The EM Algorithm in Genetics, Genomics and Public Health

The popularity of the EM algorithm owes much to the 1977 paper by Dempster, Laird and Rubin. That paper gave the algorithm its name, identified the general form and some key properties of the algorithm and established its broad applicability in scientific research. This review gives a nontechnical introduction to the algorithm for a general scientific audience, and presents a few examples characteristic of its application.Comment: Published in at http://dx.doi.org/10.1214/08-STS270 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parent-child relationships and dyadic friendship experiences as predictors of behavior problems in early adolescence

This study focused on support and conflict in parent–child relationships and dyadic friendships as predictors of behavior problems in early adolescence (n¼182; M age¼12.9 years, 51% female, 45% African American, 74% two-parent homes). Support and conflict in one relationship context were hypothesized to moderate the effects of experiences in the other relationship context. Adolescent-reported antisocial behavior was low when either parent–child relationships or friendships were low in conflict, and adolescent-reported depressed mood was low when either friendship conflict was low or parental support was high. Parent-reported antisocial behavior was high when high levels of conflict were reported in either parent–child or friendship relationships and adolescent-reported depressed mood was high when either parental or friendship support was low. Associations appear to be similar for boys and girls as no interactions involving gender were significant.

The Role of Family-Based Designs in Genome-Wide Association Studies

Genome-Wide Association Studies (GWAS) offer an exciting and promising new research avenue for finding genes for complex diseases. Traditional case-control and cohort studies offer many advantages for such designs. Family-based association designs have long been attractive for their robustness properties, but robustness can mean a loss of power. In this paper we discuss some of the special features of family designs and their relevance in the era of GWAS.Comment: Published in at http://dx.doi.org/10.1214/08-STS280 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Preconditioned iterative solution of the 2D Helmholtz equation

Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly. It is also non-Hermitian and highly indefinite and consequently difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with a new preconditioner and then solve it iteratively using a Krylov subspace method. Numerical analysis shows the preconditioner to be effective on a simple 1D test problem, and results are presented showing considerable convergence acceleration for a number of different Krylov methods for more complex problems in 2D, as well as for the more general problem of harmonic disturbances to a non-stagnant steady flow

Preconditioning harmonic unsteady potential flow calculations

This paper considers finite element discretisations of the Helmholtz equation and its generalisation arising from harmonic acoustics perturbations to a non-uniform steady potential flow. A novel elliptic, positive definite preconditioner, with a multigrid implementation, is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1D Helmholtz test problem the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2D Helmholtz equation, grid independent convergence is achieved using a QMR Krylov solver, significantly outperforming the popular SSOR preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with non-stagnant mean flow and modal boundary conditions

Fresh-Register Automata

What is a basic automata-theoretic model of computation with names and fresh-name generation? We introduce Fresh-Register Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names with previously stored ones. These finite machines extend Kaminski and Francez’s Finite-Memory Automata by being able to recognise globally fresh inputs, that is, names fresh in the whole current run. We exam-ine the expressivity of FRA’s both from the aspect of accepted languages and of bisimulation equivalence. We establish primary properties and connections between automata of this kind, and an-swer key decidability questions. As a demonstrating example, we express the theory of the pi-calculus in FRA’s and characterise bisimulation equivalence by an appropriate, and decidable in the finitary case, notion in these automata

fgui: A Method for Automatically Creating Graphical User Interfaces for Command-Line R Packages

The fgui R package is designed for developers of R packages, to help rapidly, and sometimes fully automatically, create a graphical user interface for a command line R package. The interface is built upon the Tcl/Tk graphical interface included in R. The package further facilitates the developer by loading in the help files from the command line functions to provide context sensitive help to the user with no additional effort from the developer. Passing a function as the argument to the routines in the fgui package creates a graphical interface for the function, and further options are available to tweak this interface for those who want more flexibility.

SU(N) Fermions in a One-Dimensional Harmonic Trap

We conduct a theoretical study of SU(N) fermions confined by a one-dimensional harmonic potential. Firstly, we introduce a new numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU(N) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz - derived for a Heisenberg SU(2) spin chain - is extendable to these N-component systems. Lastly, we consider balanced SU(N) Fermi gases that have an equal number of particles in each spin state for N=2, 3, 4. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N-component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.Comment: 15 pages, 6 figure