Weak Convergence of the Scaled Median of Independent Brownian Motions

We consider the median of n independent Brownian motions, and show that this process, when properly scaled, converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct estimates on the increments of the median process. An explicit formula is given for the covariance function of the limit process. The limit process is also shown to be Holder continuous with exponent gamma for all gamma < 1/4.Comment: to appear in Probability Theory and Related Field

Optical biosensor techniques for monitoring organic pollutants in the aquatic environment

The principal contribution of Southampton University to the BIOPTICAS project is in the realization of planar optical waveguide probes to determine the optical properties of attached sensing films. Three types of device are being investigated: surface plasmon resonance (SPR), directional coupler and chemiluminescence sensors. Techniques have been established for the deposition of compatible electrodes for electrochemical modulation of sensing reactions as an integral part of devices, and equipment has been set up for the fabrication of waveguides in glass substrates by field-assisted ion-exchange. The modelling and design stages for the devices are now close to completion, and we have begun the fabrication and evaluation of preliminary designs and verification of models. Interaction with partners has resulted in the establishment of standardised sensor chip formals and plans for comparative evaluations of the sensors developed in the project, using standardised sensing reactions are well in hand

Identifying Changes in the Synaptic Proteome of Cirrhotic Alcoholic Superior Frontal Gyrus

Hepatic complications are a common side-effect of alcoholism. Without the detoxification capabilities of the liver, alcohol misuse induces changes in gene and protein expression throughout the body. A global proteomics approach was used to identify these protein changes in the brain. We utilised human autopsy tissue from the superior frontal gyrus (SFG) of six cirrhotic alcoholics, six alcoholics without comorbid disease, and six non-alcoholic non-cirrhotic controls. Synaptic proteins were isolated and used in two-dimensional differential in-gel electrophoresis coupled with mass spectrometry. Many expression differences were confined to one or other alcoholic sub-group. Cirrhotic alcoholics showed 99 differences in protein expression levels from controls, of which half also differed from non-comorbid alcoholics. This may reflect differences in disease severity between the sub-groups of alcoholics, or differences in patterns of harmful drinking. Alternatively, the protein profiles may result from differences between cirrhotic and non-comorbid alcoholics in subjects’ responses to alcohol misuse. Ten proteins were identified in at least two spots on the 2D gel; they were involved in basal energy metabolism, synaptic vesicle recycling, and chaperoning. These post-translationally modified isoforms were differentially regulated in cirrhotic alcoholics, indicating a level of epigenetic control not previously observed in this disorder

Waveguide surface plasmon resonance sensors

Planar waveguide surface plasmon resonance sensors have great potential for use in the field of environmental monitoring. In this paper we present a rigorous model for the optical power transmittance of this type of sensor. This model is used to determine the change in transmitted power when a thin layer is adsorbed to the metal-clad region of the sensor, as a function of the waveguide and metal film parameters. Design curves for sensors based upon glass waveguides coated with thin gold films immersed in water are presented. Experimentally determined changes in the output power of a waveguide surface plasmon sensor, as a function of the length of the gold film, are presented and compared to theory

Waveguide surface plasmon resonance biosensor for the aqueous environment

We report the fabrication and performance of gold coated waveguide surface plasmon resonance biosensors. Biotin-avidin binding reactions at the sensor surface were observed. The output power of the sensor showed a decrease of 32% on binding a dual layer of biotin-avidin

Anomalous Pseudoscalar-Photon Vertex In and Out of Equilibrium

The anomalous pseudoscalar-photon vertex is studied in real time in and out of equilibrium in a constituent quark model. The goal is to understand the in-medium modifications of this vertex, exploring the possibility of enhanced isospin breaking by electromagnetic effects as well as the formation of neutral pion condensates in a rapid chiral phase transition in peripheral, ultrarelativistic heavy-ion collisions. In equilibrium the effective vertex is afflicted by infrared and collinear singularities that require hard thermal loop (HTL) and width corrections of the quark propagator. The resummed effective equilibrium vertex vanishes near the chiral transition in the chiral limit. In a strongly out of equilibrium chiral phase transition we find that the chiral condensate drastically modifies the quark propagators and the effective vertex. The ensuing dynamics for the neutral pion results in a potential enhancement of isospin breaking and the formation of $\pi^0$ condensates. While the anomaly equation and the axial Ward identity are not modified by the medium in or out of equilibrium, the effective real-time pseudoscalar-photon vertex is sensitive to low energy physics.Comment: Revised version to appear in Phys. Rev. D. 42 pages, 4 figures, uses Revte

