Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Are the spatial patterns of weeds scale-invariant?

In previous empirical and modelling studies of rare species and weeds, evidence of fractal behaviour has been found. We propose that weeds in modern agricultural systems may be managed close to critical population dynamic thresholds, below which their rates of increase will be negative and where scale-invariance may be expected as a consequence. We collected detailed spatial data on five contrasting species over a period of three years in a primarily arable field. Counts in 20×20 cm contiguous quadrats, 225,000 in 1998 and 84,375 thereafter, could be re-structured into a wide range of larger quadrat sizes. These were analysed using three methods based on correlation sum, incidence and conditional incidence. We found non-trivial scale invariance for species occurring at low mean densities and where they were strongly aggregated. The fact that the scale-invariance was not found for widespread species occurring at higher densities suggests that the scaling in agricultural weed populations may, indeed, be related to critical phenomena.

An ASIFT-based local registration method for satellite imagery

Imagery registration is a fundamental step, which greatly affects later processes in image mosaic, multi-spectral image fusion, digital surface modelling, etc., where the final solution needs blending of pixel information from more than one images. It is highly desired to find a way to identify registration regions among input stereo image pairs with high accuracy, particularly in remote sensing applications in which ground control points (GCPs) are not always available, such as in selecting a landing zone on an outer space planet. In this paper, a framework for localization in image registration is developed. It strengthened the local registration accuracy from two aspects: less reprojection error and better feature point distribution. Affine scale-invariant feature transform (ASIFT) was used for acquiring feature points and correspondences on the input images. Then, a homography matrix was estimated as the transformation model by an improved random sample consensus (IM-RANSAC) algorithm. In order to identify a registration region with a better spatial distribution of feature points, the Euclidean distance between the feature points is applied (named the S criterion). Finally, the parameters of the homography matrix were optimized by the Levenberg–Marquardt (LM) algorithm with selective feature points from the chosen registration region. In the experiment section, the Chang’E-2 satellite remote sensing imagery was used for evaluating the performance of the proposed method. The experiment result demonstrates that the proposed method can automatically locate a specific region with high registration accuracy between input images by achieving lower root mean square error (RMSE) and better distribution of feature points.

Psychometric properties of the parent-infant caregiving touch scale

Recent work in animals suggests that the extent of early tactile stimulation by parents of offspring is an important element in early caregiving. We evaluate the psychometric properties of a new parent-report measure designed to assess frequency of tactile stimulation across multiple caregiving domains in infancy. We describe the full item set of the Parent-Infant Caregiving Touch Scale (PICTS) and, using data from a UK longitudinal Child Health and Development Study, the response frequencies and factor structure and whether it was invariant over two time points in early development (5 and 9 weeks). When their infant was 9 weeks old, 838 mothers responded on the PICTS while a stratified subsample of 268 mothers completed PICTS at an earlier 5 week old assessment (229 responded on both occasions). Three PICTS factors were identified reflecting stroking, holding and affective communication. These were moderately to strongly correlated at each of the two time points of interest and were unrelated to, and therefore distinct from, a traditional measure of maternal sensitivity at 7-months. A wholly stable psychometry over 5 and 9-week assessments was not identified which suggests that behavior profiles differ slightly for younger and older infants. Tests of measurement invariance demonstrated that all three factors are characterized by full configural and metric invariance, as well as a moderate degree of evidence of scalar invariance for the stroking factor. We propose the PICTS as a valuable new measure of important aspects of caregiving in infancy.