One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

The effect of enteral and parenteral feeding on secretion of orexigenic peptides in infants

<p>Abstract</p> <p>Background</p> <p>The feeding in the first months of the life seems to influence the risks of obesity and affinity to some diseases including atherosclerosis. The mechanisms of these relations are unknown, however, the modification of hormonal action can likely be taken into account. Therefore, in this study the levels of ghrelin and orexin A - peripheral and central peptide from the orexigenic gut-brain axis were determined.</p> <p>Methods</p> <p>Fasting and one hour after the meal plasma concentrations of ghrelin and orexin were measured in breast-fed (group I; n = 17), milk formula-fed (group II; n = 16) and highly hydrolyzed, hypoallergic formula-fed (group III; n = 14) groups, age matched infants (mean 4 months) as well as in children with iv provision of nutrients (glucose - group IV; n = 15; total parenteral nutrition - group V; n = 14). Peptides were determined using EIA commercial kits.</p> <p>Results</p> <p>Despite the similar caloric intake in orally fed children the fasting ghrelin and orexin levels were significantly lower in the breast-fed children (0.37 ± 0.17 and 1.24 ± 0.29 ng/ml, respectively) than in the remaining groups (0.5 ± 0.27 and 1.64 ± 0.52 ng/ml, respectively in group II and 0.77 ± 0.27 and 2.04 ± 1.1 ng/ml, respectively, in group III). The postprandial concentrations of ghrelin increased to 0.87 ± 0.29 ng/ml, p < 0.002 and 0.76 ± 0.26 ng/ml, p < 0.01 in groups I and II, respectively as compared to fasting values. The decrease in concentration of ghrelin after the meal was observed only in group III (0.47 ± 0.24 ng/ml). The feeding did not influence the orexin concentration. In groups IV and V the ghrelin and orexin levels resembled those in milk formula-fed children.</p> <p>Conclusion</p> <p>The highly hydrolyzed diet strongly affects fasting and postprandial ghrelin and orexin plasma concentrations with possible negative effect on short- and long-time effects on development. Also total parenteral nutrition with the continuous stimulation and lack of fasting/postprandial modulation might be responsible for disturbed development in children fed this way.</p

Phosphorylcholine Allows for Evasion of Bactericidal Antibody by Haemophilus influenzae

The human pathogen Haemophilus influenzae has the ability to quickly adapt to different host environments through phase variation of multiple structures on its lipooligosaccharide (LPS), including phosphorylcholine (ChoP). During colonization with H. influenzae, there is a selection for ChoP+ phase variants. In a murine model of nasopharyngeal colonization, this selection is lost in the absence of adaptive immunity. Based on previous data highlighting the importance of natural antibody in limiting H. influenzae colonization, the effect of ChoP expression on antibody binding and its bactericidal activity was investigated. Flow cytometric analysis revealed that ChoP+ phase variants had decreased binding of antibody to LPS epitopes compared to ChoP− phase variants. This difference in antibody binding correlated with increased survival of ChoP+ phase variants in the presence of antibody-dependent, complement-mediated killing. ChoP+ phase variants were also more resistant to trypsin digestion, suggesting a general effect on the physical properties of the outer membrane. Moreover, ChoP-mediated protection against antibody binding correlated with increased resilience of outer membrane integrity. Collectively, these data suggest that ChoP expression provides a selective advantage during colonization through ChoP-mediated effects on the accessibility of bactericidal antibody to the cell surface

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

Seven-CpG DNA methylation age determined by single nucleotide primer extension and Illumina’s Infinium MethylationEPIC array provide highly comparable results

DNA methylation age (DNAm age, epigenetic clock) is a novel and promising biomarker of aging. It is calculated from the methylation fraction of specific cytosine phosphate guanine sites (CpG sites) of genomic DNA. Several groups have proposed epigenetic clock algorithms and these differ mostly regarding the number and location of the CpG sites considered and the method used to assess the methylation status. Most epigenetic clocks are based on a large number of CpGs, e.g. as measured by DNAm microarrays. We have recently evaluated an epigenetic clock based on the methylation fraction of seven CpGs that were determined by methylation-sensitive single nucleotide primer extension (MS-SNuPE). This method is more cost-effective when compared to array-based technologies as only a few CpGs need to be examined. However, there is only little data on the correspondence in epigenetic age estimation using the 7-CpG clock and other algorithms. To bridge this gap, in this study we measured the 7-CpG DNAm age using two methods, via MS-SNuPE and via the MethylationEPIC array, in a sample of 1,058 participants of the Berlin Aging Study II (BASE-II), assessed as part of the GendAge study. On average, participants were 75.6 years old (SD: 3.7, age range: 64.9–90.0, 52.6% female). Agreement between methods was assessed by Bland-Altman plots. DNAm age was highly correlated between methods (Pearson’s r = 0.9) and Bland-Altman plots showed a difference of 3.1 years. DNAm age by the 7-CpG formula was 71.2 years (SD: 6.9 years, SNuPE) and 68.1 years (SD: 6.4 years, EPIC array). The mean of difference in methylation fraction between methods for the seven individual CpG sites was between 0.7 and 13 percent. To allow direct conversion of DNAm age obtained from both methods we developed an adjustment formula with a randomly selected training set of 529 participants using linear regression. After conversion of the Illumina data in a second and independent validation set, the adjusted DNAm age was 71.44 years (SD: 6.1 years, n = 529). In summary, we found the results of DNAm clocks to be highly comparable. Furthermore, we developed an adjustment formula that allows for direct conversion of DNAm age estimates between methods and enables one singular clock to be used in studies that employ either the Illumina or the SNuPE method