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Gaussian Approximations of Multiple Integrals
Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional
vectors of multiple Wiener-It\^o integrals with respect to a general Gaussian
process. We establish necessary and sufficient conditions to have that, as l
diverges, the law of I(l) is asymptotically close (for example, in the sense of
Prokhorov's distance) to the law of a k-dimensional Gaussian vector having the
same covariance matrix as I(l). The main feature of our results is that they
require minimal assumptions (basically, boundedness of variances) on the
asymptotic behaviour of the variances and covariances of the elements of I(l).
In particular, we will not assume that the covariance matrix of I(l) is
convergent. This generalizes the results proved in Nualart and Peccati (2005),
Peccati and Tudor (2005) and Nualart and Ortiz-Latorre (2007). As shown in
Marinucci and Peccati (2007b), the criteria established in this paper are
crucial in the study of the high-frequency behaviour of stationary fields
defined on homogeneous spaces.Comment: 15 page
R-from-T as a common mechanism of arrhythmia initiation in long QT syndromes
Background: Long QT syndromes (LQTS) arise from many genetic and nongenetic causes with certain characteristic ECG features preceding polymorphic ventricular tachyarrhythmias (PVTs). However, how the many molecular causes result in these characteristic ECG patterns and how these patterns are mechanistically linked to the spontaneous initiation of PVT remain poorly understood. Methods: Anatomic human ventricle and simplified tissue models were used to investigate the mechanisms of spontaneous initiation of PVT in LQTS. Results: Spontaneous initiation of PVT was elicited by gradually ramping up I-Ca,I-L to simulate the initial phase of a sympathetic surge or by changing the heart rate, reproducing the different genotype-dependent clinical ECG features. In LQTS type 2 (LQT2) and LQTS type 3 (LQT3), T-wave alternans was observed followed by premature ventricular complexes (PVCs). Compensatory pauses occurred resulting in short-long-short sequences. As I-Ca,I-L increased further, PVT episodes occurred, always preceded by a short-long-short sequence. However, in LQTS type 1 (LQT1), once a PVC occurred, it always immediately led to an episode of PVT. Arrhythmias in LQT2 and LQT3 were bradycardia dependent, whereas those in LQT1 were not. In all 3 genotypes, PVCs always originated spontaneously from the steep repolarization gradient region and manifested on ECG as R-on-T. We call this mechanism R-from-T, to distinguish it from the classic explanation of R-on-T arrhythmogenesis in which an exogenous PVC coincidentally encounters a repolarizing region. In R-from-T, the PVC and the T wave are causally related, where steep repolarization gradients combined with enhanced I-Ca,I-L lead to PVCs emerging from the T wave. Since enhanced I-Ca,I-L was required for R-from-T to occur, suppressing window I-Ca,I-L effectively prevented arrhythmias in all 3 genotypes. Conclusions: Despite the complex molecular causes, these results suggest that R-from-T is likely a common mechanism for PVT initiation in LQTS. Targeting I-Ca,I-L properties, such as suppressing window I-Ca,I-L or preventing excessive I-Ca,I-L increase, could be an effective unified therapy for arrhythmia prevention in LQTS
A realization of the Lie algebra associated to a Kantor triple system
We present a nonlinear realization of the 5-graded Lie algebra associated to
a Kantor triple system. Any simple Lie algebra can be realized in this way,
starting from an arbitrary 5-grading. In particular, we get a unified
realization of the exceptional Lie algebras f_4, e_6, e_7, e_8, in which they
are respectively related to the division algebras R, C, H, O.Comment: 11 page
On structure of effective action in four-dimensional quantum dilaton supergravity
A general structure of effective action in new chiral superfield model
associated with , supergravity is investigated. This model
corresponds to finite quantum field theory and does not demand the
regularization and renormalization at effective action calculation. It is shown
that in local approximation the effective action is defined by two objects
called general superfield effective lagrangian and chiral superfield effective
lagrangian. A proper-time method is generalized for calculation of these two
effective lagrangians in superfield manner. Power expansion of the effective
action in supercovariant derivatives is formulated and the lower terms of such
an expansion are calculated in explicit superfield form
Dyonic Masses from Conformal Field Strengths in D even Dimensions
We show that D/2--form gauge fields in D even dimensions can get a mass with
both electric and magnetic contributions when coupled to conformal
field--strengths whose gauge potentials is are \frac {D-2}{2}- forms. Denoting
by e^I_\L and m^{I\L} the electric and magnetic couplings, gauge invariance
requires: e^I_\L m^{J\L}\mp e^J_\L m^{I\L}=0, where I,\L= 1... m denote the
species of gauge potentials of degree D/2 and gauge fields of degree D/2-1,
respectively. The minus and plus signs refer to the two different cases D=4n
and D=4n+2 respectively and the given constraints are respectively {\rm
{Sp}}(2m) and {\rm {O}}(m,m) invariant. For the simplest examples, (I,\L=1 for
D=4n and I,\L=1,2 for D=4n+2) both the e,m quantum numbers contribute to the
mass \m=\sqrt {e^2 +m^2} . This phenomenon generalizes to even dimensions
the coupling of massive antisymmetric tensors which appear in D=4 supergravity
Lagrangians which derive from flux compactifications in higher dimensions. For
D=4 we give the supersymmetric generalization of such couplings using N=1
superspace.Comment: 11 pages, LaTeX source, typos corrected. Version to appear on
Phys.Lett.
Back reaction of vacuum and the renormalization group flow from the conformal fixed point
We consider the GUT-like model with two scalar fields which has infinitesimal
deviation from the conformal invariant fixed point at high energy region. In
this case the dominating quantum effect is the conformal trace anomaly and the
interaction between the anomaly-generated propagating conformal factor of the
metric and the usual dimensional scalar field. This interaction leads to the
renormalization group flow from the conformal point. In the supersymmetric
conformal invariant model such an effect produces a very weak violation of
sypersymmetry at lower energies.Comment: 15 pages, LaTex, ten figures, uuencoded fil
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