How orthogonalities set Kochen-Specker sets

We look at generalisations of sets of vectors proving the Kochen-Specker theorem in 3 and 4 dimensions. It has been shown that two such sets, although unitarily inequivalent, are part of a larger 3-parameter family of vectors that share the same orthogonality graph. We find that these sets are unusual, in that the vectors in all other Kochen-Specker sets investigated here are fully determined by orthogonality conditions and thus admit no free parameters.Comment: 3 pages, contribution to the V\"axj\"o conference "Advances in Quantum Theory

A contemporary insight into Islamist extremist radicalisation and an exploration of the effectiveness of prevention and reformative strategies

The threat of Islamist extremism has become a major concern for many countries, requiring the development and implementation of effective de-radicalisation strategies. The focus of this study is to provide a contemporary insight into the radicalisation process of Islamist extremists and the effectiveness of the Prevent strategy as a de-radicalisation approach. The research methodology involved conducting a survey with 46 Prevent practitioners throughout the UK regions of the Counter Terror Commands. The design of the survey implemented a series of open-ended and closed-ended questions to gather first-hand experiences and insights. This created both qualitative and quantitative elements to the research with respondents being given the opportunity scale questions in order of their perceived importance and then elaborate on their answers with the free-text questions. The results of the study revealed several key themes and identified areas where the Prevent strategy could be improved. Specifically, the results identified prominent demographics of individuals being radicalised, the most significant locations being used to do so and new tactics employed by radicalisers and extremist groups. The study presents key findings regarding the sites of radicalisation and the platforms utilised by Islamist extremist recruiters to engage with and motivate individuals towards terrorism. It is noted that there has been a shift from traditional in-person interactions towards the online space, where new platforms, such as gaming, have emerged as a potential high level threat due to their difficulty to monitor. Recommendations are made to utilise new technologies to stay ahead of young, enterprising individuals. The findings suggest that the Prevent strategy is effective, but better communication is required to highlight successes and to gain the societal approval required due to being a voluntary service. Additional policy and procedural recommendations are made to enhance the program's efficiency and effectiveness. The limitations of this study are that it presented from a Prevent policing practitioner perspective only. Future research should consider surveying individuals who have been referred to the Channel program to provide a rounded perspective. The findings provide key discoveries and valuable information for policymakers and practitioners to assist in combating Islamist extremism and developing effective de-radicalisation strategies

Order 3 Symmetry in the Clifford Hierarchy

We investigate the action of the first three levels of the Clifford hierarchy on sets of mutually unbiased bases comprising the Ivanovic MUB and the Alltop MUBs. Vectors in the Alltop MUBs exhibit additional symmetries when the dimension is a prime number equal to 1 modulo 3 and thus the set of all Alltop vectors splits into three Clifford orbits. These vectors form configurations with so-called Zauner subspaces, eigenspaces of order 3 elements of the Clifford group highly relevant to the SIC problem. We identify Alltop vectors as the magic states that appear in the context of fault-tolerant universal quantum computing, wherein the appearance of distinct Clifford orbits implies a surprising inequivalence between some magic states.Comment: 20 pages, 2 figures. Published versio

Sex education in Iowa: sex educator characteristics and curricular materials used in public junior and senior high schools

Teachers, school counselors, and others teach sex education. They may or may not use commercially produced sex education materials. This study examined the commercially produced materials used by sex educators. This study also examined sex educator characteristics. Specifically, the problem addressed is: (a) what are the characteristics of sex educators in Iowa? and (b) what type of sex education is offered in Iowa public schools? and (c) what is the perceived usefulness of commercial sex education materials as reported by sex educators in Iowa

A second order algebraic knot concordance group

We define an algebraic group comprising symmetric chain complexes which captures the first two stages of the Cochran-Orr-Teichner solvable filtration of the knot concordance group in a single invariant. To achieve this we impose additional structure on each chain complex which puts extra control on the fundamental groups, and in particular on the way in which they can change in a concordance.Comment: 51 pages, 2 figures. This a considerably shortened version of arXiv:1109.0761, to appear in Algebraic and Geometric Topolog