Indigenous students transitioning to school : responses to pre-foundational mathematics

Australian Indigenous students' mathematics performance continues to be below that of non-Indigenous students. This occurs from the early years of school, due largely to knowledge and social differences on entry to formal schooling. This paper reports on a mathematics research project conducted in one Aboriginal community school in New South Wales, Australia. The project aimed to identify and explain the ways that young Australian Indigenous students (age 2-4 years) learn number language and processes, specifically attribute language, sorting, 1-1 correspondence and, counting. The project adopted a mixed methods approach. That is, the methodology was decolonising (Smith 1999) in that it collaborated with and gave benefit back to the Indigenous community and school being researched. It was qualitative and interpretative (Burns 2000) and incorporated an action-research teaching-experiment approach where and teachers collaborated with the researchers to try new teaching methods. This paper draws on data pertaining to students' response to diagnostic interview questions, the pre- and post-test results of the interview and photographic evidence as observations during mathematics learning time. Participants referred to in this paper include one female principal (N = 1), and the transition class of students' pre- (N = 6) and post-test (N = 3) results of the pre-foundational processes (also referred to as attributes). The results were encouraging with improvements in colour (34%), patterns (33%); capacity (38%). As a result of this project, our epistemology regarding the importance of finding out about students' pre-foundational knowledge and understandings and providing a culturally appropriate learning environment with resources has been built upon.

Tubule detection in testis images using boundary weighting and circular shortest path

In studies of germ cell transplantation, measureing tubule diameters and counting cells from different populations using antibodies as markers are very important. Manual measurement of tubule sizes and cell counts is a tedious and sanity grinding work. In this paper, we propose a new boundary weighting based tubule detection method. We first enhance the linear features of the input image and detect the approximate centers of tubules. Next, a boundary weighting transform is applied to the polar transformed image of each tubule region and a circular shortest path is used for the boundary detection. Then, ellipse fitting is carried out for tubule selection and measurement. The algorithm has been tested on a dataset consisting of 20 images, each having about 20 tubules. Experiments show that the detection results of our algorithm are very close to the results obtained manually. © 2013 IEEE.

Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

Quantification of the total neuronal structure of the fear conditioning circuit of the lateral amygdala of the rat

During Pavlovian auditory fear conditioning a previously neutral auditory stimulus (CS) gains emotional significance through pairing with a noxious unconditioned stimulus (US). These associations are believed to be formed by way of plasticity at auditory input synapses on principal neurons in the lateral nucleus of the amygdala (LA). In order to begin to understand how fear memories are stored and processed by synaptic changes in the LA, we have quantified both the entire neural number and the sub-cellular structure of LA principal neurons.We first used stereological cell counting methods on Gimsa or GABA immunostained rat brain. We identified 60,322+/-1408 neurons in the LA unilaterally (n=7). Of these 16,917+/-471 were GABA positive. The intercalated nuclei were excluded from the counts and thus GABA cells are believed to represent GABAergic interneurons. The sub-nuclei of the LA were also independently counted. We then quantified the morphometric properties of in vitro electrophysiologically identified principal neurons of the LA, corrected for shrinkage in xyz planes. The total dendritic length was 9.97+/-2.57mm, with 21+/-4 nodes (n=6). Dendritic spine density was 0.19+/-0.03 spines/um (n=6). Intra-LA axon collaterals had a bouton density of 0.1+/-0.02 boutons/um (n=5). These data begin to reveal the finite cellular and sub-cellular processing capacity of the lateral amygdala, and should facilitate efforts to understand mechanisms of plasticity in LA.

