Design of delay-tolerant space–time codes with limited feedback

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. Such a timing mismatch may cause rank deficiency of the conventional space-time codes and, thus, performance degradation. One efficient way to overcome such an issue is the delay-tolerant space-time codes (DT-STCs). The existing DT-STCs are designed assuming that the transmitter has no knowledge about the channels. In this paper, we show how the performance of DT-STCs can be improved by utilizing some feedback information. A general framework for designing DT-STC with limited feedback is first proposed, allowing for flexible system parameters such as the number of transmit/receive antennas, modulated symbols, and the length of codewords. Then, a new design method is proposed by combining Lloyd's algorithm and the stochastic gradient-descent algorithm to obtain optimal codebook of STCs, particularly for systems with linear minimum-mean-square-error receiver. Finally, simulation results confirm the performance of the newly designed DT-STCs with limited feedback.

The effects of springtime mid-latitude storms on trace gas composition determined from the MACC reanalysis

The relationship between springtime air pollution transport of ozone (O3) and carbon monoxide (CO) and mid-latitude cyclones is explored for the first time using the Monitoring Atmospheric Composition and Climate (MACC) reanalysis for the period 2003–2012. In this study, the most intense spring storms (95th percentile) are selected for two regions, the North Pacific (NP) and the North Atlantic (NA). These storms (∼60 storms over each region) often track over the major emission sources of East Asia and eastern North America. By compositing the storms, the distributions of O3 and CO within a "typical" intense storm are examined. We compare the storm-centered composite to background composites of "average conditions" created by sampling the reanalysis data of the previous year to the storm locations. Mid-latitude storms are found to redistribute concentrations of O3 and CO horizontally and vertically throughout the storm. This is clearly shown to occur through two main mechanisms: (1) vertical lifting of CO-rich and O3-poor air isentropically, from near the surface to the mid- to upper-troposphere in the region of the warm conveyor belt; and (2) descent of O3-rich and CO-poor air isentropically in the vicinity of the dry intrusion, from the stratosphere toward the mid-troposphere. This can be seen in the composite storm's life cycle as the storm intensifies, with area-averaged O3 (CO) increasing (decreasing) between 200 and 500 hPa. The influence of the storm dynamics compared to the background environment on the composition within an area around the storm center at the time of maximum intensity is as follows. Area-averaged O3 at 300 hPa is enhanced by 50 and 36% and by 11 and 7.6% at 500 hPa for the NP and NA regions, respectively. In contrast, area-averaged CO at 300 hPa decreases by 12% for NP and 5.5% for NA, and area-averaged CO at 500 hPa decreases by 2.4% for NP while there is little change over the NA region. From the mid-troposphere, O3-rich air is clearly seen to be transported toward the surface, but the downward transport of CO-poor air is not discernible due to the high levels of CO in the lower troposphere. Area-averaged O3 is slightly higher at 1000 hPa (3.5 and 1.8% for the NP and NA regions, respectively). There is an increase of CO at 1000 hPa for the NP region (3.3%) relative to the background composite and a~slight decrease in area-averaged CO for the NA region at 1000 hPa (-2.7%).

Mechanisms underlying temperature extremes in Iberia: a Lagrangian perspective

The mechanisms underlying the occurrence of temperature extremes in Iberia are analysed considering a Lagrangian perspective of the atmospheric flow, using 6-hourly ERA-Interim reanalysis data for the years 1979–2012. Daily 2-m minimum temperatures below the 1st percentile and 2-m maximum temperatures above the 99th percentile at each grid point over Iberia are selected separately for winter and summer. Four categories of extremes are analysed using 10-d backward trajectories initialized at the extreme temperature grid points close to the surface: winter cold (WCE) and warm extremes (WWE), and summer cold (SCE) and warm extremes (SWE). Air masses leading to temperature extremes are first transported from the North Atlantic towards Europe for all categories. While there is a clear relation to large-scale circulation patterns in winter, the Iberian thermal low is important in summer. Along the trajectories, air mass characteristics are significantly modified through adiabatic warming (air parcel descent), upper-air radiative cooling and near-surface warming (surface heat fluxes and radiation). High residence times over continental areas, such as over northern-central Europe for WCE and, to a lesser extent, over Iberia for SWE, significantly enhance these air mass modifications. Near-surface diabatic warming is particularly striking for SWE. WCE and SWE are responsible for the most extreme conditions in a given year. For WWE and SCE, strong temperature advection associated with important meridional air mass transports are the main driving mechanisms, accompanied by comparatively minor changes in the air mass properties. These results permit a better understanding of mechanisms leading to temperature extremes in Iberia.

