Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Productivity of crossbred dairy cows suckling their calves for 12 or 24 weeks post calving

An experiment on restricted suckling of crossbred dairy cows was conducted at the Livestock Research Centre, Tanga in northeast Tanzania. Thirty-six Bos taurus (Holstein Friesian and Jersey) x Bos indicus (East African Zebu) cows were allocated alternately as they calved to suckling their calves for either 12 or 24 weeks after calving. Cows grazed improved pastures and were offered 4 kg concentrate daily. Milking occurred twice daily by hand; calves were allowed to suck residual milk for 30 min following each milking. Calves were also allowed access to grazing and were offered a maximum of I kg concentrate daily to 24 weeks of age. Weaning age had no significant effect on lactation milk yield for human consumption, the mean (SE) yield being 1806 (102.0) L and 1705 (129. 1) L for 12- and 24-week weaning, respectively. Cows from the two treatments suffered similar losses of live weight and body condition score during lactation and neither group had returned to the original body condition score 40 weeks following calving. Post-partum anoestrous intervals were prolonged. Although not significant, cows suckling calves to 24 weeks had a mean interval to first oestrus extended by 38 days compared with cows suckling calves to 12 weeks. The mean (SE) daily live weight gains of the calves to 52 weeks were 263 (14.1) g/day and 230 (18.1) g/day for calves weaned at 12 and 24 weeks, respectively, such that 12-month weights were 119 (5.6) kg and 110 (7.3) kg, respectively. Twelve-week-weaned calves consumed more concentrate (p < 0.05) from 13 to 24 weeks than did 24-week weaned calves. Calculation of residual milk consumption removed by calves from birth to 12 weeks indicated that it accounted for 28% of total yield. No benefits in cow and calf performance and welfare were found to justify prolonging the suckling period to 24 weeks.

Longitudinal selenium status in healthy British adults: assessment using biochemical and molecular biomarkers

Human selenium (Se) requirements are currently based on biochemical markers of Se status. In rats, tissue glutathione peroxidase-1 (Gpx1) mRNA levels can be used effectively to determine Se requirements; blood Gpx1 mRNA levels decrease in Se-deficient rats, so molecular biology-based markers have potential for human nutrition assessment. To study the efficacy of molecular biology markers for assessing Se status in humans, we conducted a longitudinal study on 39 subjects (age 45 +/- 11) in Reading, UK. Diet diaries (5 day) and blood were obtained from each subject at 2, 8, 17 and 23 weeks, and plasma Se, glutathione peroxidase (Gpx3) enzyme activity, and selenoprotein mRNA levels were determined. There were no significant longitudinal effects on Se biomarkers. Se intake averaged 48 +/- 14 mu g/d. Plasma Se concentrations averaged 1.13 +/- 0.16 mu mol/l. Plasma Se v. energy-corrected Se intake (ng Se/kJ/d) was significantly correlated, but neither Gpx3 activity v. Se intake (ng Se/kJ/d) nor Gpx3 activity v. plasma Se was significantly correlated. Collectively, this indicates that subjects were on the plateaus of the response curves. Selenoprotein mRNAs were quantitated in total RNA isolated from whole blood, but mRNA levels for Gpx1, selenoprotein H, and selenoprotein W (all highly regulated by Se in rodents), as well selenoprotein P, Gpx3, and phospholipid hydroperoxide glutathione peroxidase were also not significantly correlated with plasma Se. Thus selenoprotein molecular biomarkers, as well as traditional biochemical markers, are unable to further distinguish differences in Se status in these Se replete subjects. The efficacy of molecular biomarkers to detect Se deficiency needs to be tested in Se-deficient populations.

