Recurrence Networks: Evolution and Robustness

Strozzi, Fernanda; Karmen, Poljansek; Flavio, Bono; Gutiérrez, Eugenio; Zaldı́var, J.M.

doi:10.1142/s0218127411028891

Cited by 12 publications

(14 citation statements)

References 33 publications

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“…For example, noise can hide peaks in the power spectrum of a time series, whereas recurrence network analysis and related geometric methods can conserve the basic attractor properties such as a torus-like shape even in the presence of moderate noise levels. 66,79 Hence, it can be challenging to decide about the presence of phase coherence using dynamical characteristics such as power spectral density, recurrence time distribution, or phase diffusion coefficient even after an appropriate coordinate transformation (see above) in case of noisy experimental data. These problems are partially avoided by considering the geometric viewpoint.…”

Section: Discussionmentioning

confidence: 99%

“…[54][55][56] Finally, e-recurrence networks (RNs) provide a graphtheoretical framework for quantifying various aspects of the underlying attractor's geometry. 29,[57][58][59][60][61][62][63][64][65][66][67] In the following, we will use pðsÞ and K 2 for further characterizing the dynamical complexity of the observed electrochemical oscillations. For this purpose, we will restrict our attention to the first N ¼ 10 000 points of the embedded time series in order to keep the computational efforts at an acceptable level.…”

Section: -5mentioning

confidence: 99%

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Phase coherence and attractor geometry of chaotic electrochemical oscillators

Zou

Donner

Wickramasinghe

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic complexity with increasing temperature of the system, resulting in a larger relative spread of the attractor in phase space. By allowing for feasible coordinate transformations, we demonstrate that the system, however, remains phase-coherent over the whole considered parameter range. This finding motivates a critical review of existing definitions of phase coherence that are exclusively based on dynamical characteristics and are thus potentially sensitive to projection effects in phase space. In contrast, referring to the attractor geometry, the gradual changes in some fundamental properties of the system commonly related to its phase coherence can be alternatively studied from a purely structural point of view. As a prospective example for a corresponding framework, recurrence network analysis widely avoids undesired projection effects that otherwise can lead to ambiguous results of some existing approaches to studying phase coherence. Our corresponding results demonstrate that since temperature increase induces more complex chaotic chemical reactions, the recurrence network properties describing attractor geometry also change gradually: the bimodality of the distribution of local clustering coefficients due to the attractor’s band structure disappears, and the corresponding asymmetry of the distribution as well as the average path length increase.

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Section: Discussionmentioning

confidence: 99%

Section: -5mentioning

confidence: 99%

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Zou

Donner

Wickramasinghe

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…ε networks have been applied to model systems as well as real world data like paleoclimate records and biomedical data [11,[18][19][20][21][22][23][24][25][26]. Network measures, like the average clustering coefficient C and the average path length L, have been used to discriminate between chaotic and periodic dynamics [20].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Subramaniyam

Hyttinen

2015

Phys. Rev. E

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Recently Andrezejak et al. combined the randomness and nonlinear independence test with iterative amplitude adjusted Fourier transform (iAAFT) surrogates to distinguish between the dynamics of seizure-free intracranial electroencephalographic (EEG) signals recorded from epileptogenic (focal) and nonepileptogenic (nonfocal) brain areas of epileptic patients. However, stationarity is a part of the null hypothesis for iAAFT surrogates and thus nonstationarity can violate the null hypothesis. In this work we first propose the application of the randomness and nonlinear independence test based on recurrence network measures to distinguish between the dynamics of focal and nonfocal EEG signals. Furthermore, we combine these tests with both iAAFT and truncated Fourier transform (TFT) surrogate methods, which also preserves the nonstationarity of the original data in the surrogates along with its linear structure. Our results indicate that focal EEG signals exhibit an increased degree of structural complexity and interdependency compared to nonfocal EEG signals. In general, we find higher rejections for randomness and nonlinear independence tests for focal EEG signals compared to nonfocal EEG signals. In particular, the univariate recurrence network measures, the average clustering coefficient C and assortativity R, and the bivariate recurrence network measure, the average cross-clustering coefficient C(cross), can successfully distinguish between the focal and nonfocal EEG signals, even when the analysis is restricted to nonstationary signals, irrespective of the type of surrogates used. On the other hand, we find that the univariate recurrence network measures, the average path length L, and the average betweenness centrality BC fail to distinguish between the focal and nonfocal EEG signals when iAAFT surrogates are used. However, these two measures can distinguish between focal and nonfocal EEG signals when TFT surrogates are used for nonstationary signals. We also report an improvement in the performance of nonlinear prediction error N and nonlinear interdependence measure L used by Andrezejak et al., when TFT surrogates are used for nonstationary EEG signals. We also find that the outcome of the nonlinear independence test based on the average cross-clustering coefficient C(cross) is independent of the outcome of the randomness test based on the average clustering coefficient C. Thus, the univariate and bivariate recurrence network measures provide independent information regarding the dynamics of the focal and nonfocal EEG signals. In conclusion, recurrence network analysis combined with nonstationary surrogates can be applied to derive reliable biomarkers to distinguish between epileptogenic and nonepileptogenic brain areas using EEG signals.

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“…Quite independent of the above, the field of complex networks has been extensively studied by itself and successfully applied in manifold instances in science, nature and engineering 30 31 . With significant advances being reported from various fields 32 33 34 35 36 37 38 39 40 41 42 43 , the importance of converting time series into networks is becoming increasingly clear over the last few years 44 .…”

Section: Time Series To Networkmentioning

confidence: 99%

Using complex networks towards information retrieval and diagnostics in multidimensional imaging

Banerjee

Azharuddin

Sen

et al. 2015

Sci Rep

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We present a fresh and broad yet simple approach towards information retrieval in general and diagnostics in particular by applying the theory of complex networks on multidimensional, dynamic images. We demonstrate a successful use of our method with the time series generated from high content thermal imaging videos of patients suffering from the aqueous deficient dry eye (ADDE) disease. Remarkably, network analyses of thermal imaging time series of contact lens users and patients upon whom Laser-Assisted in situ Keratomileusis (Lasik) surgery has been conducted, exhibit pronounced similarity with results obtained from ADDE patients. We also propose a general framework for the transformation of multidimensional images to networks for futuristic biometry. Our approach is general and scalable to other fluctuation-based devices where network parameters derived from fluctuations, act as effective discriminators and diagnostic markers.

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Recurrence Networks: Evolution and Robustness

Cited by 12 publications

References 33 publications

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Using complex networks towards information retrieval and diagnostics in multidimensional imaging

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