Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644

Classifying Rational G-Spectra for Finite G

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in G, as H runs over the conjugacy classes of subgroups of G. Furthermore, the Quillen equivalences of our proof are all symmetric monoidal. Thus we can understand categories of algebras or modules over a ring spectrum in terms of the algebraic model.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Twisted Edwards curves revisited

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use . It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to . This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

Prevention of postnatal distress or depression : an evaluation of an intervention at preparation for parenthood classes.

Determined the effectiveness of a psychosocial intervention, provided to expectant couples in routine antenatal classes, on the postpartum psychosocial adjustment of women and men. Preparation for Parenthood programs were randomly allocated to one of three conditions: usual service ('control'), experimental ('empathy'), or non-specific control ('baby-play'). The latter condition controlled for the non-specific effects of the intervention, these being: the provision of an extra class; asking couples to consider the early postpartum weeks; and receiving booster information after the antenatal class, and again shortly after the birth. Women and men were categorised into three levels of self-esteem, as measured antenatally: low, medium and high. 268 participants were recruited antenatally. Interview data and self-report information was collected from 202 of these women at 6 weeks postpartum, and 180 women at 6 months postpartum. The intervention consisted of a session focusing on psychosocial issues related to becoming first-time parents. Participants discussed possible postpartum concerns in separate gender groups for part of the session, and then discussed these issues with their partners

Social adaptation of children with mild intellectual disability : effects of partial integration within primary school classes

Examined the social adaptation of 32 children in grades 3–6 with mild intellectual disability: 13 Ss were partially integrated into regular primary school classes and 19 Ss were full-time in separate classes. Sociometric status was assessed using best friend and play rating measures. Consistent with previous research, children with intellectual disability were less socially accepted than were a matched group of 32 children with no learning disabilities. Children in partially integrated classes received more play nominations than those in separate classes, but had no greater acceptance as a best friend. On teachers' reports, disabled children had higher levels of inappropriate social behaviours, but there was no significant difference in appropriate behaviours. Self-assessments by integrated children were more negative than those by children in separate classes, and their peer-relationship satisfaction was lower. Ratings by disabled children of their satisfaction with peer relationships were associated with ratings of appropriate social skills by themselves and their teachers, and with self-ratings of negative behaviour. The study confirmed that partial integration can have negative consequences for children with an intellectual disability.

Using concept mapping to scaffold learning for students who experience learning difficulties in science classes

In order to develop scientific literacy students need the cognitive tools that enable them to read and evaluate science texts. One cognitive tool that has been widely used in science education to aid the development of conceptual understanding is concept mapping. However, it has been found some students experience difficulty with concept map construction. This study reports on the development and evaluation of an instructional sequence that was used to scaffold the concept-mapping process when middle school students who were experiencing difficulty with science learning used concept mapping to summarise a chapter of a science text. In this study individual differences in working memory functioning are suggested as one reason that students experience difficulty with concept map construction. The study was conducted using a design-based research methodology in the school’s learning support centre. The analysis of student work samples collected during the two-year study identified some of the difficulties and benefits associated with the use of scaffolded concept mapping with these students. The observations made during this study highlight the difficulty that some students experience with the use of concept mapping as a means of developing an understanding of science concepts and the amount of instructional support that is required for such understanding to develop. Specifically, the findings of the study support the use of multi-component, multi-modal instructional techniques to facilitate the development of conceptual understanding with students who experience difficulty with science learning. In addition, the important roles of interactive dialogue and metacognition in the development of conceptual understanding are identified.

Engaging students in large classes using Elluminate

The advancement of online teaching environments during the past several years presents an exciting opportunity to extend existing teaching methodologies. The software package known as Elluminate is one example of a virtual classroom, facilitating the provision of real time interaction, collaboration and group meetings. This paper will examine the use of Elluminate in the teaching of large classes. The use of such technology for large classes is of particular interest, as large classes are often, unfairly, associated with a reputation for being impersonal as well as notions of conveyor belt learning. In this paper the potential to extend teaching and learning opportunities using Elluminate, in the context of large classes, will be explored. It will be shown that the use of technology such as Elluminate can assist in providing students with a more flexible means of accessing academic support, as well as allowing for a customised delivery of course content so as to focus learning outcomes.

Strategies to facilitate grading consistency in large classes

First year undergraduate university classes can be very large, and big student numbers often creates a challenge for instructors to ensure assignments are graded consistently across the cohort. This session describes and demonstrates the use of interactive audience response technology (ART) with assessors (rather than students) to moderate assignment grading. Results from preliminary research indicate this method of moderating the grading of assignments is effective, and achieves more consistent outcomes for students.

Structural inquiry, human agency and the contribution of Harre and Bhaskar : a case study of Wright’s “Classes”

This paper examines the contribution of aspects of critical and referential realism to the “logic” of structural explanation through an analysis of Erik Olin Wright’s Classes and the debate surrounding this work. Wright’s Classes has been selected as a case study because it offers an opportunity to examine issues pertaining to “objective” and “subjective” determinations of class and related questions of agency and structure at the level of actual methodological strategies. A close examination of the structure of Wright’s inquiry reveals a number of places where Harre’s and Bhaskar’s approaches may contribute to the prescription of methodological strategies which could overcome some of the antinomies on which the debate on Classes is based. As a case study, the paper underlines the important “underlabourer” role of critical and referential realism and their contribution to questions of agency and structure in the context of actual stages involved in structural explanation

Sustainable assessment for large science classes : non-multiple choice, randomised assignments through a Learning Management System

This paper reports on the development of a tool that generates randomised, non-multiple choice assessment within the BlackBoard Learning Management System interface. An accepted weakness of multiple-choice assessment is that it cannot elicit learning outcomes from upper levels of Biggs’ SOLO taxonomy. However, written assessment items require extensive resources for marking, and are susceptible to copying as well as marking inconsistencies for large classes. This project developed an assessment tool which is valid, reliable and sustainable and that addresses the issues identified above. The tool provides each student with an assignment assessing the same learning outcomes, but containing different questions, with responses in the form of words or numbers. Practice questions are available, enabling students to obtain feedback on their approach before submitting their assignment. Thus, the tool incorporates automatic marking (essential for large classes), randomised tasks to each student (reducing copying), the capacity to give credit for working (feedback on the application of theory), and the capacity to target higher order learning outcomes by requiring students to derive their answers rather than choosing them. Results and feedback from students are presented, along with technical implementation details.

Multiple evolutionary rate classes in animal genome evolution

The proportion of functional sequence in the human genome is currently a subject of debate. The most widely accepted figure is that approximately 5% is under purifying selection. In Drosophila, estimates are an order of magnitude higher, though this corresponds to a similar quantity of sequence. These estimates depend on the difference between the distribution of genomewide evolutionary rates and that observed in a subset of sequences presumed to be neutrally evolving. Motivated by the widening gap between these estimates and experimental evidence of genome function, especially in mammals, we developed a sensitive technique for evaluating such distributions and found that they are much more complex than previously apparent. We found strong evidence for at least nine well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least seven classes in an alignment of four mammals, including human. We also identified at least three rate classes in human ancestral repeats. By positing that the largest of these ancestral repeat classes is neutrally evolving, we estimate that the proportion of nonneutrally evolving sequence is 30% of human ancestral repeats and 45% of the aligned portion of the genome. However, we also question whether any of the classes represent neutrally evolving sequences and argue that a plausible alternative is that they reflect variable structure-function constraints operating throughout the genomes of complex organisms.