Effects of enhanced consumption of fruit and vegetables on plasma antioxidant status and oxidative resistance of LDL in smokers supplemented with fish oil

Objective: To determine whether consumption of five portions of fruit and vegetables per day reduces the enhancement of oxidative stress induced by consumption of fish oil. Subjects: A total of 18 free-living healthy smoking volunteers, aged 18-63 y, were recruited by posters and e-mail in The University of Reading, and by leaflets in local shops. Design: A prospective study. Setting: Hugh Sinclair Unit of Human Nutrition, School of Food Biosciences, The University of Reading, Whiteknights PO Box 226, Reading RG6 6AP, UK. Intervention: All subjects consumed a daily supplement of 4 x 1 g fish oil capsules for 9 weeks. After 3 weeks, they consumed an additional five portions of fruits and vegetables per day, and then they returned to their normal diet for the last 3 weeks of the study. Fasting blood samples were taken at the ends of weeks 0, 3, 6 and 9. Results: The plasma concentrations of ascorbic acid, lutein, beta-cryptoxanthin, alpha-carotene and beta-carotene all significantly increased when fruit and vegetable intake was enhanced (P<0.05). Plasma concentrations of α-tocopherol, retinol and uric acid did not change significantly during the period of increased fruit and vegetable consumption. Plasma oxidative stability, assessed by the oxygen radical absorbance capacity (ORAC) assay, also increased from weeks 3-6 (P<0.001) but not in association with increases in measured antioxidants. Lag phase before oxidation of low-density lipoprotein (LDL) significantly decreased in the first 3 weeks of the study, reflecting the incorporation of EPA and DHA into LDL (P<0.0001). Subsequent enhanced fruit and vegetable consumption significantly reduced the susceptibility of LDL to oxidation (P<0.005). Conclusion: Fish oil reduced the oxidative stability of plasma and LDL, but the effects were partially offset by the increased consumption of fruit and vegetables.

Dietary supplementation with a natural carotenoid mixture decreases oxidative stress

Objective: To determine whether dietary supplementation with a natural carotenoid mixture counteracts the enhancement of oxidative stress induced by consumption of fish oil. Design: A randomised double-blind crossover dietary intervention. Setting: Hugh Sinclair Unit of Human Nutrition, School of Food Biosciences, The University of Reading, Whiteknights PO Box 226, Reading RG6 6AP, UK. Subjects and intervention: A total of 32 free-living healthy nonsmoking volunteers were recruited by posters and e-mails in The University of Reading. One volunteer withdrew during the study. The volunteers consumed a daily supplement comprising capsules containing fish oil (4 x 1 g) or fish oil (4 x 1 g) containing a natural carotenoid mixture (4 x 7.6 mg) for 3 weeks in a randomised crossover design separated by a 12 week washout phase. The carotenoid mixture provided a daily intake of beta-carotene (6.0 mg), alpha-carotene (1.4 mg), lycopene (4.5 mg), bixin (11.7 mg), lutein (4.4 mg) and paprika carotenoids (2.2 mg). Blood and urine samples were collected on days 0 and 21 of each dietary period. Results: The carotenoid mixture reduced the fall in ex vivo oxidative stability of low-density lipoprotein (LDL) induced by the fish oil (P = 0.045) and it reduced the extent of DNA damage assessed by the concentration of 8-hydroxy-2'-deoxyguanosine in urine (P = 0.005). There was no effect on the oxidative stability of plasma ex vivo assessed by the oxygen radical absorbance capacity test. beta- Carotene, alpha-carotene, lycopene and lutein were increased in the plasma of subjects consuming the carotenoid mixture. Plasma triglyceride levels were reduced significantly more than the reduction for the fish oil control (P = 0.035), but total cholesterol, HDL and LDL levels were not significantly changed by the consumption of the carotenoid mixture. Conclusions: Consumption of the natural carotenoid mixture lowered the increase in oxidative stress induced by the fish oil as assessed by ex vivo oxidative stability of LDL and DNA degradation product in urine. The carotenoid mixture also enhanced the plasma triglyceride-lowering effect of the fish oil.

