The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

'A load too heavy': Critical reflections on the child labor problem in Africa's small-scale mining sector

This paper provides an extended analysis of the child labor problem in the artisanal and small-scale mining (ASM) sector, focusing specifically on the situation in sub-Saharan Africa. In recent years, the issue of child labor in ASM has garnered significant attention from the International Labor Organization (ILO), which has been particularly active in raising public awareness of the problem; and, has proceeded to implement policies and collaborative project work aimed at Curtailing children's participation in ASM activities in a number of African countries. The analysis concludes with a critical appraisal of an ILO project recently launched in the Talensi-Nabdam District in the Upper East Region of Ghana, which sheds light on how the child labor problem is being tackled in practice in ASM communities in sub-Saharan Africa. (c) 2008 Elsevier Ltd. All rights reserved.

An old problem revisited - and solved: Upton and Dalton's linear production response: A note

This note presents a robust method for estimating response surfaces that consist of linear response regimes and a linear plateau. The linear response-and-plateau model has fascinated production scientists since von Liebig (1855) and, as Upton and Dalton indicated, some years ago in this Journal, the response-and-plateau model seems to fit the data in many empirical studies. The estimation algorithm evolves from Bayesian implementation of a switching-regression (finite mixtures) model and demonstrates routine application of Gibbs sampling and data augmentation-techniques that are now in widespread application in other disciplines.

Use of airborne remote sensing to detect riverside Brassica rapa to aid in risk assessment of transgenic crops

High resolution descriptions of plant distribution have utility for many ecological applications but are especially useful for predictive modeling of gene flow from transgenic crops. Difficulty lies in the extrapolation errors that occur when limited ground survey data are scaled up to the landscape or national level. This problem is epitomized by the wide confidence limits generated in a previous attempt to describe the national abundance of riverside Brassica rapa (a wild relative of cultivated rapeseed) across the United Kingdom. Here, we assess the value of airborne remote sensing to locate B. rapa over large areas and so reduce the need for extrapolation. We describe results from flights over the river Nene in England acquired using Airborne Thematic Mapper (ATM) and Compact Airborne Spectrographic Imager (CASI) imagery, together with ground truth data. It proved possible to detect 97% of flowering B. rapa on the basis of spectral profiles. This included all stands of plants that occupied >2m square (>5 plants), which were detected using single-pixel classification. It also included very small populations (<5 flowering plants, 1-2m square) that generated mixed pixels, which were detected using spectral unmixing. The high detection accuracy for flowering B. rapa was coupled with a rather large false positive rate (43%). The latter could be reduced by using the image detections to target fieldwork to confirm species identity, or by acquiring additional remote sensing data such as laser altimetry or multitemporal imagery.

The extrapolation problem and how population modeling can help

We argue that population modeling can add value to ecological risk assessment by reducing uncertainty when extrapolating from ecotoxicological observations to relevant ecological effects. We review other methods of extrapolation, ranging from application factors to species sensitivity distributions to suborganismal (biomarker and "-omics'') responses to quantitative structure activity relationships and model ecosystems, drawing attention to the limitations of each. We suggest a simple classification of population models and critically examine each model in an extrapolation context. We conclude that population models have the potential for adding value to ecological risk assessment by incorporating better understanding of the links between individual responses and population size and structure and by incorporating greater levels of ecological complexity. A number of issues, however, need to be addressed before such models are likely to become more widely used. In a science context, these involve challenges in parameterization, questions about appropriate levels of complexity, issues concerning how specific or general the models need to be, and the extent to which interactions through competition and trophic relationships can be easily incorporated.

Problems in the coupling of eye and hand in the sequential movements of children with developmental coordination disorder

Background: Shifting gaze and attention ahead of the hand is a natural component in the performance of skilled manual actions. Very few studies have examined the precise co-ordination between the eye and hand in children with Developmental Coordination Disorder (DCD). Methods This study directly assessed the maturity of eye-hand co-ordination in children with DCD. A double-step pointing task was used to investigate the coupling of the eye and hand in 7-year-old children with and without DCD. Sequential targets were presented on a computer screen, and eye and hand movements were recorded simultaneously. Results There were no differences between typically developing (TD) and DCD groups when completing fast single-target tasks. There were very few differences in the completion of the first movement in the double-step tasks, but differences did occur during the second sequential movement. One factor appeared to be the propensity for the DCD children to delay their hand movement until some period after the eye had landed on the target. This resulted in a marked increase in eye-hand lead during the second movement, disrupting the close coupling and leading to a slower and less accurate hand movement among children with DCD. Conclusions In contrast to skilled adults, both groups of children preferred to foveate the target prior to initiating a hand movement if time allowed. The TD children, however, were more able to reduce this foveation period and shift towards a feedforward mode of control for hand movements. The children with DCD persevered with a look-then-move strategy, which led to an increase in error. For the group of DCD children in this study, there was no evidence of a problem in speed or accuracy of simple movements, but there was a difficulty in concatenating the sequential shifts of gaze and hand required for the completion of everyday tasks or typical assessment items.

The role of schizotypy and creativity in a group problem-solving task

The well-studied link between psychotic traits and creativity is a subject of much debate. The present study investigated the extent to which schizotypic personality traits - as measured by O-LIFE (Oxford-Liverpool Inventory of Feelings and Experiences) - equip healthy individuals to engage as groups in everyday tasks. From a sample of 69 students, eight groups of four participants - comprised of high, medium, or low-schizotypy individuals - were assembled to work as a team to complete a creative problem-solving task. Predictably, high scorers on the O-LIFE formulated a greater number of strategies to solve the task, indicative of creative divergent thinking. However, for task success (as measured by time taken to complete the problem) an inverted U shaped pattern emerged, whereby high and low-schizotypy groups were consistently faster than medium schizotypy groups. Intriguing data emerged concerning leadership within the groups, and other tangential findings relating to anxiety, competition and motivation were explored. These findings challenge the traditional cliche that psychotic personality traits are linearly related to creative performance, and suggest that the nature of the problem determines which thinking styles are optimally equipped to solve it. (C) 2009 Elsevier Ltd. All rights reserved.