Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Radar scattering by aggregate snowflakes

The radar scattering properties of realistic aggregate snowflakes have been calculated using the Rayleigh-Gans theory. We find that the effect of the snowflake geometry on the scattering may be described in terms of a single universal function, which depends only on the overall shape of the aggregate and not the geometry or size of the pristine ice crystals which compose the flake. This function is well approximated by a simple analytic expression at small sizes; for larger snowflakes we fit a curve to Our numerical data. We then demonstrate how this allows a characteristic snowflake radius to be derived from dual wavelength radar measurements without knowledge of the pristine crystal size or habit, while at the same time showing that this detail is crucial to using such data to estimate ice water content. We also show that the 'effective radius'. characterizing the ratio of particle volume to projected area, cannot be inferred from dual wavelength radar data for aggregates. Finally, we consider the errors involved in approximating snowflakes by 'air-ice spheres', and show that for small enough aggregates the predicted dual wavelength ratio typically agrees to within a few percent, provided some care is taken in choosing the radius of the sphere and the dielectric constant of the air-ice mixture; at larger sizes the radar becomes more sensitive to particle shape, and the errors associated with the sphere model are found to increase accordingly.

Simulating current global river runoff with a global hydrological model: model revisions, validation, and sensitivity analysis

Global hydrological models (GHMs) model the land surface hydrologic dynamics of continental-scale river basins. Here we describe one such GHM, the Macro-scale - Probability-Distributed Moisture model.09 (Mac-PDM.09). The model has undergone a number of revisions since it was last applied in the hydrological literature. This paper serves to provide a detailed description of the latest version of the model. The main revisions include the following: (1) the ability for the model to be run for n repetitions, which provides more robust estimates of extreme hydrological behaviour, (2) the ability of the model to use a gridded field of coefficient of variation (CV) of daily rainfall for the stochastic disaggregation of monthly precipitation to daily precipitation, and (3) the model can now be forced with daily input climate data as well as monthly input climate data. We demonstrate the effects that each of these three revisions has on simulated runoff relative to before the revisions were applied. Importantly, we show that when Mac-PDM.09 is forced with monthly input data, it results in a negative runoff bias relative to when daily forcings are applied, for regions of the globe where the day-to-day variability in relative humidity is high. The runoff bias can be up to - 80% for a small selection of catchments but the absolute magnitude of the bias may be small. As such, we recommend future applications of Mac-PDM.09 that use monthly climate forcings acknowledge the bias as a limitation of the model. The performance of Mac-PDM.09 is evaluated by validating simulated runoff against observed runoff for 50 catchments. We also present a sensitivity analysis that demonstrates that simulated runoff is considerably more sensitive to method of PE calculation than to perturbations in soil moisture and field capacity parameters.

Environmental and human health impacts of growing genetically modified herbicide-tolerant sugar beet: a life-cycle assessment

There is ongoing debate concerning the possible environmental and human health impacts of growing genetically modified (GM) crops. Here, we report the results of a life-cycle assessment (LCA) comparing the environmental and human health impacts of conventional sugar beet growing regimes in the UK and Germany with those that might be expected if GM herbicide-tolerant (to glyphosate) sugar beet is commercialized. The results presented for a number of environmental and human health impact categories suggest that growing the GM herbicide-tolerant crop would be less harmful to the environment and human health than growing the conventional crop, largely due to lower emissions from herbicide manufacture, transport and field operations. Emissions contributing to negative environmental impacts, such as global warming, ozone depletion, ecotoxicity of water and acidification and nutrification of soil and water, were much lower for the herbicide-tolerant crop than for the conventional crop. Emissions contributing to summer smog, toxic particulate matter and carcinogenicity, which have negative human health impacts, were also substantially lower for the herbicide-tolerant crop. The environmental and human health impacts of growing GM crops need to be assessed on a case-by-case basis using a holistic approach. LCA is a valuable technique for helping to undertake such assessments.

