Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two K\"ahler Forms

In this paper, we extend our geometrical derivation of expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples. We expect that our results can be easily generalized to arbitrary toric manifold.Comment: 45 pages, 2 figures, minor errors are corrected, English is refined. Section 1 and Section 2 are enlarged. Especially in Section 2, confusion between the notion of resolution and the notion of compactification is resolved. Computation under non-zero equivariant parameters are added in Section

Phoretic Motion of Spheroidal Particles Due To Self-Generated Solute Gradients

We study theoretically the phoretic motion of a spheroidal particle, which generates solute gradients in the surrounding unbounded solvent via chemical reactions active on its surface in a cap-like region centered at one of the poles of the particle. We derive, within the constraints of the mapping to classical diffusio-phoresis, an analytical expression for the phoretic velocity of such an object. This allows us to analyze in detail the dependence of the velocity on the aspect ratio of the polar and the equatorial diameters of the particle and on the fraction of the particle surface contributing to the chemical reaction. The particular cases of a sphere and of an approximation for a needle-like particle, which are the most common shapes employed in experimental realizations of such self-propelled objects, are obtained from the general solution in the limits that the aspect ratio approaches one or becomes very large, respectively.Comment: 18 pages, 5 figures, to appear in European Physical Journal

Zonotopes and four-dimensional superconformal field theories

The a-maximization technique proposed by Intriligator and Wecht allows us to determine the exact R-charges and scaling dimensions of the chiral operators of four-dimensional superconformal field theories. The problem of existence and uniqueness of the solution, however, has not been addressed in general setting. In this paper, it is shown that the a-function has always a unique critical point which is also a global maximum for a large class of quiver gauge theories specified by toric diagrams. Our proof is based on the observation that the a-function is given by the volume of a three dimensional polytope called "zonotope", and the uniqueness essentially follows from Brunn-Minkowski inequality for the volume of convex bodies. We also show a universal upper bound for the exact R-charges, and the monotonicity of a-function in the sense that a-function decreases whenever the toric diagram shrinks. The relationship between a-maximization and volume-minimization is also discussed.Comment: 29 pages, 15 figures, reference added, typos corrected, version published in JHE

Polynomial Modular Frobenius Manifolds

The moduli space of Frobenius manifolds carries a natural involutive symmetry, and a distinguished class - so-called modular Frobenius manifolds - lie at the fixed points of this symmetry. In this paper a classification of semi-simple modular Frobenius manifolds which are polynomial in all but one of the variables is begun, and completed for three and four dimensional manifolds. The resulting examples may also be obtained from higher dimensional manifolds by a process of folding. The relationship of these results with orbifold quantum cohomology is also discussed

Amphibole: A major carrier of helium isotopes in crustal rocks

The first evidence for a specific role of amphiboles in He isotope balance of crustal rocks was presented in early contributions by Gerling et al. (1971, 1976). Since then it was shown that 4He and 3He concentrations in amphiboles generally exceed those in the host rock samples. Recently amphibole was considered as an important carrier of noble gases and other volatiles components in the course of their subduction into the mantle. This paper presents new data on the balance and mobility of noble gas isotopes and major gas constituents in amphibole separates in order to understand sources and evolution of volatile components of 2666 Ma old alkaline granites from Ponoy massif (Kola Peninsula), which underwent metamorphism 1802 Ma ago.In the amphiboles 3He, 4He and 40Ar* were dominantly produced in situ due to radioactive decay of the parent isotopes and associated nuclear reactions. A small fraction of He (≈ 3% of the total) is liberated by crushing and shows 3He/4He ratio indistinguishable from that found by total extraction. The fraction of trapped 40Ar* amounts to ≈ 40%; both these fractions presumably occupy fluid inclusions and show rather low 4He/40Ar* ≈ 0.1, a factor of ≈ 150 below the production ratio (calculated assuming no loss / gain of the species has happened since the time of metamorphism).3He has been better preserved in amphiboles compared with 4He: the retention parameter (measured amount of He / totally produced amount) for 3He (≈ 0.4) exceeds that for 4He (≈ 0.15).He extraction by fast and slow linear heating of amphiboles resulted in different release patterns. The fast heating (within 12 to 40 °C min− 1) revealed a superposition of two peaks. When heating with slower heating rate (below 8 °C min− 1) was applied, the high-temperature peak disappeared (the “disappearing site”). Extractions of He atoms from grain and powder samples at different heating rates have shown that: (1) the “disappearing site” is revealed by the fast heating analyses of different amphibole samples but not only those from the Ponoy massif; (2) amount of He liberated from the “disappearing site” is variable and generally much less than the total amount of He in the sample; (3) analysis of the powder produced in the crushing experiments never reveals the “disappearing site”; the temperature of He release from the powder is lower than that from the mm grain size sample by ≈ 50 °C. Possible explanations of the nature of the “disappearing site” are discussed. However, independently on nature of this effect, repeated gas extractions by heating at different rates would give additional information about structure and its transformation during heating of amphiboles.The simplest explanation of the observed abundances of noble gas isotopes in the amphibole separates from Ponoy granites suggests local production, redistribution and partial loss of noble gases during evolution of the massif

Long-lived oscillons from asymmetric bubbles

The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are: a) circularly symmetric; and b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly-growing instabilities not seen through the usual ``spectral'' method.Comment: RevTeX 4, 9 pages, 11 figures. Revised version with a new approach to stability. Accepted to Phys. Rev.

