On the Super-Additivity and Estimation Biases of Quantile Contributions

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions

Analogue RF over fibre links for future radar systems

The distribution of analogue RF signals within a high performance radar system is challenging due to the limited space available and the high levels of performance required. This work investigates the gain, linearity and noise performance that can be achieved by an externally modulated direct detection link designed for operation up to 20 GHz using commercially available components. The aim was to assess the suitability of such links for use in future radar systems. Good correlation has been shown between modelled and measured results demonstrating that the performance should satisfy the linearity requirements for many radar applications

Finite size scaling in three-dimensional bootstrap percolation

We consider the problem of bootstrap percolation on a three dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of Cellular Automata defined on the $d$-dimensional lattice $\{1,2,...,L\}^d$ in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability $p$, occupied sites remain occupied for ever, while empty sites are occupied by a particle if at least $\ell$ among their $2d$ nearest neighbor sites are occupied. When $d$ is fixed, the most interesting case is the one $\ell=d$: this is a sort of threshold, in the sense that the critical probability $p_c$ for the dynamics on the infinite lattice ${\Bbb Z}^d$ switches from zero to one when this limit is crossed. Finite size effects in the three-dimensional case are already known in the cases $\ell\le 2$: in this paper we discuss the case $\ell=3$ and we show that the finite size scaling function for this problem is of the form $f(L)={\mathrm{const}}/\ln\ln L$. We prove a conjecture proposed by A.C.D. van Enter.Comment: 18 pages, LaTeX file, no figur

Cosmology and the S-matrix

We study conditions for the existence of asymptotic observables in cosmology. With the exception of de Sitter space, the thermal properties of accelerating universes permit arbitrarily long observations, and guarantee the production of accessible states of arbitrarily large entropy. This suggests that some asymptotic observables may exist, despite the presence of an event horizon. Comparison with decelerating universes shows surprising similarities: Neither type suffers from the limitations encountered in de Sitter space, such as thermalization and boundedness of entropy. However, we argue that no realistic cosmology permits the global observations associated with an S-matrix.Comment: 16 pages, 5 figures; v2: minor editin

Scalable visualisation methods for modern Generalized Additive Models

In the last two decades the growth of computational resources has made it possible to handle Generalized Additive Models (GAMs) that formerly were too costly for serious applications. However, the growth in model complexity has not been matched by improved visualisations for model development and results presentation. Motivated by an industrial application in electricity load forecasting, we identify the areas where the lack of modern visualisation tools for GAMs is particularly severe, and we address the shortcomings of existing methods by proposing a set of visual tools that a) are fast enough for interactive use, b) exploit the additive structure of GAMs, c) scale to large data sets and d) can be used in conjunction with a wide range of response distributions. All the new visual methods proposed in this work are implemented by the mgcViz R package, which can be found on the Comprehensive R Archive Network

Weather-Based Crop Insurance Contracts for African Countries

Weather constitutes the major source for production risk in agriculture. Weather index can be used construct crop insurance that demand less information and can avoid moral hazard and adverse selection problems. Based on mean-variance model, theoretical results on the optimal insurance coverage and its impact from risk preference, basis risk, and premium loading are derived, which are quite consistent to the empirical results from the expected utility model. Using South Africa corn data, we investigate growers' demand and efficiency of alternative hypothetical weather index crop insurance programs. In contrast to previous work that suggests that a single-variable weather index suffices to develop an insurance contract, this study shows that the insured grower achieves a higher utility from multivariate weather indices. The most important single weather index we found in the study area was GDD, and the combination of rainfall and either temperature or GDD outperformed the single variable indices by a large margin. Depending on the growers risk preference, s/he may choose to buy o r offer such insurance for sale if the price is not actuarially fair. The risk protection value of weather-indexed-insurance follows the predictive power of the index on yield in general, though not exactly.Risk and Uncertainty, C51, C61, G22, Q14,