On the multiplicity of the hyperelliptic integrals

Let $I(t)= \oint_{\delta(t)} \omega$ be an Abelian integral, where $H=y^2-x^{n+1}+P(x)$ is a hyperelliptic polynomial of Morse type, $\delta(t)$ a horizontal family of cycles in the curves $\{H=t\}$, and $\omega$ a polynomial 1-form in the variables $x$ and $y$. We provide an upper bound on the multiplicity of $I(t)$, away from the critical values of $H$. Namely: $ord\ I(t) \leq n-1+\frac{n(n-1)}{2}$if$\deg \omega <\deg H=n+1$. The reasoning goes as follows: we consider the analytic curve parameterized by the integrals along$\delta(t)$of the$n$``Petrov'' forms of$H$(polynomial 1-forms that freely generate the module of relative cohomology of$H$), and interpret the multiplicity of$I(t)$as the order of contact of$\gamma(t)$and a linear hyperplane of$\textbf C^ n$. Using the Picard-Fuchs system satisfied by$\gamma(t)$, we establish an algebraic identity involving the wronskian determinant of the integrals of the original form$\omega$along a basis of the homology of the generic fiber of$H$. The latter wronskian is analyzed through this identity, which yields the estimate on the multiplicity of$I(t)$. Still, in some cases, related to the geometry at infinity of the curves$\{H=t\} \subseteq \textbf C^2$, the wronskian occurs to be zero identically. In this alternative we show how to adapt the argument to a system of smaller rank, and get a nontrivial wronskian. For a form$\omega$of arbitrary degree, we are led to estimating the order of contact between$\gamma(t)$and a suitable algebraic hypersurface in$\textbf C^{n+1}$. We observe that$ord I(t)$grows like an affine function with respect to$\deg \omega$.Comment: 18 page

Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry

We consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y^2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces.Comment: v2: slightly expanded expositio

Nox1 oxidase suppresses influenza a virus-induced lung inflammation and oxidative stress

Influenza A virus infection is an ongoing clinical problem and thus, there is an urgent need to understand the mechanisms that regulate the lung inflammation in order to unravel novel generic pharmacological strategies. Evidence indicates that the Nox2-containing NADPH oxidase enzyme promotes influenza A virus-induced lung oxidative stress, inflammation and dysfunction via ROS generation. In addition, lung epithelial and endothelial cells express the Nox1 isoform of NADPH oxidase, placing this enzyme at key sites to regulate influenza A virus-induced lung inflammation. The aim of this study was to investigate whether Nox1 oxidase regulates the inflammatory response and the oxidative stress to influenza infection in vivo in mice. Male WT and Nox1-deficient (Nox1−/y) mice were infected with the moderately pathogenic HkX-31 (H3N2, 1×104 PFU) influenza A virus for analysis of bodyweight, airways inflammation, oxidative stress, viral titre, lung histopathology, and cytokine/chemokine expression at 3 and 7 days post infection. HkX-31 virus infection of Nox1−/y mice resulted in significantly greater: loss of bodyweight (Day 3); BALF neutrophilia, peri-bronchial, peri-vascular and alveolar inflammation; Nox2-dependent inflammatory cell ROS production and peri-bronchial, epithelial and endothelial oxidative stress. The expression of pro-inflammatory cytokines including CCL2, CCL3, CXCL2, IL-1β, IL-6, GM-CSF and TNF-α was higher in Nox1−/y lungs compared to WT mice at Day 3, however, the expression of CCL2, CCL3, CXCL2, IFN-γ and the anti-inflammatory cytokine IL-10 were lower in lungs of Nox1−/y mice vs. WT mice at Day 7. Lung viral titre, and airways infiltration of active CD8+ and CD4+ T lymphocytes, and of Tregs were similar between WT and Nox1−/y mice. In conclusion, Nox1 oxidase suppresses influenza A virus induced lung inflammation and oxidative stress in mice particularly at the early phases of the infection. Nox1 and Nox2 oxidases appear to have opposing roles in the regulation of inflammation caused by influenza A viruses

Million-atom molecular dynamics simulation by order-N electronic structure theory and parallel computation

Parallelism of tight-binding molecular dynamics simulations is presented by means of the order-N electronic structure theory with the Wannier states, recently developed (J. Phys. Soc. Jpn. 69,3773 (2000)). An application is tested for silicon nanocrystals of more than millions atoms with the transferable tight-binding Hamiltonian. The efficiency of parallelism is perfect, 98.8 %, and the method is the most suitable to parallel computation. The elapse time for a system of $2\times 10^6$ atoms is 3.0 minutes by a computer system of 64 processors of SGI Origin 3800. The calculated results are in good agreement with the results of the exact diagonalization, with an error of 2 % for the lattice constant and errors less than 10 % for elastic constants.Comment: 5 pages, 3 figure

