705 research outputs found
Revisiting Clifford algebras and spinors III: conformal structures and twistors in the paravector model of spacetime
This paper is the third of a series of three, and it is the continuation of
math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime
structure, conformal maps are described in Minkowski spacetime as the twisted
adjoint representation of the group Spin_+(2,4), acting on paravectors.
Twistors are then presented via the paravector model of Clifford algebras and
related to conformal maps in the Clifford algebra over the lorentzian R{4,1}$
spacetime. We construct twistors in Minkowski spacetime as algebraic spinors
associated with the Dirac-Clifford algebra Cl(1,3)(C) using one lower spacetime
dimension than standard Clifford algebra formulations, since for this purpose
the Clifford algebra over R{4,1} is also used to describe conformal maps,
instead of R{2,4}. Although some papers have already described twistors using
the algebra Cl(1,3)(C), isomorphic to Cl(4,1), the present formulation sheds
some new light on the use of the paravector model and generalizations.Comment: 17 page
Large-Scale Distributed Bayesian Matrix Factorization using Stochastic Gradient MCMC
Despite having various attractive qualities such as high prediction accuracy
and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix
Factorization has not been widely adopted because of the prohibitive cost of
inference. In this paper, we propose a scalable distributed Bayesian matrix
factorization algorithm using stochastic gradient MCMC. Our algorithm, based on
Distributed Stochastic Gradient Langevin Dynamics, can not only match the
prediction accuracy of standard MCMC methods like Gibbs sampling, but at the
same time is as fast and simple as stochastic gradient descent. In our
experiments, we show that our algorithm can achieve the same level of
prediction accuracy as Gibbs sampling an order of magnitude faster. We also
show that our method reduces the prediction error as fast as distributed
stochastic gradient descent, achieving a 4.1% improvement in RMSE for the
Netflix dataset and an 1.8% for the Yahoo music dataset
On the Elliptic-Hyperbolic Transition in Whitham Modulation Theory
The dispersionless Whitham modulation equations in one space dimension and time
are generically hyperbolic or elliptic, and breakdown at the transition, which is a curve in the
frequency-wavenumber plane. In this paper, the modulation theory is reformulated with a slow
phase and different scalings resulting in a phase modulation equation near the singular curves which
is a geometric form of the two-way Boussinesq equation. This equation is universal in the same sense
as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multiperiodic,
quasiperiodic and multi-pulse localized solutions. This theory shows that the elliptic-hyperbolic
transition is a rich source of complex behaviour in nonlinear wave fields. There are several examples
of these transition curves in the literature to which the theory applies. For illustration the theory
is applied to the complex nonlinear Klein-Gordon equation which has two singular curves in the
manifold of periodic travelling waves
On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form
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
Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
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 or .Comment: 55 pages, 53 reference
Common polygenic risk for autism spectrum disorder (ASD) is associated with cognitive ability in the general population
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
POSIWID and determinism in design for behaviour change
Copyright @ 2012 Social Services Research GroupWhen designing to influence behaviour for social or environmental benefit, does designers' intent matter? Or are the effects on behaviour more important, regardless of the intent involved? This brief paper explores -- in the context of design for behaviour change -- some treatments of design, intentionality, purpose and responsibility from a variety of fields, including Stafford Beer's "The purpose of a system is what it does" and Maurice Broady's perspective on determinism. The paper attempts to extract useful implications for designers working on behaviour-related problems, in terms of analytical or reflective questions to ask during the design process
The UK prevalence of hereditary haemorrhagic telangiectasia and its association with sex, socioeconomic status and region of residence: a population-based study
Background Hereditary haemorrhagic telangiectasia (HHT) is an autosomal dominant genetic disorder of aberrant blood vessel development characterised by arteriovenous malformations. HHT is associated with significant morbidity due to complications including epistaxis, gastrointestinal bleeding and stroke. We explored the hypothesis that a diagnosis of HHT is associated with sex, socioeconomic status and geographical location.Methods We used The Health Improvement Network, a longitudinal, computerised general practice database covering 5% of the UK population to calculate prevalence estimates for HHT stratified by age, sex, socioeconomic status and geographical location.Results The 2010 UK point prevalence for HHT was 1.06/10 000 person years (95% CI 0.95 to 1.17) or 1 in 9400 individuals. The diagnosed prevalence of HHT was significantly higher in women compared with men (adjusted prevalence rate ratio (PRR) 1.53, 95% CI 1.24 to 1.88) and in those from the most affluent socioeconomic group compared with the least (adjusted PRR 1.74, 95% CI 1.14 to 2.64). The PRR varied between different regions of the UK, being highest in the South West and lowest in the West Midlands (adjusted PRR for former compared with latter 1.86, 95% CI 1.61 to 2.15).Conclusions HHT prevalence is more common in the UK population than previously demonstrated, though this updated figure is still likely to be an underestimate. HHT appears to be significantly under-diagnosed in men, which is likely to reflect their lower rates of consultation with primary care services. There is under-diagnosis in patients from lower socioeconomic groups and a marked variation in the prevalence of diagnosis between different geographical regions across the UK that requires further investigation
From Barbie to the oligarchs wife: Reading fantasy femininity and globalisation in post-Soviet Russian womens magazines
This article shows how an analysis of fantasy femininity sheds light on how norms of gender, class and national identity reflect global and local cross-cultural currents in post-Soviet Russia. Drawing on a discourse analysis of women’s magazines and in-depth interviews with readers, it shows how, in the globalized post-Soviet cultural landscape, fantasy femininity represents both change and continuity. Feminine archetypes in women’s magazines, from fairytale princesses to Barbie dolls, reflect a wider post-Soviet cultural hybridisation, and show how Western women’s magazines have adapted to the Russian context. Furthermore, the article highlights readers’ ambiguous attitudes towards post-Soviet cultural trends linked to perceived Westernisation or globalisation, such as individualism, conspicuous consumption, and glamour
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