Synchronization in large directed networks of coupled phase oscillators

We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed positive/negative coupling strengths. We compare our theory with numerical simulations and find good agreement

How accurately do adult sons and daughters report and perceive parental deaths from coronary disease?

<b>OBJECTIVES</b>: To describe how adult sons and daughters report and perceive parental deaths from heart disease <b>DESIGN</b>: Two generation family study. <b>SETTING</b>: West of Scotland. <b>SUBJECTS</b>: 1040 sons and 1298 daughters aged 30-59 from 1477 families, whose fathers and mothers were aged 45-64 in 1972-76 and have been followed up for mortality over 20 years. <b>OUTCOME</b> : Perception of a "family weakness" attributable to heart disease. RESULTS : 26% of sons and daughters had a parent who had died of coronary heart disease (CHD). The proportion was higher in older offspring (+18% per 10 year age difference) and in manual compared with non-manual groups (+37%). Eighty nine per cent of parental deaths from CHD were correctly reported by offspring. Only 23% of sons and 34% of daughters with at least one parent who had died of CHD considered that they had a family weakness attributable to heart disease. Perceptions of a family weakness were higher when one or both parents had died of CHD, when parental deaths occurred at a younger age, in daughters compared with sons and in offspring in non-manual compared with manual occupations. <b>CONCLUSIONS</b>: Only a minority of sons and daughters with experience of a parent having died from CHD perceive this in terms of a family weakness attributable to heart disease. Although men in manual occupations are most likely to develop CHD, they are least likely to interpret a parental death from CHD in terms of a family weakness. Health professionals giving advice to patients on their familial risks need to be aware of the difference between clinical definitions and lay perceptions of a family history of heart disease

Alternative criterion for two-dimensional wrapping percolation

Based on the differences between a spanning cluster and a wrapping cluster, an alternative criterion for testing wrapping percolation is provided for two-dimensional lattices. By following the Newman-Ziff method, the finite size scaling of estimates for percolation thresholds are given. The results are consistent with those from Machta's method.Comment: 4 pages, 2 figure

How robust is the evidence of an emerging or increasing female excess in physical morbidity between childhood and adolescence? Results of a systematic literature review and meta-analyses

For asthma and psychological morbidity, it is well established that higher prevalence among males in childhood is replaced by higher prevalence among females by adolescence. This review investigates whether there is evidence for a similar emerging female ‘excess’ in relation to a broad range of physical morbidity measures. Establishing whether this pattern is generalised or health outcome-specific will further understandings of the aetiology of gender differences in health. Databases (Medline; Embase; CINAHL; PsycINFO; ERIC) were searched for English language studies (published 1992–2010) presenting physical morbidity prevalence data for males and females, for at least two age-bands within the age-range 4–17 years. A three-stage screening process (initial sifting; detailed inspection; extraction of full papers), was followed by study quality appraisals. Of 11 245 identified studies, 41 met the inclusion criteria. Most (n = 31) presented self-report survey data (five longitudinal, 26 cross-sectional); 10 presented routinely collected data (GP/hospital statistics). Extracted data, supplemented by additional data obtained from authors of the included studies, were used to calculate odds ratios of a female excess, or female:male incident rate ratios as appropriate. To test whether these changed with age, the values were logged and regressed on age in random effects meta-regressions. These showed strongest evidence of an emerging/increasing female excess for self-reported measures of headache, abdominal pain, tiredness, migraine and self-assessed health. Type 1 diabetes and epilepsy, based on routinely collected data, did not show a significant emerging/increasing female excess. For most physical morbidity measures reviewed, the evidence broadly points towards an emerging/increasing female excess during the transition to adolescence, although results varied by morbidity measure and study design, and suggest that this may occur at a younger age than previously thought

Solid metabolic waste transport and stowage investigation

The basic Waste Collection System (WCS) design under consideration utilized air flow to separate the stool from the WCS user and to transport the fecal material to a slinger device for subsequent deposition on a storage bowel. The major parameters governing stool separation and transport were found to be the area of the air inlet orifices, the configuration of the air inlet orifice and the transport air flow. Separation force and transport velocity of the stool were studied. The developed inlet orifice configuration was found to be an effective design for providing fecal separation and transport. Simulated urine tests and female user tests in zero gravity established air flow rates between 0.08 and 0.25 cu sm/min (3 and 9 scfm) as satisfactory for entrapment, containment and transport of urine using an urinal. The investigation of air drying of fecal material as a substitute for vacuum drying in a WCS breadboard system showed that using baseline conditions anticipated for the shuttle cabin ambient atmosphere, flow rates of 0.14 cu sm/min (5 cfm) were adequate for drying and maintaining biological stability of the fecal material

Parametric Feedback Resonance in Chaotic Systems

If one changes the control parameter of a chaotic system proportionally to the distance between an arbitrary point on the strange attractor and the actual trajectory, the lifetime τ of the most stable unstable periodic orbit in the vicinity of this point starts to diverge with a power law. The volume in parameter space where τ becomes infinite is finite and from its nonfractal boundaries one can determine directly the local Liapunov exponents. The experimental applicability of the method is demonstrated for two coupled diode resonators

Multilayered folding with voids

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers results in geometrically-induced curvature singularities. When voids are penalized by external pressure, the system is forced to trade off these competing effects, leading to sometimes striking periodic patterns. In this paper we construct a simple model of geometrically nonlinear multi-layered structures under axial loading and pressure confinement, with non-interpenetration conditions separating the layers. Energy minimizers are characterized as solutions of a set of fourth-order nonlinear differential equations with contact-force Lagrange multipliers, or equivalently of a fourth-order free-boundary problem. We numerically investigate the solutions of this free boundary problem, and compare them with the periodic solutions observed experimentally

Positive solutions of Schr\"odinger equations and fine regularity of boundary points

Given a Lipschitz domain $\Omega$ in ${\mathbb R} ^N$ and a nonnegative potential $V$ in $\Omega$ such that $V(x)\, d(x,\partial \Omega)^2$ is bounded in $\Omega$ we study the fine regularity of boundary points with respect to the Schr\"odinger operator $L_V:= \Delta -V$ in $\Omega$. Using potential theoretic methods, several conditions equivalent to the fine regularity of $z \in \partial \Omega$ are established. The main result is a simple (explicit if $\Omega$ is smooth) necessary and sufficient condition involving the size of $V$ for $z$ to be finely regular. An essential intermediate result consists in a majorization of $\int_A | {\frac {u} {d(.,\partial \Omega)}} | ^2\, dx$ for $u$ positive harmonic in $\Omega$ and $A \subset \Omega$. Conditions for almost everywhere regularity in a subset $A$ of $\partial \Omega$ are also given as well as an extension of the main results to a notion of fine ${\mathcal L}_1 | {\mathcal L}_0$-regularity, if ${\mathcal L}_j={\mathcal L}-V_j$, $V_0,\, V_1$ being two potentials, with $V_0 \leq V_1$ and ${\mathcal L}$ a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1 is correcte

The emergence of coherence in complex networks of heterogeneous dynamical systems

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength, all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.Comment: 4 pages, 1 figure. Published versio