L1-regularisation for ill-posed problems in variational data assimilation

We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

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.

A constrained recursive least squares algorithm for adaptive combination of multiple models

In this paper, we develop a novel constrained recursive least squares algorithm for adaptively combining a set of given multiple models. With data available in an online fashion, the linear combination coefficients of submodels are adapted via the proposed algorithm.We propose to minimize the mean square error with a forgetting factor, and apply the sum to one constraint to the combination parameters. Moreover an l1-norm constraint to the combination parameters is also applied with the aim to achieve sparsity of multiple models so that only a subset of models may be selected into the final model. Then a weighted l2-norm is applied as an approximation to the l1-norm term. As such at each time step, a closed solution of the model combination parameters is available. The contribution of this paper is to derive the proposed constrained recursive least squares algorithm that is computational efficient by exploiting matrix theory. The effectiveness of the approach has been demonstrated using both simulated and real time series examples.

Naturally occurring radioactive material (NORM) from a former phosphoric acid processing plant

In recent years there has been an increasing awareness of the radiological impact of non-nuclear industries that extract and/or process ores and minerals containing naturally occurring radioactive material (NORM). These industrial activities may result in significant radioactive contamination of (by-) products, wastes and plant installations. In this study, scale samples were collected from a decommissioned phosphoric acid processing plant. To determine the nature and concentration of NORM retained in pipe-work and associated process plant, four main areas of the site were investigated: (1) the 'Green Acid Plant', where crude acid was concentrated; (2) the green acid storage tanks; (3) the Purified White Acid (PWA) plant, where inorganic impurities were removed; and (4) the solid waste, disposed of on-site as landfill. The scale samples predominantly comprise the following: fluorides (e.g. ralstonite); calcium sulphate (e.g. gypsum); and an assemblage of mixed fluorides and phosphates (e.g. iron fluoride hydrate, calcium phosphate), respectively. The radioactive inventory is dominated by U-238 and its decay chain products, and significant fractionation along the series occurs. Compared to the feedstock ore, elevated concentrations (<= 8.8 Bq/g) of U-238 Were found to be retained in installations where the process stream was rich in fluorides and phosphates. In addition, enriched levels (<= 11 Bq/g) of Ra-226 were found in association with precipitates of calcium sulphate. Water extraction tests indicate that many of the scales and waste contain significantly soluble materials and readily release radioactivity into solution. (c) 2005 Elsevier Ltd. All rights reserved.

Metrics for solar wind prediction models: Comparison of empirical, hybrid, and physics-based schemes with 8 years of L1 observations

Space weather effects on technological systems originate with energy carried from the Sun to the terrestrial environment by the solar wind. In this study, we present results of modeling of solar corona-heliosphere processes to predict solar wind conditions at the L1 Lagrangian point upstream of Earth. In particular we calculate performance metrics for (1) empirical, (2) hybrid empirical/physics-based, and (3) full physics-based coupled corona-heliosphere models over an 8-year period (1995–2002). L1 measurements of the radial solar wind speed are the primary basis for validation of the coronal and heliosphere models studied, though other solar wind parameters are also considered. The models are from the Center for Integrated Space-Weather Modeling (CISM) which has developed a coupled model of the whole Sun-to-Earth system, from the solar photosphere to the terrestrial thermosphere. Simple point-by-point analysis techniques, such as mean-square-error and correlation coefficients, indicate that the empirical coronal-heliosphere model currently gives the best forecast of solar wind speed at 1 AU. A more detailed analysis shows that errors in the physics-based models are predominately the result of small timing offsets to solar wind structures and that the large-scale features of the solar wind are actually well modeled. We suggest that additional “tuning” of the coupling between the coronal and heliosphere models could lead to a significant improvement of their accuracy. Furthermore, we note that the physics-based models accurately capture dynamic effects at solar wind stream interaction regions, such as magnetic field compression, flow deflection, and density buildup, which the empirical scheme cannot.

Polymorphisms in the apolipoprotein L1 gene and their effects on blood lipid and glucose levels in middle age males

Apolipoprotein L1 in plasma is associated with high- density lipoprotein. Novel APOL1 polymorphisms are investigated along with the association of two common haplotypes (Lys166Glu, Ile244Met, Lys271Arg) with circulating lipid and glucose levels. Although the amino acid substitutions occur in the amphipathic alpha helices region involved in lipid binding, these substitutions were found not to independently account for variability in circulating lipid and glucose levels in 149 middle age males.

Polymorphisms in the apolipoprotein L1 gene and their effects on blood lipid and glucose levels in middle age males

Apolipoprotein L1 in plasma is associated with high- density lipoprotein. Novel APOL1 polymorphisms are investigated along with the association of two common haplotypes (Lys166Glu, Ile244Met, Lys271Arg) with circulating lipid and glucose levels. Although the amino acid substitutions occur in the amphipathic alpha helices region involved in lipid binding, these substitutions were found not to independently account for variability in circulating lipid and glucose levels in 149 middle age males.

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

Comprehension of reflexives and pronouns in sequential bilingual children: do they pattern similarly to L1 children, L2 adults, or children with specific language impairment?

This paper investigates how sequential bilingual (L2) Turkish-English children comprehend English reflexives and pronouns and tests whether they pattern similarly to monolingual (L1) children, L2 adults, or children with Specific Language Impairment (SLI). Thirty nine 6- to 9-year-old L2 children with an age of onset of 30-48 months and exposure to English of 30-72 months and 33 L1 age-matched control children completed the Advanced Syntactic Test of Pronominal Reference-Revised (van der Lely, 1997). The L2 children’s performance was compared to L2 adults from Demirci (2001) and children with SLI from van der Lely & Stollwerck (1997). The L2 children’s performance in the comprehension of reflexives was almost identical to their age-matched controls, and differed from L2 adults and children with SLI. In the comprehension of pronouns, L2 children showed an asymmetry between referential and quantificational NPs, a pattern attested in younger L1 children and children with SLI. Our study provides evidence that the development of comprehension of reflexives and pronouns in these children resembles monolingual L1 acquisition and not adult L2 acquisition or acquisition of children with SLI.

Characterisation of soils containing naturally occurring radioactive material (NORM) using in situ and rapid laboratory techniques. Case study: South Terras, Cornwall

In situ analysis has become increasingly important for contaminated land investigation and remediation. At present, portable techniques are used mainly as scanning tools to assess the spread and magnitude of the contamination, and are an adjunct to conventional laboratory analyses. A site in Cornwall, containing naturally occurring radioactive material (NORM), provided an opportunity for Reading University PhD student Anna Kutner to compare analytical data collected in situ with data generated by laboratory-based methods. The preliminary results in this paper extend the author‟s poster presentation at last September‟s GeoSpec2010 conference held in Lancaster.