Structural manifestation of the delocalization error of density functional approximations: C(4N+2) rings and C(20) bowl, cage, and ring isomers.

The ground state structure of C(4N+2) rings is believed to exhibit a geometric transition from angle alternation (N < or = 2) to bond alternation (N > 2). All previous density functional theory (DFT) studies on these molecules have failed to reproduce this behavior by predicting either that the transition occurs at too large a ring size, or that the transition leads to a higher symmetry cumulene. Employing the recently proposed perspective of delocalization error within DFT we rationalize this failure of common density functional approximations (DFAs) and present calculations with the rCAM-B3LYP exchange-correlation functional that show an angle-to-bond-alternation transition between C(10) and C(14). The behavior exemplified here manifests itself more generally as the well known tendency of DFAs to bias toward delocalized electron distributions as favored by Huckel aromaticity, of which the C(4N+2) rings provide a quintessential example. Additional examples are the relative energies of the C(20) bowl, cage, and ring isomers; we show that the results from functionals with minimal delocalization error are in good agreement with CCSD(T) results, in contrast to other commonly used DFAs. An unbiased DFT treatment of electron delocalization is a key for reliable prediction of relative stability and hence the structures of complex molecules where many structure stabilization mechanisms exist.

A dual role for ErbB2 signaling in cardiac trabeculation.

Cardiac trabeculation is a crucial morphogenetic process by which clusters of ventricular cardiomyocytes extrude and expand into the cardiac jelly to form sheet-like projections. Although it has been suggested that cardiac trabeculae enhance cardiac contractility and intra-ventricular conduction, their exact function in heart development has not been directly addressed. We found that in zebrafish erbb2 mutants, which we show completely lack cardiac trabeculae, cardiac function is significantly compromised, with mutant hearts exhibiting decreased fractional shortening and an immature conduction pattern. To begin to elucidate the cellular mechanisms of ErbB2 function in cardiac trabeculation, we analyzed erbb2 mutant hearts more closely and found that loss of ErbB2 activity resulted in a complete absence of cardiomyocyte proliferation during trabeculation stages. In addition, based on data obtained from proliferation, lineage tracing and transplantation studies, we propose that cardiac trabeculation is initiated by directional cardiomyocyte migration rather than oriented cell division, and that ErbB2 cell-autonomously regulates this process.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

No-Holdback allocation rules for continuous-time assemble-to-order systems

This paper analyzes a class of common-component allocation rules, termed no-holdback (NHB) rules, in continuous-review assemble-to-order (ATO) systems with positive lead times. The inventory of each component is replenished following an independent base-stock policy. In contrast to the usually assumed first-come-first-served (FCFS) component allocation rule in the literature, an NHB rule allocates a component to a product demand only if it will yield immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain key performance expressions and compare them to those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems. © 2010 INFORMS.

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Transformation optics (TO) is a powerful tool for the design of electromagnetic and optical devices with novel functionality derived from the unusual properties of the transformation media. In general, the fabrication of TO media is challenging, requiring spatially varying material properties with both anisotropic electric and magnetic responses. Though metamaterials have been proposed as a path for achieving such complex media, the required properties arising from the most general transformations remain elusive, and cannot implemented by state-of-the-art fabrication techniques. Here, we propose faceted approximations of TO media of arbitrary shape in which the volume of the TO device is divided into flat metamaterial layers. These layers can be readily implemented by standard fabrication and stacking techniques. We illustrate our approximation approach for the specific example of a two-dimensional, omnidirectional "invisibility cloak", and quantify its performance using the total scattering cross section as a practical figure of merit. © 2012 American Institute of Physics.