Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

Ihlen, Espen Alexander F.

doi:10.3389/fphys.2012.00141

Cited by 705 publications

(704 citation statements)

References 48 publications

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“…Seasonal influenza epidemics in the USA was moderately severe in 2003-2004-2008, moderate in 2002-2003, but mild in 2011-2012(Bresee and Hayden, 2013. The virulent H3N2 influenza virus, which circulated during the moderately severe seasons of 2007-2008 and the mild season of 2011-2012 (Bresee and Hayden, 2013), show that virulence is not the only determinant of severity.…”

Section: Figuresmentioning

confidence: 99%

“…Hurst exponent, which is expressed as x( t ) = a H x(at), is related to fractal dimension D as D = 2 − H (Mandelbroit and van Ness, 1968). While the Hurst exponent of monofractal time series is independent of time and space, multifractal time series have time varying Hurst exponents (Ihlen, 2012). Detrended fluctuation analysis (DFA) algorithm estimates Hurst exponent of long-range temporal correlations, while multifractal detrended fluctuation analysis (Kantelhardt et al, 2002) detects multiple scaling of fractal time series.…”

Section: Phase Spaces Of El Niño Southern Oscillation and Influenzamentioning

confidence: 99%

“…Matlab scripts, which contained relevant algorithms, were used to test for non-linearities in time series (Barnett, 2007), for noise assisted multivariate empirical mode decomposition (Rehman and Mandic, 2010b), for time-dependent intrinsic correlation (Chen and Huang, 2010), to generate surrogate time series (Leontitsis, 2004), and for multifractal detrended fluctuation analysis (Ihlen, 2012). All Matlab scripts were implemented in Matlab-Octave programming language.…”

Section: Scripts Programming and Statistical Packagesmentioning

confidence: 99%

“…Detrended fluctuation analysis (DFA) algorithm estimates Hurst exponent of long-range temporal correlations, while multifractal detrended fluctuation analysis (Kantelhardt et al, 2002) detects multiple scaling of fractal time series. To characterize the geometry of ENSO and influenza attractors, multifractal detrended fluctuation analysis (Ihlen, 2012) of annual oscillatory components of ENSO and influenza in five geographical regions were performed.…”

Section: Phase Spaces Of El Niño Southern Oscillation and Influenzamentioning

confidence: 99%

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Deterministic Chaos, El Niño Southern Oscillation, and Seasonal Influenza Epidemics

Oluwole

2017

Front. Environ. Sci.

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Low precipitation enhances transmission of influenza viruses, which cause seasonal epidemics during the winter in northern and southern hemispheres. El Niño southern oscillation (ENSO) which modulates global precipitation is a multicomponent signal that is composed of sub-annual to multi-decadal oscillations. The dynamics of oscillatory components of ENSO and influenza are characterized, and causal relationship of annual oscillatory components is determined. Seasonality of influenza was determined in five geographical areas of north and south hemispheres. Monthly influenza time series of these regions and of ENSO were decomposed to oscillatory components. The oscillatory components were characterized in time-frequency and phase space domains. Periodicities of the oscillatory components of ENSO and influenza range from sub-annual to multidecadal. Time-dependent intrinsic correlations of instantaneous amplitude and frequencies of annual oscillatory components of ENSO and influenza are > 0.9. The dynamics of ENSO and influenza, which are dissipative with multifractal chaotic attractors, transit from quasi-periodic to chaotic regimes. Five most severe peaks of epidemic, which include 2009-2010 pandemic, occur during chaos. ENSO and influenza dynamics are phase coherent, but there is unidirectional causal effect of ENSO on influenza. Amplitude and frequency modulations of annual oscillatory components of ENSO and influenza are strongly coupled. Chaotic dynamics of ENSO determines the timing and severity of influenza epidemics. Monitoring of ENSO dynamics will aid public health surveillance of influenza epidemics.

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Section: Figuresmentioning

confidence: 99%

Section: Phase Spaces Of El Niño Southern Oscillation and Influenzamentioning

confidence: 99%

Section: Scripts Programming and Statistical Packagesmentioning

confidence: 99%

Section: Phase Spaces Of El Niño Southern Oscillation and Influenzamentioning

confidence: 99%

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Deterministic Chaos, El Niño Southern Oscillation, and Seasonal Influenza Epidemics

Oluwole

2017

Front. Environ. Sci.

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“…For the calculation methodology, Ihlen developed MATLAB code in [35] and Domański modified the algorithm in [7].…”

Section: Basic Mfdfa Algorithmmentioning

confidence: 99%

A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing

et al. 2018

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Abstract:The significant task for control performance assessment (CPA) is to review and evaluate the performance of the control system. The control system in the semiconductor industry exhibits a complex dynamic behavior, which is hard to analyze. This paper investigates the interesting crossover properties of Hurst exponent estimations and proposes a novel method for feature extraction of the nonlinear multi-input multi-output (MIMO) systems. At first, coupled data from real industry are analyzed by multifractal detrended fluctuation analysis (MFDFA) and the resultant multifractal spectrum is obtained. Secondly, the crossover points with spline fit in the scale-law curve are located and then employed to segment the entire scale-law curve into several different scaling regions, in which a single Hurst exponent can be estimated. Thirdly, to further ascertain the origin of the multifractality of control signals, the generalized Hurst exponents of the original series are compared with shuffled data. At last, non-Gaussian statistical properties, multifractal properties and Hurst exponents of the process control variables are derived and compared with different sets of tuning parameters. The results have shown that CPA of the MIMO system can be better employed with the help of fractional order signal processing (FOSP).

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Fractional Dynamics Foster Deep Learning of COPD Stage Prediction

et al. 2023

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Chronic obstructive pulmonary disease (COPD) is one of the leading causes of death worldwide. Current COPD diagnosis (i.e., spirometry) could be unreliable because the test depends on an adequate effort from the tester and testee. Moreover, the early diagnosis of COPD is challenging. The authors address COPD detection by constructing two novel physiological signals datasets (4432 records from 54 patients in the WestRo COPD dataset and 13824 medical records from 534 patients in the WestRo Porti COPD dataset). The authors demonstrate their complex coupled fractal dynamical characteristics and perform a fractional‐order dynamics deep learning analysis to diagnose COPD. The authors found that the fractional‐order dynamical modeling can extract distinguishing signatures from the physiological signals across patients with all COPD stages—from stage 0 (healthy) to stage 4 (very severe). They use the fractional signatures to develop and train a deep neural network that predicts COPD stages based on the input features (such as thorax breathing effort, respiratory rate, or oxygen saturation). The authors show that the fractional dynamic deep learning model (FDDLM) achieves a COPD prediction accuracy of 98.66% and can serve as a robust alternative to spirometry. The FDDLM also has high accuracy when validated on a dataset with different physiological signals.

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Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

Cited by 705 publications

References 48 publications

Deterministic Chaos, El Niño Southern Oscillation, and Seasonal Influenza Epidemics

Deterministic Chaos, El Niño Southern Oscillation, and Seasonal Influenza Epidemics

A Novel Method for Control Performance Assessment with Fractional Order Signal Processing and Its Application to Semiconductor Manufacturing

Fractional Dynamics Foster Deep Learning of COPD Stage Prediction

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