Multifractals. Theory and applications

Subscribe to RSS
Free download. Book file PDF easily for everyone and every device. You can download and read online Multifractals. Theory and applications file PDF Book only if you are registered here. And also you can download or read online all Book PDF file that related with Multifractals. Theory and applications book. Happy reading Multifractals. Theory and applications Bookeveryone. Download file Free Book PDF Multifractals. Theory and applications at Complete PDF Library. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Here is The CompletePDF Book Library. It's free to register here to get Book file PDF Multifractals. Theory and applications Pocket Guide.

go to site The mono- and multifractal properties we are investigating here are essentially describing different properties of the multifractal spectrum. We further observed that the Chhabra-Jensen method is the most reliable out of the three multifractal estimation methods. As was pointed out in the original publication Chhabra and Jensen, , this is most likely due to the fact that the Chhabra-Jensen method avoids a Legendre transform that the other methods require.

The Legendre transformation requires smoothing of the D q curve and can lead to errors. For further advantages of the Chhabra-Jensen method, the reader is referred to the original publication Chhabra and Jensen, A recent development, FMF method Mukli et al. Finally, our analysis highlighted the importance of choosing an adequate epoch size given a sampling frequency, in order to study events such as epileptic seizures. However, our study was based on the analysis of ictal vs.

Future work should take into account that multifractal properties may be continuously changing over time a striking example is shown in Appendix Figure E7 in Supplementary Material , and an explicitly time based approach may be needed. Along similar lines, our finding of a optimal time scale may be due to the non-stationary nature of the multifractal properties. Further theoretical work may have to develop a temporally resolved multifractal estimator, in order to fully understand this aspect.

It has been further suggested that more than one scaling exponent would be necessary to properly characterize the brain's critical dynamics Suckling et al. Hence, it has been proposed that using additional, higher-order statistical moments can better characterize such data Fraiman and Chialvo, In this work, we contribute a complementary observation: while monofractal measures of EEG appeared to essentially follow the slow changes of signal variance, multifractal characterization is capable of revealing new information.

In terms of generative processes that can produce monofractal properties, it has been suggested that a property called Self-Organized Criticality SOC Bak et al. SOC describes the capacity of a system to evolve naturally into a critical state a state in which a minimum perturbation could lead to events of all sizes. Such phenomena display power-law distributions and fractal properties as signatures Bak and Paczuski, SOC behavior has been linked to physiological control mechanisms, such as in human heart rate variability Goldberger et al.

The analysis and understanding of the non-classical SOC is, however, still under development.

  • The Secrets to Succeeding in Network Marketing Offline and Online: How To Achieve Financial Success Selling Network Marketing Products And Services?
  • Get this edition.
  • Tissue Regeneration: Where Nano Structure Meets Biology.
  • Diary of a Ohio Kid;
  • Idioms of Self-Interest: Credit, Identity, and Property in English Renaissance Literature (Literary Criticism and Cultural Theory).

In this context, our multifractal spectral analyses of human EEG data suggest that cerebral phenomena should not be modeled by a single avalanche model classical SOC , in agreement with findings in a previous study Fraiman and Chialvo, Moreover, it is hypothesized that brain dynamics are non-ergodic Bianco et al. Thus, multifractal analyses could provide a new paradigm for studying brain function and structure, as previously suggested in other studies of normal Suckling et al.

Furthermore, generative processes displaying multifractal properties could help understanding the observed multifractal changes on a mechanistic level.

Multifractal-based Image Analysis with applications in Medical Imaging (2007)

The University of Melbourne Library. Bengtsson, H. Burrough P. Generic aspects of complexity in brain imaging data and other biological systems. Goodchild M. The supports of all four patterns are fractals.

We want to emphasize that the conclusions from our work are drawn on the basis that slow changes in signal fractal features can be captured by using an epoch-wise feature extraction procedure. It is also from a feature redundancy perspective that we argue for the need of multifractal approaches over monofractal measures. We do not dispute the usefulness of monofractal measures in other general applications. In our work, we essentially performed a feature selection procedure using correlation and mutual information Guyon and Elisseeff, We evaluated how different signal feature compare on an epoch-wise basis.

Feature selection is crucial to obtain faster and cost effective models, and avoids overfitting of the available data. It might also help achieving a deeper insight into the nature of the studied phenomena Blum and Langley, ; Liu et al. A fundamental observation in our work is that an optimal time scales may exist for specific physiological processes such as epileptic seizures in terms of their multifractal dynamics Figure 7 and Appendix B in Supplementary Material.

This is further supported by similar findings in monofractal analysis Eke et al. The implications of this observation are that certain scaling exponents will only exist in specific time scales and the diversity of scaling exponents will depend on the duration of the epoch. If this is indeed the case, a temporally resolved not epoch-based multifractal method should be developed in future to adequately characterize brain dynamics.

