Cantor Spectrum for Schr\"odinger Operators with Potentials arising from Generalized Skew-shifts

We consider continuous $SL(2,\mathbb{R})$-cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove that any cocycle which is not uniformly hyperbolic can be approximated by one which is conjugate to an $SO(2,\mathbb{R})$-cocycle. Using this, we show that if a cocycle's homotopy class does not display a certain obstruction to uniform hyperbolicity, then it can be $C^0$-perturbed to become uniformly hyperbolic. For cocycles arising from Schr\"odinger operators, the obstruction vanishes and we conclude that uniform hyperbolicity is dense, which implies that for a generic continuous potential, the spectrum of the corresponding Schr\"odinger operator is a Cantor set.Comment: Final version. To appear in Duke Mathematical Journa

Non-autonomous 2-periodic Gumovski-Mira difference equations

We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.Comment: 20 pages, 11 figure

Topology and Homoclinic Trajectories of Discrete Dynamical Systems

We show that nontrivial homoclinic trajectories of a family of discrete, nonautonomous, asymptotically hyperbolic systems parametrized by a circle bifurcate from a stationary solution if the asymptotic stable bundles Es(+{\infty}) and Es(-{\infty}) of the linearization at the stationary branch are twisted in different ways.Comment: 19 pages, canceled the appendix (Properties of the index bundle) in order to avoid any text overlap with arXiv:1005.207

Light drinking in pregnancy, a risk for behavioural problems and cognitive deficits at 3 years of age?

Background The objective of this study was to determine whether there was an association between mothers’ light drinking during pregnancy and risk of behavioural problems, and cognitive deficits in their children at age 3 years. Methods Data from the first two sweeps of the nationally representative prospective UK Millennium Cohort study were used. Drinking patterns during pregnancy and behavioural and cognitive outcomes were assessed during interviews and home visits. Behavioural problems were indicated by scores falling above defined clinically 15 relevant cut-offs on the parent-report version of the Strengths and Difficulties Questionnaire (SDQ). Cognitive ability was assessed using the naming vocabulary subscale from the British Ability Scale (BAS) and the Bracken School Readiness Assessment (BSRA). Results There was a J-shaped relationship between mothers drinking 20 during pregnancy and the likelihood of high scores (above the cut-off) on the total difficulties scale of the SDQ and the conduct problems, hyperactivity and emotional symptom SDQ subscales. Children born to light drinkers were less likely to score above the cut-offs compared with children of abstinent mothers. Children 25 born to heavy drinkers were more likely to score above the cut-offs compared with children of abstinent mothers. Boys born to mothers who had up to 1–2 drinks per week or per occasion were less likely to have conduct problems (OR 0.59, 95% CI 0.45–0.77) and hyperactivity (OR 0.71, 95% CI 0.54–0.94). These effects remained 30 in fully adjusted models. Girls were less likely to have emotional symptoms (OR 0.72, 95% CI 0.51–1.01) and peer problems (OR 0.68, 95% CI 0.52–0.92) compared with those born to abstainers. These effects were attenuated in fully adjusted models. Boys born to light drinkers had higher cognitive ability test scores [standard 35 deviations, (95% CI)] BAS 0.15 (0.08–0.23) BSRA 0.24 (0.16–0.32) compared with boys born to abstainers. The difference for BAS was attenuated on adjustment for socio-economic factors, whilst the difference for BSRA remained statistically significant. Conclusions Children born to mothers who drank up to 1–2 drinks per week or per occasion during pregnancy were not at increased risk of clinically relevant behavioural difficulties or cognitive deficits compared with children of abstinent mothers. Heavy drinking 5 during pregnancy appears to be associated with behavioural problems and cognitive deficits in offspring at age 3 years whereas light drinking does not

Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

Measurement of the Electric Form Factor of the Neutron at Q^2=0.5 and 1.0 (GeV/c)^2

The electric form factor of the neutron was determined from measurements of the \vec{d}(\vec{e},e' n)p reaction for quasielastic kinematics. Polarized electrons were scattered off a polarized deuterated ammonia target in which the deuteron polarization was perpendicular to the momentum transfer. The scattered electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle detector. We find G_E^n = 0.0526 +/- 0.0033 (stat) +/- 0.0026 (sys) and 0.0454 +/- 0.0054 +/- 0.0037 at Q^2 = 0.5 and 1.0 (GeV/c)^2, respectively.Comment: 5 pages, 2 figures, as publishe

Oscillatory behaviour on a non-autonomous hybrid SIR-Model

We study the impact of some abstract agent intervention on the disease spread modelled by a SIR-model with linear growth infectivity. The intervention is meant to decrease the infectivity, which are activated by a threshold on the number of infected individuals. The coupled model is represented as a nonlinear non-autonomous hybrid system. Stability and reduction results are obtained using the notions of non-autonomous attractors, Bohl exponents, and dichotomy spectrum. Numerical examples are given where the number of infected individuals can oscillate around a equilibrium point or be a succession of bump functions, which are validated with a tool based on the notion of delta-complete decision procedures for solving satisfiability modulo theories problems over the real numbers and bounded delta-reachability. These findings seem to show that hybrid SIR-models are more flexible than standard models and generate a vast set of solution profiles. It also raises questions regarding the possibility of the agent intervention been somehow responsible for the shape and intensity of future outbreaks.publishe

