Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

Bayesian refinement of association signals for 14 loci in 3 common diseases

To further investigate susceptibility loci identified by genome-wide association studies, we genotyped 5,500 SNPs across 14 associated regions in 8,000 samples from a control group and 3 diseases: type 2 diabetes (T2D), coronary artery disease (CAD) and Graves' disease. We defined, using Bayes theorem, credible sets of SNPs that were 95% likely, based on posterior probability, to contain the causal disease-associated SNPs. In 3 of the 14 regions, TCF7L2 (T2D), CTLA4 (Graves' disease) and CDKN2A-CDKN2B (T2D), much of the posterior probability rested on a single SNP, and, in 4 other regions (CDKN2A-CDKN2B (CAD) and CDKAL1, FTO and HHEX (T2D)), the 95% sets were small, thereby excluding most SNPs as potentially causal. Very few SNPs in our credible sets had annotated functions, illustrating the limitations in understanding the mechanisms underlying susceptibility to common diseases. Our results also show the value of more detailed mapping to target sequences for functional studies. © 2012 Nature America, Inc. All rights reserved.

Ankylosing spondylitis in West Africans - evidence for a non-HLA-B27 protective effect

Objective - To determine the prevalence of ankylosing spondylitis in the Fula ethnic group in The Gambia, and relate the disease prevalence to the B27 frequency and subtype distribution of that population. Methods - 215 first degree relatives of 48 B27 positive Fula twin pairs, and 900 adult Fula males were screened for ankylosing spondylitis by clinical and, where appropriate, radiographic means. The B27 prevalence was determined by PCR/sequence specific oligonucleotides on finger prick samples from 100 unrelated Fula, and B27 subtype distribution by SSCP on unrelated B27 positive individuals. This data were then compared with the prevalence of ankylosing spondylitis among B27 positive Caucasians. Results - No case of ankylosing spondylitis was seen. Six per cent of Fula are B27 positive, of which 32% are B*2703 and 68% B*2705. Assuming the penetrance of ankylosing spondylitis in B27 positive Fula is the same as in B27 positive Caucasians, the probability of not observing any cases of ankylosing spondylitis among the Fula examined is remote (P = 6.7 x 10-6). Similarly, the chance of not seeing any cases among those expected to be either B*2705 or B*2703 was small (P = 3.2 x 10-4 for B*2705, and P = 0.02 for B*2703). Conclusions - The risk of developing ankylosing spondylitis in B27 positive Fula is lower than in B27 positive Caucasians. This is not explained by the B27 subtype distribution among Fula, and suggests the presence of some non-B27 protective factor reducing the prevalence of ankylosing spondylitis in this population.

Delay tolerant routing protocols for energy-neutral animal tracking

This paper investigates communication protocols for relaying sensor data from animal tracking applications back to base stations. While Delay Tolerant Networks (DTNs) are well suited to such challenging environments, most existing protocols do not consider the available energy that is particularly important when tracking devices can harvest energy. This limits both the network lifetime and delivery probability in energy-constrained applications to the point when routing performance becomes worse than using no routing at all. Our work shows that substantial improvement in data yields can be achieved through simple yet efficient energy-aware strategies. Conceptually, there is need for balancing the energy spent on sensing, data mulling, and delivery of direct packets to destination. We use empirical traces collected in a flying fox (fruit bat) tracking project and show that simple threshold-based energy-aware strategies yield up to 20% higher delivery rates. Furthermore, these results generalize well for a wide range of operating conditions.

Ratcheting and wear behavior of Australian rail steel: Experimental investigation of material properties and sampling method

To The ratcheting behavior of high-strength rail steel (Australian Standard AS1085.1) is studied in this work for the purpose of predicting wear and damage to the rail surface. Historically, researchers have used circular test coupons obtained from the rail head to conduct cyclic load tests, but according to hardness profile data, considerable variation exists across the rail head section. For example, the induction-hardened rail (AS1085.1) shows high hardness (400-430 HV100) up to four-millimeters into the rail head’s surface, but then drops considerably beyond that. Given that cyclic test coupons five millimeters in diameter at the gauge area are usually taken from the rail sample, there is a high probability that the original surface properties of the rail do not apply across the entire test coupon and, therefore, data representing only average material properties are obtained. In the literature, disks (47 mm in diameter) for a twin-disk rolling contact test machine have been obtained directly from the rail sample and used to validate rolling contact fatigue wear models. The question arises: How accurate are such predictions? In this research paper, the effect of rail sampling position on the ratcheting behavior of AS1085.1 rail steel was investigated using rectangular shaped specimens. Uniaxial stress-controlled tests were conducted with samples obtained at four different depths to observe the ratcheting behaviour of each. Micro-hardness measurements of the test coupons were carried out to obtain a constitutive relationship to predict the effect of depth on the ratcheting behaviour of the rail material. This work ultimately assists the selection of valid material parameters for constitutive models in the study of rail surface ratcheting.

