Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Interactions between age and apoE genotype on fasting and postprandial triglycerides levels

Objective The influences of genetic determinants on the magnitude of postprandial lipaemia are presently unclear. Here the impact of the common apolipoprotein (apo)E epsilon mutation on the postprandial triglyceride (TG) response is determined, along with an assessment of genotype penetrance according to age, body mass index and gender. Methods and results Healthy adults (n = 251) underwent a postprandial investigation, in which blood samples were taken at regular intervals after a test breakfast (0 min, 49 g fat) and lunch (330 min, 29 g fat) until 480 min after the test breakfast. There was a significant impact of apoE genotype on fasting total cholesterol (TC), (P = 0.027), LDL-cholesterol (LDL-C), (P = 0.008), and %LDL3 (P = 0.001), with higher and lower levels in the E4 and E2 carriers respectively relative to the E3/E3 genotype. Reflective of a higher fasting TG (P = 0.001), a significantly higher area under the curve for the postprandial TG response (TG AUC) was evident in the E4 carriers relative to the E3/E3 group (P = 0.038). In the group as a whole, a significant age × genotype interaction was observed for fasting TC (P = 0.021). In the participants >50 years there was a significant impact of genotype on TC (P = 0.005), LDL-C (P = 0.001) and TAG AUC (P = 0.028). Conclusions It is possible that an exaggerated postprandial lipaemia contributes to the increased coronary heart disease risk associated with carriers of the E4 allele; an effect which is more evident in older adults.

Comparison of algal and fish sources on the oxidative stability of poultry meat and its enrichment with omega-3 polyunsaturated fatty acids

Human consumption of long-chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) is below recommendations, and enriching chicken meat (by incorporating LC n-3 PUFA into broiler diets) is a viable means of increasing consumption. Fish oil is the most common LC n-3 PUFA supplement used but is unsustainable and reduces the oxidative stability of the meat. The objective of this experiment was to compare fresh fish oil (FFO) with fish oil encapsulated (EFO) in a gelatin matrix (to maintain its oxidative stability) and algal biomass at a low (LAG, 11), medium (MAG, 22), or high (HAG, 33 g/kg of diet) level of inclusion. The C22:6n-3 contents of the FFO, EFO, and MAG diets were equal. A control (CON) diet using blended vegetable oil was also made. As-hatched 1-d-old Ross 308 broilers (144) were reared (21 d) on a common starter diet then allocated to treatment pens (4 pens per treatment, 6 birds per pen) and fed treatment diets for 21 d before being slaughtered. Breast and leg meat was analyzed (per pen) for fatty acids, and cooked samples (2 pens per treatment) were analyzed for volatile aldehydes. Concentrations (mg/100 g of meat) of C20:5n-3, C22:5n-3, and C22:6n-3 were (respectively) CON: 4, 15, 24; FFO: 31, 46, 129; EFO: 18, 27, 122; LAG: 9, 19, 111; MAG: 6, 16, 147; and HAG: 9, 14, 187 (SEM: 2.4, 3.6, 13.1) in breast meat and CON: 4, 12, 9; FFO: 58, 56, 132; EFO: 63, 49, 153; LAG: 13, 14, 101; MAG: 11, 15, 102; HAG: 37, 37, 203 (SEM: 7.8, 6.7, 14.4) in leg meat. Cooked EFO and HAG leg meat was more oxidized (5.2 mg of hexanal/kg of meat) than the other meats (mean 2.2 mg/kg, SEM 0.63). It is concluded that algal biomass is as effective as fish oil at enriching broiler diets with C22:6 LC n-3 PUFA, and at equal C22:6n-3 contents, there is no significant difference between these 2 supplements on the oxidative stability of the meat that is produced.

Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

The effect of the year of wheat variety release on productivity and stability of performance on two organic and two non-organic farms

Nineteen wheat cultivars, released from 1934 to 2000, were grown at two organic and two non-organic sites in each of 3 years. Assessments included grain yield, grain protein concentration, protein yield, disease incidence and green leaf area. The superiority of each cultivar (the sum of the squares of the differences between its mean in each environment and the mean of the best cultivar there, divided by twice the number of environments; CS) was calculated for yield, grain protein concentration and protein yield, and ranked in each environment. The yield and grain protein concentration CS were more closely correlated with cultivar release date at the non-organic sites than at organic sites. This difference may be attributed to higher yield levels with larger differences among cultivars at the non-organic sites, rather than to improved stability (i.e. similar ranks) across sites. The significant difference in the correlation of protein yield CS and cultivar age between organic and non-organic sites would support evidence that the ability to take up mineral nitrogen (N) compared to soil N has been a component of the selection conditions of more modern cultivars (released after 1989). This is supported by assessment of green leaf area (GLA), where more modern cultivars in the non-organic systems had greater late-season GLA, a trend that was not identified in organic conditions. This effect could explain the poor correlation between age and protein yield CS in organic compared to non-organic conditions where modern cultivars are selected to benefit from later nitrogen (N) availability which includes the spring nitrogen applications tailored to coincide with peak crop demand. Under organic management, N release is largely based on the breakdown of fertility-building crops incorporated (ploughed-in) in the previous autumn. The release of nutrients from these residues is dependent on the soil conditions, which includes temperature and microbial populations, in addition to the potential leaching effect of high winter rainfall in the UK. In organic cereal crops, early resource capture is a major advantage for maximizing the utilization of nutrients from residue breakdown. It is concluded that selection of cultivars under conditions of high agrochemical inputs selects for cultivars that yield well under maximal conditions in terms of nutrient availability and pest, disease and weed control. The selection conditions for breeding have a tendency to select cultivars which perform relatively better in non-organic compared to organic systems.

Contribution of apolipoprotein E genotype and docosahexaenoic acid to the LDL-cholesterol response to fish oil

Objectives: To investigate the impact of apolipoprotein E (apoE) genotype on the response of the plasma lipoprotein profile to eicosapentaenoic acid (EPA) versus docosahexaenoic acid (DHA) intervention in humans. Methods and results: 38 healthy normolipidaemic males, prospectively recruited on the basis of apoE genotype (n = 20 E3/E3 and n = 18 E3/E4), completed a double-blind placebo-controlled cross-over trial, consisting of 3 × 4 week intervention arms of either control oil, EPA-rich oil (ERO, 3.3 g EPA/day) or DHA-rich oil (DRO, 3.7 g DHA/day) in random order, separated by 10 week wash-out periods. A significant genotype-independent 28% and 19% reduction in plasma triglycerides in response to ERO and DRO was observed. For total cholesterol (TC), no significant treatment effects were evident; however a significant genotype by treatment interaction emerged (P = 0.045), with a differential response to ERO and DRO in E4 carriers. Although the genotype × treatment interaction for LDL-cholesterol (P = 0.089) did not reach significance, within DRO treatment analysis indicated a 10% increase in LDL (P = 0.029) in E4 carriers with a non-significant 4% reduction in E3/E3 individuals. A genotype-independent increase in LDL mass was observed following DRO intervention (P = 0.018). Competitive uptake studies in HepG2 cells using plasma very low density lipoproteins (VLDL) from the human trial, indicated that following DRO treatment, VLDL2 fractions obtained from E3/E4 individuals resulted in a significant 32% (P = 0.002) reduction in LDL uptake relative to the control. Conclusions: High dose DHA supplementation is associated with increases in total cholesterol in E4 carriers, which appears to be due to an increase in LDL-C and may in part negate the cardioprotective action of DHA in this population subgroup.

