Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.Comment: 11 pages (Revtex) + 5 figures (postscript

Stochastic synchronization in globally coupled phase oscillators

Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure

Forecasting confined spatiotemporal chaos with genetic algorithms

A technique to forecast spatiotemporal time series is presented. it uses a Proper Ortogonal or Karhunen-Lo\`{e}ve Decomposition to encode large spatiotemporal data sets in a few time-series, and Genetic Algorithms to efficiently extract dynamical rules from the data. The method works very well for confined systems displaying spatiotemporal chaos, as exemplified here by forecasting the evolution of the onedimensional complex Ginzburg-Landau equation in a finite domain.Comment: 4 pages, 5 figure

Epigenetic Gene Promoter Methylation at Birth Is Associated With Child’s Later Adiposity

Objective: fixed genomic variation explains only a small proportion of the risk of adiposity. In animal models, maternal diet alters offspring body composition, accompanied by epigenetic changes in metabolic control genes. Little is known about whether such processes operate in humans.Research design and methods: using Sequenom MassARRAY we measured the methylation status of 68 CpGs 5? from five candidate genes in umbilical cord tissue DNA from healthy neonates. Methylation varied greatly at particular CpGs: for 31 CpGs with median methylation ?5% and a 5–95% range ?10%, we related methylation status to maternal pregnancy diet and to child’s adiposity at age 9 years. Replication was sought in a second independent cohort.Results: in cohort 1, retinoid X receptor-? (RXRA) chr9:136355885+ and endothelial nitric oxide synthase (eNOS) chr7:150315553+ methylation had independent associations with sex-adjusted childhood fat mass (exponentiated regression coefficient [?] 17% per SD change in methylation [95% CI 4–31], P = 0.009, n = 64, and ? = 20% [9–32], P < 0.001, n = 66, respectively) and %fat mass (? = 10% [1–19], P = 0.023, n = 64 and ? =12% [4–20], P = 0.002, n = 66, respectively). Regression analyses including sex and neonatal epigenetic marks explained >25% of the variance in childhood adiposity. Higher methylation of RXRA chr9:136355885+, but not of eNOS chr7:150315553+, was associated with lower maternal carbohydrate intake in early pregnancy, previously linked with higher neonatal adiposity in this population. In cohort 2, cord eNOS chr7:150315553+ methylation showed no association with adiposity, but RXRA chr9:136355885+ methylation showed similar associations with fat mass and %fat mass (? = 6% [2–10] and ? = 4% [1–7], respectively, both P = 0.002, n = 239).Conclusions: our findings suggest a substantial component of metabolic disease risk has a prenatal developmental basis. Perinatal epigenetic analysis may have utility in identifying individual vulnerability to later obesity and metabolic diseas

Noise and Periodic Modulations in Neural Excitable Media

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. To this purpose, we have considered two types of modulations; namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is present, irrespective of if the system is monostable or bistable.Comment: 13 pages, RevTex, 5 PostScript figure

Personalized glucose forecasting for type 2 diabetes using data assimilation

Type 2 diabetes leads to premature death and reduced quality of life for 8% of Americans. Nutrition management is critical to maintaining glycemic control, yet it is difficult to achieve due to the high individual differences in glycemic response to nutrition. Anticipating glycemic impact of different meals can be challenging not only for individuals with diabetes, but also for expert diabetes educators. Personalized computational models that can accurately forecast an impact of a given meal on an individual’s blood glucose levels can serve as the engine for a new generation of decision support tools for individuals with diabetes. However, to be useful in practice, these computational engines need to generate accurate forecasts based on limited datasets consistent with typical self-monitoring practices of individuals with type 2 diabetes. This paper uses three forecasting machines: (i) data assimilation, a technique borrowed from atmospheric physics and engineering that uses Bayesian modeling to infuse data with human knowledge represented in a mechanistic model, to generate real-time, personalized, adaptable glucose forecasts; (ii) model averaging of data assimilation output; and (iii) dynamical Gaussian process model regression. The proposed data assimilation machine, the primary focus of the paper, uses a modified dual unscented Kalman filter to estimate states and parameters, personalizing the mechanistic models. Model selection is used to make a personalized model selection for the individual and their measurement characteristics. The data assimilation forecasts are empirically evaluated against actual postprandial glucose measurements captured by individuals with type 2 diabetes, and against predictions generated by experienced diabetes educators after reviewing a set of historical nutritional records and glucose measurements for the same individual. The evaluation suggests that the data assimilation forecasts compare well with specific glucose measurements and match or exceed in accuracy expert forecasts. We conclude by examining ways to present predictions as forecast-derived range quantities and evaluate the comparative advantages of these ranges

Time resolved pattern evolution in a large aperture laser

We have measured quasi-instantaneous transverse patterns in a broad aperture laser. Non-ordered patterns yielding to boundary determined regular structures in progressive time-integrated recording are observed. The linear analysis and numerical integration of the full Maxwell-Bloch equations allow us to interpret the features of the experiment. We show that this system being far from threshold cannot be fully understood with a perturbative model.Comment: 7 pages, 5 GIF figures . To be published in Phys. Rev. Let

Singularites in the Bousseneq equation and in the generalized KdV equation

In this paper, two kinds of the exact singular solutions are obtained by the improved homogeneous balance (HB) method and a nonlinear transformation. The two exact solutions show that special singular wave patterns exists in the classical model of some nonlinear wave problems

Type 2 Diabetes Risk Alleles Are Associated With Reduced Size at Birth

OBJECTIVE: Low birth weight is associated with an increased risk of type 2 diabetes. The mechanisms underlying this association are unknown and may represent intrauterine programming or two phenotypes of one genotype. The fetal insulin hypothesis proposes that common genetic variants that reduce insulin secretion or action may predispose to type 2 diabetes and also reduce birth weight, since insulin is a key fetal growth factor. We tested whether common genetic variants that predispose to type 2 diabetes also reduce birth weight. RESEARCH DESIGN AND METHODS: We genotyped single-nucleotide polymorphisms (SNPs) at five recently identified type 2 diabetes loci (CDKAL1, CDKN2A/B, HHEX-IDE, IGF2BP2, and SLC30A8) in 7,986 mothers and 19,200 offspring from four studies of white Europeans. We tested the association between maternal or fetal genotype at each locus and birth weight of the offspring. RESULTS: We found that type 2 diabetes risk alleles at the CDKAL1 and HHEX-IDE loci were associated with reduced birth weight when inherited by the fetus (21 g [95% CI 11-31], P = 2 x 10(-5), and 14 g [4-23], P = 0.004, lower birth weight per risk allele, respectively). The 4% of offspring carrying four risk alleles at these two loci were 80 g (95% CI 39-120) lighter at birth than the 8% carrying none (P(trend) = 5 x 10(-7)). There were no associations between birth weight and fetal genotypes at the three other loci or maternal genotypes at any locus. CONCLUSIONS: Our results are in keeping with the fetal insulin hypothesis and provide robust evidence that common disease-associated variants can alter size at birth directly through the fetal genotype