Visibility Graph Based Time Series Analysis

[Sampling intervals dependent feature extraction for state transfer networks of epileptic signals]

Epileptic seizures and the interictal epileptiform discharges both have similar waveforms. And a method to effectively extract features that can be used to distinguish seizures is of crucial importance both in theory and clinical practice. We constructed state transfer networks by using visibility graphlet at multiple sampling intervals and analyzed network features. We found that the characteristics waveforms in ictal periods were more robust with various sampling intervals, and those feature network structures did not change easily in the range of the smaller sampling intervals. Inversely, the feature network structures of interictal epileptiform discharges were stable in range of relatively larger sampling intervals. Furthermore, the feature nodes in networks during ictal periods showed long-term correlation along the process, and played an important role in regulating system behavior. For stereo-electroencephalography at around 500 Hz, the greatest difference between ictal and the interictal epileptiform occurred at the sampling interval around 0.032 s. In conclusion, this study effectively reveals the correlation between the features of pathological changes in brain system and the multiple sampling intervals, which holds potential application value in clinical diagnosis for identifying, classifying, and predicting epilepsy.

A graph-based cardiac arrhythmia classification methodology using one-lead ECG recordings

In this study, we present a novel graph-based methodology for an accurate classification of cardiac arrhythmia diseases using a single-lead electrocardiogram (ECG). The proposed approach employs the visibility graph technique to generate graphs from time signals. Subsequently, informative features are extracted from each graph and then fed into classifiers to match the input ECG signal with the appropriate target arrhythmia class. The six target classes in this study are normal (N), left bundle branch block (LBBB), right bundle branch block (RBBB), premature ventricular contraction (PVC), atrial premature contraction (A), and fusion (F) beats. Three classification models were explored, including graph convolutional neural network (GCN), multi-layer perceptron (MLP), and random forest (RF). ECG recordings from the MIT-BIH arrhythmia database were utilized to train and evaluate these classifiers. The results indicate that the multi-layer perceptron model attains the highest performance, showcasing an average accuracy of 99.02%. Following closely, the random forest achieves a strong performance as well, with an accuracy of 98.94% while providing critical intuitions.

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.

Network Representation of fMRI Data Using Visibility Graphs: The Impact of Motion and Test-Retest Reliability

Visibility graphs provide a novel approach for analysing time-series data. Graph theoretical analysis of visibility graphs can provide new features for data mining applications in fMRI. However, visibility graphs features have not been used widely in the field of neuroscience. This is likely due to a lack of understanding of their robustness in the presence of noise (e.g., motion) and their test-retest reliability. In this study, we investigated visibility graph properties of fMRI data in the human connectome project (N = 1010) and tested their sensitivity to motion and test-retest reliability. We also characterised the strength of connectivity obtained using degree synchrony of visibility graphs. We found that strong correlation (r > 0.5) between visibility graph properties, such as the number of communities and average degrees, and motion in the fMRI data. The test-retest reliability (Intraclass correlation coefficient (ICC)) of graph theoretical features was high for the average degrees (0.74, 95% CI = [0.73, 0.75]), and moderate for clustering coefficient (0.43, 95% CI = [0.41, 0.44]) and average path length (0.41, 95% CI = [0.38, 0.44]). Functional connectivity between brain regions was measured by correlating the visibility graph degrees. However, the strength of correlation was found to be moderate to low (r < 0.35). These findings suggest that even small movement in fMRI data can strongly influence robustness and reliability of visibility graph features, thus, requiring robust motion correction strategies prior to data analysis. Further studies are necessary for better understanding of the potential application of visibility graph features in fMRI.

Relationship between magnetic rigidity cutoff and chaotic behavior in cosmic ray time series using visibility graph and network analysis techniques

Cosmic rays are highly energetic particles originating from astrophysical events outside the Solar System. In this study, we analyze the time series of cosmic ray flux measured by neutron detectors at 16 monitoring stations distributed worldwide. By applying visibility graph analysis, we explore the relationship between the magnetic rigidity cutoff (Rc) and the fractality exhibited from topology of the cosmic ray time series. Our results reveal a significant association between the magnetic rigidity cutoff and the fractality of the cosmic ray time series. Specifically, the analysis of visibility graphs and network properties demonstrates that the magnetic rigidity is inversely related to the magnetic rigidity cutoff. The identified relationship between magnetic rigidity and fractality provides insights into the chaotic nature of cosmic ray variations and their potential uses for predictability.

