Jacob Levitan

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al. on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficient related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of ~ 0.035 (for the above mentioned filter), below which individuals are at risk.

Geometry of Hamiltonian chaos.

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to an associated manifold. We find, in this way, a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this associated manifold results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions.

DISCRIMINATION BETWEEN HEALTHY AND SICK CARDIAC AUTONOMIC NERVOUS SYSTEM BY DETRENDED HEART RATE VARIABILITY ANALYSIS

Multiresolution Wavelet Transform and Detrended Fluctuation Analysis have recently been proven to be excellent methods in the analysis of Heart Rate Variability and in distinguishing between healthy subjects and patients with various dysfunctions of the cardiac nervous system. We argue that it is possible to obtain a distinction between healthy subjects/patients of at least similar quality by, first, detrending the time-series of RR-intervals by subtracting a running average based on a local window with a length of around 32 data points, then calculating the standard deviation of the detrended time-series. The results presented here indicate that the analysis can be based on very short time-series of RR-data (7–8 minutes), which is a considerable improvement relative to 24-hour Holter recordings.

Numerical study of zeno and anti-zeno effects in a local potential model

Abstract The effect of perturbation of a barrier on the passage of a wave packet is studied as an example of a perturbed unstable system. It is found that with a small periodic perturbation, significant modification of the effective lifetime occurs. The decay may be retarded (Zeno effect) or enhanced according to the relative phase of the perturbation and arrival time of the packet.

COMPARISON OF RECENT METHODS OF ANALYZING HEART RATE VARIABILITY

We compare three recently applied methods for analyzing heart rate variability: detrended fluctuation analysis (DFA), multiresolution wavelet analysis (WAV) and detrended time series analysis (DTS). In the comparison, both scale-dependent and scale-independent measures are considered. In agreement with recent results by Thurner et al.,9 we conclude that scale-dependent measures are well suited to separate healthy subjects from patients with heart disease. However, as regards the use in Kaplan-Meier cumulative survival curves, scale-independent measures (generally slope values) clearly outperform scale dependent measures (generally rms values). The comparison is mainly based on a database containing recordings from 428 patients with heart disease (myocardial infarct) and on a database containing 105 healthy subjects and 11 heart patients.

Description of complex time series by multipoles

We present a new method to describe time series with a highly complex time evolution. The time series is projected onto a two-dimensional phase–space plot which is quantified in terms of a multipole expansion where every data point is assigned a unit mass. The multipoles provide an efficient characterization of the original time series.

Heart Rate Variability Density Analysis (Dyx) and Prediction of Long‐Term Mortality after Acute Myocardial Infarction

The density HRV parameter Dyx is a new heart rate variability (HRV) measure based on multipole analysis of the Poincaré plot obtained from RR interval time series, deriving information from both the time and frequency domain. Preliminary results have suggested that the parameter may provide new predictive information on mortality in survivors of acute myocardial infarction (MI). This study compares the prognostic significance of Dyx to that of traditional linear and nonlinear measures of HRV.

Statistical analysis of the DIAMOND MI study by the multipole method

We present a new method to describe the dynamics of the beat-to-beat RR time series. The classification of the phase-space plots obtained from RR time series is performed by a calculation of parameters which describe the features of the two-dimensional plot. We demonstrate that every parameter has its specific consequence on the evaluation of the state of the cardiac function. By applying the method to the DIAMOND MI study we demonstrate that these parameters have more prognostic power than previously suggested risk markers. The results suggest that the RR intervals constitute a highly complex time series which necessitates the use of refined mathematical-statistical methods in order to reveal pathologies in the heart rate.

CHAOTIC SIGNATURES IN THE SPECTRUM OF A QUANTUM DOUBLE WELL

The spectrum of a double well constructed of a square barrier embedded in an infinite well is analyzed. Level statistics for levels slightly above the barrier show signs of Wigner statistics usually associated with quantum chaos. The correspondence with Wigner statistics improves when an ensemble of systems with slightly different barrier heights is taken, possibly reflecting an adiabatic time-dependent modulation of the barrier.

A soluble model for time dependent perturbations of an unstable quantum system

Abstract We show that a time dependent addition to the coupling constant of the Lee-Friedrichs model results in an exactly soluble model for the effect of time dependent perturbations of an unstable quantum system. For a perturbation of a single frequency, a shift in the position of the original Lee-Friedrichs pole, and the emergence of a harmonically associated sequence of other poles, are obtained by iteration of the exact difference equations for the reduced resolvent. In lowest order, line broadening can be seen directly in the structure of the shifted pole position. If the time dependence contains modulation, e.g., with two commensurate frequencies, we show that there are contributions which could lead to line narrowing as well.