Effects of chronic and acute fruit and vegetable juice consumption on cardiovascular disease risk factors

Diets low in fruit and vegetables are reportedly responsible for 2.7 million deaths annually from cardiovascular diseases (CVD) and certain cancers. A daily fruit and vegetable intake of five 80 g portions is recommended for chronic disease prevention. However, in the UK, average adult consumption is less than three portions. It is suggested that fruit juice should only count as one portion. However, fruit juices are a beneficial source of phytochemicals. The preliminary results of two randomized, controlled, crossover, dietary intervention studies investigating the effects of chronic and acute consumption of fruit and vegetable puree and juice based drinks (FVPJ) on bioavailability, antioxidant status, vascular reactivity, and risk factors for CVD are reported. In the first study, 39 volunteers consumed 200 ml FVPJ, or fruit-flavoured control, daily for six weeks. In the second study, 24 volunteers consumed 400 mL FVPJ, or sugar-matched control, on the morning of the study day. Blood and urine samples were collected throughout both studies and real-time measurements of vascular tone were performed using laser Doppler imaging with iontophoresis. Overall, the studies showed that the fruit and vegetable puree and juice based drink increased dietary phytochemicals. There was a trend towards increased vasodilation following both acute and chronic fruit juice consumption. Measurements of antioxidant status, oxidative stress and other cardiovascular disease risk factors are currently being determined.

The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.

Impact of the quantity and flavonoid content of fruits and vegetables on markers of intake in adults with an increased risk of cardiovascular disease: the FLAVURS Trial

Purpose Limited robust randomised controlled trials investigating fruit and vegetable (F&V) intake in people at risk of cardiovascular disease (CVD) exist. We aimed to design and validate a dietary strategy of increasing flavonoid-rich versus flavonoid-poor F&V consumption on nutrient biomarker profile. Methods A parallel, randomised, controlled, dose–response dietary intervention study. Participants with a CVD relative risk of 1.5 assessed by risk scores were randomly assigned to one of the 3 groups: habitual (control, CT), high-flavonoid (HF) or low-flavonoid (LF) diets. While the CT group (n = 57) consumed their habitual diet throughout, the HF (n = 58) and LF (n = 59) groups sequentially increased their daily F&V intake by an additional 2, 4 and 6 portions for 6-week periods during the 18-week study. Results Compliance to target numbers and types of F&V was broadly met and verified by dietary records, and plasma and urinary biomarkers. Mean (±SEM) number of F&V portions/day consumed by the HF and LF groups at baseline (3.8 ± 0.3 and 3.4 ± 0.3), 6 weeks (6.3 ± 0.4 and 5.8 ± 0.3), 12 weeks (7.0 ± 0.3 and 6.8 ± 0.3) and 18 weeks (7.6 ± 0.4 and 8.1 ± 0.4), respectively, was similar at baseline yet higher than the CT group (3.9 ± 0.3, 4.3 ± 0.3, 4.6 ± 0.4, 4.5 ± 0.3) (P = 0.015). There was a dose-dependent increase in dietary and urinary flavonoids in the HF group, with no change in other groups (P = 0.0001). Significantly higher dietary intakes of folate (P = 0.035), non-starch polysaccharides (P = 0.001), vitamin C (P = 0.0001) and carotenoids (P = 0.0001) were observed in both intervention groups compared with CT, which were broadly supported by nutrient biomarker analysis. Conclusions The success of improving nutrient profile by active encouragement of F&V intake in an intervention study implies the need for a more hands-on public health approach.

Effects of chronic consumption of fruit and vegetable puree-based drinks on vasodilation, plasma oxidative stability and antioxidant status

