Vertex-pursuit in random directed acyclic graphs

We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (DAGs). In Seepage, agents attempt to block the movement of an intruder who moves downward from the source node to a sink. The minimum number of such agents required to block the intruder is called the green number. We propose a generalized stochastic model for DAGs with given expected total degree sequence. Seepage and the green number is analyzed in stochastic DAGs in both the cases of a regular and power law degree sequence. For each such sequence, we give asymptotic bounds (and in certain instances, precise values) for the green number

SENSORY AND HEALTH-RELATED FRUIT QUALITY OF ORGANIC APPLES. A COMPARATIVE FIELD STUDY OVER THREE YEARS USING CONVENTIONAL AND HOLISTIC METHODS TO ASSESS FRUIT QUALITY

In a 3 years lasting field study with the ‘Golden Delicious’ cultivar, we compared fruits of 5 pairs of organic/integrated fruit farms. The orchards were similar in microclimate, soil conditions and planting system. To assess inner fruit quality we investigated at the beginning and at the end of cold storage: (i) standard parameters (firmness, sugar, malic acid., mineral content); (ii) sensorial quality by panel tests; (iii) health related components (23 phenolic compounds, nutritional fibres; vitamins); and (v) fruit «vitality quality» by holistic approaches (crystallisation in copper chloride, self degradation tests, feeding preference tests with laboratory rats). The most significant differences were found in year one of the study, and were by tendency confirmed in the following two years. In year one all fruit samples of organic orchards had significantly firmer fruit flesh (14%), a 10 % higher index of inner quality (on basis of sugar and malic acid content and fruit flesh firmness), and 15% higher taste scores than conventional ones. Phosphorus content of the fruit flesh was 31% higher in organic apples and closely correlated (r2 = 0.93) with the index of inner quality and sensory score (r2 = 0.69). No extraction method of Phosphorus in the soil (water, NH4-EDTA, citric acid, CAL) correlated with the P-content in the fruits. However, P in the fruit flesh correlated by r2 = 0.72 with the microbial activity of the soil expressed as the ratio of microbialbound Nitrogen and Carbon in the soil. With a value of 3.85 the Cmic:Nmic ratio was 44.5 % lower (thus more favourable) in organic tree strips. Flavanols, with 65.7 % of the total polyphenol content were the dominant group of polyphenols. The content of flavonols was 22.7 % higher in organic apples in the first year and 15.6 % in the average of the three years. The self-degradation test didn't provide significant differences. Laboratory rats, showed a tendency to prefer IP apples probably due to their advanced ripeness. Thus rat behaviour did not correspond with the sensory panel judgement. The picture forming method provided a correct reproducibility with repeated blind samples before and after storage (r2 = 0.83), and distinguished 100 % correctly organic an IP fruit in the first year. In the second year there was one miss qualification. The average value over three dates of the index for «vitality quality», which was especially created for this study, was 44.6 % higher with organic apples The picture forming methods correlated well with sensory scores and standard quality (r2 = 0.63) in the first year. The study revealed interesting and consumer-relevant differences between organic and integrated apples with standard and holistic methods

Geschmack- und gesundheitsrelevante Qualität von ökologisch angbauten Äpfeln: Eine 3jährige Feldvergleichsstudie mit standard- und ganzheitlichen Untersuchungsmethoden

