Time series classification based on fractal properties

The article considers classification task of fractal time series by the meta algorithms based on decision trees. Binomial multiplicative stochastic cascades are used as input time series. Comparative analysis of the classification approaches based on different features is carried out. The results indicate the advantage of the machine learning methods over the traditional estimating the degree of self-similarity.Comment: 4 pages, 2 figures, 3 equations, 1 tabl

Long-range dependencies in heart rate signals- revisited

The RR series extracted from human electrocardiogram signal (ECG) is considered as a fractal stochastic process. The manifestation of long-range dependencies is the presence of power laws in scale dependent process characteristics. Exponents of these laws: $\beta$ - describing power spectrum decay, $\alpha$ - responsible for decay of detrended fluctuations or $H$ related to, so-called, roughness of a signal, are known to differentiate hearts of healthy people from hearts with congestive heart failure. There is a strong expectation that resolution spectrum of exponents, so-called, local exponents in place of global exponents allows to study differences between hearts in details. The arguments are given that local exponents obtained in multifractal analysis by the two methods: wavelet transform modulus maxima (WTMM) and multifractal detrended fluctuation analysis (MDFA), allow to recognize the following four stages of the heart: healthy and young, healthy and advance in years, subjects with left ventricle systolic dysfunction (NYHA I--III class) and characterized by severe congestive heart failure (NYHA III-IV class).Comment: 24 page

Quantifying and containing the curse of high resolution coronal imaging

Future missions such as Solar Orbiter (SO), InterHelioprobe, or Solar Probe aim at approaching the Sun closer than ever before, with on board some high resolution imagers (HRI) having a subsecond cadence and a pixel area of about $(80km)^2$ at the Sun during perihelion. In order to guarantee their scientific success, it is necessary to evaluate if the photon counts available at these resolution and cadence will provide a sufficient signal-to-noise ratio (SNR). We perform a first step in this direction by analyzing and characterizing the spatial intermittency of Quiet Sun images thanks to a multifractal analysis. We identify the parameters that specify the scale-invariance behavior. This identification allows next to select a family of multifractal processes, namely the Compound Poisson Cascades, that can synthesize artificial images having some of the scale-invariance properties observed on the recorded images. The prevalence of self-similarity in Quiet Sun coronal images makes it relevant to study the ratio between the SNR present at SoHO/EIT images and in coarsened images. SoHO/EIT images thus play the role of 'high resolution' images, whereas the 'low-resolution' coarsened images are rebinned so as to simulate a smaller angular resolution and/or a larger distance to the Sun. For a fixed difference in angular resolution and in Spacecraft-Sun distance, we determine the proportion of pixels having a SNR preserved at high resolution given a particular increase in effective area. If scale-invariance continues to prevail at smaller scales, the conclusion reached with SoHO/EIT images can be transposed to the situation where the resolution is increased from SoHO/EIT to SO/HRI resolution at perihelion.Comment: 25 pages, 1 table, 7 figure

Wavelet and Multiscale Analysis of Network Traffic

The complexity and richness of telecommunications traffic is such that one may despair to find any regularity or explanatory principles. Nonetheless, the discovery of scaling behaviour in tele-traffic has provided hope that parsimonious models can be found. The statistics of scaling behavior present many challenges, especially in non-stationary environments. In this paper we describe the state of the art in this area, focusing on the capabilities of the wavelet transform as a key tool for unravelling the mysteries of traffic statistics and dynamics

Multiscaling analysis and modelling of bursty impulsive noise in broadband power line communication channels.

Doctor of Philosophy in Electronic Engineering. University of KwaZulu-Natal, Durban 2017.Power line communication (PLC) networks have the potential to offer broadband application services to homes and small offices cheaply since no additional wiring is required for it implementation. However, like other communication systems, it has its own challenges and the understanding of its channel characteristics is key to its optimal performance evaluation and deployment. Multipath propagation due to impedance mismatch and bursty impulsive noise are the important challenges that must be understood and their effects minimized for optimal system performance. Noise in power line communication networks is non-Gaussian and as such cannot be modelled as the convenient additive white Gaussian noise. The noise is known to be impulsive and in most cases, occurs in bursts. Therefore, it can be referred as bursty impulsive noise. Due to unique nature of this noise in power line channels, modulation and decoding schemes optimized for Gaussian channels may not necessarily work well in PLC systems. Recently developed noise models though take into consideration memory inherent in PLC noise, models capturing both long range correlations and multiscaling behaviour are not yet available in the literature. Furthermore, even though it is known that PLC noise has memory (i.e., it is correlated), the statistical properties of it is not well documented in the literature and will be the focus of this thesis. In this thesis, multiscaling behaviour of PLC noise is investigated. Both fractal and multifractal analysis methods are employed on noise data collected in three different scenarios (small offices, stand-alone apartment and University electronic laboratory) and their characteristics analysed. Multifractal analysis is employed since it is able to characterize both the strengths and frequency of occurrence of bursts in power line noise. Specifically, the contributions in this thesis are as follows: Firstly, empirical evidence is provided that PLC noise clearly manifests long range correlations behaviour. This is achieved by calculating the Hurst parameter (which is a measure of self similarity) in data from the above scenarios. Various methods employed to estimate this Hurst parameter reveal that in all the scenarios, long range dependence is evidenced. Secondly, multifractal detrended fluctuation analysis (MDFA) and multifractal detrending moving average (MDMA) analysis have been used to investigate the temporal correlations and scaling behaviour of power line channel noise measured from the three different scenarios mentioned earlier. Empirical results show that power line noise clearly manifests both long-range correlation and multifractal scaling behaviour with different strengths depending on the environments where they were captured. From the estimated singularity spectrum which is left truncated, it is evident from the two methods used that power line noise is sensitive to small fluctuations and is characterized by large scaling exponents. Multifractal analysis of the reshuffled time series noise reveal that the multifractal nature of PLC noise is as a result of long range correlation inherent in the noise and not from the heavy tailed distributions in it. Thirdly, we propose a multiplicative cascade model for PLC noise that is able to reproduce the empirical findings concerning the PLC noise time series: its local scaling behaviour and long range correlations. Model parameters are derived from the shape of multifractal spectrum of the PLC time series noise collected from measurement campaigns. Since in the recent past, the main challenge in PLC systems has been on how to model bursty impulsive PLC noise, the proposed model will be very useful in evaluating system performance of PLC networks in the presence of the bursty impulsive noise inherent in PLC networks. Moreover, bursts of different frequencies and strengths can be modelled by this proposed model and hence their effects on system performance evaluated. This will also open up investigations into designing modulation and decoding schemes that are optimal in systems prone to bursty impulsive noise