Exposure to bioaerosols in the school environment in Brisbane, Australia

Introduction: Exposure to bioaerosols in indoor environments has been linked to various adverse health effects, such as airway disorders and upper respiratory tract symptoms. The aim of this study was to assess exposure to bioaerosols in the school environment in Brisbane, Australia. Methods: Culturable fungi and endotoxin measurements were conducted in six schools between October 2010 and May 2011. Culturable fungi (2 indoor air and 1-2 outdoor air samples per school) were assessed using a Biotest RCS High Flow Air Sampler, with a flow rate of either 50L/min or 20L/min. A rose pengar agar was used for recovery, which was incubated prior to counting and partial identification. Endotoxins were sampled (8h, 2L/min) using SKC glass fibre filters (4 indoor air samples per school) and analysed using an endpoint chromogenic LAL assay. Results: The arithmetic mean for fungi concentration in indoor and outdoor air was 710 cfu/m3(125- 1900 cfu/m3) and 524 cfu/m3 (140-1250 cfu/m3), respectively. The most frequently isolated fungal genus from the outdoor air was Cladosporium (over 40 %), followed by isolated Penicillium (21%) and Aspergillus (12%). The percent of Penicillium, Cladosporium and Aspergillus in indoor air samples was 32%, 32% and 8%, respectively. The aritmetic mean of endotoxin concentration was 0.59 EU/m3 (0-2,2 EU/m3). Discussion: The results of the current study are in agreement with previously reported studies, in that airborne fungi and endotoxin concentrations varied extensively, and were mostly dependent on climatic conditions. In addition, the indoor air mycoflora largely reflected the fungal flora present in the outdoor air, with Cladosporium being the most common in both outdoor and indoor (with Penicillium) air. In indoor air, unusually high endotoxin levels, over 1 EU/m3, were detected at 2 schools. Although these schools were not affected by the recent Brisbane floods, persistent rain prior to and during the study perios could explain the results.

Large scale monitoring of crowds and building utilisation: A new database and distributed approach

Public buildings and large infrastructure are typically monitored by tens or hundreds of cameras, all capturing different physical spaces and observing different types of interactions and behaviours. However to date, in large part due to limited data availability, crowd monitoring and operational surveillance research has focused on single camera scenarios which are not representative of real-world applications. In this paper we present a new, publicly available database for large scale crowd surveillance. Footage from 12 cameras for a full work day covering the main floor of a busy university campus building, including an internal and external foyer, elevator foyers, and the main external approach are provided; alongside annotation for crowd counting (single or multi-camera) and pedestrian flow analysis for 10 and 6 sites respectively. We describe how this large dataset can be used to perform distributed monitoring of building utilisation, and demonstrate the potential of this dataset to understand and learn the relationship between different areas of a building.

Estimating the under-reporting of road crash injuries to police using multiple linked data collections

The reliance on police data for the counting of road crash injuries can be problematic, as it is well known that not all road crash injuries are reported to police which under-estimates the overall burden of road crash injuries. The aim of this study was to use multiple linked data sources to estimate the extent of under-reporting of road crash injuries to police in the Australian state of Queensland. Data from the Queensland Road Crash Database (QRCD), the Queensland Hospital Admitted Patients Data Collection (QHAPDC), Emergency Department Information System (EDIS), and the Queensland Injury Surveillance Unit (QISU) for the year 2009 were linked. The completeness of road crash cases reported to police was examined via discordance rates between the police data (QRCD) and the hospital data collections. In addition, the potential bias of this discordance (under-reporting) was assessed based on gender, age, road user group, and regional location. Results showed that the level of under-reporting varied depending on the data set with which the police data was compared. When all hospital data collections are examined together the estimated population of road crash injuries was approximately 28,000, with around two-thirds not linking to any record in the police data. The results also showed that the under-reporting was more likely for motorcyclists, cyclists, males, young people, and injuries occurring in Remote and Inner Regional areas. These results have important implications for road safety research and policy in terms of: prioritising funding and resources; targeting road safety interventions into areas of higher risk; and estimating the burden of road crash injuries.

Radon-222 activity flux measurement using activated charcoal canisters: Revisiting the methodology

The measurement of radon ((222)Rn) activity flux using activated charcoal canisters was examined to investigate the distribution of the adsorbed (222)Rn in the charcoal bed and the relationship between (222)Rn activity flux and exposure time. The activity flux of (222)Rn from five sources of varying strengths was measured for exposure times of one, two, three, five, seven, 10, and 14 days. The distribution of the adsorbed (222)Rn in the charcoal bed was obtained by dividing the bed into six layers and counting each layer separately after the exposure. (222)Rn activity decreased in the layers that were away from the exposed surface. Nevertheless, the results demonstrated that only a small correction might be required in the actual application of charcoal canisters for activity flux measurement, where calibration standards were often prepared by the uniform mixing of radium ((226)Ra) in the matrix. This was because the diffusion of (222)Rn in the charcoal bed and the detection efficiency as a function of the charcoal depth tended to counterbalance each other. The influence of exposure time on the measured (222)Rn activity flux was observed in two situations of the canister exposure layout: (a) canister sealed to an open bed of the material and (b) canister sealed over a jar containing the material. The measured (222)Rn activity flux decreased as the exposure time increased. The change in the former situation was significant with an exponential decrease as the exposure time increased. In the latter case, lesser reduction was noticed in the observed activity flux with respect to exposure time. This reduction might have been related to certain factors, such as absorption site saturation or the back diffusion of (222)Rn gas occurring at the canister-soil interface.