Morphology, geographical variation and the subspecies of marsh tit Poecile palustris in Britain and central Europe

Capsule: All British Marsh Tits belong to subspecies Poecile palustris dresseri, being smaller than nominate P. p. palustris of central Europe. Aims: Determining the subspecies of Marsh Tit in Britain to test whether ssp. P. p. palustris occurs in northern England and Scotland, by assessing regional variation in size compared with central European birds. Methods: 1147 wing length and 250 tail length measurements from 953 Marsh Tits were compared between eight British locations to test for regional variation. Biometrics were compared between birds from Britain and six locations within the continental European range of ssp. palustris. Results: There was no regional variation in wing or tail lengths among British Marsh Tits, indicating that all resident birds belong to ssp. dresseri. There was no evidence supporting the existence of ssp. palustris in northern England. British birds were significantly smaller than those from continental Europe, with proportionately shorter tails, consistent across all age and sex classes. Conclusion: All British Marsh Tits should be considered as ssp. dresseri, with ssp. palustris being limited to continental Europe. With no evidence of regional variation in size within Britain, reliable sexing methods based on biometrics could be applied in demographic studies throughout the country

An Empirical Charge Transfer Potential with Correct Dissociation Limits

The empirical valence bond (EVB) method [J. Chem. Phys. 52, 1262 (1970)] has always embodied charge transfer processes. The mechanism of that behavior is examined here and recast for use as a new empirical potential energy surface for large-scale simulations. A two-state model is explored. The main features of the model are: (1) Explicit decomposition of the total system electron density is invoked; (2) The charge is defined through the density decomposition into constituent contributions; (3) The charge transfer behavior is controlled through the resonance energy matrix elements which cannot be ignored; and (4) A reference-state approach, similar in spirit to the EVB method, is used to define the resonance state energy contributions in terms of "knowable" quantities. With equal validity, the new potential energy can be expressed as a nonthermal ensemble average with a nonlinear but analytical charge dependence in the occupation number. Dissociation to neutral species for a gas-phase process is preserved. A variant of constrained search density functional theory is advocated as the preferred way to define an energy for a given charge.Comment: Submitted to J. Chem. Phys. 11/12/03. 14 pages, 8 figure

Anharmonic Decay of Vibrational States in Amorphous Silicon

Anharmonic decay rates are calculated for a realistic atomic model of amorphous silicon. The results show that the vibrational states decay on picosecond timescales and follow the two-mode density of states, similar to crystalline silicon, but somewhat faster. Surprisingly little change occurs for localized states. These results disagree with a recent experiment.Comment: 10 pages, 4 Postscript figure

Barriers and Enablers to Weight Management Programmes for Working Men: A Qualitative Study

Gender-sensitised weight management programmes have been developed to encourage more men to access support. Whilst these programmes have proved successful for some groups of men, they are not a panacea, and the views of men who have never attended any form of structured weight management programme remain unknown. The aim of this research was to explore the views of such men towards body weight, health, and weight management programmes. Participants were recruited purposefully at their place of work. Semi-structured interviews were conducted with 16 adult men with a BMI > 25 who worked in routine manual occupations and had no previous experience of attending a weight management programme. Interviews were analysed using an inductive thematic analysis approach. Interview findings were developed into five themes: “the indestructible breadwinner,” “avoidance of feminine behaviour,” “the body conscious man,” “being one of the lads,” and “doctor knows best.” The findings suggest that these men have high levels of body consciousness, value guidance from GPs, have high levels of agency towards lifestyle choices, and wish to preserve their masculinity. The study identified various factors that help explain low participation in weight management programmes for men and potential ways to improve access. Future interventions should include gender sensitisation of resources and providing men with the opportunity to follow self-directed weight management programmes to increase participation. Individual and population-level interventions to address weight management that includes the perceived and actual needs of men working in routine manual occupations are urgently needed to address health inequalities

Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma

Vortices in thin-film superconductors are often modelled as a system of particles interacting via a repulsive logarithmic potential. Arguments are presented to show that the hypothetical (Abrikosov) crystalline state for such particles is unstable at any finite temperature against proliferation of screened disclinations. The correlation length of crystalline order is predicted to grow as $\sqrt{1/T}$ as the temperature $T$ is reduced to zero, in excellent agreement with our simulations of this two-dimensional system.Comment: 3 figure