Multivariate recurrence network analysis for characterizing horizontal oil-water two-phase flow

Multivariate joint order recurrence networks for characterization of multi-lead ECG time series from healthy and pathological heartbeat dynamics

Analysis of nonlinear dynamic characteristics of cardiac systems has been a hot topic of clinical research, and the recurrence plots have earned much attention as an effective tool for it. In this paper, we propose a novel method of multivariate joint order recurrence networks (MJORNs) to evaluate the multi-lead electrocardiography (ECG) time series with healthy and psychological heart states. The similarity between time series is studied by quantifying the structure in a joint order pattern recurrence plot. We take the time series that corresponds to each of the 12-lead ECG signals as a node in the network and use the entropy of diagonal line length that describes the complex structure of joint order pattern recurrence plot as the weight to construct MJORN. The analysis of network topology reveals differences in nonlinear complexity for healthy and heart diseased heartbeat systems. Experimental outcomes show that the values of average weighted path length are reduced in MJORN constructed from crowds with heart diseases, compared to those from healthy individuals, and the results of the average weighted clustering coefficient are the opposite. Due to the impaired cardiac fractal-like structures, the similarity between different leads of ECG is reduced, leading to a decrease in the nonlinear complexity of the cardiac system. The topological changes of MJORN reflect, to some extent, modifications in the nonlinear dynamics of the cardiac system from healthy to diseased conditions. Compared to multivariate cross recurrence networks and multivariate joint recurrence networks, our results suggest that MJORN performs better in discriminating healthy and pathological heartbeat dynamics.

Incorporation of causality structures to complex network analysis of time-varying behaviour of multivariate time series

This paper presents a new methodology for characterising the evolving behaviour of the time-varying causality between multivariate time series, from the perspective of change in the structure of the causality pattern. We propose that such evolutionary behaviour should be tracked by means of a complex network whose nodes are causality patterns and edges are transitions between those patterns of causality. In our new methodology each edge has a weight that includes the frequency of the given transition and two metrics relating to the gross and net structural change in causality pattern, which we call [Formula: see text] and [Formula: see text]. To characterise aspects of the behaviour within this network, five approaches are presented and motivated. To act as a demonstration of this methodology an application of sample data from the international oil market is presented. This example illustrates how our new methodology is able to extract information about evolving causality behaviour. For example, it reveals non-random time-varying behaviour that favours transitions resulting in predominantly similar causality patterns, and it discovers clustering of similar causality patterns and some transitional behaviour between these clusters. The example illustrates how our new methodology supports the inference that the evolution of causality in the system is related to the addition or removal of a few causality links, primarily keeping a similar causality pattern, and that the evolution is not related to some other measure such as the overall number of causality links.

Visibility-graphlet approach to the output series of a Hodgkin-Huxley neuron

The output signals of neurons that are exposed to external stimuli are of great importance for brain functionality. Traditional time-series analysis methods have provided encouraging results; however, the associated patterns and their correlations in the output signals of neurons are masked by statistical procedures. Here, graphlets are employed to extract the local temporal patterns and the transitions between them from the output signals when neurons are exposed to external stimuli with selected stimulating periods. A transition network is defined where the node is the graphlet and the direct link is the transition between two successive graphlets. The transition-network structure is affected by the simulating periods. When the stimulating period moves close to an integer multiple of the neuronal intrinsic period, only the backbone or core survives, while the other linkages disappear. Interestingly, the size of the backbone (number of nodes) equals the multiple. The transition-network structure is conservative within each stimulating region, which is defined as the range between two successive integer multiples. Nevertheless, the backbone or detailed structure is significantly altered between different stimulating regions. This alternation is induced primarily from a total of 12 active linkages. Hence, the transition network shows the structure of cross correlations in the output time-series for a single neuron.

Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions

In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint recurrence network, the cross-joint recurrence network, and the multidimensional recurrence network, which are the variants of classic recurrence networks extended for multiple time series. Generally, the fractal dimension of these recurrence networks can only be estimated numerically. The numerical analysis identifies the existence of fractality in these constructed recurrence networks. Furthermore, it is found that the numerically estimated fractal dimension of these networks can be connected to the theoretical fractal dimension of the 2D fBm graphs, because both fractal dimensions are piecewisely associated with the Hurst exponent H in a highly similar pattern, i.e., a linear decrease (if H varies from 0 to 0.5) followed by an inversely proportional-like decay (if H changes from 0.5 to 1). Although their fractal dimensions are not exactly identical, their difference can actually be deciphered by one single parameter with the value around 1. Therefore, it can be concluded that these recurrence networks constructed from the 2D fBms must inherit some fractal properties of its associated 2D fBms with respect to the fBm graphs.

Reciprocal characterization from multivariate time series to multilayer complex networks

Various transformations from time series to complex networks have recently gained significant attention. These transformations provide an alternative perspective to better investigate complex systems. We present a transformation from multivariate time series to multilayer networks for their reciprocal characterization. This transformation ensures that the underlying geometrical features of time series are preserved in their network counterparts. We identify underlying dynamical transitions of the time series through statistics of the structure of the corresponding networks. Meanwhile, this allows us to propose the concept of interlayer entropy to measure the coupling strength between the layers of a network. Specifically, we prove that under mild conditions, for the given transformation method, the application of interlayer entropy in networks is equivalent to transfer entropy in time series. Interlayer entropy is utilized to describe the information flow in a multilayer network.

A recurrence network-based convolutional neural network for fatigue driving detection from EEG

Driver fatigue is an important cause of traffic accidents, which has triggered great concern for detecting drivers' fatigue. Numerous methods have been proposed to fulfill this challenging task, including feature methods and machine learning methods. Recently, with the development of deep learning techniques, many studies achieved better results than traditional feature methods, and the combination of traditional methods and deep learning techniques gradually received attention. In this paper, we propose a recurrence network-based convolutional neural network (RN-CNN) method to detect fatigue driving. To be specific, we first conduct a simulated driving experiment to collect electroencephalogram (EEG) signals of subjects under alert state and fatigue state. Then, we construct the multiplex recurrence network (RN) from EEG signals to fuse information from the original time series. Finally, CNN is employed to extract and learn the features of a multiplex RN for realizing a classification task. The results indicate that the proposed RN-CNN method can achieve an average accuracy of 92.95%. To verify the effectiveness of our method, some existing competitive methods are compared with ours. The results show that our method outperforms the existing methods, which demonstrate the effect of the RN-CNN method.

Multivariate weighted recurrence network analysis of EEG signals from ERP-based smart home system

Smart home has been widely used to improve the living quality of people. Recently, the brain-computer interface (BCI) contributes greatly to the smart home system. We design a BCI-based smart home system, in which the event-related potentials (ERP) are induced by the image interface based on the oddball paradigm. Then, we investigate the influence of mental fatigue on the ERP classification by the Fisher linear discriminant analysis. The results indicate that the classification accuracy of ERP decreases as the brain evolves from the normal stage to the mental fatigue stage. In order to probe into the difference of the brain, cognitive process between mental fatigue and normal states, we construct multivariate weighted recurrence networks and analyze the variation of the weighted clustering coefficient and weighted global efficiency corresponding to these two brain states. The findings suggest that these two network metrics allow distinguishing normal and mental fatigue states and yield novel insights into the brain fatigue behavior resulting from a long use of the ERP-based smart home system. These properties render the multivariate recurrence network, particularly useful for analyzing electroencephalographic recordings from the ERP-based smart home system.