Model inter-comparison between statistical and dynamic model assessments of the long-term stability of blanket peat in Great Britain (1940-2099)

We compared output from 3 dynamic process-based models (DMs: ECOSSE, MILLENNIA and the Durham Carbon Model) and 9 bioclimatic envelope models (BCEMs; including BBOG ensemble and PEATSTASH) ranging from simple threshold to semi-process-based models. Model simulations were run at 4 British peatland sites using historical climate data and climate projections under a medium (A1B) emissions scenario from the 11-RCM (regional climate model) ensemble underpinning UKCP09. The models showed that blanket peatlands are vulnerable to projected climate change; however, predictions varied between models as well as between sites. All BCEMs predicted a shift from presence to absence of a climate associated with blanket peat, where the sites with the lowest total annual precipitation were closest to the presence/absence threshold. DMs showed a more variable response. ECOSSE predicted a decline in net C sink and shift to net C source by the end of this century. The Durham Carbon Model predicted a smaller decline in the net C sink strength, but no shift to net C source. MILLENNIA predicted a slight overall increase in the net C sink. In contrast to the BCEM projections, the DMs predicted that the sites with coolest temperatures and greatest total annual precipitation showed the largest change in carbon sinks. In this model inter-comparison, the greatest variation in model output in response to climate change projections was not between the BCEMs and DMs but between the DMs themselves, because of different approaches to modelling soil organic matter pools and decomposition amongst other processes. The difference in the sign of the response has major implications for future climate feedbacks, climate policy and peatland management. Enhanced data collection, in particular monitoring peatland response to current change, would significantly improve model development and projections of future change.

Interpretation bias and anxiety in childhood: stability, specificity and longitudinal associations

Background: Biases in the interpretation of ambiguous material are central to cognitive models of anxiety; however, understanding of the association between interpretation and anxiety in childhood is limited. To address this, a prospective investigation of the stability and specificity of anxious cognitions and anxiety and the relationship between these factors was conducted. Method: Sixty-five children (10–11 years) from a community sample completed measures of self-reported anxiety, depression, and conduct problems, and responded to ambiguous stories at three time points over one-year. Results: Individual differences in biases in interpretation of ambiguity (specifically “anticipated distress” and “threat interpretation”) were stable over time. Furthermore, anticipated distress and threat interpretation were specifically associated with anxiety symptoms. Distress anticipation predicted change in anxiety symptoms over time. In contrast, anxiety scores predicted change in threat interpretation over time. Conclusions: The results suggest that different cognitive constructs may show different longitudinal links with anxiety. These preliminary findings extend research and theory on anxious cognitions and their link with anxiety in children, and suggest that these cognitive processes may be valuable targets for assessment and intervention.

The impact of catechol-O-methyltransferase genotype on the acute responsiveness of vascular reactivity to a green tea extract

The beneficial effects of green tea catechins, such as the proposed improvement in endothelial function, may be influenced by phase II metabolism during and after absorption. The methylation enzyme, catechol-O-methyltransferase (COMT), has a missense mutation rs4680 (G to A), proposed to result in a 40 % reduction in enzyme activity. In the present pilot study, twenty subjects (ten of each homozygous COMT genotype) were recruited. Green tea extract capsules (836 mg green tea catechins) were given in a fasted state, and a high-carbohydrate breakfast was given after 60 min. Blood samples and vascular function measurements were taken at regular intervals. The change in digital volume pulse stiffness index (SI) from baseline was shown to be different between genotype groups at 120 and 240 min, with a lower SI in the GG individuals (P ≤ 0·044). The change in blood pressure from baseline also differed between genotype groups, with a greater increase in systolic (P = 0·023) and diastolic (P = 0·034) blood pressure at 120 min in the GG group. The AA group was shown to have a greater increase in insulin concentrations at 120 min (P = 0·019) and 180 min (P = 0·008) compared with baseline, despite similar glucose profiles. No genotypic differences were found in vascular reactivity measured using laser Doppler iontophoresis, total nitrite, lipids, plasma total antioxidant capacity or inflammatory markers after ingestion of the green tea extract. In conclusion, SI and insulin response to the glucose load differed between the COMT genotype groups, and this may be suggestive of a green tea extract and genotype interaction.