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.

Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

Meta-analysis of the influence of experimental design on effect size in peer tutoring outcomes in elementary, middle and high school settings.

A meta-analysis was undertaken on a form of cooperative learning, peer tutoring. The effects of experimental design on outcomes were explored, as measured by Effect Size (ES). 185 studies were included in the meta-analysis. Highest ES were reported for quasi-experimental studies. ES reduced as experimental design moved from single pre-test factor matched, to multiple-factor matched randomized controlled trials. ES reduced when designs used standardised, rather than self-designed measures, The implications for future meta-analyses and research in cooperative learning are explored.

Cross-age tutoring in kindergarten and elementary school settings: a systmeatic review and meta-analysis

Background: Qualified teaching staffs are neither available nor affordable to provide large numbers of children with individual attention. One solution to providing individual tuition has been the development of tutoring programs that are delivered by nonprofessional tutors, such as classmates, older children and community volunteers. Objectives: We have conducted a systematic review of cross-age tutoring interventions delivered by non-professional tutors to children between 5 and 11 years old. Only randomized controlled trials with reliable measures of academic outcomes, and continuing for at least 12 weeks, compared to instruction as usual, were included. Results: Searches of electronic databases and previous reviews, and contacts with researchers yielded 11,564 titles; after screening, 15 studies were included in the analysis. Cross-age tutoring showed small significant effects for tutees on the composite measure of reading (g=0.18, 95% CI: 0.08, 0.27, N=8251), decoding skills (g=0.29, 95% CI: 0.13, 0.44, N=7081), and reading comprehension (g=0.11, 95% CI: 0.01, 0.21, N=6945). No significant effects were detected for other reading sub-skills or for mathematics. The quality of evidence is decreased by study limitations and high heterogeneity of effects. Conclusions: The benefits for tutees of non-professional peer and cross-age tutoring can be given a positive but weak recommendation, considering the low quality of evidence and lack of cost information. Subgroup analyses suggested that highly-structured reading programs may be more useful than loosely-structured programs. Large-scale replication trials using factorial design, process evaluations, reliable outcome measures and logic models are needed to better understand under what conditions, and for whom, cross-age non-professional tutoring may be effective.

Cross-age tutoring in kindergarten and elementary school settings: A systematic review and meta-analysis

This systematic review summarizes effects of peer tutoring delivered to children between 5 and 11 years old by non-professional tutors, such as classmates, older children and adult community peer volunteers. Inclusion criteria for the review included tutoring studies with a randomized controlled trial design, reliable measures of academic outcomes, and duration of at least 12 weeks. Searches of electronic databases, previous reviews, and contacts with researchers yielded 11,564 titles. After screening, 15 studies were included in the analysis. Cross-age tutoring showed small significant effects for tutees on the composite measure of reading (g = 0.18, 95% CI: 0.08, 0.27, N = 8251), decoding skills (g = 0.29, 95% CI: 0.13, 0.44, N = 7081), and reading comprehension (g = 0.11, 95% CI: 0.01, 0.21, N = 6945). No significant effects were detected for other reading sub-skills or for mathematics. The benefits to tutees of non-professional cross-age peer tutoring can be given a positive, but weak recommendation. Effect Sizes were modest and in the range −0.02 to 0.29. Questions regarding study limitations, lack of cost information, heterogeneity of effects, and the relatively small number of studies that have used a randomized controlled trial design means that the evidence base is not as strong as it could be. Subgroup analyses of included studies indicated that highly-structured reading programmes were of more benefit than those that were loosely-structured. Large-scale replication trials using factorial designs, reliable outcome measures, process evaluations and logic models are needed to better understand under what conditions, and for whom, cross-age non-professional peer tutoring may be most effective.

Quantum Chromatic Numbers via Operator Systems

We define several new types of quantum chromatic numbers of a graph and characterize them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.

Operator and Workflow Optimization for High-Performance Analytics

We make a case for studying the impact of intra-node parallelism on the performance of data analytics. We identify four performance optimizations that are enabled by an increasing number of processing cores on a chip. We discuss the performance impact of these opimizations on two analytics operators and we identify how these optimizations affect each another.

The influence of experimental design on the magnitude of the effect size -peer tutoring for elementary, middle and high school settings: A meta-analysis

A meta-analysis was undertaken on a form of cooperative learning, peer tutoring. The effects of experimental design on outcomes were explored, as measured by Effect Size (ES). Forty three articles with 82 effect size studies were included in the meta-analysis. Highest ES were reported for quasi-experimental studies. ES reduced as experimental design moved from single pre-test factor matched, to multiple-factor matched randomized controlled trials. ES reduced when designs used standardised, rather than self-designed measures. The implications for future meta-analyses and research in cooperative learning are explored.