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.

Decoding an olfactory mechanism of kin recognition and inbreeding avoidance in a primate.

BACKGROUND: Like other vertebrates, primates recognize their relatives, primarily to minimize inbreeding, but also to facilitate nepotism. Although associative, social learning is typically credited for discrimination of familiar kin, discrimination of unfamiliar kin remains unexplained. As sex-biased dispersal in long-lived species cannot consistently prevent encounters between unfamiliar kin, inbreeding remains a threat and mechanisms to avoid it beg explanation. Using a molecular approach that combined analyses of biochemical and microsatellite markers in 17 female and 19 male ring-tailed lemurs (Lemur catta), we describe odor-gene covariance to establish the feasibility of olfactory-mediated kin recognition. RESULTS: Despite derivation from different genital glands, labial and scrotal secretions shared about 170 of their respective 338 and 203 semiochemicals. In addition, these semiochemicals encoded information about genetic relatedness within and between the sexes. Although the sexes showed opposite seasonal patterns in signal complexity, the odor profiles of related individuals (whether same-sex or mixed-sex dyads) converged most strongly in the competitive breeding season. Thus, a strong, mutual olfactory signal of genetic relatedness appeared specifically when such information would be crucial for preventing inbreeding. That weaker signals of genetic relatedness might exist year round could provide a mechanism to explain nepotism between unfamiliar kin. CONCLUSION: We suggest that signal convergence between the sexes may reflect strong selective pressures on kin recognition, whereas signal convergence within the sexes may arise as its by-product or function independently to prevent competition between unfamiliar relatives. The link between an individual's genome and its olfactory signals could be mediated by biosynthetic pathways producing polymorphic semiochemicals or by carrier proteins modifying the individual bouquet of olfactory cues. In conclusion, we unveil a possible olfactory mechanism of kin recognition that has specific relevance to understanding inbreeding avoidance and nepotistic behavior observed in free-ranging primates, and broader relevance to understanding the mechanisms of vertebrate olfactory communication.