In a 3 years lasting field study with the ‘Golden Delicious’ cultivar, we compared fruits of 5 pairs of organic/integrated fruit farms. The orchards were similar in microclimate, soil conditions and planting system. To assess inner fruit quality we investigated at the beginning and at the end of cold storage: (i) standard parameters (firmness, sugar, malic acid., mineral content); (ii) sensorial quality by panel tests; (iii) health related components (23 phenolic compounds, nutritional fibres; vitamins); and (v) fruit «vitality quality» by holistic approaches (crystallisation in copper chloride, self degradation tests, feeding preference tests with laboratory rats). The most significant differences were found in year one of the study, and were by tendency confirmed in the following two years. In year one all fruit samples of organic orchards had significantly firmer fruit flesh (14%), a 10 % higher index of inner quality (on basis of sugar and malic acid content and fruit flesh firmness), and 15% higher taste scores than conventional ones. Phosphorus content of the fruit flesh was 31% higher in organic apples and closely correlated (r2 = 0.93) with the index of inner quality and sensory score (r2 = 0.69). No extraction method of Phosphorus in the soil (water, NH4-EDTA, citric acid, CAL) correlated with the P-content in the fruits. However, P in the fruit flesh correlated by r2 = 0.72 with the microbial activity of the soil expressed as the ratio of microbialbound Nitrogen and Carbon in the soil. With a value of 3.85 the Cmic:Nmic ratio was 44.5 % lower (thus more favourable) in organic tree strips. Flavanols, with 65.7 % of the total polyphenol content were the dominant group of polyphenols. The content of flavonols was 22.7 % higher in organic apples in the first year and 15.6 % in the average of the three years. The self-degradation test didn't provide significant differences. Laboratory rats, showed a tendency to prefer IP apples probably due to their advanced ripeness. Thus rat behaviour did not correspond with the sensory panel judgement. The picture forming method provided a correct reproducibility with repeated blind samples before and after storage (r2 = 0.83), and distinguished 100 % correctly organic an IP fruit in the first year. In the second year there was one miss qualification. The average value over three dates of the index for «vitality quality», which was especially created for this study, was 44.6 % higher with organic apples The picture forming methods correlated well with sensory scores and standard quality (r2 = 0.63) in the first year. The study revealed interesting and consumer-relevant differences between organic and integrated apples with standard and holistic methods

Self-similar solutions of semilinear wave equations with a focusing nonlinearity

We prove that in three space dimensions a nonlinear wave equation $u_{tt}-\Delta u = u^p$ with $p\geq 7$ being an odd integer has a countable family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio

Effect of phospholipids and bile acids on cholesterol nucleation time and vesicular/micellar cholesterol in gallbladder bile of patients with cholesterol stones

Supersaturation and rapid nucleation of cholesterol in bile are of key importance in the pathogenesis of cholesterol gallstones. While the effects of bile acids and phospholipids on cholesterol saturation of bile have been extensively studied, their influence on the cholesterol nucleation time has not been compared. We, therefore, investigated whether increases of bile acid or phospholipid concentrations in bile by in vitro supplementation affect the cholesterol nucleation time. Bile samples were obtained at surgery from patients with cholesterol gallstones. Prior to the nucleation assay the bile samples were divided into 0.5-ml aliquots and supplemented with 1.25, 2.5, 5.0, and 10.0 mumol/ml of different phosphatidylcholines (PC-dimyristoyl, PC- dipalmitoyl, PC-distearoyl, and extracted biliary PCs) or with 5.0, 10.0, and 20.0 mumol/ml of bile acids (glycine or taurine conjugates of cholic acid, deoxycholic acid, or chenodeoxycholic acid). The increase of phosphatidylcholine or bile acid concentration decreased the mean cholesterol saturation index to a similar extent (PC: 0.1-0.3; BA: 0.1- 0.2). Supplementations of bile with increasing amounts of synthetic or biliary PCs caused a marked prolongation of the nucleation time in bile from 1.5 +/- 0.2 up to > or = 21 days or 2.5 +/- 0.7 up to > or = 21 days. Concurrently, biliary cholesterol was shifted from vesicles to mixed micelles and the cholesterol/phospholipid ratio of the remaining vesicles was progressively lowered. In contrast, the addition of bile acids to gallbladder bile did not affect the cholesterol nucleation time (2.2 +/- 0.3 days), the percentage of vesicular cholesterol, or the cholesterol/phospholipid ratio of vesicles and micelles