A Patient Suffering From Neurodegenerative Disease May Have a Strengthened Fractal Gait Rhythm

Scale invariance in stride series, namely, the series shows similar patterns across multiple time scales, is used widely as a non-invasive identifier of health assessment. Detailed calculations in the literature with standard tools, such as de-trended fluctuation analysis and wavelet transform modulus maxima seem to lead a conclusion that patients suffering from neurodegenerative diseases have weakened fractal gait rhythm compared with healthy persons. These variance-based methods are dynamical mechanism dependent, namely, for some dynamical process the scale invariance cannot be detected qualitatively, while for some others the scale invariance can be detected correctly, but the estimated value of scaling exponent is not correct. Generally, we have limited knowledge on the dynamical mechanism. What is more, the stride series for the patients have a typical finite length of ~300, which may lead to unreasonable statistical fluctuations to the evaluation procedure. Hence, how a neurodegenerative disorder disease affects the scale invariance is still an open problem. In this paper the balanced estimation of diffusion entropy (cBEDE) is used to overcome the limitations. The volunteers include healthy individuals and patients with/without freezing of gait (FOG). It is found that scale invariance exists widely in the gait time series for all the individuals. The average of scaling exponents for patients suffering from FOG is similar with or larger than that for healthy individuals, and similar with that for patients without FOG. The patients not suffering from FOG have an average of scaling exponent significantly larger than that for healthy people. From the results estimated by cBEDE, we can conclude that a patient may have an increased scaling exponent, which is contradictory qualitatively with that in the literatures.

Abrupt transitions in time series with uncertainties

Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.

Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series

In order to explore the characteristics of the evolution behavior of the time-varying relationships between multivariate time series, this paper proposes an algorithm to transfer this evolution process to a complex network. We take the causality patterns as nodes and the succeeding sequence relations between patterns as edges. We used four time series as sample data. The results of the analysis reveal some statistical evidences that the causalities between time series is in a dynamic process. It implicates that stationary long-term causalities are not suitable for some special situations. Some short-term causalities that our model recognized can be referenced to the dynamic adjustment of the decisions. The results also show that weighted degree of the nodes obeys power law distribution. This implies that a few types of causality patterns play a major role in the process of the transition and that international crude oil market is statistically significantly not random. The clustering effect appears in the transition process and different clusters have different transition characteristics which provide probability information for predicting the evolution of the causality. The approach presents a potential to analyze multivariate time series and provides important information for investors and decision makers.

Constructing ordinal partition transition networks from multivariate time series

A growing number of algorithms have been proposed to map a scalar time series into ordinal partition transition networks. However, most observable phenomena in the empirical sciences are of a multivariate nature. We construct ordinal partition transition networks for multivariate time series. This approach yields weighted directed networks representing the pattern transition properties of time series in velocity space, which hence provides dynamic insights of the underling system. Furthermore, we propose a measure of entropy to characterize ordinal partition transition dynamics, which is sensitive to capturing the possible local geometric changes of phase space trajectories. We demonstrate the applicability of pattern transition networks to capture phase coherence to non-coherence transitions, and to characterize paths to phase synchronizations. Therefore, we conclude that the ordinal partition transition network approach provides complementary insight to the traditional symbolic analysis of nonlinear multivariate time series.

Multiplex multivariate recurrence network from multi-channel signals for revealing oil-water spatial flow behavior

The exploration of the spatial dynamical flow behaviors of oil-water flows has attracted increasing interests on account of its challenging complexity and great significance. We first technically design a double-layer distributed-sector conductance sensor and systematically carry out oil-water flow experiments to capture the spatial flow information. Based on the well-established recurrence network theory, we develop a novel multiplex multivariate recurrence network (MMRN) to fully and comprehensively fuse our double-layer multi-channel signals. Then we derive the projection networks from the inferred MMRNs and exploit the average clustering coefficient and the spectral radius to quantitatively characterize the nonlinear recurrent behaviors related to the distinct flow patterns. We find that these two network measures are very sensitive to the change of flow states and the distributions of network measures enable to uncover the spatial dynamical flow behaviors underlying different oil-water flow patterns. Our method paves the way for efficiently analyzing multi-channel signals from multi-layer sensor measurement system.

