Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

Complete two-loop effective potential approximation to the lightest Higgs scalar boson mass in supersymmetry

I present a method for accurately calculating the pole mass of the lightest Higgs scalar boson in supersymmetric extensions of the Standard Model, using a mass-independent renormalization scheme. The Higgs scalar self-energies are approximated by supplementing the exact one-loop results with the second derivatives of the complete two-loop effective potential in Landau gauge. I discuss the dependence of this approximation on the choice of renormalization scale, and note the existence of particularly poor choices which fortunately can be easily identified and avoided. For typical input parameters, the variation in the calculated Higgs mass over a wide range of renormalization scales is found to be of order a few hundred MeV or less, and is significantly improved over previous approximations.Comment: 5 pages, 1 figure. References added, sample test model parameters listed, minor wording change

A Chimeric Nucleobase - Phenylazo Derivative as an Intrinsic Nucleobase Quencher

Molecular beacons are important bioanalytical probes which are most often constructed from a single-stranded oligonucleotide which has been labeled at opposite termini with a fluorophore and a quencher. When the fluorophore and quencher are in close proximity, no fluorescence is observed due to FRET (Fluorescence Resonance Energy Transfer). DABCYL (4-dimethylaminoazobenzene- 4\u27-carboxylic acid) has been used as a quencher in the molecular beacon to absorbs excitation energy from a fluorophore and to dissipate the energy as heat. However, DABCYL is unable to form a base-pair and is conventionally placed as an overhanging residue. This produces a derivative wherein the chromophore has substantial mobility and limits the types of other conjugates that can be prepared. In order to overcome these limitations, we have embarked on the synthesis of deoxyribonucleoside and peptide nucleic acid (PNA) analogue possessing DMPAU (5-[(4-dimethylaminophenyl) diazenyl]uracil) as the nucleobase. DMPAU has DABCYL-like properties due to the installation of an azo moiety at the 5-position of the uracil base. This base is designed to have the ability to form a complementary base pair with adenosine by canonical hydrogen bonding and also to quench the fluorescence emission in a molecular beacon construct. Both DMPAUridine and DMPAU PNA analogue are determined to have same UV-Vis absorbance ranges as DABCYL and reasonable quenching effect to the fluorophore

Stressed, but not defenceless: no obvious influence of irradiation levels on antifeeding and antifouling defences of tropical macroalgae

The production of defence metabolites is assumed to be costly in metabolic terms. If this holds true, low-light stress should reduce the ability of seaweeds to defend themselves chemically against herbivory and fouling. We investigated the effect of energy limitation on the defensive status of seaweeds by assessing their attractiveness to mesograzers and their activity against a bivalve macrofouler in comparison with non-stressed conspecifics. The macroalgae Codium decorticatum (Woodw.) M. Howe, Osmundaria obtusiloba (C. Agardh) R. E. Norris, Pterocladiella capillacea (S. G. Gmel.) Santel. and Hommer., Sargassum vulgare C. Agardh and Stypopodium zonale (Lamour.) Papenf. collected at the southeastern Brazilian coast were exposed to six levels of irradiation (between 1 and 180 μmol photons m−2 s−1) for 10–14 days. After this period, algae from all treatment levels were: (a) processed as artificial food and offered to an amphipod community dominated by Elasmopus brasiliensis Dana and (b) extracted to test for differences in settlement rates of the fouling mussel Perna perna L. on filter paper loaded with the crude extracts. Generally, photosynthesis rates and growth were reduced under low light conditions. Attractiveness to herbivores and macrofoulers, however, was insensitive to energy limitation. We discuss possible explanations for the observed absence of a relationship between light availability and algal defence including the change in nutritional value of the algal tissue, the allocation of resources towards defence instead of growth and the absence of costs for defence

Uplifted supersymmetric Higgs region

We show that the parameter space of the Minimal Supersymmetric Standard Model includes a region where the down-type fermion masses are generated by the loop-induced couplings to the up-type Higgs doublet. In this region the down-type Higgs doublet does not acquire a vacuum expectation value at tree level, and has sizable couplings in the superpotential to the tau leptons and bottom quarks. Besides a light standard-like Higgs boson, the Higgs spectrum includes the nearly degenerate states of a heavy spin-0 doublet which can be produced through their couplings to the $b$ quark and decay predominantly into \tau^+\tau^- or \tau\nu.Comment: 14 pages; Signs in Eqns. (3.1) and (4.2) corrected, appendix include

