359 research outputs found
Parallel spinors and holonomy groups
In this paper we complete the classification of spin manifolds admitting
parallel spinors, in terms of the Riemannian holonomy groups. More precisely,
we show that on a given n-dimensional Riemannian manifold, spin structures with
parallel spinors are in one to one correspondence with lifts to Spin_n of the
Riemannian holonomy group, with fixed points on the spin representation space.
In particular, we obtain the first examples of compact manifolds with two
different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2
A Bayesian semiparametric Markov regression model for juvenile dermatomyositis
Juvenile dermatomyositis (JDM) is a rare autoimmune disease that may lead to serious complications, even to death. We develop a 2-state Markov regression model in a Bayesian framework to characterise disease progression in JDM over time and gain a better understanding of the factors influencing disease risk. The transition probabilities between disease and remission state (and vice versa) are a function of time-homogeneous and time-varying covariates. These latter types of covariates are introduced in the model through a latent health state function, which describes patient-specific health over time and accounts for variability among patients. We assume a nonparametric prior based on the Dirichlet process to model the health state function and the baseline transition intensities between disease and remission state and vice versa. The Dirichlet process induces a clustering of the patients in homogeneous risk groups. To highlight clinical variables that most affect the transition probabilities, we perform variable selection using spike and slab prior distributions. Posterior inference is performed through Markov chain Monte Carlo methods. Data were made available from the UK JDM Cohort and Biomarker Study and Repository, hosted at the UCL Institute of Child Health
Manifolds with small Dirac eigenvalues are nilmanifolds
Consider the class of n-dimensional Riemannian spin manifolds with bounded
sectional curvatures and diameter, and almost non-negative scalar curvature.
Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of
the Dirac operator on such a manifold has small eigenvalues, then the
manifold is diffeomorphic to a nilmanifold and has trivial spin structure.
Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a
non-trivial spin structure, then there exists a uniform lower bound on the r-th
eigenvalue of the square of the Dirac operator. If a manifold with almost
nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume
is not too small, then we show that the metric is close to a Ricci-flat metric
on M with a parallel spinor. In dimension 4 this implies that M is either a
torus or a K3-surface
On the supersymmetries of anti de Sitter vacua
We present details of a geometric method to associate a Lie superalgebra with
a large class of bosonic supergravity vacua of the type AdS x X, corresponding
to elementary branes in M-theory and type II string theory.Comment: 16 page
Comparison of the Utility and Validity of Three Scoring Tools to Measure Skin Involvement in Patients With Juvenile Dermatomyositis
OBJECTIVE: To compare the abbreviated Cutaneous Assessment Tool (CAT), Disease Activity Score (DAS), and Myositis Intention to Treat Activity Index (MITAX) and correlate them with the physician's 10-cm skin visual analog scale (VAS) in order to define which tool best assesses skin disease in patients with juvenile dermatomyositis. METHODS: A total of 71 patients recruited to the UK Juvenile Dermatomyositis Cohort and Biomarker Study were included and assessed for skin disease using the CAT, DAS, MITAX, and skin VAS. The Childhood Myositis Assessment Scale (CMAS), manual muscle testing of 8 groups (MMT8), muscle enzymes, inflammatory markers, and physician's global VAS were recorded. Relationships were evaluated using Spearman's correlations and predictors with linear regression. Interrater reliability was assessed using intraclass correlation coefficients. RESULTS: All 3 tools showed correlation with the physician's global VAS and skin VAS, with DAS skin showing the strongest correlation with skin VAS. DAS skin and CAT activity were inversely correlated with CMAS and MMT8, but these correlations were moderate. No correlations were found between the skin tools and inflammatory markers or muscle enzymes. DAS skin and CAT were the quickest to complete (meanâ±âSD 0.68â±â0.1 minutes and 0.63â±â0.1 minutes, respectively). CONCLUSION: The 3 skin tools were quick and easy to use. The DAS skin correlated best with the skin VAS. The addition of CAT in a bivariate model containing the physician's global VAS was a statistically significant estimator of skin VAS score. We propose that there is scope for a new skin tool to be devised and tested, which takes into account the strengths of the 3 existing tools
The Singularity Problem for Space-Times with Torsion
The problem of a rigorous theory of singularities in space-times with torsion
is addressed. We define geodesics as curves whose tangent vector moves by
parallel transport. This is different from what other authors have done,
because their definition of geodesics only involves the Christoffel connection,
though studying theories with torsion. We propose a preliminary definition of
singularities which is based on timelike or null geodesic incompleteness, even
though for theories with torsion the paths of particles are not geodesics. The
study of the geodesic equation for cosmological models with torsion shows that
the definition has a physical relevance. It can also be motivated, as done in
the literature, remarking that the causal structure of a space-time with
torsion does not get changed with respect to general relativity. We then prove
how to extend Hawking's singularity theorem without causality assumptions to
the space-time of the ECSK theory. This is achieved studying the generalized
Raychaudhuri equation in the ECSK theory, the conditions for the existence of
conjugate points and properties of maximal timelike geodesics. Hawking's
theorem can be generalized, provided the torsion tensor obeys some conditions.
Thus our result can also be interpreted as a no-singularity theorem if these
additional conditions are not satisfied. In other words, it turns out that the
occurrence of singularities in closed cosmological models based on the ECSK
theory is less generic than in general relativity. Our work is to be compared
with previous papers in the literature. There are some relevant differences,
because we rely on a different definition of geodesics, we keep the field
equations of the ECSK theory in their original form rather than casting them in
a form similar to general relativity with a modified energy momentum tensor,Comment: 17 pages, plain-tex, published in Nuovo Cimento B, volume 105, pages
75-90, year 199
On Four-Point Functions of Half-BPS Operators in General Dimensions
We study four-point correlation functions of half-BPS operators of arbitrary
weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using
harmonic superspace techniques, we derive the superconformal Ward identities
for these correlators and present them in a universal form. We then solve these
identities, employing Jack polynomial expansions. We show that the general
solution is parameterized by a set of arbitrary two-variable functions, with
the exception of the case d=4, where in addition functions of a single variable
appear. We also discuss the operator product expansion using recent results on
conformal partial wave amplitudes in arbitrary dimension.Comment: The discussion of the case d=6 expanded; references added/correcte
Nonstandard Drinfeld-Sokolov reduction
Subject to some conditions, the input data for the Drinfeld-Sokolov
construction of KdV type hierarchies is a quadruplet (\A,\Lambda, d_1, d_0),
where the are -gradations of a loop algebra \A and \Lambda\in \A
is a semisimple element of nonzero -grade. A new sufficient condition on
the quadruplet under which the construction works is proposed and examples are
presented. The proposal relies on splitting the -grade zero part of \A
into a vector space direct sum of two subalgebras. This permits one to
interpret certain Gelfand-Dickey type systems associated with a nonstandard
splitting of the algebra of pseudo-differential operators in the
Drinfeld-Sokolov framework.Comment: 19 pages, LaTeX fil
A natural Finsler--Laplace operator
We give a new definition of a Laplace operator for Finsler metric as an
average with regard to an angle measure of the second directional derivatives.
This definition uses a dynamical approach due to Foulon that does not require
the use of connections nor local coordinates. We show using 1-parameter
families of Katok--Ziller metrics that this Finsler--Laplace operator admits
explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio
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