Written numeracy assessment in the early years: The challenges of pronouns and noun groups

We examine the challenges of pronouns and noun groups in the Australian Curriculum, Assessment and Reporting Authority’s (ACARA) Year 3 National Assessment Program - Literacy and Numeracy (NAPLAN) Numeracy Example Test (ACARA, 2015a). Framed by discourses of Literacy as a General Capability (ACARA, 2015b) in the Australian Curriculum: Mathematics (ACARA, 2015c), the pronouns and noun groups used in the Example Test are mapped onto the Australian Curriculum: English Content Descriptions (ACARA, 2015d). The findings are that some of the pronouns and noun groups used in the Example Test are more complex than what Year 3 children are expected to achieve in the Australian Curriculum: English. We thus stress the need for early years teachers of mathematics to account for the unique mathematical register of written mathematics problems so that young children are not only prepared for high-stakes written numeracy assessments, but are also enabled as a numerically literate citizen.

Functional evaluation of genetic variants associated with endometriosis near GREB1

STUDY QUESTION: Do DNA variants in the growth regulation by estrogen in breast cancer 1 (GREB1) region regulate endometrial GREB1 expression and increase the risk of developing endometriosis in women? SUMMARY ANSWER: We identified new single nucleotide polymorphisms (SNPs) with strong association with endometriosis at the GREB1 locus although we did not detect altered GREB1 expression in endometriosis patients with defined genotypes. WHAT IS ALREADY KNOWN: Genome-wide association studies have identified the GREB1 region on chromosome 2p25.1 for increasing endometriosis risk. The differential expression of GREB1 has also been reported by others in association with endometriosis disease phenotype. STUDY DESIGN, SIZE, DURATION: Fine mapping studies comprehensively evaluated SNPs within the GREB1 region in a large-scale data set (>2500 cases and >4000 controls). Publicly available bioinformatics tools were employed to functionally annotate SNPs showing the strongest association signal with endometriosis risk. Endometrial GREB1 mRNA and protein expression was studied with respect to phases of the menstrual cycle (n = 2-45 per cycle stage) and expression quantitative trait loci (eQTL) analysis for significant SNPs were undertaken for GREB1 [mRNA (n = 94) and protein (n = 44) in endometrium]. PARTICIPANTS/MATERIALS, SETTING, METHODS: Participants in this study are females who provided blood and/or endometrial tissue samples in a hospital setting. The key SNPs were genotyped using Sequenom MassARRAY. The functional roles and regulatory annotations for identified SNPs are predicted by various publicly available bioinformatics tools. Endometrial GREB1 expression work employed qRT-PCR, western blotting and immunohistochemistry studies. MAIN RESULTS AND THE ROLE OF CHANCE: Fine mapping results identified a number of SNPs showing stronger association (0.004 < P < 0.032) with endometriosis risk than the original GWAS SNP (rs13394619) (P = 0.034). Some of these SNPs were predicted to have functional roles, for example, interaction with transcription factor motifs. The haplotype (a combination of alleles) formed by the risk alleles from two common SNPs showed significant association (P = 0.026) with endometriosis and epistasis analysis showed no evidence for interaction between the two SNPs, suggesting an additive effect of SNPs on endometriosis risk. In normal human endometrium, GREB1 protein expression was altered depending on the cycle stage (significantly different in late proliferative versus late secretory, P < 0.05) and cell type (glandular epithelium, not stromal cells). However, GREB1 expression in endometriosis cases versus controls and eQTL analyses did not reveal any significant changes. LIMITATIONS, REASONS FOR CAUTION: In silico prediction tools are generally based on cell lines different to our tissue and disease of interest. Functional annotations drawn from these analyses should be considered with this limitation in mind. We identified cell-specific and hormone-specific changes in GREB1 protein expression. The lack of a significant difference observed following our GREB1 expression studies may be the result of moderate power on mixed cell populations in the endometrial tissue samples. WIDER IMPLICATIONS OF THE FINDINGS: This study further implicates the GREB1 region on chromosome 2p25.1 and the GREB1 gene with involvement in endometriosis risk. More detailed functional studies are required to determine the role of the novel GREB1 transcripts in endometriosis pathophysiology. STUDY FUNDING/COMPETING INTERESTS: Funding for this work was provided by NHMRC Project Grants APP1012245, APP1026033, APP1049472 and APP1046880. There are no competing interests.