Stomatal conductance and not stomatal density determines the long-term reduction in leaf transpiration of poplar in elevated CO2

Using a free-air CO2 enrichment (FACE) experiment, poplar trees (Populus · euramericana clone I214) were exposed to either ambient or elevated [CO2] from planting, for a 5-year period during canopy development, closure, coppice and re-growth. In each year, measurements were taken of stomatal density (SD, number mm2) and stomatal index (SI, the proportion of epidermal cells forming stomata). In year 5, measurements were also taken of leaf stomatal conductance (gs, lmol m2 s1), photosynthetic CO2 fixation (A, mmol m2 s1), instantaneous water-use efficiency (A/E) and the ratio of intercellular to atmospheric CO2 (Ci:Ca). Elevated [CO2] caused reductions in SI in the first year, and in SD in the first 2 years, when the canopy was largely open. In following years, when the canopy had closed, elevated [CO2] had no detectable effects on stomatal numbers or index. In contrast, even after 5 years of exposure to elevated [CO2], gs was reduced, A/E was stimulated, and Ci:Ca was reduced relative to ambient [CO2]. These outcomes from the long-term realistic field conditions of this forest FACE experiment suggest that stomatal numbers (SD and SI) had no role in determining the improved instantaneous leaf-level efficiency of water use under elevated [CO2]. We propose that altered cuticular development during canopy closure may partially explain the changing response of stomata to elevated [CO2], although the mechanism for this remains obscure.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

Heliospheric modulation of galactic cosmic rays during grand solar minima: past and future variations

Galactic cosmic ray flux at Earth is modulated by the heliospheric magnetic field. Heliospheric modulation potential, Φ, during grand solar minima is investigated using an open solar flux (OSF) model with OSF source based on sunspot number, R, and OSF loss on heliospheric current sheet inclination. Changing dominance between source and loss means Φ varies in- (anti-) phase with R during strong (weak) cycles, in agreement with Φ estimates from ice core records of 10Be concentration, which are in-phase during most of the last 300 years, but anti-phase during the Maunder Minimum. Model results suggest “flat” OSF cycles, such as solar cycle 20 result from OSF source and loss terms temporarily balancing throughout the cycle. Thus even if solar activity continues to decline steadily, the long-term drop in OSF through SC21 to SC23 may plateau during SC24, though reemerge in SC25 with the inverted phase relation.

Measuring variation in potato roots in both field and glasshouse: the search for useful yield predictors and a simple screen for root traits

Aims Potatoes have an inadequate rooting system for efficient acquisition of water and minerals and use disproportionate amounts of irrigation and fertilizer. This research determines whether significant variation in rooting characteristics of potato exists, which characters correlate with final yield and whether a simple screen for rooting traits could be developed. Methods Twenty-eight genotypes of Solanum tuberosum groups Tuberosum and Phureja were grown in the field; eight replicate blocks to final harvest, while entire root systems were excavated from four blocks. Root classes were categorised and measured. The same measurements were made on these genotypes in the glasshouse, 2 weeks post emergence. Results In the field, total root length varied from 40 m to 112 m per plant. Final yield was correlated negatively with basal root specific root length and weakly but positively with total root weight. Solanum tuberosum group Phureja genotypes had more numerous roots and proportionally more basal than stolon roots compared with Solanum tuberosum, group Tuberosum genotypes. There were significant correlations between glasshouse and field measurements. Conclusions Our data demonstrate that variability in rooting traits amongst commercially available potato genotypes exists and a robust glasshouse screen has been developed. By measuring potato roots as described in this study, it is now possible to assess rooting traits of large populations of potato genotypes.

Shoot yield drives phosphorus use efficiency in Brassica oleracea and correlates with root architecture traits

The environmental and financial costs of using inorganic phosphate fertilizers to maintain crop yield and quality are high. Breeding crops that acquire and use phosphorus (P) more efficiently could reduce these costs. The variation in shoot P concentration (shoot-P) and various measures of P use efficiency (PUE) were quantified among 355 Brassica oleracea L. accessions, 74 current commercial cultivars, and 90 doubled haploid (DH) mapping lines from a reference genetic mapping population. Accessions were grown at two or more external P concentrations in glasshouse experiments; commercial and DH accessions were also grown in replicated field experiments. Within the substantial species-wide diversity observed for shoot-P and various measures of PUE in B. oleracea, current commercial cultivars have greater PUE than would be expected by chance. This may be a consequence of breeding for increased yield, which is a significant component of most measures of PUE, or early establishment. Root development and architecture correlate with PUE; in particular, lateral root number, length, and growth rate. Significant quantitative trait loci associated with shoot-P and PUE occur on chromosomes C3 and C7. These data provide information to initiate breeding programmes to improve PUE in B. oleracea.

The current status of anticoagulant resistance in rats and mice in the UK

Introduction: Resistance to anticoagulants in Norway rats (Rattus norvegicus) and house mice (Mus domesticus) has been studied in the UK since the early 1960s. In no other country in the world is our understanding of resistance phenomena so extensive and profound. Almost every aspect of resistance in the key rodent target species has been examined in laboratory and field trials and results obtained by independent researchers have been published. It is the principal purpose of this document to present a short synopsis of this information. More recently, however, the development of genetical techniques has provided a definitive means of detection of resistant genotypes among pest rodent populations. Preliminary information from a number of such surveys will also be presented. Resistance in Norway rats: A total of nine different anticoagulant resistance mutations (single nucleotide polymorphisms or SNPs) are found among Norway rats in the UK. In no other country worldwide are present so many different forms of Norway rat resistance. Among these nine SNPs, five are known to confer on rats that carry them a significant degree of resistance to anticoagulant rodenticides. These mutations are: L128Q, Y139S, L120Q, Y139C and Y139F. The latter three mutations confer, to varying degrees, practical resistance to bromadiolone and difenacoum, the two second-generation anticoagulants in predominant use in the UK. It is the recommendation of RRAG that bromadiolone and difenacoum should not be used against rats carrying the L120Q, Y139C and Y139F mutations because this will promote the spread of resistance and jeopardise the long-term efficacy of anticoagulants. Brodifacoum, flocoumafen and difethialone are effective against these three genotypes but cannot presently be used because of the regulatory restriction that they can only be applied against rats that are living and feeding predominantly indoors. Our understanding of the geographical distribution of Norway rat resistance in incomplete but is rapidly increasing. In particular, the mapping of the focus of L120Q Norway rat resistance in central-southern England by DNA sequencing is well advanced. We now know that rats carrying this resistance mutation are present across a large part of the counties of Hampshire, Berkshire and Wiltshire, and the resistance spreads into Avon, Oxfordshire and Surrey. It is also found, perhaps as outlier foci, in south-west Scotland and East Sussex. L120Q is currently the most severe form of anticoagulant resistance found in Norway rats and is prevalent over a considerable part of central-southern England. A second form of advanced Norway rat resistance is conferred by the Y139C mutation. This is noteworthy because it occurs in at least four different foci that are widely geographically dispersed, namely in Dumfries and Galloway, Gloucestershire, Yorkshire and Norfolk. Once again, bromadiolone and difenacoum are not recommended for use against rats carrying this genotype and a concern of RRAG is that continued applications of resisted active substances may result in Y139C becoming more or less ubiquitous across much of the UK. Another type of advanced resistance, the Y139F mutation, is present in Kent and Sussex. This means that Norway rats, carrying some degree of resistance to bromadiolone and difenacoum, are now found from the south coast of Kent, west into the city of Bristol, to Yorkshire in the north-east and to the south-west of Scotland. This difficult situation can only deteriorate further where these three genotypes exist and resisted anticoagulants are predominantly used against them. Resistance in house mice: House mouse is not so well understood but the presence in the UK of two resistant genotypes, L128S and Y139C, is confirmed. House mice are naturally tolerant to anticoagulants and such is the nature of this tolerance, and the presence of genetical resistance, that house mice resistant to the first-generation anticoagulants are considered to be widespread in the UK. Consequently, baits containing warfarin, sodium warfarin, chlorophacinone and coumatetralyl are not approved for use against mice. This regulatory position is endorsed by RRAG. Baits containing brodifacoum, flocoumafen and difethialone are effective against house mice and may be applied in practice because house mouse infestations are predominantly indoors. There are some reports of resistance among mice in some areas to the second-generation anticoagulant bromadiolone, while difenacoum remains largely efficacious. Alternatives to anticoagulants: The use of habitat manipulation, that is the removal of harbourage, denial of the availability of food and the prevention of ingress to structures, is an essential component of sustainable rodent pest management. All are of importance in the management of resistant rodents and have the advantage of not selecting for resistant genotypes. The use of these techniques may be particularly valuable in preventing the build-up of rat infestations. However, none can be used to remove any sizeable extant rat infestation and for practical reasons their use against house mice is problematic. Few alternative chemical interventions are available in the European Union because of the removal from the market of zinc phosphide, calciferol and bromethalin. Our virtual complete reliance on the use of anticoagulants for the chemical control of rodents in the UK, and more widely in the EU, calls for improved schemes for resistance management. Of course, these might involve the use of alternatives to anticoagulant rodenticides. Also important is an increasing knowledge of the distribution of resistance mutations in rats and mice and the use of only fully effective anticoagulants against them.

