Geometric Algebras and Extensors

This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the theory of its deformations leading to metric geometric algebras Cl(V,G) and some special types of extensors. Those tools permit obtaining, the remarkable golden formula relating calculations in Cl(V,G) with easier ones in Cl(V,G_{E}) (e.g., a noticeable relation between the Hodge star operators associated to G and G_{E}). Several useful examples are worked in details fo the purpose of transmitting the "tricks of the trade".Comment: This paper (to appear in Int. J. Geom. Meth. Mod. Phys. 4 (6) 2007) is an improved version of material appearing in math.DG/0501556, math.DG/0501557, math.DG/050155

A cohort study of influences, health outcomes and costs of patients' health-seeking behaviour for minor ailments from primary and emergency care settings

To compare health-related and cost-related outcomes of consultations for symptoms suggestive of minor ailments in emergency departments (EDs), general practices and community pharmacies

Estimating the burden of minor ailment consultations in general practices and emergency departments through retrospective review of routine data in North East Scotland

Minor ailment attendances in general practices and emergency departments (EDs) place significant burden on health care resources

Cystic fibrosis mice carrying the missense mutation G551D replicate human genotype phenotype correlations

We have generated a mouse carrying the human G551D mutation in the cystic fibrosis transmembrane conductance regulator gene (CFTR) by a one-step gene targeting procedure. These mutant mice show cystic fibrosis pathology but have a reduced risk of fatal intestinal blockage compared with 'null' mutants, in keeping with the reduced incidence of meconium ileus in G551D patients. The G551D mutant mice show greatly reduced CFTR-related chloride transport, displaying activity intermediate between that of cftr(mlUNC) replacement ('null') and cftr(mlHGU) insertional (residual activity) mutants and equivalent to approximately 4% of wild-type CFTR activity. The long-term survival of these animals should provide an excellent model with which to study cystic fibrosis, and they illustrate the value of mouse models carrying relevant mutations for examining genotype-phenotype correlations

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

Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained generalized supersymmetries admit a dual formulation. For both real and complex spinors generalized supersymmetries are constructed and classified as dimensional reductions of supersymmetries from {\em oxidized} space-times (i.e. the maximal space-times associated to $n$-component Clifford irreps). We apply these results to sistematically construct a class of models describing superparticles in presence of bosonic tensorial central charges, deriving the consistency conditions for the existence of the action, as well as the constrained equations of motion. Examples of these models (which, in their twistorial formulation, describe towers of higher-spin particles) were first introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and Lukierski (for complex spinors).Comment: 32 pages, LaTe

Topological transversals to a family of convex sets

Let $\mathcal F$ be a family of compact convex sets in $\mathbb R^d$. We say that $\mathcal F$ has a \emph{topological $\rho$-transversal of index $(m,k)$} ($\rho<m$, $0<k\leq d-m$) if there are, homologically, as many transversal $m$-planes to $\mathcal F$ as $m$-planes containing a fixed $\rho$-plane in $\mathbb R^{m+k}$. Clearly, if $\mathcal F$ has a $\rho$-transversal plane, then $\mathcal F$ has a topological $\rho$-transversal of index $(m,k),$ for $\rho<m$ and $k\leq d-m$. The converse is not true in general. We prove that for a family $\mathcal F$ of $\rho+k+1$ compact convex sets in $\mathbb R^d$ a topological $\rho$-transversal of index $(m,k)$ implies an ordinary $\rho$-transversal. We use this result, together with the multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann category of the Grassmannian, and different versions of the colorful Helly theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences

Hermitian versus holomorphic complex and quaternionic generalized supersymmetries of the M-theory. A classification

Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language,"generalized supertranslations") is provided. In each given space-time the maximal, saturated, generalized supersymmetry, compatible with the division-algebra constraint that can be consistently imposed on spinors and on superalgebra generators, is furnished. Constraining the superalgebra generators in both the complex and the quaternionic cases gives rise to the two classes of constrained hermitian and holomorphic generalized supersymmetries. In the complex case these two classes of generalized supersymmetries can be regarded as complementary. The quaternionic holomorphic supersymmetry only exists in certain space-time dimensions and can admit at most a single bosonic scalar central charge. The results here presented pave the way for a better understanding of the various $M$ algebra-type of structures which can be introduced in different space-time signatures and in association with different division algebras, as well as their mutual relations. In a previous work, e.g., the introduction of a complex holomorphic generalized supersymmetry was shown to be necessary in order to perform the analytic continuation of the standard $M$-theory to the 11-dimensional Euclidean space. As an application of the present results, it is shown that the above algebra also admits a 12-dimensional, Euclidean, $F$-algebra presentation.Comment: 25 pages, LaTe

Referrals of women with a family history of breast cancer from primary care to cancer genetics services in South East Scotland

As part of a cluster randomised trial to assess an alternative model of cancer genetics services, we gathered data on all referrals from general practitioners (GPs) to cancer genetics services in South East Scotland over a 4-year period. The referral rate per 1000 patients rose by 48% from 0.21 in the 2-year period before the trial to 0.31 during the trial. This increase was much greater in the trial group offered the GP clinic service (64% increase compared to a 38% increase in those referred to the regional service). Thus, the offer of a more local service appeared to have a marked effect on GP management of these women. Referral rates to cancer genetics services from general practices varied widely with higher referral rates from practices with more female partners. There was a negative correlation between referral rates and practice area deprivation scores. However, this was not found during the trial in the group which offered clinics in general practice, the provision of clinic appointments nearer to the homes of more socially deprived women resulting in improved access to women from deprived areas. The interaction with the GP appears to be associated with an inappropriate level of interest in and expectation of the appropriateness of genetic testing. The provision of the clinics within general practice did not result in higher levels of confidence among GPs in managing these women