Superensembles of linear viscoelastic models of polymer melts

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

Characterisation of Escherichia fergusonii isolates from farm animals using an Escherichia coli virulence gene array and tissue culture adherence assays

Escherichia fergusonii has been associated with a wide variety of intestinal and extra-intestinal infections in both humans and animals but, despite strong circumstantial evidence, the degree to which the organism is responsible for the pathologies identified remains uncertain. Thirty isolates of E fergusonii collected between 2003 and 2004 were screened using an Escherichia coli virulence gene array to test for the presence of homologous virulence genes in E. fergusonii. The iss (increased serum survival) gene was present in 13/30 (43%) of the test strains and the prfB (P-related fimbriae regulatory) and ireA (siderophore receptor IreA) genes were also detected jointly in 3/30 (10%) strains. No known virulence genes were detected in 14/30 (47%) of strains. Following confirmatory PCR and sequence analysis, the E. fergusonii prfB, iss and ireA genes shared a high degree of sequence similarity to their counterparts in E. coli, and a particular resemblance was noted with the E. coli strain APEC O1 pathogenicity island. In tissue culture adherence assays, nine E. fergusonii isolates associated with HEp-2 cells with a 'localised adherence' or 'diffuse adherence' phenotype, and they proved to be moderately invasive. The E fergusonii isolates in this study possess both some phenotypic and genotypic features linked to known pathotypes of E coli, and support existing evidence that strains of E fergusonii may act as an opportunistic pathogens, although their specific virulence factors may need to be explored. Crown Copyright (c) 2008 Published by Elsevier Ltd. All rights reserved.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Development of a dense SNP-based linkage map of an apple rootstock progeny using the Malus Infinium whole genome genotyping array

Background A whole-genome genotyping array has previously been developed for Malus using SNP data from 28 Malus genotypes. This array offers the prospect of high throughput genotyping and linkage map development for any given Malus progeny. To test the applicability of the array for mapping in diverse Malus genotypes, we applied the array to the construction of a SNPbased linkage map of an apple rootstock progeny. Results Of the 7,867 Malus SNP markers on the array, 1,823 (23.2 %) were heterozygous in one of the two parents of the progeny, 1,007 (12.8 %) were heterozygous in both parental genotypes, whilst just 2.8 % of the 921 Pyrus SNPs were heterozygous. A linkage map spanning 1,282.2 cM was produced comprising 2,272 SNP markers, 306 SSR markers and the S-locus. The length of the M432 linkage map was increased by 52.7 cM with the addition of the SNP markers, whilst marker density increased from 3.8 cM/marker to 0.5 cM/marker. Just three regions in excess of 10 cM remain where no markers were mapped. We compared the positions of the mapped SNP markers on the M432 map with their predicted positions on the ‘Golden Delicious’ genome sequence. A total of 311 markers (13.7 % of all mapped markers) mapped to positions that conflicted with their predicted positions on the ‘Golden Delicious’ pseudo-chromosomes, indicating the presence of paralogous genomic regions or misassignments of genome sequence contigs during the assembly and anchoring of the genome sequence. Conclusions We incorporated data for the 2,272 SNP markers onto the map of the M432 progeny and have presented the most complete and saturated map of the full 17 linkage groups of M. pumila to date. The data were generated rapidly in a high-throughput semi-automated pipeline, permitting significant savings in time and cost over linkage map construction using microsatellites. The application of the array will permit linkage maps to be developed for QTL analyses in a cost-effective manner, and the identification of SNPs that have been assigned erroneous positions on the ‘Golden Delicious’ reference sequence will assist in the continued improvement of the genome sequence assembly for that variety.