Furthermore, the slow temporal changes in multifractal dynamics need to be characterized in a systematic way. Using epileptic seizures as an example, Appendix Figure E7 in Supplementary Material shows that dramatic changes in multifractal properties can sometimes be seen before an epileptic seizure. This observation requires further investigation to address questions such as: are all epileptic seizures characterized by pre-ictal changes in multifractal properties?

Do other physiological processes, such as sleep, influence this finding? To answer these questions, we will most likely also need well-characterized experimental conditions, where seizures can be triggered in a controlled manner. Finally, it is well-recognized that epileptic seizures are spatio-temporal processes see e. Data-driven unsupervised approaches, such as dimensionality reduction, may help summarize spatial aspects. Additionally, the challenge will be to develop a spatio-temporal multifractal analysis approach that can also deal with the challenges of low spatial sampling resolution in EEG recordings.

Our work has highlighted several challenges that need to be considered when analysing multifractal properties of EEG signals; namely choice of the appropriate estimation method, estimation parameters, and the influence of the time series variance on signal features. We have suggested some solutions to these problems, such as the used of the Chhabra-Jensen approach combined with an epoch-wise standardization approach, which has shown potential capabilities as a signal feature for machine learning applications.

We have also highlighted possible process-specific challenges. In terms of epileptic seizures, future work is required to analyse a larger number of patients in order to draw firmer conclusions on the potential clinical relevance of multifractal analyses. Furthermore, the study of mechanistic generative models of EEG may shed light on why those multifractal changes occur. For example, a generative process of potential interest could feature a modified version of Bak—Tang—Wiesenfeld model Bak et al. In this paper, we have analyzed the monofractal and multifractal properties of human EEG recordings.

1st Edition

We have shown that monofractal estimates are influenced by the standard deviation of the time series, thus not capturing features beyond signal variance. For multifractal estimation, we have shown that the Chhabra-Jensen approach is the most stable, and we have developed a method of signal pre-processing to remove the influence caused by the variance of the signal. Using the suggested approach, the multifractal estimates do not correlate with traditional EEG measures, thus yielding additional information about the signal and being a relevant signal feature.

Finally, our results also indicate a preferential time scale to identify differences in multifractal properties between ictal and interictal state recordings in patients with epilepsy. LF: data curation, funding acquisition, investigation, and visualization. LF and YW: formal analysis and validation. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to thank Benjamin H. Peter Taylor for helpful comments throughout the project. Acharya, R. Non-linear analysis of EEG signals at various sleep stages. Methods Prog. Argoul, F. Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade. Nature , 51— Bak, P. Complexity, contingency, and criticality. Baldassano, S. Crowdsourcing seizure detection: algorithm development and validation on human implanted device recordings. Brain , — Bassett, D.

Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Adaptive reconfiguration of fractal small-world human brain functional networks. Beggs, J. Neuronal avalanches in neocortical circuits. Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures.

Bengtsson, H. R package version 3. Bianco, S. Brain, music, and non-Poisson renewal processes. E Biswas, A. Ouadfeul InTech , — Blum, A. Selection of relevant features and examples in machine learning. Google Scholar. Brinkmann, B. Large-scale electrophysiology: acquisition, compression, encryption, and storage of big data.

Methods , — Crowdsourcing reproducible seizure forecasting in human and canine epilepsy. Bullmore, E. Generic aspects of complexity in brain imaging data and other biological systems. NeuroImage 47, — Wavelets and statistical analysis of functional magnetic resonance images of the human brain. Methods Med.

Cannon, M. Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series. Physica A. Chhabra, A. Chialvo, D. Emergent complex neural dynamics. Critical brain dynamics at large scale. Neural Syst. Ciuciu, P. Scale-free and multifractal time dynamics of fMRI signals during rest and task. Consolini, G.

Multifractal structure of auroral electrojet index data. Costa, I. Altered functional performance in patients with fibromyalgia. Davies, R. Tests for Hurst effect. Biometrika 74, 95— Davis, A. The landsat scale break in stratocumulus as a three-dimensional radiative transfer effect: implications for cloud remote sensing. Scale-free brain functional networks. Eke, A. Physiological time series: distinguishing fractal noises from motions. Fractal characterization of complexity in temporal physiological signals.

Esteller, R.

Journal list menu

Falconer, K. Fractal Geometry. Feder, J. Fraiman, D. What kind of noise is brain noise: anomalous scaling behavior of the resting brain activity fluctuations. On multifractals: a non-linear study of actigraphy data. A , — Freestone, D. Seizure prediction: science fiction or soon to become reality? Gneiting, T. Stochastic models that separate fractal dimension and the hurst effect. SIAM Rev. Goldberger, A. PhysioBank, physioToolkit, and physioNet : components of a new research resource for complex physiologic signals.

