Determinants of short-period heart rate variability in the general population

Decreased heart rate variability (HRV) is associated with a worse prognosis in a variety of diseases and disorders. We evaluated the determinants of short-period HRV in a random sample of 149 middle-aged men and 137 women from the general population. Spectral analysis was used to compute low-frequency (LF), high-frequency (HF) and total-frequency power. HRV showed a strong inverse association with age and heart rate in both sexes with a more pronounced effect of heart rate on HRV in women. Age and heart rate-adjusted LF was significantly higher in men and HF higher in women. Significant negative correlations of BMI, triglycerides, insulin and positive correlations of HDL cholesterol with LF and total power occurred only in men. In multivariate analyses, heart rate and age persisted as prominent independent predictors of HRV. In addition, BMI was strongly negatively associated with LF in men but not in women, We conclude that the more pronounced vagal influence in cardiac regulation in middle-aged women and the gender-different influence of heart rate and metabolic factors on HRV may help to explain the lower susceptibility of women for cardiac arrhythmias. Copyright (C) 2001 S. Karger AG, Basel

Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2

The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere. In this paper, instead of the uniform distribution, we introduce Brownian motion on a sphere to yield the parametric motion of the energy levels. As a result, the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the GSE universality class. Moreover, by starting the Brownian motion from a point distribution on the sphere, we gradually increase the effect of the spin and calculate the form factor describing the transition from the GOE (Gaussian Orthogonal Ensemble) class to the GSE class.Comment: 25 pages, 2 figure

Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

Laughlin states on the Poincare half-plane and its quantum group symmetry

We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.Comment: 9 pages,Late

Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph

We study the spectral statistics of the Dirac operator on a rose-shaped graph---a graph with a single vertex and all bonds connected at both ends to the vertex. We formulate a secular equation that generically determines the eigenvalues of the Dirac rose graph, which is seen to generalise the secular equation for a star graph with Neumann boundary conditions. We derive approximations to the spectral pair correlation function at large and small values of spectral spacings, in the limit as the number of bonds approaches infinity, and compare these predictions with results of numerical calculations. Our results represent the first example of intermediate statistics from the symplectic symmetry class.Comment: 26 pages, references adde

NGC 2419, M92, and the Age Gradient in the Galactic Halo

The WFPC2 camera on HST has been used to obtain deep main sequence photometry of the low-metallicity ([Fe/H]=-2.14), outer-halo globular cluster NGC 2419. A differential fit of the NGC 2419 CMD to that of the similarly metal-poor \ standard cluster M92 shows that they have virtually identical principal sequences and thus the same age to well within 1 Gyr. Since other low-metallicity clusters throughout the Milky Way halo have this same age to within the 1-Gyr precision of the differential age technique, we conclude that the earliest star (or globular cluster) formation began at essentially the same time everywhere in the Galactic halo throughout a region now almost 200 kpc in diameter. Thus for the metal-poorest clusters in the halo there is no detectable age gradient with Galactocentric distance. To estimate the absolute age of NGC 2419 and M92, we fit newly computed isochrones transformed through model-atmosphere calculations to the (M_V,V-I) plane, with assumed distance scales that represent the range currently debated in the literature. Unconstrained isochrone fits give M_V(RR) = 0.55 \pm 0.06 and a resulting age of 14 to 15 Gyr. Incorporating the full effects of helium diffusion would further reduce this estimate by about 1 Gyr. A distance scale as bright as M_V(RR) = 0.15 for [Fe/H] = -2, as has recently been reported, would leave several serious problems which have no obvious solution in the context of current stellar models.Comment: 32 pages, aastex, 9 postscript figures; accepted for publication in AJ, September 1997. Also available by e-mail from [email protected]

Semiclassical Approach to Chaotic Quantum Transport

We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and other related quantities require trajectory quadruplets; simple diagrammatic rules allow to find the contributions of these pairs and quadruplets. Both pure symmetry classes and the crossover due to an external magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version

Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Cosmic String Network Evolution in arbitrary Friedmann-Lemaitre models

We use the velocity-dependent one-scale model by Martins & Shellard to investigate the evolution of a GUT long cosmic string network in arbitrary Friedmann-Lemaitre models. Four representative models are used to show that in general there is no scaling solution. The implications for structure formation are briefly discussed.Comment: 8 pages, 4 postscript figures included, submitted to Phys. Rev.