Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

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.

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.

Dietary long-chain n-3 PUFAs increase LPL gene expression in adipose tissue of subjects with an atherogenic lipoprotein phenotype

We sought to test the hypothesis that dietary long-chain n-3 PUFA (LC n-3 PUFA) in fish oil stimulate the gene expression of lipoprotein lipase (LPL) in human adipose tissue (AT). In a randomized, double blind, placebo-controlled, cross-over study, 51 male subjects expressing an atherogenic lipoprotein phenotype (ALP) had their diets supplemented with fish oil for 6 weeks. As we previously reported for this group, supplementation with LC n-3 PUFA produced a decrease in fasting plasma triglyceride (TG) (−35%, P < 0.05), attenuation of the postprandial TG response (area and incremental area under the curve; AUC and IAUC, P < 0.05), and a decrease in small, dense LDL. The present study extended these observations by showing that these changes were accompanied by a marked increase in the concentration of LPL mRNA in adipose tissue (AT-LPL mRNA, +55%, P = 0.003) and post-heparin LPL activity (PH-LPL, +31%, P = 0.036). There was also evidence of an association between LPL gene expression and polymorphism in the apolipoprotein E gene. We conclude that the favorable influence of dietary n-3 PUFA on the ALP may be mediated, in part, through an increase in the plasma activity and gene expression of lipoprotein lipase in human adipose tissue.

Lack of association between lipaemia and central adiposity in subjects with an atherogenic lipoprotein phenotype (ALP)

OBJECTIVE: To investigate the associations between indices of adiposity and cardiovascular risk factors in individuals with an atherogenic lipoprotein phenotype (ALP). SUBJECTS: Fifty-five men, aged 34-69 y, body mass index (BMI) 22-35 kg/m2, with an ALP lipid profile (triglycerides (TG) 1.5-4.0 mmol/l, HDL<1.1 mmol/l; %LDL-3>40% total LDL). DESIGN: Each participant provided a fasting blood sample and underwent an 8 h postprandial assessment and had anthropometric measurements taken. OUTCOME MEASURES: BMI, waist circumference (W), waist-to-hip ratio (W/H), sum of skinfolds (SSK), fasting and postprandial concentrations of glucose, insulin and plasma lipids, post-heparin lipase activity, and apoE genotype. RESULTS: The expected positive associations between BMI, W and SSK and fasting and postprandial insulin were observed (r=0.42-0.65). Little association between glucose responses and any measures of adiposity was evident. Unexpectedly, there were no positive associations between measures of central adiposity (W and W/H) and fasting and postprandial TG responses, with a trend towards negative associations in this study group (TG AUC vs W, r=-0.23, P=0.097; TG IAUC vs W/H, r=-0.26, P=0.068). Subgroup analysis indicated that lack of a positive association between central adiposity and postprandial TG values was more evident in those with one E4 allele (r=-0.42, P=0.077) relative to non-E4 carriers (r=-0.16, P=0.430). The expected positive associations between insulin and TG responses were not observed (r=-0.03 to -0.36). CONCLUSION: In this ALP group the expected positive association between TG responses and a centralized distribution of body fat was not observed, particularly in individuals with an apoE4 genotype. Our findings are not in line with the view that there is a clear causal relationship between insulin resistance and the lipid abnormalities associated with ALP.

ApoE polymorphism and fish oil supplementation in subjects with an antherogenic lipoprotein phenotype

The study assessed the efficacy of fish oil supplementation in counteracting the classic dyslipidemia of the atherogenic lipoprotein phenotype (ALP). In addition, the impact of the common apolipoprotein E (apoE) polymorphism on the fasting and postprandial lipid profile and on responsiveness to the dietary intervention was established. Fifty-five ALP males (aged 34 to 69 years, body mass index 22 to 35 kg/m2, triglyceride [TG] levels 1.5 to 4.0 mmol/L, high density lipoprotein cholesterol [HDL-C] <1.1 mmol/l, and percent low density lipoprotein [LDL]-3 >40% total LDL) completed a randomized placebo-controlled crossover trial of fish oil (3.0 g eicosapentaenoic acid/docosahexaenoic acid per day) and placebo (olive oil) capsules with the 6-week treatment arms separated by a 12-week washout period. In addition to fasting blood samples, at the end of each intervention arm, a postprandial assessment of lipid metabolism was carried out. Fish oil supplementation resulted in a reduction in fasting TG level of 35% (P<0.001), in postprandial TG response of 26% (TG area under the curve, P<0.001), and in percent LDL-3 of 26% (P<0.05). However, no change in HDL-C levels was evident (P=0.752). ANCOVA showed that baseline HDL-C levels were significantly lower in apoE4 carriers (P=0.035). The apoE genotype also had a striking impact on lipid responses to fish oil intervention. Individuals with an apoE2 allele displayed a marked reduction in postprandial incremental TG response (TG incremental area under the curve, P=0.023) and a trend toward an increase in lipoprotein lipase activity relative to non-E2 carriers. In apoE4 individuals, a significant increase in total cholesterol and a trend toward a reduction in HDL-C relative to the common homozygous E3/E3 profile was evident. Our data demonstrate the efficacy of fish oil fatty acids in counteracting the proatherogenic lipid profile of the ALP but also that the apoE genotype influences responsiveness to this dietary treatment.

Inter-relationships between small, dense low-density lipoprotein (LDL), plasma triacylglycerol and LDL apoprotein B in an atherogenic lipoprotein phenotype in free-living subjects

A predominance of small, dense low-density lipoprotein (LDL) is a major component of an atherogenic lipoprotein phenotype, and a common, but modifiable, source of increased risk for coronary heart disease in the free-living population. While much of the atherogenicity of small, dense LDL is known to arise from its structural properties, the extent to which an increase in the number of small, dense LDL particles (hyper-apoprotein B) contributes to this risk of coronary heart disease is currently unknown. This study reports a method for the recruitment of free-living individuals with an atherogenic lipoprotein phenotype for a fish-oil intervention trial, and critically evaluates the relationship between LDL particle number and the predominance of small, dense LDL. In this group, volunteers were selected through local general practices on the basis of a moderately raised plasma triacylglycerol (triglyceride) level (>1.5 mmol/l) and a low concentration of high-density-lipoprotein cholesterol (<1.1 mmol/l). The screening of LDL subclasses revealed a predominance of small, dense LDL (LDL subclass pattern B) in 62% of the cohort. As expected, subjects with LDL subclass pattern B were characterized by higher plasma triacylglycerol and lower high-density lipoprotein cholesterol (<1.1 mmol/l) levels and, less predictably, by lower LDL cholesterol and apoprotein B levels (P<0.05; LDL subclass A compared with subclass B). While hyper-apoprotein B was detected in only five subjects, the relative percentage of small, dense LDL-III in subjects with subclass B showed an inverse relationship with LDL apoprotein B (r=-0.57; P<0.001), identifying a subset of individuals with plasma triacylglycerol above 2.5 mmol/l and a low concentration of LDL almost exclusively in a small and dense form. These findings indicate that a predominance of small, dense LDL and hyper-apoprotein B do not always co-exist in free-living groups. Moreover, if coronary risk increases with increasing LDL particle number, these results imply that the risk arising from a predominance of small, dense LDL may actually be reduced in certain cases when plasma triacylglycerol exceeds 2.5 mmol/l.

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.