Measurement of complex coupling coefficients of directional coupling by thermo-optic modulation

Directional coupling between two parallel singlemode optical waveguides is the functional principle underlying numerous integrated optical devices, such as modulators, filters and sensors. As the coupling efficiency depends critically on the synchronism of wave propagation and on the field overlap of the two guides, tight tolerances apply in waveguide fabrication, and a precise determination of the coupling parameters is essential

The intrinsic charm contribution to the proton spin

The charm quark contribution to the first moment of $g_1(x,Q^2)$ is calculated using a heavy mass expansion of the divergence of the singlet axial current. It is shown to be small.Comment: LATEX, 6 page

Real-time nonequilibrium dynamics in hot QED plasmas: dynamical renormalization group approach

We study the real-time nonequilibrium dynamics in hot QED plasmas implementing a dynamical renormalization group and using the hard thermal loop (HTL) approximation. The focus is on the study of the relaxation of gauge and fermionic mean fields and on the quantum kinetics of the photon and fermion distribution functions. For semihard photons of momentum eT << k << T we find to leading order in the HTL that the gauge mean field relaxes in time with a power law as a result of infrared enhancement of the spectral density near the Landau damping threshold. The dynamical renormalization group reveals the emergence of detailed balance for microscopic time scales larger than 1/k while the rates are still varying with time. The quantum kinetic equation for the photon distribution function allows us to study photon production from a thermalized quark-gluon plasma (QGP) by off-shell effects. We find that for a QGP at temperature T ~ 200 MeV and of lifetime 10 < t < 50 fm/c the hard (k ~ T) photon production from off-shell bremsstrahlung (q -> q \gamma and \bar{q} -> \bar{q}\gamma) at O(\alpha) grows logarithmically in time and is comparable to that produced from on-shell Compton scattering and pair annihilation at O(\alpha \alpha_s). Fermion mean fields relax as e^{-\alpha T t ln(\omega_P t)} with \omega_P=eT/3 the plasma frequency, as a consequence of the emission and absorption of soft magnetic photons. A quantum kinetic equation for hard fermions is obtained directly in real time from a field theoretical approach improved by the dynamical renormalization group. The collision kernel is time-dependent and infrared finite.Comment: RevTeX, 46 pages, including 5 EPS figures, published versio

Dynamical Renormalization Group Approach to Quantum Kinetics in Scalar and Gauge Theories

We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of the distribution function in perturbation theory. The solution of this equation of motion reveals secular terms that grow in time, the dynamical renormalization group resums these secular terms in real time and leads directly to the quantum kinetic equation. We used this method to study the relaxation in a cool gas of pions and sigma mesons in the O(4) chiral linear sigma model. We obtain in relaxation time approximation the pion and sigma meson relaxation rates. We also find that in large momentum limit emission and absorption of massless pions result in threshold infrared divergence in sigma meson relaxation rate and lead to a crossover behavior in relaxation. We then study the relaxation of charged quasiparticles in scalar electrodynamics (SQED). While longitudinal, Debye screened photons lead to purely exponential relaxation, transverse photons, only dynamically screened by Landau damping lead to anomalous relaxation, thus leading to a crossover between two different relaxational regimes. We emphasize that infrared divergent damping rates are indicative of non-exponential relaxation and the dynamical renormalization group reveals the correct relaxation directly in real time. Finally we also show that this method provides a natural framework to interpret and resolve the issue of pinch singularities out of equilibrium and establish a direct correspondence between pinch singularities and secular terms. We argue that this method is particularly well suited to study quantum kinetics and transport in gauge theories.Comment: RevTeX, 40 pages, 4 eps figures, published versio