Computing trisections of 4-manifolds

Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to algorithmically construct a trisection, which describes a $4$-dimensional manifold as a union of three $4$-dimensional handlebodies. The complexity of the $4$-manifold is captured in a collection of curves on a surface, which guide the gluing of the handelbodies. The algorithm begins with a description of a manifold as a union of pentachora, or $4$-dimensional simplices. It transforms this description into a trisection. This results in the first explicit complexity bounds for the trisection genus of a $4$-manifold in terms of the number of pentachora ($4$-simplices) in a triangulation.Comment: 15 pages, 9 figure

Gravitational waves from the sound of a first order phase transition

We report on the first three-dimensional numerical simulations of first-order phase transitions in the early Universe to include the cosmic fluid as well as the scalar field order parameter. We calculate the gravitational wave (GW) spectrum resulting from the nucleation, expansion, and collision of bubbles of the low-temperature phase, for phase transition strengths and bubble wall velocities covering many cases of interest. We find that the compression waves in the fluid continue to be a source of GWs long after the bubbles have merged, a new effect not taken properly into account in previous modeling of the GW source. For a wide range of models, the main source of the GWs produced by a phase transition is, therefore, the sound the bubbles make

Numerical simulations of acoustically generated gravitational waves at a first order phase transition

We present details of numerical simulations of the gravitational radiation produced by a first order thermal phase transition in the early Universe. We confirm that the dominant source of gravitational waves is sound waves generated by the expanding bubbles of the low-temperature phase. We demonstrate that the sound waves have a power spectrum with a power-law form between the scales set by the average bubble separation (which sets the length scale of the fluid flow Lf) and the bubble wall width. The sound waves generate gravitational waves whose power spectrum also has a power-law form, at a rate proportional to Lf and the square of the fluid kinetic energy density. We identify a dimensionless parameter ˜ ΩGW characterizing the efficiency of this “acoustic” gravitational wave production whose value is 8π ˜ ΩGW≃0.8±0.1 across all our simulations. We compare the acoustic gravitational waves with the standard prediction from the envelope approximation. Not only is the power spectrum steeper (apart from an initial transient) but the gravitational wave energy density is generically larger by the ratio of the Hubble time to the phase transition duration, which can be 2 orders of magnitude or more in a typical first order electroweak phase transition

Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic

Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic

Effects of spinosad on honey bees (Apis mellifera): Findings from over ten years of testing and commercial use

Background: Spinosad is widely used as an insecticide in crop protection against thysanopteran, lepidopteran and dipteran species. As such it is intrinsically toxic to insects and among them to the honey bee (Apis mellifera). An updated risk assessment is presented in the context of the regulatory evaluation of spinosad products and is in accordance with the latest recommendation of regulatory guidance documents. Results: The intrinsic toxicity to the honey bee as observed in laboratory conditions through oral and contact tests on adults does not appear to impair honey bee colonies when exposed to treated attractive crops in tunnel conditions. Reasons for this could include reduced availability of residues of the product on plant surface compared to laboratory conditions, together with a fast dissipation from treated plants and the absence of active degradation products. Conclusions: Spinosad products present a negligible impact on honey bees when used under the current label recommendations and conditions of agricultural use. This conclusion deduced from data available for the regulatory risk assessment has been confirmed by the feedback of surveys on incidents, which address the potential impact of spinosad products under realistic conditions of exposure, including other environmental and chemical factors that are common in cropped areas. Keywords: honey bee, pesticide, risk assessment, risk management, spinosa

Shape of the acoustic gravitational wave power spectrum from a first order phase transition

We present results from large-scale numerical simulations of a first order thermal phase transition in the early Universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted k(-3) behavior, where k is the wave number, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-k decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wave number behavior of the velocity power spectrum is consistent with a causal k(3), except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about 0.05c, produced from bubbles with a mean separation of about 10(-2) of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.Peer reviewe

Associations of Maternal Prenatal Smoking with Early Childhood Physical Aggression, Hyperactivity-Impulsivity, and Their Co-Occurrence

This study investigated associations between maternal prenatal smoking and physical aggression (PA), hyperactivity-impulsivity (HI) and co-occurring PA and HI between ages 17 and 42 months in a population sample of children born in Québec (Canada) in 1997/1998 (N=1745). Trajectory model estimation showed three distinct developmental patterns for PA and four for HI. Multinomial regression analyses showed that prenatal smoking significantly predicted children’s likelihood to follow different PA trajectories beyond the effects of other perinatal factors, parental psychopathology, family functioning and parenting, and socio-economic factors. However, prenatal smoking was not a significant predictor of HI in a model with the same control variables. Further multinomial regression analyses showed that, together with gender, presence of siblings and maternal hostile reactive parenting, prenatal smoking independently predicted co-occurring high PA and high HI compared to low levels of both behaviors, to high PA alone, and to high HI alone. These results show that maternal prenatal smoking predicts multiple behavior regulation problems in early childhood

Unprecedented Fe delivery from the Congo River margin to the South Atlantic Gyre

Rivers are a major supplier of particulate and dissolved material to the ocean, but their role as sources of bio-essential dissolved iron (dFe) is thought to be limited due to rapid, efficient Fe removal during estuarine mixing. Here, we use trace element and radium isotope data to show that the influence of the Congo River margin on surface Fe concentrations is evident over 1000 km from the Congo outflow. Due to an unusual combination of high Fe input into the Congo-shelf-zone and rapid lateral transport, the Congo plume constitutes an exceptionally large offshore dFe flux of 6.8 ± 2.3 × 108 mol year−1. This corresponds to 40 ± 15% of atmospheric dFe input into the South Atlantic Ocean and makes a higher contribution to offshore Fe availability than any other river globally. The Congo River therefore contributes significantly to relieving Fe limitation of phytoplankton growth across much of the South Atlantic