Estimates on the coverage of parameter space using populations of models

In this paper we provide estimates for the coverage of parameter space when using Latin Hypercube Sampling, which forms the basis of building so-called populations of models. The estimates are obtained using combinatorial counting arguments to determine how many trials, k, are needed in order to obtain specified parameter space coverage for a given value of the discretisation size n. In the case of two dimensions, we show that if the ratio (Ø) of trials to discretisation size is greater than 1, then as n becomes moderately large the fractional coverage behaves as 1-exp-ø. We compare these estimates with simulation results obtained from an implementation of Latin Hypercube Sampling using MATLAB.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

Adjusting body cell mass for size in women of differing nutritional status

Background: Body cell mass (BCM) may be estimated in clinical practice to assess functional nutritional status, eg, in patients with anorexia nervosa. Interpretation of the data, especially in younger patients who are still growing, requires appropriate adjustment for size. Previous investigations of this general issue have addressed chemical rather than functional components of body composition and have not considered patients at the extremes of nutritional status, in whom the ability to make longitudinal comparisons is of particular importance. Objective: Our objective was to determine the power by which height should be raised to adjust BCM for height in women of differing nutritional status. Design: BCM was estimated by K-40 counting in 58 healthy women, 33 healthy female adolescents, and 75 female adolescents with anorexia nervosa. The relation between BCM and height was explored in each group by using log-log regression analysis. Results: The powers by which height should be raised to adjust BCM,A,ere 1.73. 1.73, and 2.07 in the women, healthy female adolescents, and anorexic female adolescents, respectively. A simplified version of the index, BCM/height(2), was appropriate for all 3 categories and was negligibly correlated with height. Conclusions: In normal-weight women, the relation between height and BCM is consistent with that reported previously between height and fat-free mass. Although the consistency of the relation between BCM and fat-free mass decreases with increasing weight loss, the relation between height and BCM is not significantly different between normal-weight and underweight women. The index BCM/height(2) is easy to calculate and applicable to both healthy and underweight women. This information may be helpful in interpreting body-composition data in clinical practice.

Value of total body potassium in assessing the nutritional status of children with end-stage liver disease

Malnutrition is a common problem in children with end-stage liver disease (ESLD), and accurate assessment of nutritional status is essential in managing these children. In a retrospective study, we compared nutritional assessment by anthropometry with that by body composition. We analyzed all consecutive measurements of total body potassium (TBK, n = 186) of children less than 3 years old with ESLD awaiting transplantation found in our database. The TBK values obtained by whole body counting of 40K were compared with reference TRK values of healthy children. The prevalence of malnutrition, as assessed by weight (weight Z score < -2) was 28%, which was significantly lower (chi-square test, p < 0.0001) than the prevalence of malnutrition (76%) assessed by TBK (< 90% of expected TRK for age). These results demonstrated that body weight underestimated the nutritional deficit and stressed the importance of measuring body composition as part of assessing nutritional status of children with ESLD.

Nutritional status of children with cystic fibrosis measured by total body potassium as a marker of body cell mass: Lack of sensitivity of anthropometric measures

Objective: To investigate measures aimed at defining the nutritional status of cystic fibrosis (CF) populations, this study compared standard anthropometric measurements and total body potassium (TBK) as indicators of malnutrition. Methods: Height, weight, and TBK measurements of 226 children with CF from Royal Children's Hospital, Brisbane, Australia, were analyzed. Z scores for height for age, weight for age, and weight for height were analyzed by means of the National Centre for Health Statistics reference. TBK was measured by means of whole body counting and compared with predicted TBK for age. Two criteria were evaluated with respect to malnutrition: (1) a z score < -2.0 and (2) a TBK for age <80% of predicted. Results: Males and females with CF had lower mean height-for-age and weight-for-age z scores than the National Centre for Health Statistics reference (P < .01), but mean weight-for-height z score was not significantly different. There were no significant gender differences. According to anthropometry, only 7.5% of this population were underweight and 7.6% were stunted. However, with TBK as an indicator of nutritional status, 29.9% of males and 22.0% of females were malnourished. Conclusion: There are large differences in the percentage of patients with CF identified as malnourished depending on whether anthropometry or body composition data are used as the nutritional indicator. At an individual level, weight-based indicators are not sensitive indicators of suboptimal nutritional status in CF, significantly underestimating the extent of malnutrition. Current recommendations in which anthropometry is used as the indicator of malnutrition in CF should be revised.

Fatigue Laws Via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner's rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson's Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading', Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner's rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.