Phase resetting effects for robust cycles between chaotic sets

In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible. This paper introduces and discusses an instructive example of an ODE where one can observe and analyse robust cycling behaviour. By design, we can show that there is a robust cycle between invariant sets that may be chaotic saddles (whose internal dynamics correspond to a Rossler system), and/or saddle equilibria. For this model, we distinguish between cycling that include phase resetting connections (where there is only one connecting trajectory) and more general non-phase resetting cases where there may be an infinite number (even a continuum) of connections. In the non-phase resetting case there is a question of connection selection: which connections are observed for typical attracted trajectories? We discuss the instability of this cycling to resonances of Lyapunov exponents and relate this to a conjecture that phase resetting cycles typically lead to stable periodic orbits at instability whereas more general cases may give rise to `stuck on' cycling. Finally, we discuss how the presence of positive Lyapunov exponents of the chaotic saddle mean that we need to be very careful in interpreting numerical simulations where the return times become long; this can critically influence the simulation of phase-resetting and connection selection

The prevalence of, and factors associated with, paying for sex among men resident in Britain: findings from the third national survey of sexual attitudes and lifestyles (Natsal-3)

Objectives Men who pay for sex (MPS) are considered a bridging population for sexually transmitted infections (STI). However, the extent, characteristics and role of MPS in transmission is poorly understood. We investigate these questions using data from Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3). Methods We performed complex survey analyses of data from 6293 men aged 16–74 years resident in Britain who completed Natsal-3, a probability sample survey undertaken during 2010–2012, using computer-assisted personal interviewing and computer-assisted self-interview. Results 11.0% (95% CI10.1% to 11.9%) of all men reported ever paying for sex. Among MPS, 18.4% (95% CI 18.2% to 18.7%) of their lifetime sexual partners were paid. 3.6% (95% CI 3.1% to 4.2%) of men had paid for sex in the past 5 years. Partners of MPS constitute 14.7% of all reported partners and MPS report 15.6% of all reported STI diagnoses in the past 5 years. Paying for sex in the past 5 years was strongly associated with reporting larger numbers of sexual partners (adjusted OR, AOR for 5+ partners, past 5 years, 31.50, 95% CI 18.69 to 53.09). After adjusting for partner numbers, paying for sex remained strongly associated with reporting new foreign partners outside the UK (AOR 7.96; 95% CI 4.97 to 12.73) and STI diagnosis/es (AOR 2.34; 95% CI 1.44 to 3.81), all in the past 5 years. Among men ever paying for sex, 62.6% (95% CI 58.3% to 66.8%) reported paying for sex outside the UK, most often in Europe and Asia. Conclusions MPS in Britain remain at greater risk of STI acquisition and onward transmission than men who do not. They report high numbers of partners, but the minority are paid partners. They are an important core group in STI transmission

Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection

We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this ‘cycling chaos’ manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets interspersed with short transitions between neighbourhoods of these sets. Such behaviour is robust to perturbations that preserve the symmetry of the system; we examine bifurcations of this state. We discuss a scenario where an attracting cycling chaotic state is created at a blowout bifurcation of a chaotic attractor in an invariant subspace. This differs from the standard scenario for the blowout bifurcation in that in our case, the blowout is neither subcritical nor supercritical. The robust cycling chaotic state can be followed to a point where it loses stability at a resonance bifurcation and creates a series of large period attractors. The model we consider is a ninth-order truncated ordinary differential equation (ODE) model of three-dimensional incompressible convection in a plane layer of conducting fluid subjected to a vertical magnetic field and a vertical temperature gradient. Symmetries of the model lead to the existence of invariant subspaces for the dynamics; in particular there are invariant subspaces that correspond to regimes of two-dimensional flows, with variation in the vertical but only one of the two horizontal directions. Stable two-dimensional chaotic flow can go unstable to three-dimensional flow via the cross-roll instability. We show how the bifurcations mentioned above can be located by examination of various transverse Liapunov exponents. We also consider a reduction of the ODE to a map and demonstrate that the same behaviour can be found in the corresponding map. This allows us to describe and predict a number of observed transitions in these models. The dynamics we describe is new but nonetheless robust, and so should occur in other applications

On asimuthal anisotropy in fragmentation of classical relativistic string

A fragmenting relativistic string is widely used for modelling particle production via quark-gluon strings formed in hadron inelastic interactions of high energies. In this note we focus on motion and fragmentation of relativistic string with non-zero transverse separation of its ends and study this scenario as a possible mechanism bringing anisotropy into the asimuthal angle disribution of produced particles in inelastic interactions of hadrons.Comment: 12 pages, 6 figure

An evolutionarily-unique heterodimeric voltage-gated cation channel found in aphids

We describe the identification in aphids of a unique heterodimeric voltage-gated sodium channel which has an atypical ion selectivity filter and, unusually for insect channels, is highly insensitive to tetrodotoxin. We demonstrate that this channel has most likely arisen by adaptation (gene fission or duplication) of an invertebrate ancestral mono(hetero)meric channel. This is the only identifiable voltage-gated sodium channel homologue in the aphid genome(s), and the channel’s novel selectivity filter motif (DENS instead of the usual DEKA found in other eukaryotes) may result in a loss of sodium selectivity, as indicated experimentally in mutagenised Drosophila channels

