Retrieval of mesospheric electron densities using an optimal estimation inverse method

We present a new method to determine mesospheric electron densities from partially reflected medium frequency radar pulses. The technique uses an optimal estimation inverse method and retrieves both an electron density profile and a gradient electron density profile. As well as accounting for the absorption of the two magnetoionic modes formed by ionospheric birefringence of each radar pulse, the forward model of the retrieval parameterises possible Fresnel scatter of each mode by fine electronic structure, phase changes of each mode due to Faraday rotation and the dependence of the amplitudes of the backscattered modes upon pulse width. Validation results indicate that known profiles can be retrieved and that χ2 tests upon retrieval parameters satisfy validity criteria. Application to measurements shows that retrieved electron density profiles are consistent with accepted ideas about seasonal variability of electron densities and their dependence upon nitric oxide production and transport.

On variational data assimilation in continuous time

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalization of what is known as weakly constrained four-dimensional variational assimilation (4D-Var) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two-point boundary value problem. For imperfect models, the trade-off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. This trade-off turns out to be trivial if the model is perfect. However, even in this situation, allowing for minute deviations from the perfect model is shown to have positive effects, namely to regularize the problem. The presented formalism is dynamical in character. No statistical assumptions on dynamical or observational noise are imposed.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Reframing 'crisis' in fair trade coffee production: trajectories of agrarian change in Nicaragua

A focus on crisis provides a methodological window to understand how agrarian change shapes producer engagement in fair trade. This orientation challenges a seperation between the market and development, situating fair trade within global processes that incorporate agrarian histories of social change and conflict. Reframing crisis as a condition of agrarian life, rather than emphasizing its cyclical manifestation within the global economy, reveals how market-driven development encompasses the material conditions of peoples' existence in ambiguous and contradictory ways. Drawing on the case of coffee production in Nicaragua, experiences of crisis demonstrate that greater attention needs to be paid to the socioeconomic and political dimensions of development within regional commodity assemblages to address entrenched power relations and unequal access to land and resources. This questions moral certainties when examining the paradox of working in and against the market, and suggests that a better understanding of specific trajectories of development could improve fair trade's objective of enhancing producer livelihoods.

Optimal sting use in the feeding behavior of the scorpion Hadrurus spadix

Since venom is costly to produce and stinging is not obligatory in prey capture for scorpions, the need to optimize use of resources suggests that venom should be reserved for prey that cannot otherwise be overpowered, (i.e., larger and/or more active prey). In accordance with these predictions, sting use by Hadrurus spadix Stahnke 1940 increased with prey size, reaching 100% once prey items were longer than the scorpion’s pedipalp patella length, and with prey activity, which we manipulated by varying prey temperature. Surprisingly, the scorpions were slower to capture less active (cooler) prey than those that exhibited higher rates of activity. We suggest this is because prey are located by vibrations in the substrate, with less active prey producing fewer vibrations. Keywords: Optimal foraging, venom, pectines

Optimal tax theory and the taxation of housing in the US and the UK

First, we survey recent research in the application of optimal tax theory to housing. This work suggests that the under-taxation of housing for owner occupation distorts investment so that owner occupiers are encouraged to over-invest in housing. Simulations of the US economy suggest that this is true there. But, the theoretical work excludes consideration of land and the simulations exclude consideration of taxes other than income taxes. These exclusions are important for the US and UK economies. In the US, the property tax is relatively high. We argue that excluding the property tax is wrong, so that, when the property tax is taken into account, owner occupied housing is not undertaxed in the US. In the UK, property taxes are relatively low but the cost of land has been increasing in real terms for forty years as a result of a policy of constraining land for development. The price of land for housing is now higher than elsewhere. Effectively, an implicit tax is paid by first time buyers which has reduced housing investment. When land is taken into account over-investment in housing is not encouraged in the UK either.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Optimal beamforming in MIMO systems with HPA nonlinearity

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance.

Optimal frame length for keeping normalized goodput with lowest requirement on BER

This paper presents an adaptive frame length mechanism based on a cross-layer analysis of intrinsic relations between the MAC frame length, bit error rate (BER) of the wireless link and normalized goodput. The proposed mechanism selects the optimal frame length that keeps the service normalized goodput at required levels while satisfying the lowest requirement on the BER, thus increasing the transmission reliability. Numerical results are provided and show that an optimal frame length satisfying the lowest BER requirement does indeed exist. The performance of BER requirement as a function of the MAC frame length is evaluated and compared for transmission scenarios with and without automatic repeat request (ARQ). Furthermore, issues related to the MAC overhead length are also discussed to illuminate the functionality and performance of the proposed mechanism.