Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis

Computer simulation of syringomyelia in dogs

Syringomyelia is a pathological condition in which fluid-filled cavities (syringes) form and expand in the spinal cord. Syringomyelia is often linked with obstruction of the craniocervical junction and a Chiari malformation, which is similar in both humans and animals. Some brachycephalic toy breed dogs such as Cavalier King Charles Spaniels (CKCS) are particularly predisposed. The exact mechanism of the formation of syringomyelia is undetermined and consequently with the lack of clinical explanation, engineers and mathematicians have resorted to computer models to identify possible physical mechanisms that can lead to syringes. We developed a computer model of the spinal cavity of a CKCS suffering from a large syrinx. The model was excited at the cranial end to simulate the movement of the cerebrospinal fluid (CSF) and the spinal cord due to the shift of blood volume in the cranium related to the cardiac cycle. To simulate the normal condition, the movement was prescribed to the CSF. To simulate the pathological condition, the movement of CSF was blocked

Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning

This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53 The final publication is available at www.springerlink.com Published version: http://dx.doi.org/10.3758/BF0321390

Transverse Electronic Transport through DNA Nucleotides with Functionalized Graphene Electrodes

Graphene nanogaps and nanopores show potential for the purpose of electrical DNA sequencing, in particular because single-base resolution appears to be readily achievable. Here, we evaluated from first principles the advantages of a nanogap setup with functionalized graphene edges. To this end, we employed density functional theory and the non-equilibrium Green's function method to investigate the transverse conductance properties of the four nucleotides occurring in DNA when located between the opposing functionalized graphene electrodes. In particular, we determined the electrical tunneling current variation as a function of the applied bias and the associated differential conductance at a voltage which appears suitable to distinguish between the four nucleotides. Intriguingly, we observe for one of the nucleotides a negative differential resistance effect.Comment: 19 pages, 7 figure

Two-year outcomes after transcatheter or surgical aortic-valve replacement.

BACKGROUND: The Placement of Aortic Transcatheter Valves (PARTNER) trial showed that among high-risk patients with aortic stenosis, the 1-year survival rates are similar with transcatheter aortic-valve replacement (TAVR) and surgical replacement. However, longer-term follow-up is necessary to determine whether TAVR has prolonged benefits. METHODS: At 25 centers, we randomly assigned 699 high-risk patients with severe aortic stenosis to undergo either surgical aortic-valve replacement or TAVR. All patients were followed for at least 2 years, with assessment of clinical outcomes and echocardiographic evaluation. RESULTS: The rates of death from any cause were similar in the TAVR and surgery groups (hazard ratio with TAVR, 0.90; 95% confidence interval [CI], 0.71 to 1.15; P=0.41) and at 2 years (Kaplan-Meier analysis) were 33.9% in the TAVR group and 35.0% in the surgery group (P=0.78). The frequency of all strokes during follow-up did not differ significantly between the two groups (hazard ratio, 1.22; 95% CI, 0.67 to 2.23; P=0.52). At 30 days, strokes were more frequent with TAVR than with surgical replacement (4.6% vs. 2.4%, P=0.12); subsequently, there were 8 additional strokes in the TAVR group and 12 in the surgery group. Improvement in valve areas was similar with TAVR and surgical replacement and was maintained for 2 years. Paravalvular regurgitation was more frequent after TAVR (P<0.001), and even mild paravalvular regurgitation was associated with increased late mortality (P<0.001). CONCLUSIONS: A 2-year follow-up of patients in the PARTNER trial supports TAVR as an alternative to surgery in high-risk patients. The two treatments were similar with respect to mortality, reduction in symptoms, and improved valve hemodynamics, but paravalvular regurgitation was more frequent after TAVR and was associated with increased late mortality. (Funded by Edwards Lifesciences; ClinicalTrials.gov number, NCT00530894.)

Simultaneous genetic analysis of longitudinal means and covariance structure in the simplex model using twin data

A longitudinal model based on the simplex model is presented to analyze simultaneously means and covariance structure using univariate longitudinal twin data. The objective of the model is to decompose the mean trend into components which can be attributed to those genetic and environmental factors which give rise to phenotypic individual differences and a component of unknown constitution which does not involve individual differences. Illustrations are given using simulated data and repeatedly measured weight obtained in a sample of 82 female twin pairs on sbc occasions. KEY WORDS: repeated measures; genetic and environmental covariance structure; mean trend; longitudinal twin data; genetic simplex mode; LISREL

Individual differences in puberty onset in girls: Bayesian estimation of heritabilities and genetic correlations

We report heritabilities for individual differences in female pubertal development at the age of 12. Tanner data on breast and pubic hair development in girls and data on menarche were obtained from a total of 184 pairs of monozygotic and dizygotic twins. Genetic correlations were estimated to determine to what extent the same genes are involved in different aspects of physical development in puberty. A Bayesian estimation approach was taken, using Markovchain Monte Carlo simulation to estimate model parameters. All three phenotypes were to a significant extent heritable and showed high genetic correlations, suggesting that a common set of genes is involved in the timing of puberty in general. However, gonadarche (menarche and breast development) and adrenarche (pubic hair) are affected by different environmental factors, which does not support the three phenotypes to be regarded as indicators of a unitary physiological factor. © 2006 Springer Science+Business Media, Inc