Low temperature phase diagram and critical behaviour of the four-state chiral clock model

The low temperature behaviour of the four-state chiral clock ($CC_4$) model is reexamined using a systematic low temperature series expansion of the free energy. Previously obtained results for the low temperature phases are corrected and the low temperature phase diagram is derived. In addition, the phase transition from the modulated region to the high temperature paraphase is shown to belong to the universality class of the 3d-XY model.Comment: 17 pages in ioplppt style, 3 figure

A Bayesian framework for verification and recalibration of ensemble forecasts: How uncertain is NAO predictability?

Predictability estimates of ensemble prediction systems are uncertain due to limited numbers of past forecasts and observations. To account for such uncertainty, this paper proposes a Bayesian inferential framework that provides a simple 6-parameter representation of ensemble forecasting systems and the corresponding observations. The framework is probabilistic, and thus allows for quantifying uncertainty in predictability measures such as correlation skill and signal-to-noise ratios. It also provides a natural way to produce recalibrated probabilistic predictions from uncalibrated ensembles forecasts. The framework is used to address important questions concerning the skill of winter hindcasts of the North Atlantic Oscillation for 1992-2011 issued by the Met Office GloSea5 climate prediction system. Although there is much uncertainty in the correlation between ensemble mean and observations, there is strong evidence of skill: the 95% credible interval of the correlation coefficient of [0.19,0.68] does not overlap zero. There is also strong evidence that the forecasts are not exchangeable with the observations: With over 99% certainty, the signal-to-noise ratio of the forecasts is smaller than the signal-to-noise ratio of the observations, which suggests that raw forecasts should not be taken as representative scenarios of the observations. Forecast recalibration is thus required, which can be coherently addressed within the proposed framework.Comment: 36 pages, 10 figure

Heat and groundwater transport between the Antarctic Ice Sheet and subglacial sedimentary basins from electromagnetic geophysical measurements

Numerical models of contemporary as well as paleo-ice sheets suggest that groundwater and heat exchanges between subglacial sedimentary basins and the ice sheet above, can be substantial and influence the flow of ice above. So far, an approach for the measurement and assessment of such heat fluxes has not been available. Here, we summarise existing evidence for groundwater and heat exchanges between contemporary and paleo ice sheets and the substrate below. We then explain the utility of electromagnetic geophysical measurements in elucidating such exchanges, and present magnetotelluric synthetic models of the deep sedimentary basin beneath the Institute Ice Stream in West Antarctica by way of illustration. Finally, we propose a simple empirical model by which heat exchanges between subglacial sedimentary basins and the overlying ice sheet can be estimated to first-order from electromagnetic data

Strong Resonance of Light in a Cantor Set

The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately $6/|\eta_\mathrm{r}|$, where $\eta_\mathrm{r}$ is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime $\tau_\mathrm{r}=4.3$ms and of the enhancement factor $M=7.8\times10^7$ is found at the resonant frequency $\omega_\mathrm{r}=367$GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant $\epsilon=10$.Comment: 20 pages, 11 figures, to be published in Journal of the Physical Society of Japa

Max-and-Smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models

This is the final version. Available on open access from International Society for Bayesian Analysis (ISBA) via the DOI in this record. With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs) where one or more of the likelihood parameters are modeled by latent additive Gaussian processes. Max-and-Smooth consists of two-steps. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to either (a) the maximum likelihood estimate and the inverse observed information, respectively, or (b) the mean and covariance of the normalized likelihood function. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. Since the approximated likelihood function is Gaussian, the approximate posterior density of the latent parameters of the LGM (conditional on the hyperparameters) is also Gaussian, thus facilitating efficient posterior inference in high dimensions. Furthermore, the approximate marginal posterior distribution of the hyperparameters is tractable, and as a result, the hyperparameters can be sampled independently of the latent parameters. In the case of a large number of independent data replicates, sparse precision matrices, and high-dimensional latent vectors, the speedup is substantial in comparison to an MCMC scheme that infers the posterior density from the exact likelihood function. The proposed inference scheme is demonstrated on one spatially referenced real dataset and on simulated data mimicking spatial, temporal, and spatio-temporal inference problems. Our results show that Max-and-Smooth is accurate and fast.NER

Dysplasia epiphysealis hemimelica of the distal ulna: a case report and review of the literature

Dysplasia epiphysealis hemimelica (DEH) or Trevor's Disease is a very rare disease with an estimated incidence of one in 1.000.000. The majority of cases reported affect the lower limb and only 25 case reports of 33 cases with affection of the upper limb have been published. Here we present a case of DEH affecting the distal ulnar epiphysis and the lunate in an eleven-year-old girl, a DEH location described extremely rarely before. We firstly do not only present clinical and radiological findings (plane radiographs, CT, MRI), but also the surgical approach and the histopathological results of DEH in this uncommon location. Although extremely rare, DEH should be considered also in non-typical locations

Impurity-induced diffusion bias in epitaxial growth

We introduce two models for the action of impurities in epitaxial growth. In the first, the interaction between the diffusing adatoms and the impurities is ``barrier''-like and, in the second, it is ``trap''-like. For the barrier model, we find a symmetry breaking effect that leads to an overall down-hill current. As expected, such a current produces Edwards-Wilkinson scaling. For the trap model, no symmetry breaking occurs and the scaling behavior appears to be of the conserved-KPZ type.Comment: 5 pages(with the 5 figures), latex, revtex3.0, epsf, rotate, multico

An orthogonal biocatalytic approach for the safe generation and use of HCN in a multistep continuous preparation of chiral O-acetylcyanohydrins

An enantioselective preparation of O-acetylcyanohydrins has been accomplished by a three-step telescoped continuous process. The modular components enabled accurate control of two sequential biotransformations, safe handling of an in situ generated hazardous gas, and in-line stabilization of products. This method proved to be advantageous over the batch protocols in terms of reaction time (40 vs 345 min) and ease of operation, opening up access to reactions which have often been neglected due to safety concerns.We gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) within the research training group GRK 1166 “Biocatalysis in non-conventional media (BioNoCo)”, and the EPSRC (Award Nos. EP/K009494/1 and EP/K039520/1)This is the final version of the article. It first appeared from Georg Thieme Verlag KG via http://dx.doi.org/10.1055/s-0035-156064