No evidence for genetic association with the let-7 microRNA-binding site or other common KRAS variants in risk of endometriosis

STUDY QUESTION Is there a contribution of the minor allele at the KRAS single nucleotide polymorphism (SNP) rs61764370 in the let-7 microRNA-binding site to endometriosis risk? SUMMARY ANSWER We found no evidence for association between endometriosis risk and rs61764370 or any other SNPs in KRAS. WHAT IS KNOWN ALREADY The rs61764370 SNP in the 3' untranslated region of the KRAS gene is predicted to disrupt a complementary binding site (LCS6) for the let-7 microRNA, and was recently reported to be at a high frequency (31%) in 132 women of varying ancestry with endometriosis compared with frequencies in a database of population controls (up to 7.6% depending on ancestry), suggesting a strong effect of this KRAS SNP in the aetiology of endometriosis. STUDY DESIGN, SIZE AND DURATION This was a case-control study with a total of 11 206 subjects. The study was performed between February 2012 and July 2012. PARTICIPANTS/MATERIALS, SETTINGAND METHODS We first investigated a possible association between common markers in KRAS and endometriosis risk from our genome-wide association (GWA) data in 3194 surgically confirmed endometriosis cases and 7060 controls of European ancestry. Although rs61764370 was not genotyped on the GWA arrays, five SNPs typed in the study were highly correlated with this variant. The rs61764370 and two SNPs highly correlated with rs61764370 were then genotyped in 933 endometriosis cases and 952 controls using the Sequenom MassARRAY platform. MAIN RESULTS AND THE ROLE OF CHANCE There was no evidence for an association between rs61764370 and endometriosis risk P = 0.411 and odds ratio = 1.10 (95% confidence intervals: 0.88-1.36). We also found no evidence for an association between the highly correlated SNP rs17387019 and endometriosis. Their minor allele frequencies in cases and controls were of 0.087-0.091 similar to the population frequency reported previously for this variant in controls. Analyses of endometriosis cases with revised American Fertility Society stage III/IV disease also showed no evidence for an association between these SNPs and endometriosis risk. LIMITATIONS AND REASONS FOR CAUTION The GWA and genotyped data sets were not independent since individuals and cases from some families overlap. Controls in our GWA study were not screened for endometriosis. WIDER IMPLICATIONS OF THE FINDINGS The key SNP, rs61764370, was genotyped in a subset of samples. Our results do not support the suggestion that carrying the minor allele at rs61764370 contributes to a significant number of endometriosis cases and rs61764370 is, therefore, unlikely to be a useful marker of endometriosis risk. STUDY FUNDING/COMPETING INTEREST(S) The research was funded by grants from the Australian National Health and Medical Research Council and Wellcome Trust. None of the authors has competing interests for the study.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.

On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

Forced Oscillations of a Contained Rotating Stratified Fluid

The motion generated by forced oscillations in an incompressible inviscid rotating and/or stratified fluid is examined under linear theory taking the density variation on the inertia terms. The solution consists of numerous internal modes in addition to the mode which oscillates with forcing frequency. Resonance occurs when the forcing frequency is equal to one of the frequencies of the internal modes. Some of these modes grow linearly or exponentially with time rendering the motion unstable and eventually may lead to turbulence. Most of the results discussed here will be missed under Boussinesq approximation.

On the Analysis of Thick Rectangular Plates

Abstract is not available.

A Method of Characteristics for Solving Two-dimensional Unsteady Flow Problems

The aim of this investigation is to evolve a method of solving two-dimensional unsteady flow problems by the method of characteristics. This involves the reduction of the given system of equations to an equivalent system where only interior derivatives occur on a characteristic surface. From this system, four special bicharacteristic directional derivatives are chosen. A finite difference scheme is prescribed for solving the equations. General rectangular lattices are also considered. As an example, we investigate the propagation of an initial pressure distribution in a medium at rest.

On the Solution of Certain Simultaneous Pairs of Dual Integral Equations

Mit einer direkten Methode, bei der der Erdelyi-Kober- und der modifizierte Hankel-Operator Anwendung finden, werden gewisse Systeme aus zwei bzw. drei Paaren dualer Integralgleichungen mit Bessel-Kernen in geschlossener Form gelöst. Für bestimmte Funktionenklassen und Ordnungen der Bessel-Funktionen ist die Vorgehensweise angebrachter und geeigneter als die bereits existierenden Methoden.