Improving a global model from the boundary layer: total turbulent energy and the neutral limit Prandtl number

Model intercomparisons have identified important deficits in the representation of the stable boundary layer by turbulence parametrizations used in current weather and climate models. However, detrimental impacts of more realistic schemes on the large-scale flow have hindered progress in this area. Here we implement a total turbulent energy scheme into the climate model ECHAM6. The total turbulent energy scheme considers the effects of Earth’s rotation and static stability on the turbulence length scale. In contrast to the previously used turbulence scheme, the TTE scheme also implicitly represents entrainment flux in a dry convective boundary layer. Reducing the previously exaggerated surface drag in stable boundary layers indeed causes an increase in southern hemispheric zonal winds and large-scale pressure gradients beyond observed values. These biases can be largely removed by increasing the parametrized orographic drag. Reducing the neutral limit turbulent Prandtl number warms and moistens low-latitude boundary layers and acts to reduce longstanding radiation biases in the stratocumulus regions, the Southern Ocean and the equatorial cold tongue that are common to many climate models.

A tillering inhibition gene influences root-shoot carbon partitioning and pattern of water use to improve wheat productivity in rainfed environments

Genetic modification of shoot and root morphology has potential to improve water and nutrient 19 uptake of wheat crops in rainfed environments. Near-isogenic lines (NILs) varying for a tillering 20 inhibition (tin) gene and representing multiple genetic backgrounds were investigated in contrasting 21 controlled environments for shoot and root growth. Leaf area, shoot and root biomass were similar 22 until tillering whereupon reduced tillering in tin-containing NILs produced reductions of up to 60% in 23 total leaf area and biomass, and increases in total root length of up to 120% and root biomass to 24 145%. Together, root-to-shoot ratio increased two-fold with the tin gene. The influence of tin on shoot 25 and root growth was greatest in the cv. Banks genetic background, particularly in the biculm-selected 26 NIL, and was typically strongest in cooler environments. A separate de-tillering study confirmed 27 greater root-to-shoot ratios with regular tiller removal in non-tin containing genotypes. In validating 28 these observations in a rainfed field study, the tin allele had a negligible effect on seedling growth but 29 was associated with significantly (P<0.05) reduced tiller number (-37%), leaf area index (-26%) and 30 spike number (-35%) to reduce plant biomass (-19%) at anthesis. Root biomass, root-to-shoot ratio at 31 early stem elongation and root depth at maturity were increased in tin-containing NILs. Soil water use 32 was slowed in tin-containing NILs resulting in greater water availability, greater stomatal 33 conductance, cooler canopy temperatures and maintenance of green leaf area during grain-filling. 34 Together these effects contributed to increases in harvest index and grain yield. In both the controlled 35 and field environments, the tin gene was commonly associated with increased root length and biomass 36 but the significant influence of genetic background and environment suggests careful assessment of 37 tin-containing progeny in selection for genotypic increases in root growth.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.