Limit Theorems For Quantum Walks Associated with Hadamard Matrices

We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given

The impact of private sector provision on equitable provision of coronary revascularisation

Objective: To investigate the impact of including private sector data on assessments of equity of coronary revascularisation provision using NHS data only. Design: Analyses of Hospital Episodes Statistics and private sector data by age, sex, and PCT of residence. For each PCT, the share of London's total population and revascularisations (all admissions, NHS-funded, and privately-funded admissions) were calculated. GINI coefficients were derived to provide an index of inequality across sub-populations, with parametric bootstrapping to estimate confidence intervals. Setting: London Participants London residents undergoing coronary revascularisation April 2001 - December 2003. Intervention Coronary artery bypass graft or angioplasty Main outcome measures: Directly-standardised revascularisation rates, GINI coefficients. Results: NHS-funded age-standardised revascularisation rates varied from 95.2 to 193.9 per 100,000 and privately funded procedures from 7.6 to 57.6. Although the age distribution did not vary by funding, the proportion of revascularisations among women that were privately funded (11.0%) was lower than among men (17.0%). Privately funded rates were highest in PCTs with the lowest death rates (p=0.053). NHS-funded admission rates were not related to deprivation nor age-standardised deaths rates from coronary heart disease. Privately-funded admission rates were lower in more deprived PCTs. NHS provision was significantly more egalitarian (Gini coefficient 0.12) than the private sector (0.35). Including all procedures was significantly less equal (0.13) than NHS funded care alone. Conclusion: Private provision exacerbates geographical inequalities. Those responsible for commissioning care for defined populations must have access to consistent data on provision of treatment wherever it takes place

Assessing time knowledge in children aged 10 to 11 years

The acquisition of time knowledge involves learning how to read clocks, estimate time, read dates and learn about temporal sequences. Evidence suggests that many of these competencies are acquired by 10 years of age although not all children may follow this developmental path. The main purpose of this study was to collect normative data for a screening tool that assesses time knowledge. These data identify the prevalence and pattern of difficulties with time knowledge among a UK sample of Year 6 pupils (aged 10 to 11 years). The Time Screening Assessment tool (Doran, Dutt & Pembery, 2015), designed to assess time knowledge, was administered individually to a sample of 79 children. Findings revealed a median overall score of 32 out of a maximum score of 36. 25% of children performed at or close to ceiling, however seven children scored more than -1.5 standard deviations below the mean. The value of these findings to practitioners working with children in schools is discussed

Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology

Models have made numerous contributions to evolutionary biology, but misunderstandings persist regarding their purpose. By formally testing the logic of verbal hypotheses, proof-of-concept models clarify thinking, uncover hidden assumptions, and spur new directions of study. thumbnail image credit: modified from the Biodiversity Heritage Librar

The effect of weld residual stresses and their re-distribution with crack growth during fatigue under constant amplitude loading

In this work the evolution of the residual stresses in a MIG-welded 2024-T3 aluminium alloy M(T) specimen during in situ fatigue crack growth at constant load amplitude has been measured with neutron diffraction. The plastic relaxation and plasticity-induced residual stresses associated with the fatigue loading were found to be small compared with the stresses arising due to elastic re-distribution of the initial residual stress field. The elastic re-distribution was modelled with a finite element simulation and a good correlation between the experimentally-determined and the modelled stresses was found. A significant mean stress effect on the fatigue crack growth rate was seen and this was also accurately predicted using the measured initial residual stresses

Global bifurcation of homoclinic trajectories of discrete dynamical systems

We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving the topological properties of the asymptotic stable bundles.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1111.140

Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe

New Ultraviolet Extinction Curves for Interstellar Dust in M31

New low-resolution UV spectra of a sample of reddened OB stars in M31 were obtained with HST/STIS to study the wavelength dependence of interstellar extinction and the nature of the underlying dust grain populations. Extinction curves were constructed for four reddened sightlines in M31 paired with closely matching stellar atmosphere models. The new curves have a much higher S/N than previous studies. Direct measurements of N(H I) were made using the Ly$\alpha$ absorption lines enabling gas-to-dust ratios to be calculated. The sightlines have a range in galactocentric distance of 5 to 14 kpc and represent dust from regions of different metallicities and gas-to-dust ratios. The metallicities sampled range from Solar to 1.5 Solar. The measured curves show similarity to those seen in the Milky Way and the Large Magellanic Cloud. The Maximum Entropy Method was used to investigate the dust composition and size distribution for the sightlines observed in this program finding that the extinction curves can be produced with the available carbon and silicon abundances if the metallicity is super-Solar.Comment: ApJ, in press, 9 pages, 5 figure

Protocol for the United Kingdom Rotator Cuff Study (UKUFF) : a randomised controlled trial of open and arthroscopic rotator cuff repair

This project was funded by the NIHR Health Technology Assessment programme (project number 05/47/02). J. L. Rees has received a grant from Oxford University which is related to this paper. J. Dawson reports that Oxford University has received a grant from HTA which is related to this paper, as well as a study grant.Peer reviewedPublisher PD

Antilocalization of Coulomb Blockade in a Ge-Si Nanowire

The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a Ge-Si nanowire quantum dot. Strong spin-orbit coupling in this hole-gas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the open-wire regime places a bound on the spin-orbit length ($l_{so}$ < 20 nm), consistent with values extracted in the Coulomb blockade regime ($l_{so}$ < 25 nm).Comment: Supplementary Information available at http://bit.ly/19pMpd