms one-and two-particle reduced density matrices, quantities that are spin-independent and readily available within GUGA formalism. Next, evaluation using Shavitt l...