Photoplethysmography-based cuffless blood pressure estimation: an image encoding and fusion approach

Objective.Photoplethysmography (PPG) is a promising wearable technology that detects volumetric changes in microcirculation using a light source and a sensor on the skin's surface. PPG has been shown to be useful for non-invasive blood pressure (BP) measurement. Deep learning-based BP measurements are now gaining popularity. However, almost all methods focus on 1D PPG. We aimed to design an end-to-end approach for estimating BP using image encodings from a 2D perspective.Approach.In this paper, we present a BP estimation approach based on an image encoding and fusion (BP-IEF) technique. We convert the PPG into five image encodings and use them as input. The proposed BP-IEF consists of two parts: an encoder and a decoder. In addition, three kinds of well-known neural networks are taken as the fundamental architecture of the encoder. The decoder is a hybrid architecture that consists of convolutional and fully connected layers, which are used to fuse features from the encoder.Main results.The performance of the proposed BP-IEF is evaluated on the UCI database in both non-mixed and mixed manners. On the non-mixed dataset, the root mean square error and mean absolute error for systolic BP (SBP) are 13.031 mmHg and 9.187 mmHg respectively, while for diastolic BP (DBP) they are 5.049 mmHg and 3.810 mmHg. On the mixed dataset, the corresponding values for SBP are 4.623 mmHg and 3.058 mmHg, while for DBP the values are 2.350 mmHg and 1.608 mmHg. In addition, both SBP and DBP estimation on the mixed dataset achieved grade A compared to the British Hypertension Society standard. The DBP estimation on the non-mixed dataset also achieved grade A.Significance.The results indicate that the proposed approach has the potential to improve on the current mobile healthcare for cuffless BP measurement.

Assessment of Multivariate Information Transmission in Space-Time-Frequency Domain: A Case Study for EEG Signals

OBJECTIVE

Multivariate signal (MS) analysis, especially the assessment of its information transmission (for example, from the perspective of network science), is the key to our understanding of various phenomena in biology, physics and economics. Although there is a large amount of literature demonstrating that MS can be decomposed into space-time-frequency domain information, there seems to be no research confirming that multivariate information transmission (MIT) in these three domains can be quantified. Therefore, in this study, we attempted to combine dynamic mode decomposition (DMD) and parallel communication model (PCM) together to realize it.

METHODS

We first regarded MS as a large-scale system and then used DMD to decompose it into specific subsystems with their own intrinsic oscillatory frequencies. At the same time, the transition probability matrix (TPM) of information transmission within and between MS at two consecutive moments in each subsystem can also be calculated. Then, communication parameters (CPs) derived from each TPM were calculated in order to quantify the MIT in the space-time-frequency domain. In this study, multidimensional electroencephalogram (EEG) signals were used to illustrate our method.

RESULTS

Compared with traditional EEG brain networks, this method shows greater potential in EEG analysis to distinguish between patients and healthy controls.

CONCLUSION

This study demonstrates the feasibility of measuring MIT in the space-time-frequency domain simultaneously.

SIGNIFICANCE

This study shows that MIT analysis in the space-time-frequency domain is not only completely different from the MS decomposition in these three domains, but also can reveal many new phenomena behind MS that have not yet been discovered.

Cuff-Less Blood Pressure Estimation via Small Convolutional Neural Networks

Deep learning-based cuff-less blood pressure (BP) estimation methods have recently gained increased attention as they can provide accurate BP estimation with only one physiological signal as input. In this paper, we present a simple and effective method for cuff-less BP estimation by training a small-scale convolutional neural network (CNN), modified from LeNet-5, with images created from short segments of the photoplethysmogram (PPG) signal via visibility graph (VG). Results show that the trained modified LeNet-5 model achieves an error performance of 0.184±7.457 mmHg for the systolic BP (SBP), and 0.343±4.065 mmHg for the diastolic BP (DBP) in terms of the mean error (ME) and the standard deviation (SD) of error between the estimated and reference BP. Both the SBP and the DBP accuracy rank grade A under the British Hypertension Society (BHS) protocol, demonstrating that our proposed method is an accurate way for cuff-less BP estimation.

