Dejin Yu

Uncovering non-linear structure in human ECG recordings

We employ surrogate data techniques and a new correlation dimension estimation algorithm, the Gaussian kernel algorithm, to uncover non-linearity in human electrocardiogram recordings during normal (sinus) rhythm, ventricular tachycardia (VT) and ventricular fibrillation (VF). We conclude that all three rhythms are not linear (i.e. distinct from a monotonic non-linear transformation of linearly filtered noise) and have significant correlations over a period greater than the inter-beat interval. Furthermore, we observe that sinus rhythm and VT exhibit a correlation dimension of approximately 2.3 and 2.4, respectively. The correlation dimension of VF exceeds 3.2. The entropy of sinus rhythm, VT and VF is approximately 0.69, 0.55, and 0.67 nats/s, respectively. These results indicate that techniques from non-linear dynamical systems theory should help us understand the mechanism underlying ventricular arrhythmia, and that these rhythms are likely to be a combination of low dimensional chaos and noise. 2002 Elsevier Science Ltd. All rights reserved.

Sbs self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre

Abstract High fidelity, polarised, optical phase conjugation via stimulated Brillouin scattering of CW laser radiation in a multimode silica fibre is reported. A power threshold of ∼70 mW and reflectivity of 70% were obtained in a 4.23 km length of fibre with a Nd:YAG laser.

Space time-index plots for probing dynamical nonstationarity

Abstract We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.

A new self-diffraction pattern formation in defocusing liquid media

Abstract We report on steady-state dark spot formation in the center of the far field of a divergent Gaussian beam transmitted through a thin absorbing defocusing liquid medium. The size of the dark region is found to be approximately conserved with increase of incident pump power. Theoretical analysis shows a good quantitative agreement with our experimental measurements, establishing the physical origin of such a pattern formation to arise from interplay between wavefront curvature of the input Gaussian beam and strong spatial self-phase modulation by thermally-induced refractive index change in the medium, which we show to be dominated by longitudinal thermal diffusion.

Detecting dynamical nonstationarity in time series data

Nonlinear time series analysis is becoming an ever more powerful tool to explore complex phenomena and uncover underlying patterns from irregular data recorded from experiments. However, the existence of dynamical nonstationarity in time series data causes many results of such analysis to be questionable and inconclusive. It is increasingly recognized that detecting dynamical nonstationarity is a crucial precursor to data analysis. In this paper, we present a test procedure to detect dynamical nonstationarity by directly inspecting the dependence of nonlinear statistical distributions on absolute time along a trajectory in phase space. We test this method using a broad range of data, chaotic, stochastic and power-law noise, both computer-generated and observed, and show that it provides a reliable test method in analyzing experimental data. (c) 1999 American Institute of Physics.

Measuring temporal complexity of ventricular fibrillation

Abstract Temporal complexity of early ventricular fibrillation (VF) is re-assessed through measuring the correlation dimension D 2 , entropy K 2 and high-dimensional component σ from electrocardiogram (ECG) recordings using the Gaussian kernel algorithm. Seven representative ECG traces of induced VF among 53 pig subjects are selected for analysis. VF is found to have 80–90% low-dimensional deterministic dynamics with D 2 varying around 5 and 10–20% high-dimensional extents.

Non-linear noise reduction and detecting chaos: some evidence from the S&P composite price index

Academic and applied researchers in economics have, in the last 10 years, become increasingly interested in the topic of chaotic dynamics. In this paper we undertake non-linear dynamical analysis of one representative time series taken from financial markets, namely the Standard and Poors (S&P) Composite Price Index. The data is based upon (adjusted) daily data from 1928 to 1987 comprising 16 127 observations. The results in the paper, based on the Grassberger–Procaccia (GP) correlation dimension measurement in conjunction with non-linear noise filtering and the surrogate technique, show strong evidence of chaos in one of these series, the S&P 500. The analysis shows that the accuracy of results improves with the increase in the number of recording points and the length of the time series, 5000 data points being sufficient to identify deterministic dynamics.

Analysis of dark spot formation in absorbing liquid media

Abstract A theoretical analysis based on coupled field-matter equations is given to describe the recently observed phenomenon of a central dark spot formation of a Gaussian beam transmitted through an absorbing defocusing liquid medium. We find that such a pattern formation, which is accompanied by normal defocusing rings in the far field, originates from interplay between the wave-front curvature of the Gaussian beam and strong spatial self-phase medulation arising from thermally induced refractive index change in the medium. Results of numerical analysis for a thin medium are shown to be in a good quantitative agreement with our experimental findings. Further, the dark spot formation is also predicted by using a focused Gaussian beam and self-focusing medium.

Detecting false benign in breast cancer diagnosis

Reports a method for breast cancer diagnosis using a robust heteroscedastic probabilistic neural network. The network has the inherent property of clustering patients into several groups, each of which has a distinct significance level: e.g. the larger the significance level of a benign (malignant) group, the more typical the benign (malignant) symptoms. From this, false benign patients can be identified through investigating the probabilistic relationships between each benign group with a small significance level and malignant groups. A false benign analysis table has thus been designed based on this approach. By detecting false benign, the misclassification rate of malignant patients can be reduced to a minimum without significantly increasing the misclassification rate of benign patients. In applying this method to Wisconsin diagnostic breast cancer data, the correct classification rates are 100% for malignant and 98% for benign.

Chaotic stimulated Brillouin scattering: theory and experiment

Abstract We report our recent experimental observation and theoretical analysis of nonlinear dynamics in stimulated Brillouin scattering (SBS) generated in single mode fibre in the presence of weak external feedback. Both experiment and theory establish that the noise, which initiates this process and dominates the emission near the SBS threshold, is dramatically suppressed from the onset of SBS emission, giving rise to various highly deterministic dynamical features. Further in this analysis we identify the critical role of nonlinear refraction on the nonlinear dynamical behaviour.