Confronting expectation in grade 4: Tossing two coins

This study focuses on the experiences of 91 Grade 4 students who had been introduced to expectation and variation through trials of tossing a single coin many times. They were then given two coins to toss simultaneously and asked to state their expectation of the chances for the possible outcomes, in a similar manner expressed for a single coin. This paper documents the journey of the students in discovering that generally their initial expectation for two coins was incorrect and that despite variation, a large number of tosses could confirm a new expectation.

Expectation and variation with a virtual die

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the advantage they offer is a familiar context within which to explore much more complex concepts. If the basic chance mechanism of the device is understood, it is possible to enter quickly into an arena of more complex concepts. This is what happened with a two hour activity engaged in by four classes of Grade 6 students in the same school. The activity targeted the concepts of variation and expectation. The teachers held extended discussions with their classes on variation and expectation at the beginning of the activity, with students contributing examples of the two concepts from their own experience. These notions are quite sophisticated for Grade 6, but the underlying concepts describe phenomena that students encounter every day. For example, time varies continuously; sporting results vary from game to game; the maximum temperature varies from day to day. However, there is an expectation about tomorrow’s maximum temperature based on the expert advice from the weather bureau. There may also be an expectation about a sporting result based on the participants’ previous results. It is this juxtaposition that makes life interesting. Variation hence describes the differences we see in phenomena around us. In a scenario displaying variation, expectation describes the effort to characterise or summarise the variation and perhaps make a prediction about the message arising from the scenario. The explicit purpose of the activity described here was to use the familiar scenario of rolling a die to expose these two concepts. Because the students had previously experienced rolling physical dice they knew instinctively about the variation that occurs across many rolls and about the theoretical expectation that each side should “come up” one-sixth of the time. They had observed the instances of the concepts in action, but had not consolidated the underlying terminology to describe it. As the two concepts are so fundamental to understanding statistics, we felt it would be useful to begin building in the familiar environment of rolling a die. Because hand-held dice limit the explorations students can undertake, the classes used the soft-ware TinkerPlots (Konold & Miller, 2011) to simulate rolling a die multiple times.

Whole exome sequencing is an efficient and sensitive method for detection of germline mutations in patients with phaeochromcytomas and paragangliomas

Background Genetic testing is recommended when the probability of a disease-associated germline mutation exceeds 10%. Germline mutations are found in approximately 25% of individuals with phaeochromcytoma (PCC) or paraganglioma (PGL); however, genetic heterogeneity for PCC/PGL means many genes may require sequencing. A phenotype-directed iterative approach may limit costs but may also delay diagnosis, and will not detect mutations in genes not previously associated with PCC/PGL. Objective To assess whether whole exome sequencing (WES) was efficient and sensitive for mutation detection in PCC/PGL. Methods Whole exome sequencing was performed on blinded samples from eleven individuals with PCC/PGL and known mutations. Illumina TruSeq™ (Illumina Inc, San Diego, CA, USA) was used for exome capture of seven samples, and NimbleGen SeqCap EZ v3.0 (Roche NimbleGen Inc, Basel, Switzerland) for five samples (one sample was repeated). Massive parallel sequencing was performed on multiplexed samples. Sequencing data were called using Genome Analysis Toolkit and annotated using annovar. Data were assessed for coding variants in RET, NF1, VHL, SDHD, SDHB, SDHC, SDHA, SDHAF2, KIF1B, TMEM127, EGLN1 and MAX. Target capture of five exome capture platforms was compared. Results Six of seven mutations were detected using Illumina TruSeq™ exome capture. All five mutations were detected using NimbleGen SeqCap EZ v3.0 platform, including the mutation missed using Illumina TruSeq™ capture. Target capture for exons in known PCC/PGL genes differs substantially between platforms. Exome sequencing was inexpensive (<$A800 per sample for reagents) and rapid (results <5 weeks from sample reception). Conclusion Whole exome sequencing is sensitive, rapid and efficient for detection of PCC/PGL germline mutations. However, capture platform selection is critical to maximize sensitivity.

The role of environmental factors in the spatial distribution of Japanese encephalitis in mainland China

Japanese encephalitis (JE) is the most common cause of viral encephalitis and an important public health concern in the Asia-Pacific region, particularly in China where 50% of global cases are notified. To explore the association between environmental factors and human JE cases and identify the high risk areas for JE transmission in China, we used annual notified data on JE cases at the center of administrative township and environmental variables with a pixel resolution of 1 km×1 km from 2005 to 2011 to construct models using ecological niche modeling (ENM) approaches based on maximum entropy. These models were then validated by overlaying reported human JE case localities from 2006 to 2012 onto each prediction map. ENMs had good discriminatory ability with the area under the curve (AUC) of the receiver operating curve (ROC) of 0.82-0.91, and low extrinsic omission rate of 5.44-7.42%. Resulting maps showed JE being presented extensively throughout southwestern and central China, with local spatial variations in probability influenced by minimum temperatures, human population density, mean temperatures, and elevation, with contribution of 17.94%-38.37%, 15.47%-21.82%, 3.86%-21.22%, and 12.05%-16.02%, respectively. Approximately 60% of JE cases occurred in predicted high risk areas, which covered less than 6% of areas in mainland China. Our findings will help inform optimal geographical allocation of the limited resources available for JE prevention and control in China, find hidden high-risk areas, and increase the effectiveness of public health interventions against JE transmission.