Synchronization Analysis In Epileptic EEG Signals Via State Transfer Networks Based On Visibility Graph Technique

Epilepsy is a persistent and recurring neurological condition in a community of brain neurons that results from sudden and abnormal electrical discharges. This paper introduces a new form of assessment and interpretation of the changes in electroencephalography (EEG) recordings from different brain regions in epilepsy disorders based on graph analysis and statistical rescale range analysis. In this study, two different states of epilepsy EEG data (preictal and ictal phases), obtained from 17 subjects (18 channels each), were analyzed by a new method called state transfer network (STN). The analysis performed by STN yields a network metric called motifs, which are averaged over all channels and subjects in terms of their persistence level in the network. The results showed an increase of overall motif persistence during the ictal over the preictal phase, reflecting the synchronization increase during the seizure phase (ictal). An evaluation of intermotif cross-correlation indicated a definite manifestation of such synchronization. Moreover, these findings are compared with several other well-known methods such as synchronization likelihood (SL), visibility graph similarity (VGS), and global field synchronization (GFS). It is hinted that the STN method is in good agreement with approaches in the literature and more efficient. The most significant contribution of this research is introducing a novel nonlinear analysis technique of generalized synchronization. The STN method can be used for classifying epileptic seizures based on the synchronization changes between multichannel data.

Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash

In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.

Identifiable Temporal Feature Selection via Horizontal Visibility Graph Towards Smart Medical Applications

With the proliferation of IoMT (Internet of Medical Things), billions of connected medical devices are constantly producing oceans of time series sensor data, dubbed as time series for short. Considering these time series reflect various functional states of the human body, how to effectively detect the corresponding abnormalities is of great significance for smart healthcare. Accordingly, we develop a horizontal visibility graph-based temporal classification model for disease diagnosis. We conduct extensive comparison experiments on the benchmark datasets to justify the superiority of our method in term of accuracy and efficiency. Besides, we have released the codes and parameters to facilitate the community research. We propose an identifiable temporal feature selection via horizontal visibility graph for time series classification (TSC) based disease diagnosis. We conduct comparison experiments on the benchmark datasets to justify the superiority of our method in term of accuracy and efficiency. As a side contribution, we have released the codes and parameters to facilitate the community research ( https://github.com/sdujicun/SSVG ).

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.

Visibility graph based temporal community detection with applications in biological time series

Temporal behavior is an essential aspect of all biological systems. Time series have been previously represented as networks. Such representations must address two fundamental problems on how to: (1) Create appropriate networks to reflect the characteristics of biological time series. (2) Detect characteristic dynamic patterns or events as network temporal communities. General community detection methods use metrics comparing the connectivity within a community to random models, or are based on the betweenness centrality of edges or nodes. However, such methods were not designed for network representations of time series. We introduce a visibility-graph-based method to build networks from time series and detect temporal communities within these networks. To characterize unevenly sampled time series (typical of biological experiments), and simultaneously capture events associated to peaks and troughs, we introduce the Weighted Dual-Perspective Visibility Graph (WDPVG). To detect temporal communities in individual signals, we first find the shortest path of the network between start and end nodes, identifying high intensity nodes as the main stem of our community detection algorithm that act as hubs for each community. Then, we aggregate nodes outside the shortest path to the closest nodes found on the main stem based on the closest path length, thereby assigning every node to a temporal community based on proximity to the stem nodes/hubs. We demonstrate the validity and effectiveness of our method through simulation and biological applications.

Augmenting Neuromuscular Disease Detection Using Optimally Parameterized Weighted Visibility Graph

In this contribution, we propose a novel neuromuscular disease detection framework employing weighted visibility graph (WVG) aided analysis of electromyography signals. WVG converts a time series into an undirected graph, while preserving the signal properties. However, conventional WVG is sensitive to noise and has high computational complexity which is problematic for lengthy and noisy time series analysis. To address this issue in this article, we investigate the performance of WVG by varying two important parameters, namely penetrable distance and scale factor, both of which have shown promising results by eliminating the problem of signal adulteration and decreasing the computational complexity, respectively. We also aim to unfold the combined effect of these two aforesaid parameters on the WVG performance to discriminate between myopathy, amyotrophic lateral sclerosis (ALS) and healthy EMG signals. Using graph theory based features we demonstrated that the discriminating capability between the three classes increased significantly with the increase in both penetrable distance and scale factor values. Three binary (healthy vs. myopathy, myopathy vs. ALS and healthy vs. ALS) and one multiclass problems (healthy vs. myopathy vs. ALS) have been addressed in this study and for each problem, we obtained optimum parameter values determined on the basis of F-value computed using one way analysis of variance (ANOVA) test. Using optimal parameter values, we obtained mean accuracy of 98.57%, 98.09% and 99.45%, respectively for three binary and 99.05% for the multi-class classification problem. Additionally, the computational time was reduced by 96% with optimally selected WVG parameters compared to traditional WVG.

