Random division of an interval

The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily

Prevalence of childhood disability and the characteristics and circumstances of disabled children in the UK : secondary analysis of the Family Resources Survey

Background: Robust data on the prevalence of childhood disability and the circumstances and characteristics of disabled children is crucial to understanding the relationship between impairment and social disadvantage. It is also crucial for public policy development aimed at reducing the prevalence of childhood disability and providing appropriate and timely service provision. This paper reports prevalence rates for childhood disability in the United Kingdom (UK) and describes the social and household circumstances of disabled children, comparing these where appropriate to those of non-disabled children. Methods: Data were generated from secondary analysis of the Family Resources Survey, a national UK cross-sectional survey, (2004/5) which had data on 16,012 children aged 0-18 years. Children were defined as disabled if they met the Disability Discrimination Act (DDA) definition (1995 and 2005). Frequency distributions and cross-tabulations were run to establish prevalence estimates, and describe the circumstances of disabled children. To establish the association between individual social and material factors and childhood disability when other factors were controlled for, logistic regression models were fitted on the dependent variable 'DDA defined disability'. Results: 7.3% (CI 6.9, 7.7) of UK children were reported by as disabled according to the DDA definition. Patterns of disability differed between sexes with boys having a higher rate overall and more likely than girls to experience difficulties with physical coordination; memory, concentration and learning; communication. Disabled children lived in different personal situations from their non-disabled counterparts, and were more likely to live with low-income, deprivation, debt and poor housing. This was particularly the case for disabled children from black/minority ethnic/ mixed parentage groups and lone-parent households. Childhood disability was associated with lone parenthood and parental disability and these associations persisted when social disadvantage was controlled for. Conclusion: These analyses suggest that UK disabled children experience higher levels of poverty and personal and social disadvantage than other children. Further research is required to establish accurate prevalence estimates of childhood disability among different black and minority ethnic groups and to understand the associations between childhood disability and lone parenthood and the higher rates of sibling and parental disability in households with disabled children

Automatic Mapping of Discontinuity Persistence on Rock Masses Using 3D Point Clouds

Finding new ways to quantify discontinuity persistence values in rock masses in an automatic or semi-automatic manner is a considerable challenge, as an alternative to the use of traditional methods based on measuring patches or traces with tapes. Remote sensing techniques potentially provide new ways of analysing visible data from the rock mass. This work presents a methodology for the automatic mapping of discontinuity persistence on rock masses, using 3D point clouds. The method proposed herein starts by clustering points that belong to patches of a given discontinuity. Coplanar clusters are then merged into a single group of points. Persistence is measured in the directions of the dip and strike for each coplanar set of points, resulting in the extraction of the length of the maximum chord and the area of the convex hull. The proposed approach is implemented in a graphic interface with open source software. Three case studies are utilized to illustrate the methodology: (1) small-scale laboratory setup consisting of a regular distribution of cubes with similar dimensions, (2) more complex geometry consisting of a real rock mass surface in an excavated cavern and (3) slope with persistent sub-vertical discontinuities. Results presented good agreement with field measurements, validating the methodology. Complexities and difficulties related to the method (e.g. natural discontinuity waviness) are reported and discussed. An assessment on the applicability of the method to the 3D point cloud is also presented. Utilization of remote sensing data for a more objective characterization of the persistence of planar discontinuities affecting rock masses is highlighted herein