1,182 research outputs found

    Fundamental representations and algebraic properties of biquaternions or complexified quaternions

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    The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates, semi-norms, polar forms, and inner and outer products. The notation is consistent throughout, even between representations, providing a clear account of the many ways in which the component parts of a biquaternion may be manipulated algebraically

    Benchmark Framework for Virtual Students’ Behaviours

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    This paper demonstrates the integration and evaluation of different atmosphere models into Virtual Reality (VR) training for teacher education. We developed three behaviour models to simulate different levels of class discipline. We evaluated their performances using a combination of objective and subjective measurements. Our initial results suggest that the more believable and distinguishable classroom atmospheres are produced by creating more consistent behaviours across virtual students. Our results confirm the importance of similar behaviours to elicit a particular atmosphere

    A randomised controlled trial of breast cancer genetics services in South East Scotland:Psychological impact

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    This study compared the psychological impact of two models of breast cancer genetics services in South East Scotland. One hundred and seventy general practices were randomised to refer patients to the existing standard regional service or the novel community based service. Participants completed postal questionnaires at baseline (n¼373), 4 weeks (n¼276) and 6 months (n¼263) to assess perceived risk of breast cancer, subjective and objective understanding of genetics and screening issues, general psychological\ud distress, cancer worry and health behaviours. For participants in both arms of the trial, there were improvements in subjective and objective understanding up to 4 weeks which were generally sustained up to 6 months. However, improvements in subjective understanding for the women at low risk of breast cancer (i.e. not at significantly increased risk) in the standard service arm did not reach statistical significance. Cancer worry was significantly reduced at 6 months for participants in both arms of the trial. The two models of cancer genetics services tested were generally comparable in terms of the participants’ psychological outcomes. Therefore,\ud decisions regarding the implementation of the novel community-based service should be based on the resources required and client satisfaction with the service

    Common polygenic risk for autism spectrum disorder (ASD) is associated with cognitive ability in the general population

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    Acknowledgements Generation Scotland has received core funding from the Chief Scientist Office of the Scottish Government Health Directorates CZD/16/6 and the Scottish Funding Council HR03006. We are grateful to all the families who took part, the general practitioners and the Scottish School of Primary Care for their help in recruiting them and the whole Generation Scotland team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, volunteers, managers, receptionists, health-care assistants and nurses. We acknowledge with gratitude the financial support received for this work from the Dr Mortimer and Theresa Sackler Foundation. For the Lothian Birth Cohorts (LBC1921 and LBC1936), we thank Paul Redmond for database management assistance; Alan Gow, Martha Whiteman, Alison Pattie, Michelle Taylor, Janie Corley, Caroline Brett and Caroline Cameron for data collection and data entry; nurses and staff at the Wellcome Trust Clinical Research Facility, where blood extraction and genotyping was performed; staff at the Lothian Health Board; and the staff at the SCRE Centre, University of Glasgow. The research was supported by a program grant from Age UK (Disconnected Mind) and by grants from the Biotechnology and Biological Sciences Research Council (BBSRC). The work was undertaken by The University of Edinburgh Centre for Cognitive Ageing and Cognitive Epidemiology, part of the cross council Lifelong Health and Wellbeing Initiative (MR/K026992/1). Funding from the Medical Research Council (MRC) and BBSRC is gratefully acknowledged. DJM is an NRS Career Research Fellow funded by the CSO. BATS were funded by the Australian Research Council (A79600334, A79906588, A79801419, DP0212016, DP0664638, and DP1093900) and the National Health and Medical Research Council (389875) Australia. MKL is supported by a Perpetual Foundation Wilson Fellowship. SEM is supported by a Future Fellowship (FT110100548) from the Australian Research Council. GWM is supported by a National Health and Medical Research Council (NHMRC), Australia, Fellowship (619667). We thank the twins and siblings for their participation, Marlene Grace, Ann Eldridge and Natalie Garden for cognitive assessments, Kerrie McAloney, Daniel Park, David Smyth and Harry Beeby for research support, Anjali Henders and staff in the Molecular Epidemiology Laboratory for DNA sample processing and preparation and Scott Gordon for quality control and management of the genotypes. This work is supported by a Stragetic Award from the Wellcome Trust, reference 104036/Z/14/Z.Peer reviewedPublisher PD

    The Seven-sphere and its Kac-Moody Algebra

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    We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under S7S^7 are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

    Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

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    This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over R\bf R or C\bf C.Comment: 55 pages, 53 reference

    Comparative analysis of new sport types - potential candidates for inclusion in the winter Olympic games

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    The aim of this analysis is to compare and to assess modern sport types and to define one of them as the most suitable for inclusion in the program of the Olympic Winter Games(OWG). As the object of study most suitable sport types were chosen in accordance with the existing criteria for the assessment of the International Olympic Committee. As a result of ranking ski orienteering has the highest potential as the most popular sport having the best coverage in the media and the most convenient for carrying out competitions on existing winter biathlon stadiums or track

    On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

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    Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199
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