Permutation Entropy as a Measure of Information Gain/Loss in the Different Symbolic Descriptions of Financial Data

Financial markets give a large number of trading opportunities. However, over-complicated systems make it very difficult to be effectively used by decision-makers. Volatility and noise present in the markets evoke a need to simplify the market picture derived for the decision-makers. Symbolic representation fits in this concept and greatly reduces data complexity. However, at the same time, some information from the market is lost. Our motivation is to answer the question: What is the impact of introducing different data representation on the overall amount of information derived for the decision-maker? We concentrate on the possibility of using entropy as a measure of the information gain/loss for the financial data, and as a basic form, we assume permutation entropy with later modifications. We investigate different symbolic representations and compare them with classical data representation in terms of entropy. The real-world data covering the time span of 10 years are used in the experiments. The results and the statistical verification show that extending the symbolic description of the time series does not affect the permutation entropy values.

Coastal Mangrove Response to Marine Erosion: Evaluating the Impacts of Spatial Distribution and Vegetation Growth in Bangkok Bay from 1987 to 2017

Long time-series monitoring of mangroves to marine erosion in the Bay of Bangkok, using Landsat data from 1987 to 2017, shows responses including landward retreat and seaward extension. Quantitative assessment of these responses with respect to spatial distribution and vegetation growth shows differing relationships depending on mangrove growth stage. Using transects perpendicular to the shoreline, we calculated the cross-shore mangrove extent (width) to represent spatial distribution, and the normalized difference vegetation index (NDVI) was used to represent vegetation growth. Correlations were then compared between mangrove seaside changes and the two parameters—mangrove width and NDVI—at yearly and 10-year scales. Both spatial distribution and vegetation growth display positive impacts on mangrove ecosystem stability: At early growth stages, mangrove stability is positively related to spatial distribution, whereas at mature growth the impact of vegetation growth is greater. Thus, we conclude that at early growth stages, planting width and area are more critical for stability, whereas for mature mangroves, management activities should focus on sustaining vegetation health and density. This study provides new rapid insights into monitoring and managing mangroves, based on analyses of parameters from historical satellite-derived information, which succinctly capture the net effect of complex environmental and human disturbances.

Sampling frequency dependent visibility graphlet approach to time series

Recent years have witnessed special attention on complex network based time series analysis. To extract evolutionary behaviors of a complex system, an interesting strategy is to separate the time series into successive segments, map them further to graphlets as representatives of states, and extract from the state (graphlet) chain transition properties, called graphlet based time series analysis. Generally speaking, properties of time series depend on the time scale. In reality, a time series consists of records that are sampled usually with a specific frequency. A natural question is how the evolutionary behaviors obtained with the graphlet approach depend on the sampling frequency? In the present paper, a new concept called the sampling frequency dependent visibility graphlet is proposed to answer this problem. The key idea is to extract a new set of series in which the successive elements have a specified delay and obtain the state transition network with the graphlet based approach. The dependence of the state transition network on the sampling period (delay) can show us the characteristics of the time series at different time scales. Detailed calculations are conducted with time series produced by the fractional Brownian motion, logistic map and Rössler system, and the empirical sentence length series for the famous Chinese novel entitled A Story of the Stone. It is found that the transition networks for fractional Brownian motions with different Hurst exponents all share a backbone pattern. The linkage strengths in the backbones for the motions with different Hurst exponents have small but distinguishable differences in quantity. The pattern also occurs in the sentence length series; however, the linkage strengths in the pattern have significant differences with that for the fractional Brownian motions. For the period-eight trajectory generated with the logistic map, there appear three different patterns corresponding to the conditions of the sampling period being odd/even-fold of eight or not both. For the chaotic trajectory of the logistic map, the backbone pattern of the transition network for sampling 1 saturates rapidly to a new structure when the sampling period is larger than 2. For the chaotic trajectory of the Rössler system, the backbone structure of the transition network is initially formed with two self-loops, the linkage strengths of which decrease monotonically with the increase of the sampling period. When the sampling period reaches 9, a new large loop appears. The pattern saturates to a complex structure when the sampling period is larger than 11. Hence, the new concept can tell us new information on the trajectories. It can be extended to analyze other series produced by brains, stock markets, and so on.

