Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Bound on quantum computation time: Quantum error correction in a critical environment

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user. © 2010 The American Physical Society.

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.

Uncovering compounds by synergy of cluster expansion and high-throughput methods.

Predicting from first-principles calculations whether mixed metallic elements phase-separate or form ordered structures is a major challenge of current materials research. It can be partially addressed in cases where experiments suggest the underlying lattice is conserved, using cluster expansion (CE) and a variety of exhaustive evaluation or genetic search algorithms. Evolutionary algorithms have been recently introduced to search for stable off-lattice structures at fixed mixture compositions. The general off-lattice problem is still unsolved. We present an integrated approach of CE and high-throughput ab initio calculations (HT) applicable to the full range of compositions in binary systems where the constituent elements or the intermediate ordered structures have different lattice types. The HT method replaces the search algorithms by direct calculation of a moderate number of naturally occurring prototypes representing all crystal systems and guides CE calculations of derivative structures. This synergy achieves the precision of the CE and the guiding strengths of the HT. Its application to poorly characterized binary Hf systems, believed to be phase-separating, defines three classes of alloys where CE and HT complement each other to uncover new ordered structures.

Ras controls melanocyte expansion during zebrafish fin stripe regeneration.

Regenerative medicine for complex tissues like limbs will require the provision or activation of precursors for different cell types, in the correct number, and with the appropriate instructions. These strategies can be guided by what is learned from spectacular events of natural limb or fin regeneration in urodele amphibians and teleost fish. Following zebrafish fin amputation, melanocyte stripes faithfully regenerate in tandem with complex fin structures. Distinct populations of melanocyte precursors emerge and differentiate to pigment regenerating fins, yet the regulation of their proliferation and patterning is incompletely understood. Here, we found that transgenic increases in active Ras dose-dependently hyperpigmented regenerating zebrafish fins. Lineage tracing and marker analysis indicated that increases in active Ras stimulated the in situ amplification of undifferentiated melanocyte precursors expressing mitfa and kita. Active Ras also hyperpigmented early fin regenerates of kita mutants, which are normally devoid of primary regeneration melanocytes, suppressing defects in precursor function and survival. By contrast, this protocol had no noticeable impact on pigmentation by secondary regulatory melanocyte precursors in late-stage kita regenerates. Our results provide evidence that Ras activity levels control the repopulation and expansion of adult melanocyte precursors after tissue loss, enabling the recovery of patterned melanocyte stripes during zebrafish appendage regeneration.

Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.

Error recovery in cyberphysical digital microfluidic biochips

Droplet-based digital microfluidics technology has now come of age, and software-controlled biochips for healthcare applications are starting to emerge. However, today's digital microfluidic biochips suffer from the drawback that there is no feedback to the control software from the underlying hardware platform. Due to the lack of precision inherent in biochemical experiments, errors are likely during droplet manipulation; error recovery based on the repetition of experiments leads to wastage of expensive reagents and hard-to-prepare samples. By exploiting recent advances in the integration of optical detectors (sensors) into a digital microfluidics biochip, we present a physical-aware system reconfiguration technique that uses sensor data at intermediate checkpoints to dynamically reconfigure the biochip. A cyberphysical resynthesis technique is used to recompute electrode-actuation sequences, thereby deriving new schedules, module placement, and droplet routing pathways, with minimum impact on the time-to-response. © 2012 IEEE.

Expansion of the alpha 2-adrenergic receptor family: cloning and characterization of a human alpha 2-adrenergic receptor subtype, the gene for which is located on chromosome 2.

Pharmacologic, biochemical, and genetic analyses have demonstrated the existence of multiple alpha 2-adrenergic receptor (alpha 2AR) subtypes. We have cloned a human alpha 2AR by using the polymerase chain reaction with oligonucleotide primers homologous to conserved regions of the previously cloned alpha 2ARs, the genes for which are located on human chromosomes 4 (C4) and 10 (C10). The deduced amino acid sequence encodes a protein of 450 amino acids whose putative topology is similar to that of the family of guanine nucleotide-binding protein-coupled receptors, but whose structure most closely resembles that of the alpha 2ARs. Competition curve analysis of the binding properties of the receptor expressed in COS-7 cells with a variety of adrenergic ligands demonstrates a unique alpha 2AR pharmacology. Hybridization with somatic cell hybrids shows that the gene for this receptor is located on chromosome 2. Northern blot analysis of various rat tissues shows expression in liver and kidney. The unique pharmacology and tissue localization of this receptor suggest that this is an alpha 2AR subtype not previously identified by classical pharmacological or ligand binding approaches.

Hybrid error correction and de novo assembly of single-molecule sequencing reads.

Single-molecule sequencing instruments can generate multikilobase sequences with the potential to greatly improve genome and transcriptome assembly. However, the error rates of single-molecule reads are high, which has limited their use thus far to resequencing bacteria. To address this limitation, we introduce a correction algorithm and assembly strategy that uses short, high-fidelity sequences to correct the error in single-molecule sequences. We demonstrate the utility of this approach on reads generated by a PacBio RS instrument from phage, prokaryotic and eukaryotic whole genomes, including the previously unsequenced genome of the parrot Melopsittacus undulatus, as well as for RNA-Seq reads of the corn (Zea mays) transcriptome. Our long-read correction achieves >99.9% base-call accuracy, leading to substantially better assemblies than current sequencing strategies: in the best example, the median contig size was quintupled relative to high-coverage, second-generation assemblies. Greater gains are predicted if read lengths continue to increase, including the prospect of single-contig bacterial chromosome assembly.

Identification of dopamine receptors across the extant avian family tree and analysis with other clades uncovers a polyploid expansion among vertebrates.

Dopamine is an important central nervous system transmitter that functions through two classes of receptors (D1 and D2) to influence a diverse range of biological processes in vertebrates. With roles in regulating neural activity, behavior, and gene expression, there has been great interest in understanding the function and evolution dopamine and its receptors. In this study, we use a combination of sequence analyses, microsynteny analyses, and phylogenetic relationships to identify and characterize both the D1 (DRD1A, DRD1B, DRD1C, and DRD1E) and D2 (DRD2, DRD3, and DRD4) dopamine receptor gene families in 43 recently sequenced bird genomes representing the major ordinal lineages across the avian family tree. We show that the common ancestor of all birds possessed at least seven D1 and D2 receptors, followed by subsequent independent losses in some lineages of modern birds. Through comparisons with other vertebrate and invertebrate species we show that two of the D1 receptors, DRD1A and DRD1B, and two of the D2 receptors, DRD2 and DRD3, originated from a whole genome duplication event early in the vertebrate lineage, providing the first conclusive evidence of the origin of these highly conserved receptors. Our findings provide insight into the evolutionary development of an important modulatory component of the central nervous system in vertebrates, and will help further unravel the complex evolutionary and functional relationships among dopamine receptors.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.