Evolution of scaling behaviors embedded in sentence series from A Story of the Stone

The novel entitled A Story of the Stone provides us precise details of life and social structure of the 18th century China. Its writing lasted a long duration of about 10 years, in which the author’s habit may change significantly. It had been published anonymously up to the beginning of the 20th century, which left a mystery of the author’s attribution. In the present work we focus our attention on scaling behavior embedded in the sentence series from this novel, hope to find how the ideas are organized from single sentences to the whole text. Especially we are interested in the evolution of scale invariance to monitor the changes of the author’s language habit and to find some clues on the author’s attribution. The sentence series are separated into a total of 69 non-overlapping segments with a length of 500 sentences each. The correlation dependent balanced estimation of diffusion entropy (cBEDE) is employed to evaluate the scaling behaviors embedded in the short segments. It is found that the total, the part attributed currently to Xueqin Cao (X-part), and the other part attributed to E Gao (E-part), display scale invariance in a large scale up to 10³ sentences, while their scaling exponents are almost identical. All the segments behave scale invariant in considerable wide scales, most of which reach one third of the length. In the curve of scaling exponent versus segment number, the X-part has rich patterns with averagely larger values, while the E-part has a U-shape with a significant low bottom. This finding is a new clue to support the attribution of the E-part to E Gao.

Constructing Robust Cooperative Networks using a Multi-Objective Evolutionary Algorithm

The design and construction of network structures oriented towards different applications has attracted much attention recently. The existing studies indicated that structural heterogeneity plays different roles in promoting cooperation and robustness. Compared with rewiring a predefined network, it is more flexible and practical to construct new networks that satisfy the desired properties. Therefore, in this paper, we study a method for constructing robust cooperative networks where the only constraint is that the number of nodes and links is predefined. We model this network construction problem as a multi-objective optimization problem and propose a multi-objective evolutionary algorithm, named MOEA-Net_rc, to generate the desired networks from arbitrary initializations. The performance of MOEA-Net_rc is validated on several synthetic and real-world networks. The results show that MOEA-Net_rc can construct balanced candidates and is insensitive to the initializations. MOEA-Net_rc can find the Pareto fronts for networks with different levels of cooperation and robustness. In addition, further investigation of the robustness of the constructed networks revealed the impact on other aspects of robustness during the construction process.

Reconstructing Networks from Profit Sequences in Evolutionary Games via a Multiobjective Optimization Approach with Lasso Initialization

Evolutionary games (EG) model a common type of interactions in various complex, networked, natural and social systems. Given such a system with only profit sequences being available, reconstructing the interacting structure of EG networks is fundamental to understand and control its collective dynamics. Existing approaches used to handle this problem, such as the lasso, a convex optimization method, need a user-defined constant to control the tradeoff between the natural sparsity of networks and measurement error (the difference between observed data and simulated data). However, a shortcoming of these approaches is that it is not easy to determine these key parameters which can maximize the performance. In contrast to these approaches, we first model the EG network reconstruction problem as a multiobjective optimization problem (MOP), and then develop a framework which involves multiobjective evolutionary algorithm (MOEA), followed by solution selection based on knee regions, termed as MOEANet, to solve this MOP. We also design an effective initialization operator based on the lasso for MOEA. We apply the proposed method to reconstruct various types of synthetic and real-world networks, and the results show that our approach is effective to avoid the above parameter selecting problem and can reconstruct EG networks with high accuracy.

Multivariate weighted recurrence network inference for uncovering oil-water transitional flow behavior in a vertical pipe

Exploring the dynamical behaviors of high water cut and low velocity oil-water flows remains a contemporary and challenging problem of significant importance. This challenge stimulates us to design a high-speed cycle motivation conductance sensor to capture spatial local flow information. We systematically carry out experiments and acquire the multi-channel measurements from different oil-water flow patterns. Then we develop a novel multivariate weighted recurrence network for uncovering the flow behaviors from multi-channel measurements. In particular, we exploit graph energy and weighted clustering coefficient in combination with multivariate time-frequency analysis to characterize the derived complex networks. The results indicate that the network measures are very sensitive to the flow transitions and allow uncovering local dynamical behaviors associated with water cut and flow velocity. These properties render our method particularly useful for quantitatively characterizing dynamical behaviors governing the transition and evolution of different oil-water flow patterns.

