A subdivision-based implementation of non-uniform local refinement with THB-splines

Paper accepted for 15th IMA International Conference on Mathematics on Surfaces, 2017. Abstract: Local refinement of spline basis functions is an important process for spline approximation and local feature modelling in computer aided design (CAD). This paper develops an efficient local refinement method for non-uniform and general degree THB-splines(Truncated hierarchical B-splines). A non-uniform subdivision algorithm is improved to efficiently subdivide a single non-uniform B-spline basis function. The subdivision scheme is then applied to locally hierarchically refine non-uniform B-spline basis functions. The refined basis functions are non-uniform and satisfy the properties of linear independence, partition of unity and are locally supported. The refined basis functions are suitable for spline approximation and numerical analysis. The implementation makes it possible for hierarchical approximation to use the same non-uniform B-spline basis functions as existing modelling tools have used. The improved subdivision algorithm is faster than classic knot insertion. The non-uniform THB-spline approximation is shown to be more accurate than uniform low degree hierarchical local refinement when applied to two classical approximation problems

Bayesian Analysis of Individual Level Personality Dynamics

A Bayesian technique with analyses of within-person processes at the level of the individual is presented. The approach is used to examine if the patterns of within-person responses on a 12 trial simulation task are consistent with the predictions of ITA theory (Dweck, 1999). ITA theory states that the performance of an individual with an entity theory of ability is more likely to spiral down following a failure experience than the performance of an individual with an incremental theory of ability. This is because entity theorists interpret failure experiences as evidence of a lack of ability, which they believe is largely innate and therefore relatively fixed; whilst incremental theorists believe in the malleability of abilities and interpret failure experiences as evidence of more controllable factors such as poor strategy or lack of effort. The results of our analyses support ITA theory at both the within- and between-person levels of analyses and demonstrate the benefits of Bayesian techniques for the analysis of within-person processes. These include more formal specification of the theory and the ability to draw inferences about each individual, which allows for more nuanced interpretations of individuals within a personality category, such as differences in the individual probabilities of spiralling. While Bayesian techniques have many potential advantages for the analyses of within-person processes at the individual level, ease of use is not one of them for psychologists trained in traditional frequentist statistical techniques

Haemophilus influenzae and smoking-related obstructive airways disease

Background: Intralumenal bacteria play a critical role in the pathogenesis of acute infective episodes and airway inflammation. Antigens from colonizing bacteria such as nontypeable Haemophilus influenzae (NTHi) may contribute to chronic lung disease through an immediate hypersensitivity response. The objective of this study was to determine the presence of specific NTHi-IgE antibodies in subjects with chronic bronchitis (CB) and COPD who had smoked. Methods: Serum, sputum, and saliva samples were collected from subjects with CB and moderate–severe COPD and healthy aged-matched controls. Total IgE and specific NTHi IgE were measured by enzyme linked immmunosorbent assay. Throat swabs were examined for the presence of NTHi. Results: The results demonstrate that: i) specific NTHi IgE antibodies occur at a low level in healthy subjects; ii) those with both CB and moderate–severe COPD have elevated specific NTHi IgE antibody compared with healthy controls, with higher levels in those with most severe disease; iii) IgE levels are greater in those with moderate–severe COPD than in those with CB. They demonstrate specific NTHi IgE antibody is regularly found at higher than normal levels in COPD. Conclusion: The detection of IgE antibody to colonizing bacteria in all subjects with CB or moderate–severe COPD identifies a possible mechanism of bronchospasm in these subjects amenable to specific intervention therapy