Limited utility of exercise stress testing in the evaluation of suspected acute coronary syndrome in patients aged less than 40 years with intermediate risk features

Objective National guidelines for management of intermediate risk patients with suspected acute coronary syndrome, in whom AMI has been excluded, advocate provocative testing to final risk stratify these patients into low risk (negative testing) or high risk (positive testing suggestive of unstable angina). Adults less than 40 years have a low pretest probability of acute coronary syndrome. The utility of exercise stress testing in young adults with chest pain suspected of acute coronary syndrome who have National Heart Foundation intermediate risk features was evaluated Methods A retrospective analysis of exercise stress testing performed on patients less than 40 years was evaluated. Patients were enrolled on a chest pain pathway and had negative serial ECGs and cardiac biomarkers before exercise stress testing to rule-out acute coronary syndrome. Chart review was completed on patients with positive stress tests. Results The 3987 patients with suspected intermediate risk acute coronary syndrome underwent exercise stress testing. One thousand and twenty-seven (25.8%) were aged less than 40 years (age 33.3 ± 4.8 years). Four of these 1027 patients had a positive exercise stress test (0.4% incidence of positive exercise stress testing). Of those, three patients had subsequent non-invasive functional testing that yielded a negative result. One patient declined further investigations. Assuming this was a true positive exercise stress test, the incidence of true positive exercise stress testing would have been 0.097% (95% confidence interval: 0.079–0.115%) (one of 1027 patients). Conclusions Routine exercise stress testing has limited value in the risk stratification of adults less than 40 years with suspected intermediate risk of acute coronary syndrome

Optimizing the quantum dot: Plasmon interaction in a nano gap waveguide

Spontaneous emission (SE) of a Quantum emitter depends mainly on the transmission strength between the upper and lower energy levels as well as the Local Density of States (LDOS)[1]. When a QD is placed in near a plasmon waveguide, LDOS of the QD is increased due to addition of the non-radiative decay and a plasmonic decay channel to free space emission[2-4]. The slow velocity and dramatic concentration of the electric field of the plasmon can capture majority of the SE into guided plasmon mode (Гpl ). This paper focused on studying the effect of waveguide height on the efficiency of coupling QD decay into plasmon mode using a numerical model based on finite elemental method (FEM). Symmetric gap waveguide considered in this paper support single mode and QD as a dipole emitter. 2D simulation models are done to find normalized Гpl and 3D models are used to find probability of SE decaying into plasmon mode ( β) including all three decay channels. It is found out that changing gap height can increase QD-plasmon coupling, by up to a factor of 5 and optimally placed QD up to a factor of 8. To make the paper more realistic we briefly studied the effect of sharpness of the waveguide edge on SE emission into guided plasmon mode. Preliminary nano gap waveguide fabrication and testing are already underway. Authors expect to compare the theoretical results with experimental outcomes in the future

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

Methods for constructing uncertainty intervals for queries of Bayesian nets

In this paper the issue of finding uncertainty intervals for queries in a Bayesian Network is reconsidered. The investigation focuses on Bayesian Nets with discrete nodes and finite populations. An earlier asymptotic approach is compared with a simulation-based approach, together with further alternatives, one based on a single sample of the Bayesian Net of a particular finite population size, and another which uses expected population sizes together with exact probabilities. We conclude that a query of a Bayesian Net should be expressed as a probability embedded in an uncertainty interval. Based on an investigation of two Bayesian Net structures, the preferred method is the simulation method. However, both the single sample method and the expected sample size methods may be useful and are simpler to compute. Any method at all is more useful than none, when assessing a Bayesian Net under development, or when drawing conclusions from an ‘expert’ system.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Practical determination of cane wagon derailment forces for the Australian sugar industry

Derailments are a significant cost to the Australian sugar industry with damage to rail infrastructure and rolling stock in excess of $2 M per annum. Many factors can contribute to cane rail derailments. The more prevalent factors are discussed. Derailment statistics on likely causes for cane rail derailments are presented with the case of empty wagons on the main line being the highest contributor to business cost. Historically, the lateral to vertical wheel load ratio, termed the derailment ratio, has been used to indicate the derailment probability of rolling stock. When the derailment ratio reaches the Nadal limit of 0.81 for cane rail operations, there is a high probability that a derailment will occur. Contributing factors for derailments include the operating forces, the geometric variables of the rolling stock and the geometric deviations of the railway track. These combined, have the capacity to affect the risk of derailment for a cane rail transport operating system. The derailment type that is responsible for creating the most damage to assets and creating mill stops is the flange climb derailment, as these derailments usually occur at speed with a full rake of empty wagons. The typical forces that contribute to the flange climb derailment case for cane rail operations are analysed and a practical derailment model is developed to enable operators to better appreciate the most significant contributing factors to this type of derailment. The paper aims to: (a) improve awareness of the significance of physical operating parameters so that these principles can be included in locomotive driver training and (b) improve awareness of track and wagon variables related to the risk of derailment so that maintainers of the rail system can allocate funds for maintenance more effectively.