Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices within DIIS. This differs from the traditional DIIS of Pulay, which uses an object function derived from the commutator of the density and Fock matrices. Our results show that the present algorithm, abbreviated ADIIS, is more robust and efficient than the energy-DIIS (EDIIS) approach. In particular, several examples demonstrate that the combination of ADIIS and DIIS ("ADIIS+DIIS") is highly reliable and efficient in accelerating SCF convergence.

Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Experimental evidence that phenotypic divergence in predators drives community divergence in prey.

Studies of adaptive divergence have traditionally focused on the ecological causes of trait diversification, while the ecological consequences of phenotypic divergence remain relatively unexplored. Divergence in predator foraging traits, in particular, has the potential to impact the structure and dynamics of ecological communities. To examine the effects of predator trait divergence on prey communities, we exposed zooplankton communities in lake mesocosms to predation from either anadromous or landlocked (freshwater resident) alewives, which have undergone recent and rapid phenotypic differentiation in foraging traits (gape width, gill raker spacing, and prey size-selectivity). Anadromous alewives, which exploit large prey items, significantly reduced the mean body size, total biomass, species richness, and diversity of crustacean zooplankton relative to landlocked alewives, which exploit smaller prey. The zooplankton responses observed in this experiment are consistent with patterns observed in lakes. This study provides direct evidence that phenotypic divergence in predators, even in its early stages, can play a critical role in determining prey community structure.

Response to Comment on "Whole-genome analyses resolve early branches in the tree of life of modern birds".

Mitchell et al. argue that divergence-time estimates for our avian phylogeny were too young because of an "inappropriate" maximum age constraint for the most recent common ancestor of modern birds and that, as a result, most modern bird orders diverged before the Cretaceous-Paleogene mass extinction event 66 million years ago instead of after. However, their interpretations of the fossil record and timetrees are incorrect.