Background: Fruit and vegetable-rich diets are associated with a reduced cardiovascular disease (CVD) risk. This protective effect may be a result of the phytochemicals present within fruits and vegetables (F&V). However, there can be considerable variation in the content of phytochemical composition of whole F&V depending on growing location, cultivar, season and agricultural practices, etc. Therefore, the present study investigated the effects of consuming fruits and vegetables as puree-based drinks (FVPD) daily on vasodilation, phytochemical bioavailability, antioxidant status and other CVD risk factors. FVPD was chosen to provide a standardised source of F&V material that could be delivered from the same batch to all subjects during each treatment arm of the study. Methods: Thirty-nine subjects completed the randomised, controlled, cross-over dietary intervention. Subjects were randomised to consume 200 mL of FVPD (or fruit-flavoured control), daily for 6 weeks with an 8-week washout period between treatments. Dietary intake was measured using two 5-day diet records during each cross-over arm of the study. Blood and urine samples were collected before and after each intervention and vasodilation assessed in 19 subjects using laser Doppler imaging with iontophoresis. Results: FVPD significantly increased dietary vitamin C and carotenoids (P < 0.001), and concomitantly increased plasma α- and β-carotene (P < 0.001) with a near-significant increase in endothelium-dependent vasodilation (P = 0.060). Conclusions: Overall, the findings obtained in the present study showed that FVPD were a useful vehicle to increase fruit and vegetable intake, significantly increasing dietary and plasma phytochemical concentrations with a trend towards increased endothelium-dependent vasodilation.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

Change in convergence and accommodation after two weeks of eye exercises in typical young adults

Abstract: Introduction Although eye exercises appear to help heterophoria, convergence insufficiency and intermittent strabismus, true treatment effects can be confounded by placebo, practice and encouragement factors. This study assessed objective changes in vergence and accommodation responses in typical naïve young adults after two weeks of exercises compared to control conditions to assess the extent of treatment effects occur above other factors. Methods 156 asymptomatic young adults were randomly assigned to 6 exercise groups or 2 no-treatment groups. Treatment targeted i) accommodation, ii)vergence, iii) both, iv) convergence>accommodation, v)accommodation>convergence, or vi) a placebo. All were re-tested under identical conditions, except for the second control group who were additionally encouraged during testing. Objective accommodation and vergence were assessed to a range of targets moving in depth containing combinations of blur, disparity and proximity/looming cues. Results Response gain improved more for less naturalistic targets where more improvement was possible. Convergence exercises improved vergence for near across all targets (P=.035). Mean accommodation changed similarly,but non-significantly. No other treatment group differed significantly from the non-encouraged control group, while encouraging effort produced significantly increased vergence (P=.004) and accommodation (P=.005) gains in the other control group. Conclusions True treatment effects were small, only significantly better after vergence exercises to a non-accommodative target, and were rarely related to response they were designed to improve. Exercising accommodation without convergence made no difference to accommodation to cues containing detail. Additional effort improved objective responses the most, so should be controlled carefully in research, and considered when auditing treatment.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Evidence for interplay between genes and maternal stress in utero: monoamine oxidase A polymorphism moderates effects of life events during pregnancy on infant negative emotionality at 5 weeks

The low activity variant of the monoamine oxidase A (MAOA) functional promoter polymorphism, MAOA-LPR, in interaction with adverse environments (G × E) is associated with child and adult antisocial behaviour disorders. MAOA is expressed during foetal development so in utero G × E may influence early neurodevelopment. We tested the hypothesis that MAOA G × E during pregnancy predicts infant negative emotionality soon after birth. In an epidemiological longitudinal study starting in pregnancy, using a two stage stratified design, we ascertained MAOA-LPR status (low vs. high activity variants) from the saliva of 209 infants (104 boys and 105 girls), and examined predictions to observed infant negative emotionality at 5 weeks post-partum from life events during pregnancy. In analyses weighted to provide estimates for the general population, and including possible confounders for life events, there was an MAOA status by life events interaction (P = 0.017). There was also an interaction between MAOA status and neighbourhood deprivation (P = 0.028). Both interactions arose from a greater effect of increasing life events on negative emotionality in the MAOA-LPR low activity, compared with MAOA-LPR high activity infants. The study provides the first evidence of moderation by MAOA-LPR of the effect of the social environment in pregnancy on negative emotionality in infancy, an early risk for the development of child and adult antisocial behaviour disorders.