A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

HLA class I associations of ankylosing spondylitis in the white population in the United Kingdom

Objective - To investigate the HLA class I associations of ankylosing spondylitis (AS) in the white population, with particular reference to HLA-B27 subtypes. Methods - HLA-B27 and -B60 typing was performed in 284 white patients with AS. Allele frequencies of HLA-B27 and HLA-B60 from 5926 white bone marrow donors were used for comparison. HLA-B27 subtyping was performed by single strand conformation polymorphism (SSCP) in all HLA-B27 positive AS patients, and 154 HLA-B27 positive ethnically matched blood donors. Results - The strong association of HLA-B27 and AS was confirmed (odds ratio (OR) 171, 95% confidence interval (CI) 135 to 218; p < 10-99). The association of HLA-B60 with AS was confirmed in HLA-B27 positive cases (OR 3.6, 95% CI 2.1 to 6.3; p < 5 x 10-5), and a similar association was demonstrated in HLA-B27 negative AS (OR 3.5, 95% CI 1.1 to 11.4; p < 0.05). No significant difference was observed in the frequencies of HLA-B27 allelic subtypes in patients and controls (HLA-B*2702, three of 172 patients v five of 154 controls; HLA-B*2705, 169 of 172 patients v 147 of 154 controls; HkA-B*2708, none of 172 patients v two of 154 controls), and no novel HLA-B27 alleles were detected. Conclusion - HLA-B27 and -B60 are associated with susceptibility to AS, but differences in BLA-B27 subtype do not affect susceptibility to AS in this white population.

Comparison of the Cosmed K4 b2 and the Deltatrac II™ metabolic cart in measuring resting energy expenditure in adults

Background and Aims: The objective of the study was to compare data obtained from the Cosmed K4 b2 and the Deltatrac II™ metabolic cart for the purpose of determining the validity of the Cosmed K4 b2 in measuring resting energy expenditure. Methods: Nine adult subjects (four male, five female) were measured. Resting energy expenditure was measured in consecutive sessions using the Cosmed K4 b2, the Deltatrac II™ metabolic cart separately and the Cosmed K4 b2 and Deltatrac II™ metabolic cart simultaneously, performed in random order. Resting energy expenditure (REE) data from both devices were then compared with values obtained from predictive equations. Results: Bland and Altman analysis revealed a mean bias for the four variables, REE, respiratory quotient (RQ), VCO2, VO2 between data obtained from Cosmed K4 b2 and Deltatrac II™ metabolic cart of 268 ± 702 kcal/day, -0.0±0.2, 26.4±118.2 and 51.6±126.5 ml/min, respectively. Corresponding limits of agreement for the same four variables were all large. Also, Bland and Altman analysis revealed a larger mean bias between predicted REE and measured REE using Cosmed K4 b2 data (-194±603 kcal/day) than using Deltatrac™ metabolic cart data (73±197 kcal/day). Conclusions: Variability between the two devices was very high and a degree of measurement error was detected. Data from the Cosmed K4 b2 provided variable results on comparison with predicted values, thus, would seem an invalid device for measuring adults. © 2002 Elsevier Science Ltd. All rights reserved.

A critical appraisal of the relational management paradigm in an international setting: A future research agenda

Purpose In the mainstream relationship management literature, critical appraisal of the relationship paradigm in an international setting is virtually non-existent. The extant literature reveals a gap in terms of linking relationship management theories with international management. Furthermore, little research attention has been paid to synthesise the existing theories in a cohesive manner towards developing a theoretical paradigm in the interface of the importer-supplier relationship dyad. Thus, the purpose of this paper is to strengthen the theoretical grounds of relationship marketing in an international setting in an importer-exporter relationship context. Design/methodology/approach The paper follows a comprehensive review approach and applies the fundamental theory of trust and commitment to identify the relational factors. More precisely, the paper identifies and applies other relevant theories such as internationalisation process theory, resource-based theory of the firm, dependence theory and transaction cost theory in developing an innovative theoretical paradigm. Findings Based on the integration of extant theories, this paper proposes a new direction in the theoretical realm of the trust and commitment building process within an importer and supplier relationship management paradigm. The research concludes that trust and commitment are the focal factors within the international relational paradigm. Research limitations/implications The proposed research direction suggests an emerging framework integrating mainstream theoretical variables of trust and commitment in importer and foreign-supplier context. This novel framework has the potential for use in further research. Originality/value This paper advances a grounded theoretical exploration within an international management domain in the context of importers and foreign-suppliers.

Esophageal stricture in children: Fiber-optic endoscopy and dilatation under fluoroscopic control

We made a retrospective analysis of the efficacy and complication rate of 268 esophageal dilatation procedures performed under fluoroscopic control using the fiber-optic endoscope in 45 children with esophageal stricture. Antegrade and retrograde stricture dilatation was performed under general anesthetic, mainly as an outpatient procedure. Thirty-six children had an esophageal stricture following tracheoesophageal fistula and/or esophageal atresia repair, and nine children had severe corrosive stricture of the esophagus following lye ingestion. The procedure was well tolerated and effective. © 1992 Raven Press, Ltd., New York.

Meta-analyses identify 13 loci associated with age at menopause and highlight DNA repair and immune pathways

To newly identify loci for age at natural menopause, we carried out a meta-analysis of 22 genome-wide association studies (GWAS) in 38,968 women of European descent, with replication in up to 14,435 women. In addition to four known loci, we identified 13 loci newly associated with age at natural menopause (at P < 5 x 10(-8)). Candidate genes located at these newly associated loci include genes implicated in DNA repair (EXO1, HELQ, UIMC1, FAM175A, FANCI, TLK1, POLG and PRIM1) and immune function (IL11, NLRP11 and PRRC2A (also known as BAT2)). Gene-set enrichment pathway analyses using the full GWAS data set identified exoDNase, NF-kappaB signaling and mitochondrial dysfunction as biological processes related to timing of menopause.

G-protein beta3 subunit gene (GNB3) variant in causation of essential hypertension

-Essential hypertensives display enhanced signal transduction through pertussis toxin-sensitive G proteins. The T allele of a C825T variant in exon 10 of the G protein beta3 subunit gene (GNB3) induces formation of a splice variant (Gbeta3-s) with enhanced activity. The T allele of GNB3 was shown recently to be associated with hypertension in unselected German patients (frequency=0.31 versus 0.25 in control). To confirm and extend this finding in a different setting, we performed an association study in Australian white hypertensives. This involved an extensively examined cohort of 110 hypertensives, each of whom were the offspring of 2 hypertensive parents, and 189 normotensives whose parents were both normotensive beyond age 50 years. Genotyping was performed by polymerase chain reaction and digestion with BseDI, which either cut (C allele) or did not cut (T allele) the 268-bp polymerase chain reaction product. T allele frequency in the hypertensive group was 0.43 compared with 0.25 in the normotensive group (chi2=22; P=0.00002; odds ratio=2.3; 95% CI=1.7 to 3.3). The T allele tracked with higher pretreatment blood pressure: diastolic=105+/-7, 109+/-16, and 128+/-28 mm Hg (mean+/-SD) for CC, CT, and TT, respectively (P=0.001 by 1-way ANOVA). Blood pressures were higher in female hypertensives with a T allele (P=0.006 for systolic and 0.0003 for diastolic by ANOVA) than they were in male hypertensives. In conclusion, the present study of a group with strong family history supports a role for a genetically determined, physiologically active splice variant of the G protein beta3 subunit gene in the causation of essential hypertension.