An Ensemble Smoother with Error Estimates

A smoother introduced earlier by van Leeuwen and Evensen is applied to a problem in which real obser vations are used in an area with strongly nonlinear dynamics. The derivation is new , but it resembles an earlier derivation by van Leeuwen and Evensen. Again a Bayesian view is taken in which the prior probability density of the model and the probability density of the obser vations are combined to for m a posterior density . The mean and the covariance of this density give the variance-minimizing model evolution and its errors. The assumption is made that the prior probability density is a Gaussian, leading to a linear update equation. Critical evaluation shows when the assumption is justified. This also sheds light on why Kalman filters, in which the same ap- proximation is made, work for nonlinear models. By reference to the derivation, the impact of model and obser vational biases on the equations is discussed, and it is shown that Bayes’ s for mulation can still be used. A practical advantage of the ensemble smoother is that no adjoint equations have to be integrated and that error estimates are easily obtained. The present application shows that for process studies a smoother will give superior results compared to a filter , not only owing to the smooth transitions at obser vation points, but also because the origin of features can be followed back in time. Also its preference over a strong-constraint method is highlighted. Further more, it is argued that the proposed smoother is more efficient than gradient descent methods or than the representer method when error estimates are taken into account

The role of evaporating showers in the transfer of sting-jet momentum to the surface

The most damaging winds in a severe extratropical cyclone often occur just ahead of the evaporating ends of cloud filaments emanating from the so-called cloud head. These winds are associated with low-level jets (LLJs), sometimes occurring just above the boundary layer. The question then arises as to how the high momentum is transferred to the surface. An opportunity to address this question arose when the severe ‘St Jude's Day’ windstorm travelled across southern England on 28 October 2013. We have carried out a mesoanalysis of a network of 1 min resolution automatic weather stations and high-resolution Doppler radar scans from the sensitive S-band Chilbolton Advanced Meteorological Radar (CAMRa), along with satellite and radar network imagery and numerical weather prediction products. We show that, although the damaging winds occurred in a relatively dry region of the cyclone, there was evidence within the LLJ of abundant precipitation residues from shallow convective clouds that were evaporating in a localized region of descent. We find that pockets of high momentum were transported towards the surface by the few remaining actively precipitating convective clouds within the LLJ and also by precipitation-free convection in the boundary layer that was able to entrain evaporatively cooled air from the LLJ. The boundary-layer convection was organized in along-wind rolls separated by 500 to about 3000 m, the spacing varying according to the vertical extent of the convection. The spacing was greatest where the strongest winds penetrated to the surface. A run with a medium-resolution version of the Weather Research and Forecasting (WRF) model was able to reproduce the properties of the observed LLJ. It confirmed the LLJ to be a sting jet, which descended over the leading edge of a weaker cold-conveyor-belt jet.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Genetics and hyperlipidaemia

Hannah is a 30 year old single mother with two young children. She is of Chinese descent and moved to the UK six years ago; she has a good level of English. Recently her mother suffered a heart attack, which prompted Hannah’s first visit to the general practitioner (GP). Meanwhile Hannah performed a predictive genetic test independently through an online company, which showed an increased risk of developing cardiovascular disease (CVD); she has the ɛ4 variant of the APOE gene. The company has recommended a daily supplement and dietary changes. Blood tests showed raised blood lipids and her GP referred Hannah to a dietitian for lifestyle management. Hannah is very concerned and anxious about her health.

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.