Gender differences in the associations between age trends of social media interaction and well-being among 10-15 year olds in the UK

Background Adolescents are among the highest consumers of social media while research has shown that their well-being decreases with age. The temporal relationship between social media interaction and well-being is not well established. The aim of this study was to examine whether the changes in social media interaction and two well-being measures are related across ages using parallel growth models. Methods Data come from five waves of the youth questionnaire, 10-15 years, of the Understanding Society, the UK Household Longitudinal Study (pooled n =9859). Social media interaction was assessed through daily frequency of chatting on social websites. Well-being was measured by happiness with six domains of life and the Strengths and Difficulties Questionnaire. Results Findings suggest gender differences in the relationship between interacting on social media and well-being. There were significant correlations between interacting on social media and well-being intercepts and between social media interaction and well-being slopes among females. Additionally higher social media interaction at age 10 was associated with declines in well-being thereafter for females, but not for males. Results were similar for both measures of well-being. Conclusions High levels of social media interaction in early adolescence have implications for well-being in later adolescence, particularly for females. The lack of an association among males suggests other factors might be associated with their reduction in well-being with age. These findings contribute to the debate on causality and may inform future policy and interventions

Work-family life courses and BMI trajectories in three British birth cohorts.

BACKGROUND/OBJECTIVES: Combining work and family responsibilities has previously been associated with improved health in mid-life, yet little is known about how these associations change over time (both biographical and historical) and whether this extends to body mass index (BMI) trajectories for British men and women. The purpose of this study was to investigate relationships between work-family life courses and BMI trajectories across adulthood (16-42 years) for men and women in three British birth cohorts. SUBJECTS/METHODS: Multiply imputed data from three nationally representative British birth cohorts were used-the MRC National Survey of Health and Development (NSHD; 1946 birth cohort, n=3012), the National Child Development Study (NCDS; 1958 birth cohort, n=9614) and the British Cohort Study (BCS; 1970 birth cohort, n=8140). A typology of work-family life course types was developed using multi-channel sequence analysis, linking annual information on work, partnerships and parenthood from 16 to 42 years. Work-family life courses were related to BMI trajectories using multi-level growth models. Analyses adjusted for indicators of prior health, birthweight, child BMI, educational attainment and socioeconomic position across the life course, and were stratified by gender and cohort. RESULTS: Work-family life courses characterised by earlier transitions to parenthood and weaker long-term links to employment were associated with greater increases in BMI across adulthood. Some of these differences, particularly for work-family groups, which are becoming increasingly non-normative, became more pronounced across cohorts (for example, increases in BMI between 16 and 42 years in long-term homemaking women: NSHD: 4.35 kg m-2, 95% confidence interval (CI): 3.44, 5.26; NCDS: 5.53 kg m-2, 95% CI: 5.18, 5.88; BCS: 6.69 kg m-2, 95% CI: 6.36, 7.02). CONCLUSIONS: Becoming a parent earlier and weaker long-term ties to employment are associated with greater increases in BMI across adulthood in British men and women.Rebecca Lacey, Anne McMunn, Amanda Sacker and Meena Kumari received funding from the European Research Council (grant number: ERC-2011-StG_20101124, PI: Anne McMunn). Steven Bell also received funding from the European Research Council (grant number: ERCStG-2012-309337_Alcohol-Lifecourse, PI: Annie Britton) and UK Medical Research Council/Alcohol Research UK (MR/M006638/1). Amanda Sacker, Anne McMunn and Meena Kumari additionally received support from the Economic and Social Research Council’s International Centre for Life Course Studies in Society and Health (grant number: ES/J019119/1). DK is supported by the UK Medical Research Council (MC_UU_12019/1). The MRC National Survey of Health and Development is funded by the UK Medical Research Council. Peggy McDonough and Diana Worts were supported by the Canadian Institutes of Health Research grant MOP 119526 and the Social Sciences and Humanities Research Council grant 43512-1267

Repeated exposure to socioeconomic disadvantage and health selection as life course pathways to mid-life depressive and anxiety disorders

The biomedical examination was funded by Medical Research Council [G0000934], awarded under the Health of the Public initiative. Charlotte Clark is supported by an Engineering and Physical Sciences Research Fellowship. Bryan Rodgers is supported by Research Fellowships Nos 148948 and 366758 and by Program Grant No. 179805 from the National Health and Medical Research Council of Australia. Research at the Institute of Child Health and Great Ormond Street Hospital for Children NHS Trust benefits from R&D funding received from the NHS Executive