Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions

We argue that two dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three dimensional curved manifolds. Specifically, the Yang-Mills field strength tensor computes the Riemannian curvature tensor of the ambient space in a thin neighborhood of the surface. In this sense the two dimensional gauge theory then serves as a source of three dimensional gravity. In particular, if the three dimensional manifold is flat it corresponds to the vacuum of the Yang-Mills theory. This implies that all solutions to the original Gauss-Codazzi surface equations determine two dimensional integrable models with a SU(2) Lax pair. Furthermore, the three dimensional SU(2) Chern-Simons theory describes the Hamiltonian dynamics of two dimensional Riemann surfaces in a four dimensional flat space-time

Measurement of the branching ratio for beta-delayed alpha decay of 16N

While the 12C(a,g)16O reaction plays a central role in nuclear astrophysics, the cross section at energies relevant to hydrostatic helium burning is too small to be directly measured in the laboratory. The beta-delayed alpha spectrum of 16N can be used to constrain the extrapolation of the E1 component of the S-factor; however, with this approach the resulting S-factor becomes strongly correlated with the assumed beta-alpha branching ratio. We have remeasured the beta-alpha branching ratio by implanting 16N ions in a segmented Si detector and counting the number of beta-alpha decays relative to the number of implantations. Our result, 1.49(5)e-5, represents a 24% increase compared to the accepted value and implies an increase of 14% in the extrapolated S-factor

Epitope-Specific Regulation of Memory Programming by Differential Duration of Antigen Presentation to Influenza-Specific CD8+ T Cells

SummaryMemory CD8+ T cells are programmed during the primary response for robust secondary responsiveness. Here we show that CD8+ T cells responding to different epitopes of influenza virus received qualitatively different signals during the primary response that altered their secondary responsiveness. Nucleoprotein (NP)-specific CD8+ T cells encountered antigen on CD40-licensed, CD70-expressing, CD103−CD11bhi dendritic cells (DCs) at later times in the primary response. As a consequence, they maintained CD25 expression and responded to interleukin-2 (IL-2) and CD27, which together programmed their robust secondary proliferative capacity and interferon-γ (IFN-γ)-producing ability. In contrast, polymerase (PA)-specific CD8+ T cells did not encounter antigen-bearing, CD40-activated DCs at later times in the primary response, did not receive CD27 and CD25 signals, and were not programmed to become memory CD8+ T cells with strong proliferative and cytokine-producing ability. As a result, CD8+ T cells responding to abundant antigens, like NP, dominated the secondary response

Individualised risk assessment for diabetic retinopathy and optimisation of screening intervals: a scientific approach to reducing healthcare costs.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked Files. This article is open access.To validate a mathematical algorithm that calculates risk of diabetic retinopathy progression in a diabetic population with UK staging (R0-3; M1) of diabetic retinopathy. To establish the utility of the algorithm to reduce screening frequency in this cohort, while maintaining safety standards.The cohort of 9690 diabetic individuals in England, followed for 2 years. The algorithms calculated individual risk for development of preproliferative retinopathy (R2), active proliferative retinopathy (R3A) and diabetic maculopathy (M1) based on clinical data. Screening intervals were determined such that the increase in risk of developing certain stages of retinopathy between screenings was the same for all patients and identical to mean risk in fixed annual screening. Receiver operating characteristic curves were drawn and area under the curve calculated to estimate the prediction capability.The algorithm predicts the occurrence of the given diabetic retinopathy stages with area under the curve =80% for patients with type II diabetes (CI 0.78 to 0.81). Of the cohort 64% is at less than 5% risk of progression to R2, R3A or M1 within 2 years. By applying a 2 year ceiling to the screening interval, patients with type II diabetes are screened on average every 20 months, which is a 40% reduction in frequency compared with annual screening.The algorithm reliably identifies patients at high risk of developing advanced stages of diabetic retinopathy, including preproliferative R2, active proliferative R3A and maculopathy M1. Majority of patients have less than 5% risk of progression between stages within a year and a small high-risk group is identified. Screening visit frequency and presumably costs in a diabetic retinopathy screening system can be reduced by 40% by using a 2 year ceiling. Individualised risk assessment with 2 year ceiling on screening intervals may be a pragmatic next step in diabetic retinopathy screening in UK, in that safety is maximised and cost reduced by about 40%.Icelandic Research Counci

Efficient computation of matched solutions of the Kapchinskij-Vladimirskij envelope equations for periodic focusing lattices

A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to all physically achievable system parameters -- including where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.Comment: 20 pages, 5 figures, Mathematica source code provide

Customer Focused Price Optimisation

Tesco want to better understand how to set online prices for their general merchandise (i.e. not groceries or clothes) in the UK. Because customers can easily compare prices from different retailers we expect they will be very sensitive to price, so it is important to get it right. There are four aspects of the problem. • Forecasting: Estimating the customer demand as a function of the price chosen (especially hard for products with no sales history or infrequent sales). • Objective function: What exactly should Tesco aim to optimise? Sales volume? Profit? Profit margin? Conversion rates? • Optimisation: How to choose prices for many related products to optimise the chosen objective function. • Evalution: How to demonstrate that the chosen prices are optimal, especially to people without a mathematical background. Aggregate sales data was provided for about 400 products over about 2 years so that quantitive approaches could be tested. For some products competitors’ prices were also provided

Rational sequences for the conductance in quantum wires from affine Toda field theories

We analyse the expression for the conductance of a quantum wire which is decribed by an integrable quantum field theory. In the high temperature regime we derive a simple formula for the filling fraction. This expression involves only the inverse of a matrix which contains the information of the asymptotic phases of the scattering matrix and the solutions of the constant thermodynamic Bethe ansatz equations. Evaluating these expressions for minimal affine Toda field theory we recover several sequences of rational numbers, which are multiples of the famous Jain sequence for the filling fraction occurring in the context of the fractional quantum Hall effect. For instance we obtain $\nu= 4 m/(2m +1)$ for $A_{4m-1}$-minimal affine Toda field theory. The matrices involved have in general non-rational entries and are not part of previous classification schemes based on integral lattices.Comment: 9 pages Latex, version to appear in Journal of Physics