Visibility graphlet approach to chaotic time series

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.

Pattern transitions of oil-water two-phase flow with low water content in rectangular horizontal pipes probed by terahertz spectrum

The flow-pattern transition has been a challenging problem in two-phase flow system. We propose the terahertz time-domain spectroscopy (THz-TDS) to investigate the behavior underlying oil-water flow in rectangular horizontal pipes. The low water content (0.03-2.3%) in oil-water flow can be measured accurately and reliably from the relationship between THz peak amplitude and water volume fraction. In addition, we obtain the flow pattern transition boundaries in terms of flow rates. The critical flow rate Qc of the flow pattern transitions decreases from 0.32 m3 h to 0.18 m3 h when the corresponding water content increases from 0.03% to 2.3%. These properties render THz-TDS particularly powerful technology for investigating a horizontal oil-water two-phase flow system.

Visibility Graph Based Time Series Analysis

Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.

Signatures of chaotic and stochastic dynamics uncovered with ε -recurrence networks

An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, ε -recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global ε -recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rössler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global ε -recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high noise levels and short data lengths. Furthermore, ε -recurrence network analysis of the real-world epileptic data revealed the capability of these network measures in capturing dynamical transitions using short window sizes. ε -recurrence network analysis is a powerful method in uncovering the signatures of chaotic and stochastic dynamics based on the geometrical properties of time series.

A Network of Networks Perspective on Global Trade

Mutually intertwined supply chains in contemporary economy result in a complex network of trade relationships with a highly non-trivial topology that varies with time. In order to understand the complex interrelationships among different countries and economic sectors, as well as their dynamics, a holistic view on the underlying structural properties of this network is necessary. This study employs multi-regional input-output data to decompose 186 national economies into 26 industry sectors and utilizes the approach of interdependent networks to analyze the substructure of the resulting international trade network for the years 1990-2011. The partition of the network into national economies is observed to be compatible with the notion of communities in the sense of complex network theory. By studying internal versus cross-subgraph contributions to established complex network metrics, new insights into the architecture of global trade are obtained, which allow to identify key elements of global economy. Specifically, financial services and business activities dominate domestic trade whereas electrical and machinery industries dominate foreign trade. In order to further specify each national sector's role individually, (cross-)clustering coefficients and cross-betweenness are obtained for different pairs of subgraphs. The corresponding analysis reveals that specific industrial sectors tend to favor distinct directionality patterns and that the cross-clustering coefficient for geographically close country pairs is remarkably high, indicating that spatial factors are still of paramount importance for the organization of trade patterns in modern economy. Regarding the evolution of the trade network's substructure, globalization is well-expressed by trends of several structural characteristics (e.g., link density and node strength) in the interacting network framework. Extreme events, such as the financial crisis 2008/2009, are manifested as anomalies superimposed to these trends. The marked reorganization of trade patterns, associated with this economic crisis in comparison to "normal" annual fluctuations in the network structure is traced and quantified by a new widely applicable generalization of the Hamming distance to weighted networks.

Investigation on Law and Economics Based on Complex Network and Time Series Analysis

The research focuses on the cooperative relationship and the strategy tendency among three mutually interactive parties in financing: small enterprises, commercial banks and micro-credit companies. Complex network theory and time series analysis were applied to figure out the quantitative evidence. Moreover, this paper built up a fundamental model describing the particular interaction among them through evolutionary game. Combining the results of data analysis and current situation, it is justifiable to put forward reasonable legislative recommendations for regulations on lending activities among small enterprises, commercial banks and micro-credit companies. The approach in this research provides a framework for constructing mathematical models and applying econometrics and evolutionary game in the issue of corporation financing.

