Weakly coupled one-dimensional Mott insulators

We consider a model of one-dimensional Mott insulators coupled by a weak interchain tunnelling $t_\perp$. We first determine the single-particle Green's function of a single chain by exact field-theoretical methods and then take the tunnelling into account by means of a Random Phase Approximation (RPA). In order to embed this approximation into a well-defined expansion with a small parameter, the Fourier transform $T_\perp(k)$ of the interchain coupling is assumed to have a small support in momentum space such that every integration over transverse wave vector yields a small factor $\kappa_0^2 \ll 1$. When \tp(0) exceeds a critical value, a small Fermi surface develops in the form of electron and hole pockets. We demonstrate that Luttinger's theorem holds both in the insulating and in the metallic phases. We find that the quasi-particle residue $Z$ increases very fast through the transition and quickly reaches a value of about $0.4-0.6$. The metallic state close to the transition retains many features of the one-dimensional system in the form of strong incoherent continua.Comment: 14 pages, 13 figure

Balance conditions in variational data assimilation for a high-resolution forecast model

This paper explores the role of balance relationships for background error covariance modelling as the model's grid box decreases to convective-scales. Data assimilation (DA) analyses are examined from a simplified convective-scale model and DA system (called ABC-DA) with a grid box size of 1.5km in a 2D 540km (longitude), 15km (height) domain. The DA experiments are performed with background error covariance matrices B modelled and calibrated by switching on/off linear balance (LB) and hydrostatic balance (HB), and by observing a subset of the ABC variables, namely v, meridional wind, r', scaled density (a pressure-like variable), and b', buoyancy (a temperature-like variable). Calibration data are sourced from two methods of generating proxies of forecast errors. One uses forecasts from different latitude slices of a 3D parent model (here called the `latitude slice method'), and the other uses sets of differences between forecasts of different lengths but valid at the same time (the National Meteorological Center method). Root-mean-squared errors computed over the domain from identical twin DA experiments suggest that there is no combination of LB/HB switches that give the best analysis for all model quantities. It is frequently found though that the B-matrices modelled with both LB and HB do perform the best. A clearer picture emerges when the errors are examined at different spatial scales. In particular it is shown that switching on HB in B mostly has a neutral/positive effect on the DA accuracy at `large' scales, and switching off the HB has a neutral/positive effect at `small' scales. The division between `large' and `small' scales is between 10 and 100km. Furthermore, one hour forecast error correlations computed between control parameters find that correlations are small at large scales when balances are enforced, and at small scales when balances are not enforced (ideal control parameters have zero cross correlations). This points the way to modelling B with scale-dependent balances

Dynamic protein methylation in chromatin biology

Post-translational modification of chromatin is emerging as an increasingly important regulator of chromosomal processes. In particular, histone lysine and arginine methylation play important roles in regulating transcription, maintaining genomic integrity, and contributing to epigenetic memory. Recently, the use of new approaches to analyse histone methylation, the generation of genetic model systems, and the ability to interrogate genome wide histone modification profiles has aided in defining how histone methylation contributes to these processes. Here we focus on the recent advances in our understanding of the histone methylation system and examine how dynamic histone methylation contributes to normal cellular function in mammals

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform

A regime-dependent balanced control variable based on potential vorticity

In this paper it is argued that rotational wind is not the best choice of leading control variable for variational data assimilation, and an alternative is suggested and tested. A rotational wind parameter is used in most global variational assimilation systems as a pragmatic way of approximately representing the balanced component of the assimilation increments. In effect, rotational wind is treated as a proxy for potential vorticity, but one that it is potentially not a good choice in flow regimes characterised by small Burger number. This paper reports on an alternative set of control variables which are based around potential vorticity. This gives rise to a new formulation of the background error covariances for the Met Office's variational assimilation system, which leads to flow dependency. It uses similar balance relationships to traditional schemes, but recognises the existence of unbalanced rotational wind which is used with a new anti-balance relationship. The new scheme is described and its performance is evaluated and compared to a traditional scheme using a sample of diagnostics