Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

Solving inherent problems of anomaly detection by cooperation

Anomaly detection compensates shortcomings of signature-based detection such as protecting against Zero-Day exploits. However, Anomaly Detection can be resource-intensive and is plagued by a high false-positive rate. In this work, we address these problems by presenting a Cooperative Intrusion Detection approach for the AIS, the Artificial Immune System, as an example for an anomaly detection approach. In particular we show, how the cooperative approach reduces the false-positive rate of the detection and how the overall detection process can be organized to account for the resource constraints of the participating devices. Evaluations are carried out with the novel network simulation environment NeSSi as well as formally with an extension to the epidemic spread model SIR

Problems and awareness of support services among University students

Although Australian universities have allocated significant resources toward the development of student support services, administrators have little systematic information about the problems undergraduate university students experience or students' knowledge about available support services. The author surveyed 441 students in an urban, nonresidential university to examine the prevalence of difficulties associated with learning, sexual harassment, discrimination, emotional distress, health problems, course and career concerns, financial difficulties, and difficulties with lecturers; he also assessed students' knowledge of support services in each of these areas. Course concerns were the most common problem, followed by emotional distress, worry about career choices, financial difficulties, and problems with lecturers. More than half of the students were unaware of the support services available to them to address a range of concerns from sexual harassment and discrimination to emotional distress. Approximately 20% of the students reported having used university counseling or career services. Implications for targeting specific areas for outreach programs are discussed.

Prediction of multilocus identity-by-descent

Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in randommating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X ABC at each of ordered loci A, B, and C can be well approximated by XABC = XABXBC/XB and generalizes to X123. . .k = X12X23. . .Xk-1,k/ Xk-2, where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBD L are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.

Candidate gene analysis for quantitative traits using the transmission disequilibrium test : the example of the melanocortin 4-receptor in pigs

Population-wide associations between loci due to linkage disequilibrium can be used to map quantitative trait loci (QTL) with high resolution. However, spurious associations between markers and QTL can also arise as a consequence of population stratification. Statistical methods that cannot differentiate between loci associations due to linkage disequilibria from those caused in other ways can render false-positive results. The transmission-disequilibrium test (TDT) is a robust test for detecting QTL. The TDT exploits within-family associations that are not affected by population stratification. However, some TDTs are formulated in a rigid-form, with reduced potential applications. In this study we generalize TDT using mixed linear models to allow greater statistical flexibility. Allelic effects are estimated with two independent parameters: one exploiting the robust within-family information and the other the potentially biased between-family information. A significant difference between these two parameters can be used as evidence for spurious association. This methodology was then used to test the effects of the fourth melanocortin receptor (MC4R) on production traits in the pig. The new analyses supported the previously reported results; i.e., the studied polymorphism is either causal of in very strong linkage disequilibrium with the causal mutation, and provided no evidence for spurious association.

Dealing with heterogeneity problems and causal effect estimation in entrepreneurship research

This paper deals with causal effect estimation strategies in highly heterogeneous empirical settings such as entrepreneurship. We argue that the clearer used of modern tools developed to deal with the estimation of causal effects in combination with our analysis of different sources of heterogeneity in entrepreneurship can lead to entrepreneurship with higher internal validity. We specifically lend support from the counterfactual logic and modern research of estimation strategies for causal effect estimation.

Hydrogen Gas Sensor Based on Highly Ordered Polyaniline/Multiwall Carbon Nanotubes Composite

In this work, the structural and gas sensing properties of an electropolymerized, polyaniline (PANI)/multiwall carbon nanotube (MWNT) composite based surface acoustic wave (SAW) sensor are reported. Thin films made of PANI nanofibers were deposited onto 36 lithium tantalate (LiTaO3) SAW transducers using electropolymerization and were subsequently dedoped. Scanning electron microscopy (SEM) revealed the compact growth of the composites which is much denser than that of PANI nanofibers. The PANI/MWNT composite based SAW sensor was then exposed to different concentrations of hydrogen (H2) gas at room temperature with a demonstrated electrical response.

What are the health needs, familial and social problems of Thai migrants in a local community in Australia? A focus group study

This study explored the health needs, familial and social problems of Thai migrants in a local community in Brisbane, Australia. Five focus groups with Thai migrants were conducted. The qualitative data were examined using thematic content analysis that is specifically designed for focus group analysis. Four themes were identified: (1) positive experiences in Australia, (2) physical health problems, (3) mental health problems, and (4) familial and social health problems. This study revealed key health needs related to chronic disease and mental health, major barriers to health service use, such as language skills, and facilitating factors, such as the Thai Temple. We concluded that because the health needs, familial and social problems of Thai migrants were complex and culture bound, the development of health and community services for Thai migrants needs to take account of the ways in which Thai culture both negatively impacts health and offer positive solutions to problems.

