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.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Aligning asset allocation and real estate investment: some lessons from the last cycle

Asset allocation is concerned with the development of multi--‐asset portfolio strategies that are likely to meet an investor’s objectives based on the interaction of expected returns, risk, correlation and implementation from a range of distinct asset classes or beta sources. Challenges associated with the discipline are often particularly significant in private markets. Specifically, composition differences between the ‘index’ or ‘benchmark’ universe and the investible universe mean that there can often be substantial and meaningful deviations between the investment characteristics implied in asset allocation decisions and those delivered by investment teams. For example, while allocation decisions are often based on relatively low--‐risk diversified real estate ‘equity’ exposure, implementation decisions frequently include exposure to higher risk forms of the asset class as well as investments in debt based instruments. These differences can have a meaningful impact on the contribution of the asset class to the overall portfolio and, therefore, lead to a potential misalignment between asset allocation decisions and implementation. Despite this, the key conclusion from this paper is not that real estate investors should become slaves to a narrowly defined mandate based on IPD / NCREIF or other forms of benchmark replication. The discussion suggests that such an approach would likely lead to the underutilization of real estate in multi--‐asset portfolio strategies. Instead, it is that to achieve asset allocation alignment, real estate exposure should be divided into multiple pools representing distinct forms of the asset class. In addition, the paper suggests that associated investment guidelines and processes should be collaborative and reflect the portfolio wide asset allocation objectives of each pool. Further, where appropriate they should specifically target potential for ‘additional’ beta or, more marginally, ‘alpha’.

What limits insect fecundity? Body size- and temperature-dependent egg maturation and oviposition in a butterfly

1. Large female insects usually have high potential fecundity. Therefore selection should favour an increase in body size given that these females get opportunities to realize their potential advantage by maturing and laying more eggs. However, ectotherm physiology is strongly temperature-dependent, and activities are carried out sufficiently only within certain temperature ranges. Thus it remains unclear if the fecundity advantage of a large size is fully realized in natural environments, where thermal conditions are limiting. 2. Insect fecundity might be limited by temperature at two levels; first eggs need to mature, and then the female needs time for strategic ovipositing of the egg. Since a female cannot foresee the number of oviposition opportunities that she will encounter on a given day, the optimal rate of egg maturation will be governed by trade-offs associated with egg- and time-limited oviposition. As females of different sizes will have different amounts of body reserves, size-dependent allocation trade-offs between the mother’s condition and her egg production might be expected. 3. In the temperate butterfly Pararge aegeria , the time and temperature dependence of oviposition and egg maturation, and the interrelatedness of these two processes were investigated in a series of laboratory experiments, allowing a decoupling of the time budgets for the respective processes. 4. The results show that realized fecundity of this species can be limited by both the temperature dependence of egg maturation and oviposition under certain thermal regimes. Furthermore, rates of oviposition and egg maturation seemed to have regulatory effects upon each other. Early reproductive output was correlated with short life span, indicating a cost of reproduction. Finally, large females matured more eggs than small females when deprived of oviposition opportunities. Thus, the optimal allocation of resources to egg production seems dependent on female size. 5. This study highlights the complexity of processes underlying rates of egg maturation and oviposition in ectotherms under natural conditions. We further discuss the importance of temperature variation for egg- vs. time-limited fecundity and the consequences for the evolution of female body size in insects.

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.

The potential inefficiency of using marketing margins in applied commodity price analysis, forecasting and risk management

This paper examines the implications of using marketing margins in applied commodity price analysis. The marketing-margin concept has a long and distinguished history, but it has caused considerable controversy. This is particularly the case in the context of analyzing the distribution of research gains in multi-stage production systems. We derive optimal tax schemes for raising revenues to finance research and promotion in a downstream market, derive the rules for efficient allocation of the funds, and compare the rules with an without the marketing-margin assumption. Applying the methodology to quarterly time series on the Australian beef-cattle sector and, with several caveats, we conclude that, during the period 1978:2 - 1988:4, the Australian Meat and Livestock Corporation optimally allocated research resources.

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