Communications Biophysics

Contains reports on two research projects

Communications Biophysics

Contains reports on two research projects.United States Air Force (Contract AF19(604)-4112)United States National Institute of Neurological Diseases and Blindness, U.S. Public Health Service (BT-437)United States National Institute of Neurological Diseases and Blindness (B 369 Physiology)United States Navy, Office of Naval Research, (NR 101-445))United States Air Force, Office of Scientific Research (AF-49-(638)-98)

Communications Biophysics

Contains research objectives and reports on one research project.U.S. Air Force under Contract AF19(604)-411

Communications Biophysics

Contains reports on two research projects.United States Air Force (Contract AF19(604)-4112)United States Air Force, Office of Scientific Research, Air Research and Development Command (Contract AF 61 (052)-107)Rockefeller Foundatio

Communications Biophysics

Contains reports on two research projects

Communications Biophysics

Contains reports on three research projects

Multiple Imputation with Survey Weights: A Multilevel Approach

Abstract Multiple imputation is now well established as a practical and flexible method for analyzing partially observed data, particularly under the missing at random assumption. However, when the substantive model is a weighted analysis, there is concern about the empirical performance of Rubin’s rules and also about how to appropriately incorporate possible interaction between the weights and the distribution of the study variables. One approach that has been suggested is to include the weights in the imputation model, potentially also allowing for interactions with the other variables. We show that the theoretical criterion justifying this approach can be approximately satisfied if we stratify the weights to define level-two units in our data set and include random intercepts in the imputation model. Further, if we let the covariance matrix of the variables have a random distribution across the level-two units, we also allow imputation to reflect any interaction between weight strata and the distribution of the variables. We evaluate our proposal in a number of simulation scenarios, showing it has promising performance both in terms of coverage levels of the model parameters and bias of the associated Rubin’s variance estimates. We illustrate its application to a weighted analysis of factors predicting reception-year readiness in children in the UK Millennium Cohort Study.</jats:p

Communications Biophysics

Contains reports on two research projects

Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

Communications Biophysics

Contains research objectives and reports on two research projects