Managing memory and reducing I/O cost for correlation matrix calculation in bioinformatics

The generation of a correlation matrix from a large set of long gene sequences is a common requirement in many bioinformatics problems such as phylogenetic analysis. The generation is not only computationally intensive but also requires significant memory resources as, typically, few gene sequences can be simultaneously stored in primary memory. The standard practice in such computation is to use frequent input/output (I/O) operations. Therefore, minimizing the number of these operations will yield much faster run-times. This paper develops an approach for the faster and scalable computing of large-size correlation matrices through the full use of available memory and a reduced number of I/O operations. The approach is scalable in the sense that the same algorithms can be executed on different computing platforms with different amounts of memory and can be applied to different problems with different correlation matrix sizes. The significant performance improvement of the approach over the existing approaches is demonstrated through benchmark examples.

Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

The ancient gene C12orf29 : an exploration of its role in the chordate body plan

The sheep (Ovis aries) is commonly used as a large animal model in skeletal research. Although the sheep genome has been sequenced there are still only a limited number of annotated mRNA sequences in public databases. A complementary DNA (cDNA) library was constructed to provide a generic resource for further exploration of genes that are actively expressed in bone cells in sheep. It was anticipated that the cDNA library would provide molecular tools for further research into the process of fracture repair and bone homeostasis, and add to the existing body of knowledge. One of the hallmarks of cDNA libraries has been the identification of novel genes and in this library the full open reading frame of the gene C12orf29 was cloned and characterised. This gene codes for a protein of unknown function with a molecular weight of 37 kDa. A literature search showed that no previous studies had been conducted into the biological role of C12orf29, except for some bioinformatics studies that suggested a possible link with cancer. Phylogenetic analyses revealed that C12orf29 had an ancient pedigree with a homologous gene found in some bacterial taxa. This implied that the gene was present in the last common eukaryotic ancestor, thought to have existed more than 2 billion years ago. This notion was further supported by the fact that the gene is found in taxa belonging to the two major eukaryotic branches, bikonts and unikonts. In the bikont supergroup a C12orf29-like gene was found in the single celled protist Naegleria gruberi, whereas in the unikont supergroup, encompassing the metazoa, the gene is universal to all chordate and, therefore, vertebrate species. It appears to have been lost to the majority of cnidaria and protostomes taxa; however, C12orf29-like genes have been found in the cnidarian freshwater hydra and the protostome Pacific oyster. The experimental data indicate that C12orf29 has a structural role in skeletal development and tissue homeostasis, whereas in silico analysis of the human C12orf29 promoter region suggests that its expression is potentially under the control of the NOTCH, WNT and TGF- developmental pathways, as well SOX9 and BAPX1; pathways that are all heavily involved in skeletogenesis. Taken together, this investigation provides strong evidence that C12orf29 has a very important role in the chordate body plan, in early skeletal development, cartilage homeostasis, and also a possible link with spina bifida in humans.

Screening in early childhood for risk of later mental health problems : a longitudinal study

Depression in childhood or adolescence is associated with increased rates of depression in adulthood. Does this justify efforts to detect (and treat) those with symptoms of depression in early childhood or adolescence? The aim of this study was to determine how well symptoms of anxiety/depression (A-D) in early childhood and adolescence predict adult mental health. The study sample is taken from a population-based prospective birth cohort study. Of the 8556 mothers initially approached to participate 8458 agreed, of whom 7223 mothers gave birth to a live singleton baby. Children were screened using modified Child Behaviour Checklist (CBCL) scales for internalizing and total problems (T-P) at age 5 and the CBCL and Youth Self Report (YSR) A-D subscale and T-P scale at age 14. At age 21, a sub-sample of 2563 young adults in this cohort were administered the CIDI-Auto. Results indicated that screening at age 5 would detect few later cases of significant mental ill-health. Using a cut-point of 20% for internalizing at child age 5 years the CBCL had sensitivities of only 25% and 18% for major depression and anxiety disorders at 21 years, respectively. At age 14, the YSR generally performed a little better than the CBCL as a screening instrument, but neither performed at a satisfactory level. Of the children who were categorised as having YSR A-D at 14 years 30% and 37% met DSM-IV criteria for major depression and anxiety disorders, respectively, at age 21. Our findings challenge an existing movement encouraging the detection and treatment of those with symptoms of mental illness in early childhood.