Comment on ``Piecewise potential vorticity inversion: Elementary tests''

Egger (2008) constructs some idealised experiments to test the usefulness of piecewise potential vorticity inversion (PPVI) in the diagnosis of Rossby wave dynamics and baroclinic development. He concludes that, ``PPVI does not help us to understand the dynamics of linear Rossby waves. It provides local tendencies of the streamfunction which are unrelated to the true ones. The same way, the motion of baroclinic waves in shear flow cannot be understood by using PPVI. Moreover, the effect of boundary temperatures as determined by PPVI is unrelated to the flow evolution.'' He goes further in arguing that we should not consider velocities as ``induced'' by PV anomalies defined by carving up the global domain. However, these conclusions partly reflect the limitations of his idealised experiments and the manner in which the PV components were partitioned from one another.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

Characterising the background errors for the boundary-layer capping inversion

The one-dimensional variational assimilation of vertical temperature information in the presence of a boundary-layer capping inversion is studied. For an optimal analysis of the vertical temperature profile, an accurate representation of the background error covariances is essential. The background error covariances are highly flow-dependent due to the variability in the presence, structure and height of the boundary-layer capping inversion. Flow-dependent estimates of the background error covariances are shown by studying the spread in an ensemble of forecasts. A forecast of the temperature profile (used as a background state) may have a significant error in the position of the capping inversion with respect to observations. It is shown that the assimilation of observations may weaken the inversion structure in the analysis if only magnitude errors are accounted for as is the case for traditional data assimilation methods used for operational weather prediction. The positional error is treated explicitly here in a new data assimilation scheme to reduce positional error, in addition to the traditional framework to reduce magnitude error. The distribution of the positional error of the background inversion is estimated for use with the new scheme.

Notations and conventions in molecular spectroscopy: part 3. Permutation and permutation-inversion symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 3 in a series, deals with symmetry notation referring to groups that involve nuclear permutations and the inversion operation. Further parts will follow, dealing inter alia with vibration-rotation spectroscopy and electronic spectroscopy.

The dynamics of a polar low assessed using potential vorticity inversion

The dynamics of a polar low are examined using a piecewise potential vorticity (PV) inversion method. In previous studies of this and other polar lows, structural evolution has been described in terms of regions of anomalous PV. In this study the relative importance of different PV anomalies and the interactions between them have been quantified using PV diagnostics. The intensification of the polar low occurred in three stages (in contrast to previous studies of polar lows that have only identified two stages). The dynamical characteristics of stages one and two are consistent with the proposed type C cyclogenesis mechanism. A diabatically-generated lower-tropospheric PV anomaly dominated intensification after initial triggering by a positive upper-level PV anomaly. A phase tilt between the upper and lower levels was maintained through retardation of the positive upper-level anomaly by the effects of latent heat release. Stage three was a period of growth dominated by wind-induced surface heat exchange (WISHE), which contributed at least 18% to the amplitude of the mature surface polar low.

Characterisation of an s-type low molecular weight glutenin subunit of wheat and its proline and glutamine-rich repetitive domain

The low molecular weight glutenin subunits (LMW-GS) are major components of the glutenin polymers which determine the elastomeric properties of wheat (Triticum aestivum L.) gluten and dough. They comprise a complex mixture of components and have proved to be difficult to purify for detailed characterisation. The mature LMW subunit proteins comprise two structural domains, with one domain consisting of repeated sequences based on short peptide motifs. DNA sequences encoding this domain and a whole subunit were expressed in Escherichia coli and the recombinant proteins purified. Detailed comparisons by spectroscopy (CD, FT-IR) and dynamic light scattering indicated that the repetitive and non-repetitive domains of the proteins formed different structures with the former having an extended conformation with an equilibrium between poly-L-proline II-like structure and type II’ b-turns, and the latter a more compact globular structure rich in a-helix. Although the structures of these two domains appear to form independently, dynamic light scattering of the whole subunit dissolved in trifluoroethanol(TFE) suggested that they interact, leading to a more compact conformation. These observations may have relevance to the role of the LMW-GS in gluten structure and functionality.

Nuclear magnetic resonance structure shows that the severe acute respiratory syndrome coronavirus-unique domain contains a macrodomain fold

The nuclear magnetic resonance (NMR) structure of a central segment of the previously annotated severe acute respiratory syndrome (SARS)-unique domain (SUD-M, for "middle of the SARS-unique domain") in SARS coronavirus (SARS-CoV) nonstructural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3 residues 528 to 648, and there is a flexibly extended N-terminal tail with the residues 513 to 527 and a C-terminal flexible tail of residues 649 to 651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527 to 651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly(A) and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In a further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1 ''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows three-dimensional structure homology with several helicases and nucleoside triphosphate-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.