A unified approach to the solution of plane problems of Magneto-elasticity with special reference to a hole in a thin infinite conducting plate

Under certain specific assumption it has been observed that the basic equations of magneto-elasticity in the case of plane deformation lead to a biharmonic equation, as in the case of the classical plane theory of elasticity. The method of solving boundary value problems has been properly modified and a unified approach in solving such problems has been suggested with special reference to problems relating thin infinite plates with a hole. Closed form expressions have been obtained for the stresses due to a uniform magnetic field present in the plane of deformation of a thin infinite conducting plate with a circular hole, the plate being deformed by a tension acting parallel to the direction of the magnetic field.

Solutions of Boundary Layer Equations Governing Free Convective and Magnetohydrodynamic Flows through Parametric Differentiation

In der vorliegenden Arbeit wird die Methode der parametrischen Differentiation angewendet, um ein System nichtlinearer Gleichungen zu lösen, das zwei- und dreidimensionale freie, konvektive Grenzschichströmungen bzw. eine zweidimensionale magnetohydrodynamische Grenzschichtströmung beherrscht. Der Hauptvorteil dieser Methode besteht darin, daß die nichlinearen Gleichungen auf lineare reduziert werden und die Nichtlinearität auf ein System von Gleichungen erster Ordnung beschränkt wird, das, verglichen mit den ursprünglichen Nichtlinearen Gleichungen, viel leichter gelöst werden kann. Ein anderer Vorzug der Methode ist, daß sie es ermöglicht, die Lösung von einer bekannten, zu einem bestimmten Parameterwert gehörigen Lösung aus durch schrittweises Vorgehen die Lösung für den gesamten Parameterbereich zu erhalten. Die mit dieser Methode gewonnenen Ergebnisse stimmen gut mit den entsprechenden, mit anderen numerischen Verfahren erzielten überein.

Dependence Logic: Investigations into Higher-Order Semantics Defined on Teams

This thesis is a study of a rather new logic called dependence logic and its closure under classical negation, team logic. In this thesis, dependence logic is investigated from several aspects. Some rules are presented for quantifier swapping in dependence logic and team logic. Such rules are among the basic tools one must be familiar with in order to gain the required intuition for using the logic for practical purposes. The thesis compares Ehrenfeucht-Fraïssé (EF) games of first order logic and dependence logic and defines a third EF game that characterises a mixed case where first order formulas are measured in the formula rank of dependence logic. The thesis contains detailed proofs of several translations between dependence logic, team logic, second order logic and its existential fragment. Translations are useful for showing relationships between the expressive powers of logics. Also, by inspecting the form of the translated formulas, one can see how an aspect of one logic can be expressed in the other logic. The thesis makes preliminary investigations into proof theory of dependence logic. Attempts focus on finding a complete proof system for a modest yet nontrivial fragment of dependence logic. A key problem is identified and addressed in adapting a known proof system of classical propositional logic to become a proof system for the fragment, namely that the rule of contraction is needed but is unsound in its unrestricted form. A proof system is suggested for the fragment and its completeness conjectured. Finally, the thesis investigates the very foundation of dependence logic. An alternative semantics called 1-semantics is suggested for the syntax of dependence logic. There are several key differences between 1-semantics and other semantics of dependence logic. 1-semantics is derived from first order semantics by a natural type shift. Therefore 1-semantics reflects an established semantics in a coherent manner. Negation in 1-semantics is a semantic operation and satisfies the law of excluded middle. A translation is provided from unrestricted formulas of existential second order logic into 1-semantics. Also game theoretic semantics are considerd in the light of 1-semantics.

Stresses and Displacements under a Flexible Circular Foundation in the Presence of Friction or Adhesion

Die Vorliegende Arbeit beschäftigt sich mit den Spannungen und Verschiebungen an einem elastischen Halbraum unter einem kreisförmigen biegsamen Fundament, wenn an der Kontaktfläche vollkommenes Haften besteht. Das gemischte Randwertproblem wird mit Hilfe von Hankel-Transformationen auf duale Integralgleichungen von Titchmarsh- Typ zurückgeführt. Für die Berechnung der Spannungen und Verschiebungen werden Gaußsche Quadraturformeln benutzt. Die Ergebnisse werden mit denen verglichen, die man bei glattem Fundament erhält, und der Einfluß der Poisson-Zahl auf die Spannungen und Verschiebungen wird deutlich gemacht. Schließlich werden die Ergebnisse für den praktischen Gebrauch in Diagrammen und Tabellen zusammengefaßt.

Intrinsic equations of steady rotating, incompressible viscous fluid flow

The equations governing the flow of a steady rotating incompressible viscous fluid are expressed in intrinsic form along the vortex lines and their normals. Using these equations the effects of rotation on the geometric properties of viscous fluid flows are studied. A particular flow in which the vortex lines are right circular helices is discussed.