Circulation , e—e Fractal dynamics in physiology: alterations with disease and aging. Use of the Higuchi's fractal dimension for the analysis of MEG recordings from Alzheimer's disease patients. Gong, P. Scale-invariant fluctuations of the dynamical synchronization in human brain electrical activity.

Gu, G. Detrending moving average algorithm for multifractals. Guyon, I. An introduction to variable and feature selection. Higuchi, T. Approach to an irregular time series on the basis of the fractal theory. D 31, — Guyon and Elisseeff, Hsu, W. Wavelet-based fractal features with active segment selection: application to single-trial EEG data. Hu, K. Non-random fluctuations and multi-scale dynamics regulation of human activity.

A Stat. Reduction of scale invariance of activity fluctuations with aging and Alzheimer's disease: involvement of the circadian pacemaker. Ihlen, E. Introduction to multifractal detrended fluctuation analysis in Matlab. Ince, R. A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula. Brain Mapp.

Ivanov, P. Multifractality in human heartbeat dynamics. Nature , — Kantelhardt, J. Multifractal detrended fluctuation analysis of nonstationary time series. A , 87— Karoly, P. The circadian profile of epilepsy improves seizure forecasting. Kestener, P. Three-dimensional wavelet-based multifractal method: the need for revisiting the multifractal description of turbulence dissipation data.

Kroese, D. Schmidt Cham: Springer International Publishing , — Kuhlmann, L. Seizure prediction-ready for a new era. Li, X. Fractal spectral analysis of pre-epileptic seizures in terms of criticality. Neural Eng. Linkenkaer-Hansen, K. Long-range temporal correlations and scaling behavior in human brain oscillations. Lipa, P. From strong to weak intermittency. B , — Liu, H. Toward integrating feature selection algorithms for classification and clustering. IEEE Trans. Data Eng. Lovejoy, S. Scaling and multifractal fields in the solid earth and topography.

Lutzenberger, W. Fractal dimension of electroencephalographic time series and underlying brain processes. Mandelbrot, B. The Fractal Geometry of Nature, Vol. Fractional brownian motions, fractional noises and applications. Martinerie, J. Reply to "Prediction of epileptic seizures: are nonlinear methods relevant? McSharry, P. Meneveau, C. Simple multifractal cascade model for fully developed turbulence. The multifractal nature of turbulent energy dissipation.

CiteSeerX — Multifractal-based Image Analysis with applications in Medical Imaging

Fluid Mech. Miranda, J. Multifractal characterization of saprolite particle-size distributions after topsoil removal. Geoderma , — Mormann, F. Seizure prediction: the long and winding road. Mukli, P. Multifractal formalism by enforcing the universal behavior of scaling functions.

Murcio, R. Multifractal to monofractal evolution of the London street network. Nagy, Z. Decomposing multifractal crossovers. Neuwirth, E. Rcolorbrewer: Colorbrewer Palettes. R package version 1. Papo, D. Functional significance of complex fluctuations in brain activity: from resting state to cognitive neuroscience. Editorial: on the relation of dynamics and structure in brain networks. Chaos Interdisc. Paz-Ferreiro, J. Multifractal analysis of soil porosity based on mercury injection and nitrogen adsorption.

Vadose Zone J. Assessing soil particle-size distribution on experimental plots with similar texture under different management systems using multifractal parameters. Geoderma , 47— Pechlivanidis, I. Earth Syst. Peng, C. Mosaic organization of DNA nucleotides. E 49, — Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series.

Pereda, E. Non-linear behaviour of human EEG: fractal exponent versus correlation dimension in awake and sleep stages. Peterson, B. R Core Team Racz, F. Multifractal dynamics of resting-state functional connectivity in the prefrontal cortex. Saeys, Y. A review of feature selection techniques in bioinformatics. Bioinformatics 23, — She, Z. Universal scaling laws in fully developed turbulence. Shevchenko, G. Sreenivasan, K.

Supermanifolds: Theory and Applications. Rigidity theory and applications. Wavelets: Theory and applications. Supermanifolds : theory and applications. Matrices theory and applications. Superconductivity — Theory and Applications. Herbicides, Theory and Applications. Nucleation Theory and Applications. Games, Theory and Applications. Supermanifolds: theory and applications. Buildings: Theory and applications.

Plasticity: Theory and Applications. Graph theory and applications. Matrices: Theory and applications. Recommend Documents.

Aïe Aïe Aïe !

Subdifferentials: Theory and applications Contents Preface Chapter 1. Convex Correspondences and Operators 1. Convex Sets. Axler F. Gehring K. Ribet This page intentionally left bla Distributions: Theory and Applications J.