A priori data-driven multi-clustered reservoir generation algorithm for echo state network

Echo state networks (ESNs) with multi-clustered reservoir topology perform better in reservoir computing and robustness than those with random reservoir topology. However, these ESNs have a complex reservoir topology, which leads to difficulties in reservoir generation. This study focuses on the reservoir generation problem when ESN is used in environments with sufficient priori data available. Accordingly, a priori data-driven multi-cluster reservoir generation algorithm is proposed. The priori data in the proposed algorithm are used to evaluate reservoirs by calculating the precision and standard deviation of ESNs. The reservoirs are produced using the clustering method; only the reservoir with a better evaluation performance takes the place of a previous one. The final reservoir is obtained when its evaluation score reaches the preset requirement. The prediction experiment results obtained using the Mackey-Glass chaotic time series show that the proposed reservoir generation algorithm provides ESNs with extra prediction precision and increases the structure complexity of the network. Further experiments also reveal the appropriate values of the number of clusters and time window size to obtain optimal performance. The information entropy of the reservoir reaches the maximum when ESN gains the greatest precision.

The evolution of your success lies at the centre of your co-authorship network

Collaboration among scholars and institutions is progressively becoming essential to the success of research grant procurement and to allow the emergence and evolution of scientific disciplines. Our work focuses on analysing if the volume of collaborations of one author together with the relevance of his collaborators is somewhat related to his research performance over time. In order to prove this relation we collected the temporal distributions of scholars' publications and citations from the Google Scholar platform and the co-authorship network (of Computer Scientists) underlying the well-known DBLP bibliographic database. By the application of time series clustering, social network analysis and non-parametric statistics, we observe that scholars with similar publications (citations) patterns also tend to have a similar centrality in the co-authorship network. To our knowledge, this is the first work that considers success evolution with respect to co-authorship.

Multi-frequency complex network from time series for uncovering oil-water flow structure

Uncovering complex oil-water flow structure represents a challenge in diverse scientific disciplines. This challenge stimulates us to develop a new distributed conductance sensor for measuring local flow signals at different positions and then propose a novel approach based on multi-frequency complex network to uncover the flow structures from experimental multivariate measurements. In particular, based on the Fast Fourier transform, we demonstrate how to derive multi-frequency complex network from multivariate time series. We construct complex networks at different frequencies and then detect community structures. Our results indicate that the community structures faithfully represent the structural features of oil-water flow patterns. Furthermore, we investigate the network statistic at different frequencies for each derived network and find that the frequency clustering coefficient enables to uncover the evolution of flow patterns and yield deep insights into the formation of flow structures. Current results present a first step towards a network visualization of complex flow patterns from a community structure perspective.

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

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.

Identification and quantification analysis of nonlinear dynamics properties of combustion instability in a diesel engine

The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.

Evaluation of scaling invariance embedded in short time series

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

Chaotic behavior of light-assisted physical aging in arsenoselenide glasses

The theory of strange attractors is shown to be adequately applicable for analyzing the kinetics of light-assisted physical aging revealed in structural relaxation of Se-rich As-Se glasses below glass transition. Kinetics of enthalpy losses is used to determine the phase space reconstruction parameters. Observed chaotic behaviour (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, false nearest neighbours, etc.) reconstructed via the TISEAN program package is treated within a microstructure model describing multistage aging behaviour in arsenoselenide glasses. This simulation testifies that photoexposure acts as an initiating factor only at the beginning stage of physical aging, thus facilitating further atomic shrinkage of a glassy backbone.

Multi-scale dynamics of glow discharge plasma through wavelets: self-similar behavior to neutral turbulence and dissipation

The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization ability of the continuous Morlet wavelet is found to identify the scale dependent periodic modulations efficiently, as also the emergence of neutral turbulence and dissipation, whereas the discrete Daubechies basis set has been used for detrending the temporal behavior to reveal the multi-fractality of the underlying dynamics. The scaling exponents and the Hurst exponent have been estimated through wavelet based detrended fluctuation analysis, and also Fourier methods and rescale range analysis.

Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model

This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph

A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque et al., Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa et al., Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form [Formula: see text], in which [Formula: see text] is the node degree and [Formula: see text] is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to [Formula: see text] chaotic maps, 2 chaotic flows and [Formula: see text] different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.