Fracture in the Elderly Multidisciplinary Rehabilitation (FEMuR):study protocol for a phase II randomised feasibility study of a multidisciplinary rehabilitation package following hip fracture [ ISRCTN22464643 ]

Background Proximal femoral fracture is a common, major health problem in old age resulting in loss of functional independence and a high-cost burden on society, with estimated health and social care costs of £2.3 billion per year in the UK. Rehabilitation has the potential to maximise functional recovery and maintain independent living, but evidence of effectiveness is lacking. Usual rehabilitation care is delivered by a multi-disciplinary team in the hospital and in the community. An ‘enhanced rehabilitation’ intervention has been developed consisting of a workbook, goal-setting diary and extra therapy sessions, designed to improve self-efficacy and increase the amount and quality of the practice of physical exercise and activities of daily living. Methods/design This paper describes the design of a phase II study comprising an anonymous cohort of all proximal femoral fracture patients admitted to the three acute hospitals in Betsi Cadwaladr University Health Board over a 6-month period with a randomised feasibility study comparing the enhanced rehabilitation intervention with usual care. These will assess the feasibility of a future definitive randomised controlled trial and concurrent economic evaluation in terms of recruitment, retention, outcome measure completion, compliance with the intervention and fidelity of delivery, health service use data, willingness to be randomised and effect size for a future sample size calculation. Focus groups will provide qualitative data to contribute to the assessment of the acceptability of the intervention amongst patients, carers and rehabilitation professionals and the feasibility of delivering the planned intervention. The primary outcome measure is function assessed by the Barthel Index. Secondary outcomes measure the ability to perform activities of daily living, anxiety and depression, potential mediators of outcomes such as hip pain, self-efficacy and fear of falling, health utility, health service use, objectively assessed physical function and adverse events. Participants’ preference for rehabilitation services will be assessed in a discrete choice experiment. Discussion Phase II studies are an opportunity to not only assess the feasibility of trial methods but also to compare different methods of outcome measurement and novel methods of obtaining health service use data from routinely collected patient information. Trial registration Current Controlled Trials ISRCTN22464643, UKCRN16677

Electromagnetic wave propagation in rain and polarization effects

This paper summarizes our study on microwave and millimeter-wave propagation in rain with special emphasis on the effects of polarization. Starting from a recount of our past findings, we will discuss developments with these and how they are connected with subsequent research

Vintage venoms: proteomic and pharmacological stability of snake venoms stored for up to eight decades

For over a century, venom samples from wild snakes have been collected and stored around the world. However, the quality of storage conditions for "vintage" venoms has rarely been assessed. The goal of this study was to determine whether such historical venom samples are still biochemically and pharmacologically viable for research purposes, or if new sample efforts are needed. In total, 52 samples spanning 5 genera and 13 species with regional variants of some species (e.g., 14 different populations of Notechis scutatus) were analysed by a combined proteomic and pharmacological approach to determine protein structural stability and bioactivity. When venoms were not exposed to air during storage, the proteomic results were virtually indistinguishable from that of fresh venom and bioactivity was equivalent or only slightly reduced. By contrast, a sample of Acanthophis antarcticus venom that was exposed to air (due to a loss of integrity of the rubber stopper) suffered significant degradation as evidenced by the proteomics profile. Interestingly, the neurotoxicity of this sample was nearly the same as fresh venom, indicating that degradation may have occurred in the free N- or C-terminus chains of the proteins, rather than at the tips of loops where the functional residues are located. These results suggest that these and other vintage venom collections may be of continuing value in toxin research. This is particularly important as many snake species worldwide are declining due to habitat destruction or modification. For some venoms (such as N. scutatus from Babel Island, Flinders Island, King Island and St. Francis Island) these were the first analyses ever conducted and these vintage samples may represent the only venom ever collected from these unique island forms of tiger snakes. Such vintage venoms may therefore represent the last remaining stocks of some local populations and thus are precious resources. These venoms also have significant historical value as the Oxyuranus venoms analysed include samples from the first coastal taipan (Oxyuranus scutellatus) collected for antivenom production (the snake that killed the collector Kevin Budden), as well as samples from the first Oxyuranus microlepidotus specimen collected after the species' rediscovery in 1976. These results demonstrate that with proper storage techniques, venom samples can retain structural and pharmacological stability. This article is part of a Special Issue entitled: Proteomics of non-model organisms. Biological significance: •These results show that with proper storage venoms are useful for decades.•These results have direct implications for the use of rare venoms

Primary Invasive Aspergillosis of the Digestive Tract: Report of Two Cases and Review of the Literature

BACKGROUND: Disseminated aspergillosis is thought to occur as a result of vascular invasion from the lungs with subsequent bloodstream dissemination, and portals of entry other than sinuses and/or the respiratory tract remain speculative. METHODS: We report two cases of primary aspergillosis in the digestive tract and present a detailed review of eight of the 23 previously-published cases for which detailed data are available. RESULTS AND CONCLUSION: These ten cases presented with symptoms suggestive of typhlitis, with further peritonitis requiring laparotomy and small bowel segmental resection. All cases were characterized by the absence of pulmonary disease at the time of histologically-confirmed gastrointestinal involvement with vascular invasion by branched Aspergillus hyphae. These cases suggest that the digestive tract may represent a portal of entry for Aspergillus species in immunocompromised patients