Collider signals from slow decays in supersymmetric models with an intermediate-scale solution to the mu problem

The problem of the origin of the mu parameter in the Minimal Supersymmetric Standard Model can be solved by introducing singlet supermultiplets with non-renormalizable couplings to the ordinary Higgs supermultiplets. The Peccei-Quinn symmetry is broken at a scale which is the geometric mean between the weak scale and the Planck scale, yielding a mu term of the right order of magnitude and an invisible axion. These models also predict one or more singlet fermions which have electroweak-scale masses and suppressed couplings to MSSM states. I consider the case that such a singlet fermion, containing the axino as an admixture, is the lightest supersymmetric particle. I work out the relevant couplings in several of the simplest models of this type, and compute the partial decay widths of the next-to-lightest supersymmetric particle involving leptons or jets. Although these decays will have an average proper decay length which is most likely much larger than a typical collider detector, they can occasionally occur within the detector, providing a striking signal. With a large sample of supersymmetric events, there will be an opportunity to observe these decays, and so gain direct information about physics at very high energy scales.Comment: 24 pages, LaTeX, 4 figure

The oxygen isotopic composition of phosphate in river water and its potential sources in the Upper River Taw catchment, UK

The need to reduce both point and diffuse phosphorus pollution to aquatic ecosystems is widely recognised and in order to achieve this, identification of the different pollutant sources is essential. Recently, a stable isotope approach using oxygen isotopes within phosphate (δ18OPO4) has been used in phosphorus source tracing studies. This approach was applied in a one-off survey in September 2013 to the River Taw catchment in south-west England where elevated levels of phosphate have been reported. River water δ18OPO4 along the main channel varied little, ranging from + 17.1 to + 18.8‰. This was no > 0.3‰ different to that of the isotopic equilibrium with water (Eδ18OPO4). The δ18OPO4 in the tributaries was more variable (+ 17.1 to + 18.8‰), but only deviated from Eδ18OPO4 by between 0.4 and 0.9‰. Several potential phosphate sources within the catchment were sampled and most had a narrow range of δ18OPO4 values similar to that of river Eδ18OPO4. Discharge from two waste water treatment plants had different and distinct δ18OPO4 from one another ranging between + 16.4 and + 19.6‰ and similar values to that of a dairy factory final effluent (+ 16.5 to + 17.8‰), mains tap water (+ 17.8 to + 18.4‰), and that of the phosphate extracted from river channel bed sediment (+ 16.7 to + 17.6‰). Inorganic fertilizers had a wide range of values (+ 13.3 to + 25.9‰) while stored animal wastes were consistently lower (+ 12.0 to + 15.0‰) than most other sources and Eδ18OPO4. The distinct signals from the waste water treatment plants were lost within the river over a short distance suggesting that rapid microbial cycling of phosphate was occurring, because microbial cycling shifts the isotopic signal towards Eδ18OPO4. This study has added to the global inventory of phosphate source δ18OPO4 values, but also demonstrated the limitations of this approach to identifying phosphate sources, especially at times when microbial cycling is high

Differential requirements for the chemokine receptor CCR7 in T cell activation during Listeria monocytogenes infection

Effective priming of T cell responses depends on cognate interactions between naive T cells and professional antigen-presenting cells (APCs). This contact is the result of highly coordinated migration processes, in which the chemokine receptor CCR7 and its ligands, CCL19 and CCL21, play a central role. We used the murine Listeria monocytogenes infection model to characterize the role of the CCR7/CCR7 ligand system in the generation of T cell responses during bacterial infection. We demonstrate that efficient priming of naive major histocompatibility complex (MHC) class Ia–restricted CD8+ T cells requires CCR7. In contrast, MHC class Ib–restricted CD8+ T cells and MHC class II–restricted CD4+ T cells seem to be less dependent on CCR7; memory T cell responses are independent of CCR7. Infection experiments with bone marrow chimeras or mice reconstituted with purified T cell populations indicate that CCR7 has to be expressed on CD8+ T cells and professional APCs to promote efficient MHC class Ia–restricted T cell priming. Thus, different T cell subtypes and maturation stages have discrete requirements for CCR7

Cigarette Smoking, Birthweight and Osteoporosis in Adulthood: Results from the Hertfordshire Cohort Study

We looked for interaction between early environment and adult lifestyle in determination of bone mineral content (BMC) and bone mineral density (BMD) among 498 men and 468 women for whom birth records were available. Participants completed a health questionnaire, and bone densitometry (DXA) of the lumbar spine and femoral neck performed