Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

A sociocultural analysis of language learning: New forms of literacy practices in a language and culture awareness programme

This paper reports on a sociocultural study conducted in a Catholic primary school in the Australian outback and provides insights into how policy related to Languages Other Than English (LOTE) programmes is implemented in a specific location and interwoven within the literacy practices of children, parents and teachers. A case study that tracked a Year Four student's learning and development during a Language and Culture Awareness Programme is discussed within a discourse of cultural and linguistic practices. Significant aspects of the student's learning related to a phenomenon called multi-tiered scaffolding temporarily disrupted the established literacy practices in the school community. Implications of the research for second-language teaching and learning in Australian primary schools are elaborated.

Cosegregation analysis of natriuretic peptide genes and blood pressure in the spontaneously hypertensive rat

1. The natriuretic peptide precursor A (Nppa) and B (Nppb) genes are candidate genes for hypertension and cardiac hypertrophy in the spontaneously hypertensive rat (SHR). The purpose of the present study was to determine the role of the Nppa and Nppb genes in the development of hypertension in the SHR. 2. A cohort (n = 162) of F2 segregating intercross animals was established between strains of hypertensive SHR and normotensive Wistar-Kyoto rats. Blood pressure and heart weight were measured in each rat at 12-16 weeks of age. Rats were genotyped using 11 informative microsatellite markers, distributed in the vicinity of the Nppa marker on rat chromosome 5 including an Nppb marker. The phenotype values were compared with genotype using the computer package MAP-MAKER 3.0 (Whitehead Institute, Boston, MA, USA) to determine whether there was a link between the genetic variants of the natriuretic peptide family and blood pressure or cardiac hypertrophy. 3. A strong correlation was observed between the Nppa marker and blood pressure. A quantitative trait locus (QTL) for blood pressure on chromosome 5 was identified between the Nppa locus and the D5Mgh15 marker, less than 2 cM from the Nppa locus. The linkage score for the blood pressure QTL on chromosome 5 was 3.8 and the QTL accounted for 43% of the total variance of systolic blood pressure, 54% of diastolic blood pressure and 59% of mean blood pressure. No association was found between the Nppb gene and blood pressure. This is the first report of linkage between the Nppa marker and blood pressure in the rat. There was no correlation between the Nppa or Nppb genes or other markers in this region and either heart weight or left ventricular weight in F2 rats. 4. These findings suggest the existence of a blood pressure-dependent Nppa marker variant or a gene close to Nppa predisposing to spontaneous hypertension in the rat. It provides a strong foundation for further detailed genetic studies in congenic strains, which may help to narrow down the location of this gene and lead to positional cloning.

Cluster analysis of high-dimensional data: A case study

Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.

Survey-gap analysis in expeditionary research: where do we go from here?

Research expeditions into remote areas to collect biological specimens provide vital information for understanding biodiversity. However, major expeditions to little-known areas are expensive and time consuming, time is short, and well-trained people are difficult to find. In addition, processing the collections and obtaining accurate identifications takes time and money. In order to get the maximum return for the investment, we need to determine the location of the collecting expeditions carefully. In this study we used environmental variables and information on existing collecting localities to help determine the sites of future expeditions. Results from other studies were used to aid in the selection of the environmental variables, including variables relating to temperature, rainfall, lithology and distance between sites. A survey gap analysis tool based on 'ED complementarity' was employed to select the sites that would most likely contribute the most new taxa. The tool does not evaluate how well collected a previously visited site survey site might be; however, collecting effort was estimated based on species accumulation curves. We used the number of collections and/or number of species at each collecting site to eliminate those we deemed poorly collected. Plants, birds, and insects from Guyana were examined using the survey gap analysis tool, and sites for future collecting expeditions were determined. The south-east section of Guyana had virtually no collecting information available. It has been inaccessible for many years for political reasons and as a result, eight of the first ten sites selected were in that area. In order to evaluate the remainder of the country, and because there are no immediate plans by the Government of Guyana to open that area to exploration, that section of the country was not included in the remainder of the study. The range of the ED complementarity values dropped sharply after the first ten sites were selected. For plants, the group for which we had the most records, areas selected included several localities in the Pakaraima Mountains, the border with the south-east, and one site in the north-west. For birds, a moderately collected group, the strongest need was in the north-west followed by the east. Insects had the smallest data set and the largest range of ED complementarity values; the results gave strong emphasis to the southern parts of the country, but most of the locations appeared to be equidistant from one another, most likely because of insufficient data. Results demonstrate that the use of a survey gap analysis tool designed to solve a locational problem using continuous environmental data can help maximize our resources for gathering new information on biodiversity. (c) 2005 The Linnean Society of London.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulae for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.

Analysis of line x environment interactions for yield in navy beans. 2. Pattern analysis of lines and environment within years

Seven years of multi-environment yield trials of navy bean (Phaseolus vulgaris L.) grown in Queensland were examined. As is common with plant breeding evaluation trials, test entries and locations varied between years. Grain yield data were analysed for each year using cluster and ordination analyses (pattern analyses). These methods facilitate descriptions of genotype performance across environments and the discrimination among genotypes provided by the environments. The observed trends for genotypic yield performance across environments were partly consistent with agronomic and disease reactions at specific environments and also partly explainable by breeding and selection history. In some cases, similarities in discrimination among environments were related to geographic proximity, in others management practices, and in others similarities occurred between geographically widely separated environments which differed in management practices. One location was identified as having atypical line discrimination. The analysis indicated that the number of test locations was below requirements for adequate representation of line x environment interaction. The pattern analyses methods used were an effective aid in describing the patterns in data for each year and illustrated the variations in adaptive patterns from year to year. The study has implications for assessing the number and location of test sites for plant breeding multi-environment trials, and for the understanding of genetic traits contributing to line x environment interactions.