Eliminating the Hadronic Uncertainty

The Standard Model Lagrangian requires the values of the fermion masses, the Higgs mass and three other experimentally well-measured quantities as input in order to become predictive. These are typically taken to be $\alpha$, $G_\mu$ and $M_Z$. Using the first of these, however, introduces a hadronic contribution that leads to a significant error. If a quantity could be found that was measured at high energy with sufficient precision then it could be used to replace $\alpha$ as input. The level of precision required for this to happen is given for a number of precisely-measured observables. The $W$ boson mass must be measured with an error of $\pm13$\,MeV, $\Gamma_Z$ to $0.7$\,MeV and polarization asymmetry, $A_{LR}$, to $\pm0.002$ that would seem to be the most promising candidate. The r\^ole of renormalized parameters in perturbative calculations is reviewed and the value for the electromagnetic coupling constant in the $\overline{\rm MS}$ renormalization scheme that is consistent with all experimental data is obtained to be $\alpha^{-1}_{\overline{\rm MS}}(M^2_Z)=128.17$.Comment: 8 pages LaTeX2

Importance Sampling: Intrinsic Dimension and Computational Cost

The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee accurate approximations. Intuitively, some notion of distance between the target and the proposal should determine the computational cost of the method. A major challenge is to quantify this distance in terms of parameters or statistics that are pertinent for the practitioner. The subject has attracted substantial interest from within a variety of communities. The objective of this paper is to overview and unify the resulting literature by creating an overarching framework. A general theory is presented, with a focus on the use of importance sampling in Bayesian inverse problems and filtering.Comment: Statistical Scienc

Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schr\"odinger system

We study a nonlinear system of partial differential equations in which a complex field (the Higgs field) evolves according to a nonlinear Schroedinger equation, coupled to an electromagnetic field whose time evolution is determined by a Chern-Simons term in the action. In two space dimensions, the Chern-Simons dynamics is a Galileo invariant evolution for A, which is an interesting alternative to the Lorentz invariant Maxwell evolution, and is finding increasing numbers of applications in two dimensional condensed matter field theory. The system we study, introduced by Manton, is a special case (for constant external magnetic field, and a point interaction) of the effective field theory of Zhang, Hansson and Kivelson arising in studies of the fractional quantum Hall effect. From the mathematical perspective the system is a natural gauge invariant generalization of the nonlinear Schroedinger equation, which is also Galileo invariant and admits a self-dual structure with a resulting large space of topological solitons (the moduli space of self-dual Ginzburg-Landau vortices). We prove a theorem describing the adiabatic approximation of this system by a Hamiltonian system on the moduli space. The approximation holds for values of the Higgs self-coupling constant close to the self-dual (Bogomolny) value of 1. The viability of the approximation scheme depends upon the fact that self-dual vortices form a symplectic submanifold of the phase space (modulo gauge invariance). The theorem provides a rigorous description of slow vortex dynamics in the near self-dual limit.Comment: Minor typos corrected, one reference added and DOI give

MCMC methods for functions modifying old algorithms to make\ud them faster

Many problems arising in applications result in the need\ud to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems

Electrochemical detection of TNT at cobalt phthalocyanine mediated screen-printed electrodes and application to detection of airborne vapours

We describe the use of cobalt phthalocyanine as a mediator to improve the sensitivity for the electrochemical detection of TNT. Commercial screen-printed electrodes containing cobalt phthalocyanine were employed for determination of TNT. Improved sensitivities compared to screen-printed carbon electrodes without phthalocyanine were observed, current response for cyclic voltammetric measurements at modified electrodes being at least double that of unmodified electrodes. A synergistic effect between oxygen and TNT reduction was also observed. Correlation between TNT concentrations and sensor output was observed between 0–200 µM TNT. Initial proof-of-concept experiments combining electrochemical determinations, with the use of an air-sampling cyclone, are also reported

Acoustic characterization of crack damage evolution in sandstone deformed under conventional and true triaxial loading

We thank the Associate Editor, Michelle Cooke, and the reviewers, Ze'ev Reches and Yves Guéguen, for useful comments which helped to improve the manuscript. We thank J.G. Van Munster for providing access to the true triaxial apparatus at KSEPL and for technical support during the experimental program. We thank R. Pricci for assistance with technical drawings of the apparatus. This work was partly funded by NERC award NE/N002938/1 and by a NERC Doctoral Studentship, which we gratefully acknowledge. Supporting data are included in a supporting information file; any additional data may be obtained from J.B. (e-mail: [email protected]).Peer reviewedPublisher PD

Magnetoresistance, Micromagnetism and Domain Wall Effects in Epitaxial Fe and Co Structures with Stripe Domains

We review our recent magnetotransport and micromagnetic studies of lithographically defined epitaxial thin film structures of bcc Fe and hcp Co with stripe domains. Micromagnetic structure and resistivity anisotropy are shown to be the predominant sources of low field magnetoresistance (MR) in these microstructures, with domain wall (DW) effects smaller but observable (DW-MR $\lesssim 1$). In Fe, at low temperature, in a regime in which fields have a significant effect on electron trajectories, a novel negative DW contribution to the resistivity is observed. In hcp Co microstructures, temperature dependent transport measurements for current perpendicular and parallel to walls show that any additional resistivity due to DW scattering is very small.Comment: 7 pages, 8 figures, to appear in Journal of Applied Physics 199