The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0int for all q≥1.

Zero attracting recursive least squares algorithms

The l1-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.

On the time for fold surfaces to order during the crystallization of polyethylene from the melt and its dependence on molecular parameters

New experiments underpin the interpretation of the basic division in crystallization behaviour of polyethylene in terms of whether or not there is time for the fold surface to order before the next molecular layer is added at the growth front. For typical growth rates, in Regime 11, polyethylene lamellae form with disordered {001} fold surfaces then transform, with lamellar thickening and twisting, towards the more-ordered condition found for slower crystallization in Regime 1, in which lamellae form with and retain {201} fold surfaces. Several linear and linear-low-density polyethylenes have been used to show that, for the same polymer crystallized alone or in a blend, the growth rate at which the change in initial lamellar condition occurs is reasonably constant thereby supporting the concept of a specific time for surfaces to attain the ordered {201}) state. This specific time, in the range from milliseconds to seconds, increases with molecular length, and in linear-low-density polymer, for higher branch contents. (c) 2006 Elsevier Ltd. All rights reserved.

The infra-red spectra of silyl fluoride and silyl fluoride-d3

Infra-red spectra have been recorded for silyl fluoride and silyl fluoride-d3 at a resolution of circa 0·3 cm-1. Rotational structure has been observed for parallel fundamentals in both molecules, and for all perpendicular fundamentals. In both SiH3F and SiD3F the A1 and E species deformation modes interact strongly via a Coriolis perturbation; this has been analysed, and the band origin of v5 for SiH3F is reassigned. A hybrid-orbital force field based on the experimental data is also reported.

Influence of apoA-V gene variants on postprandial triglyceride metabolism: impact of gender

Although apolipoprotein AN (apoA-V) polymorphisms have been consistently associated with fasting triglyceride (TG) levels, their impact on postprandial lipemia remains relatively unknown. In this study, we investigate the impact of two common apoA-V polymorphisms (-1131 T>C and S19W) and apoA-V haplotypes on fasting and postprandial lipid metabolism in adults in the United Kingdom (n = 259). Compared with the wild-type TT, apoA-V -1131 TC heterozygotes had 15% (P = 0.057) and 21% (P = 0.002) higher fasting TG and postprandial TG area under the curve (AUC), respectively. Significant (P = 0.038) and nearly significant (P = 0.057) gender X genotype interactions were observed for fasting TG and TG AUC, with a greater impact of genotype in males. Lower HDL-cholesterol was associated with the rare TC genotype (P = 0.047). Significant linkage disequilibrium was found between the apoA-V -1131 T>C and the apoC-III 3238 C>G variants, with univariate analysis indicating an impact of this apoC-III single nucleotide polymorphism (SNP) on TG AUC (P = 0.015). However, in linear regression analysis, a significant independent association with TG AUC (P = 0.007) was only evident for the apoA-V -1131 T>C SNP, indicating a greater relative importance of the apoA-V genotype.

Rethinking construction: the Generic Design and Construction Process Protocol

The complexity of construction projects and the fragmentation of the construction industry undertaking those projects has effectively resulted in linear, uncoordinated and highly variable project processes in the UK construction sector. Research undertaken at the University of Salford resulted in the development of an improved project process, the Process Protocol, which considers the whole lifecycle of a construction project whilst integrating its participants under a common framework. The Process Protocol identifies the various phases of a construction project with particular emphasis on what is described in the manufacturing industry as the ‘fuzzy front end’. The participants in the process are described in terms of the activities that need to be undertaken in order to achieve a successful project and process execution. In addition, the decision-making mechanisms, from a client perspective, are illustrated and the foundations for a learning organization/industry are facilitated within a consistent Process Protocol.

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

Contrasting effects of necrotrophic and biotrophic plant pathogens on the aphid Aphis fabae

Phytophagous insects have to contend with a wide variation in food quality brought about by a variety of factors intrinsic and extrinsic to the plant. One of the most important factors is infection by plant pathogenic fungi. Necrotrophic and biotrophic plant pathogenic fungi may have contrasting effects on insect herbivores due to their different infection mechanisms and induction of different resistance pathways, although this has been little studied and there has been no study of their combined effect. We studied the effect of the biotrophic rust fungus Uromyces viciae-fabae (Pers.) Schroet (Basidiomycota: Uredinales: Pucciniaceae) and the necrotrophic fungus Botrytis cinerea Pers. (Ascomycota: Helotiales: Sclerotiniaceae) singly and together on the performance of the aphid Aphis fabae Scop. (Hemiptera: Aphididae) on Vicia faba (L.) (Fabaceae). Alone, botrytis had an inhibitory effect on individual A. fabae development, survival and fecundity, while rust infection consistently enhanced individual aphids’ performance. These effects varied in linear relation to lesion or pustule density. However, whole-plant infection by either pathogen resulted in a smaller aphid population of smaller aphids than on uninfected plants, indicating a lowering of aphid carrying capacity with infection. When both fungi were applied simultaneously to a leaf they generally cancelled the effect of each other out, resulting in most performance parameters being similar to the controls, although fecundity was reduced. However, sequential plant infection (pathogens applied five days apart) led to a 70% decrease in fecundity and 50% reduction in intrinsic rate of increase. The application of rust before botrytis had a greater inhibitory effect on aphids than applying botrytis before rust. Rust infection increased leaf total nitrogen concentration by 30% while infection by botrytis with or without rust led to a 38% decrease. The aphids’ responses to the two plant pathogens individually is consistent with the alteration in plant nutrient content by infection and also the induction of different plant defence pathways and the possible cross-talk between them. This is the first demonstration of the complex effects of the dual infection of a plant by contrasting pathogens on insect herbivores. Key words: Vicia faba, Botrytis cinerea, Uromyces viciae-fabae, tripartite interactions, induced resistance

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Decadal predictability of the Atlantic Ocean in a coupled GCM: forecast skill and optimal perturbations using Linear Inverse Modelling

The decadal predictability of three-dimensional Atlantic Ocean anomalies is examined in a coupled global climate model (HadCM3) using a Linear Inverse Modelling (LIM) approach. It is found that the evolution of temperature and salinity in the Atlantic, and the strength of the meridional overturning circulation (MOC), can be effectively described by a linear dynamical system forced by white noise. The forecasts produced using this linear model are more skillful than other reference forecasts for several decades. Furthermore, significant non-normal amplification is found under several different norms. The regions from which this growth occurs are found to be fairly shallow and located in the far North Atlantic. Initially, anomalies in the Nordic Seas impact the MOC, and the anomalies then grow to fill the entire Atlantic basin, especially at depth, over one to three decades. It is found that the structure of the optimal initial condition for amplification is sensitive to the norm employed, but the initial growth seems to be dominated by MOC-related basin scale changes, irrespective of the choice of norm. The consistent identification of the far North Atlantic as the most sensitive region for small perturbations suggests that additional observations in this region would be optimal for constraining decadal climate predictions.