Prevalence of infertility and help seeking among 15 000 women and men

STUDY QUESTION: What is the prevalence of infertility and of help seeking among women and men in Britain? SUMMARY ANSWER: One in eight women and one in ten men aged 16-74 years had experienced infertility, defined by unsuccessfully attempting pregnancy for a year or longer, and little more than half of these people sought medical or professional help. WHAT IS KNOWN ALREADY: Estimates of infertility and help seeking in Britain vary widely and are not easily comparable because of different definitions and study populations. STUDY DESIGN, SIZE, DURATION: A cross-sectional population survey was conducted between 2010 and 2012 with a sample of 15 162 women and men aged 16-74 years. PARTICIPANTS/MATERIALS, SETTING, METHODS: Participants completed the Natsal-3 questionnaire, using computer-assisted personal interviewing (CAPI) and computer-assisted self-interview (CASI). MAIN RESULTS AND THE ROLE OF CHANCE: The reported prevalence of infertility was 12.5% (CI 95% 11.7-13.3) among women and 10.1% (CI 95% 9.2-11.1) among men. Increased prevalence was associated with later cohabitation with a partner, higher socio-economic status and, for those who had a child, becoming parents at older ages. The reported prevalence of help seeking was 57.3% (CI 95% 53.6-61.0) among women and 53.2% (CI 95% 48.1-58.1) among men. Help seekers were more likely to be better educated and in higher status occupations and, among those who had a child, to have become parents later in life. LIMITATIONS, REASONS FOR CAUTION: These data are cross-sectional so it is not possible to establish temporality or infer causality. Self-reported data may be subject to recall bias. WIDER IMPLICATIONS OF THE FINDINGS: The study provides estimates of infertility and help seeking in Britain and the results indicate that the prevalence of infertility is higher among those delaying parenthood. Those with higher educational qualifications and occupational status are more likely to consult with medical professionals for fertility problems than others and these inequalities in help seeking should be considered by clinical practice and public health. STUDY FUNDING/COMPETING INTERESTS: Funding was provided by grants from the Medical Research Council and the Wellcome Trust, with support from the Economic and Social Research Council and the Department of Health. AMJ is a Governor of the Wellcome Trust. Other authors have no competing interests

Mirror Symmetry and Other Miracles in Superstring Theory

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam's 'no miracles argument' that, I argue, many string theorists in fact espouse. String theory leads to many surprising, useful, and well-confirmed mathematical 'predictions' - here I focus on mirror symmetry. These predictions are made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for framework that generated them. I attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a high (philosophical) price.Comment: For submission to a Foundations of Physics special issue on "Forty Years Of String Theory: Reflecting On the Foundations" (edited by G. `t Hooft, E. Verlinde, D. Dieks and S. de Haro)

Adjustment to colostomy: stoma acceptance, stoma care self-efficacy and interpersonal relationships

‘The definitive version is available at www.blackwell-synergy.com.’ Copyright Blackwell Publishing. DOI: 10.1111/j.1365-2648.2007.04446.xThis paper is a report of a study to examine adjustment and its relationship with stoma acceptance and social interaction, and the link between stoma care self-efficacy and adjustment in the presence of acceptance and social interactions.Peer reviewe

Transverse Phase Locking for Vortex Motion in Square and Triangular Pinning Arrays

We analyze transverse phase locking for vortex motion in a superconductor with a longitudinal DC drive and a transverse AC drive. For both square and triangular arrays we observe a variety of fractional phase locking steps in the velocity versus DC drive which correspond to stable vortex orbits. The locking steps are more pronounced for the triangular arrays which is due to the fact that the vortex motion has a periodic transverse velocity component even for zero transverse AC drive. All the steps increase monotonically in width with AC amplitude. We confirm that the width of some fractional steps in the square arrays scales as the square of the AC driving amplitude. In addition we demonstrate scaling in the velocity versus applied DC driving curves at depinning and on the main step, similar to that seen for phase locking in charge-density wave systems. The phase locking steps are most prominent for commensurate vortex fillings where the interstitial vortices form symmetrical ground states. For increasing temperature, the fractional steps are washed out very quickly, while the main step gains a linear component and disappears at melting. For triangular pinning arrays we again observe transverse phase locking, with the main and several of the fractional step widths scaling linearly with AC amplitude.Comment: 10 pages, 14 postscript figure

Nucleation of a sodium droplet on C60

We investigate theoretically the progressive coating of C60 by several sodium atoms. Density functional calculations using a nonlocal functional are performed for NaC60 and Na2C60 in various configurations. These data are used to construct an empirical atomistic model in order to treat larger sizes in a statistical and dynamical context. Fluctuating charges are incorporated to account for charge transfer between sodium and carbon atoms. By performing systematic global optimization in the size range 1<=n<=30, we find that Na_nC60 is homogeneously coated at small sizes, and that a growing droplet is formed above n=>8. The separate effects of single ionization and thermalization are also considered, as well as the changes due to a strong external electric field. The present results are discussed in the light of various experimental data.Comment: 17 pages, 10 figure