Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

Mathematics and reading difficulty subtypes: Minor phonological influences on mathematics for 5-7 year olds

Linguistic influences in mathematics have previously been explored throughsubtyping methodology and by taking advantage of the componential nature ofmathematics and variations in language requirements that exist across tasks. Thepresent longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5-7 years. Initially, 256 children were screened for mathematics and reading difficulties using standardised measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the MD (n=26), MDRD (n=32), reading difficulty (RD, n=22) and typically achieving (TA, n=35) subtypes. These children were tested at four time points, separated by six monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypescould have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.

Perceptual Watermarking for Discrete Shearlet Transform

This paper presents a new perceptual watermarking model for Discrete Shearlet transform (DST). DST provides the optimal representation [10] of the image features based on multi-resolution and multi-directional analysis. This property can be exploited on for watermark embedding to achieve the watermarking imperceptibility by introducing the human visual system using Chou’s model. In this model, a spatial JND profile is adapted to fit the sub-band structure. The combination of DST and the Just-Noticeable Distortion (JND) profile improves the levels of robustness against certain attacks while minimizing the distortion; by assigning a visibility threshold of distortion to each DST sub-band coefficient in the case of grey scale image watermarking.

A-level Mathematics Options – Views of Secondary-level Teachers

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules with the pure maths representing two thirds of the assessment. The applied maths section includes mechanics, statistics and (sometimes) decision maths. A combination of mechanics and statistics tends to be the most popular choice by far. The current study aims to understand how maths teachers in secondary education make decisions regarding the curriculum options and offers useful insight to those currently designing the new A-level specifications.

Semi-structured interviews were conducted with A-level maths teachers representing 27 grammar schools across Northern Ireland. Teachers were generally in agreement regarding the importance of pure maths and the balance between pure and applied within the A-level maths curriculum. A wide variety of opinions existed concerning the applied options. While many believe that the basic mechanics-statistics (M1-S1) combination is most accessible, it was also noted that the M1-M2 combination fits neatly alongside A-level physics. Lack of resources, timetabling constraints and competition with other subjects in the curriculum hinder uptake of A-level Further Maths.

Teachers are very conscious of the need to obtain high grades to benefit both their pupils and the school’s reputation. The move to a linear assessment system in England while Northern Ireland retains the modular system is likely to cause some schools to review their choice of exam board although there is disagreement as to whether a modular or linear system is more advantageous for pupils. The upcoming change in the specification offers an opportunity to refresh the assessment also and reduce the number of leading questions. However, teachers note that there are serious issues with GCSE maths and these have implications for A-level.

Discrete cyclic di-GMP-dependent control of bacterial predation versus axenic growth in Bdellovibrio bacteriovorus

Bdellovibrio bacteriovorus is a Delta-proteobacterium that oscillates between free-living growth and predation on Gram-negative bacteria including important pathogens of man, animals and plants. After entering the prey periplasm, killing the prey and replicating inside the prey bdelloplast, several motile B. bacteriovorus progeny cells emerge. The B. bacteriovorus HD100 genome encodes numerous proteins predicted to be involved in signalling via the secondary messenger cyclic di-GMP (c-di-GMP), which is known to affect bacterial lifestyle choices. We investigated the role of c-di-GMP signalling in B. bacteriovorus, focussing on the five GGDEF domain proteins that are predicted to function as diguanylyl cyclases initiating c-di-GMP signalling cascades. Inactivation of individual GGDEF domain genes resulted in remarkably distinct phenotypes. Deletion of dgcB (Bd0742) resulted in a predation impaired, obligately axenic mutant, while deletion of dgcC (Bd1434) resulted in the opposite, obligately predatory mutant. Deletion of dgcA (Bd0367) abolished gliding motility, producing bacteria capable of predatory invasion but unable to leave the exhausted prey. Complementation was achieved with wild type dgc genes, but not with GGAAF versions. Deletion of cdgA (Bd3125) substantially slowed predation; this was restored by wild type complementation. Deletion of dgcD (Bd3766) had no observable phenotype. In vitro assays showed that DgcA, DgcB, and DgcC were diguanylyl cyclases. CdgA lacks enzymatic activity but functions as a c-di-GMP receptor apparently in the DgcB pathway. Activity of DgcD was not detected. Deletion of DgcA strongly decreased the extractable c-di-GMP content of axenic Bdellovibrio cells. We show that c-di-GMP signalling pathways are essential for both the free-living and predatory lifestyles of B. bacteriovorus and that obligately predatory dgcC- can be made lacking a propensity to survive without predation of bacterial pathogens and thus possibly useful in anti-pathogen applications. In contrast to many studies in other bacteria, Bdellovibrio shows specificity and lack of overlap in c-di-GMP signalling pathways.

, Lexicographic Preferences in Discrete Choice Experiments: Consequences on Individual-Specific Willingness to Pay Estimates

In discrete choice experiments respondents are generally assumed to consider all of the attributes across each of the alternatives, and to choose their most preferred. However, results in this paper indicate that many respondents employ simplified lexicographic decision-making rules, whereby they have a ranking of the attributes, but their choice of an alternative is based solely on the level of their most important attribute(s). Not accounting for these simple decision-making heuristics introduces systemic errors and leads to biased point estimates, as they are a violation of the continuity axiom and a departure from the use of compensatory decision-making. In this paper the implications of lexicographic preferences are examined. In particular, using a mixed logit specification this paper investigates the sensitivity of individual-specific willingness to pay (WTP) estimates conditional on whether lexicographic decision-making rules are accounted for in the modelling of discrete choice responses. Empirical results are obtained from a discrete choice experiment that was carried out to address the value of a number of rural landscape attributes in Ireland

Learning, fatigue and preference formation in discrete choice experiments

While the repeated nature of Discrete Choice Experiments is advantageous from a sampling efficiency perspective, patterns of choice may differ across the tasks, due, in part, to learning and fatigue. Using probabilistic decision process models, we find in a field study that learning and fatigue behavior may only be exhibited by a small subset of respondents. Most respondents in our sample show preference and variance stability consistent with rational pre-existent and
well formed preferences. Nearly all of the remainder exhibit both learning and fatigue effects. An important aspect of our approach is that it enables learning and fatigue effects to be explored, even though they were not envisaged during survey design or data collection.

Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials.