246 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
Covariance and Fisher information in quantum mechanics
Variance and Fisher information are ingredients of the Cramer-Rao inequality.
We regard Fisher information as a Riemannian metric on a quantum statistical
manifold and choose monotonicity under coarse graining as the fundamental
property of variance and Fisher information. In this approach we show that
there is a kind of dual one-to-one correspondence between the candidates of the
two concepts. We emphasis that Fisher informations are obtained from relative
entropies as contrast functions on the state space and argue that the scalar
curvature might be interpreted as an uncertainty density on a statistical
manifold.Comment: LATE
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
A Reilly formula and eigenvalue estimates for differential forms
We derive a Reilly-type formula for differential p-forms on a compact
manifold with boundary and apply it to give a sharp lower bound of the spectrum
of the Hodge Laplacian acting on differential forms of an embedded hypersurface
of a Riemannian manifold. The equality case of our inequality gives rise to a
number of rigidity results, when the geometry of the boundary has special
properties and the domain is non-negatively curved. Finally we also obtain, as
a by-product of our calculations, an upper bound of the first eigenvalue of the
Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 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
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
D-Matter
We study the properties and phenomenology of particle-like states originating
from D-branes whose spatial dimensions are all compactified. They are
non-perturbative states in string theory and we refer to them as D-matter. In
contrast to other non-perturbative objects such as 't Hooft-Polyakov monopoles,
D-matter states could have perturbative couplings among themselves and with
ordinary matter. The lightest D-particle (LDP) could be stable because it is
the lightest state carrying certain (integer or discrete) quantum numbers.
Depending on the string scale, they could be cold dark matter candidates with
properties similar to that of wimps or wimpzillas. The spectrum of excited
states of D-matter exhibits an interesting pattern which could be distinguished
from that of Kaluza-Klein modes, winding states, and string resonances. We
speculate about possible signatures of D-matter from ultra-high energy cosmic
rays and colliders.Comment: 25 pages, 5 figures, references adde
Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
In spacetimes admitting Yano tensors the classical theory of the spinning
particle possesses enhanced worldline supersymmetry. Quantum mechanically
generators of extra supersymmetries correspond to operators that in the
classical limit commute with the Dirac operator and generate conserved
quantities. We show that the result is preserved in the full quantum theory,
that is, Yano symmetries are not anomalous. This was known for Yano tensors of
rank two, but our main result is to show that it extends to Yano tensors of
arbitrary rank. We also describe the conformal Yano equation and show that is
invariant under Hodge duality. There is a natural relationship between Yano
tensors and supergravity theories. As the simplest possible example, we show
that when the spacetime admits a Killing spinor then this generates Yano and
conformal Yano tensors. As an application, we construct Yano tensors on
maximally symmetric spaces: they are spanned by tensor products of Killing
vectors.Comment: 1+32 pages, no figures. Accepted for publication on Classical and
Quantum Gravity. New title and abstract. Some material has been moved to the
Appendix. Concrete formulas for Yano tensors on some special holonomy
manifolds have been provided. Some corrections included, bibliography
enlarge
Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling
We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement
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
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