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.

Decoding cortical brain states from widefield calcium imaging data using visibility graph

Widefield optical imaging of neuronal populations over large portions of the cerebral cortex in awake behaving animals provides a unique opportunity for investigating the relationship between brain function and behavior. In this paper, we demonstrate that the temporal characteristics of calcium dynamics obtained through widefield imaging can be utilized to infer the corresponding behavior. Cortical activity in transgenic calcium reporter mice (n=6) expressing GCaMP6f in neocortical pyramidal neurons is recorded during active whisking (AW) and no whisking (NW). To extract features related to the temporal characteristics of calcium recordings, a method based on visibility graph (VG) is introduced. An extensive study considering different choices of features and classifiers is conducted to find the best model capable of predicting AW and NW from calcium recordings. Our experimental results show that temporal characteristics of calcium recordings identified by the proposed method carry discriminatory information that are powerful enough for decoding behavior.

Categorisation of polyphonic musical signals by using modularity community detection in audio-associated visibility network

This article proposes a method to numerically characterise the homogeneity of polyphonic musical signals through community detection in audio-associated visibility networks and to detect patterns that allow the categorisation of these signals into two types of grouping based on this numerical characterization. To implement this methodology, we first calculate the variance fluctuation series in fixed-size windows of an audio stretch. Next we map this series onto a visibility graph, where the nodes are the points of the series, and the edges are defined by the visibility between each pair of points. Then, we measure the quality of the partitions of the network using the modularity and Louvain optimisation. We observed that a greater or lesser homogeneity of the magnitudes of the signal transients is related to a higher or lower modularity of the audio-associated visibility network. We also note that these differences are related to musical choices that can establish important differences between musical styles. In this article, we show that the modularity is able to give relevant information to allow the categorisation of 120 musical signs labelled in percussive and symphonic music.

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.

Visibility Graph from Adaptive Optimal Kernel Time-Frequency Representation for Classification of Epileptiform EEG

Detecting epileptic seizure from EEG signals constitutes a challenging problem of significant importance. Combining adaptive optimal kernel time-frequency representation and visibility graph, we develop a novel method for detecting epileptic seizure from EEG signals. We construct complex networks from EEG signals recorded from healthy subjects and epilepsy patients. Then we employ clustering coefficient, clustering coefficient entropy and average degree to characterize the topological structure of the networks generated from different brain states. In addition, we combine energy deviation and network measures to recognize healthy subjects and epilepsy patients, and further distinguish brain states during seizure free interval and epileptic seizures. Three different experiments are designed to evaluate the performance of our method. The results suggest that our method allows a high-accurate classification of epileptiform EEG signals.

Directed weighted network structure analysis of complex impedance measurements for characterizing oil-in-water bubbly flow

Characterizing the flow structure underlying the evolution of oil-in-water bubbly flow remains a contemporary challenge of great interests and complexity. In particular, the oil droplets dispersing in a water continuum with diverse size make the study of oil-in-water bubbly flow really difficult. To study this issue, we first design a novel complex impedance sensor and systematically conduct vertical oil-water flow experiments. Based on the multivariate complex impedance measurements, we define modalities associated with the spatial transient flow structures and construct modality transition-based network for each flow condition to study the evolution of flow structures. In order to reveal the unique flow structures underlying the oil-in-water bubbly flow, we filter the inferred modality transition-based network by removing the edges with small weight and resulting isolated nodes. Then, the weighted clustering coefficient entropy and weighted average path length are employed for quantitatively assessing the original network and filtered network. The differences in network measures enable to efficiently characterize the evolution of the oil-in-water bubbly flow structures.

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.

Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series

Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.

Long-Range Correlations in Sentence Series from A Story of the Stone

A sentence is the natural unit of language. Patterns embedded in series of sentences can be used to model the formation and evolution of languages, and to solve practical problems such as evaluating linguistic ability. In this paper, we apply de-trended fluctuation analysis to detect long-range correlations embedded in sentence series from A Story of the Stone, one of the greatest masterpieces of Chinese literature. We identified a weak long-range correlation, with a Hurst exponent of 0.575±0.002 up to a scale of 10⁴. We used the structural stability to confirm the behavior of the long-range correlation, and found that different parts of the series had almost identical Hurst exponents. We found that noisy records can lead to false results and conclusions, even if the noise covers a limited proportion of the total records (e.g., less than 1%). Thus, the structural stability test is an essential procedure for confirming the existence of long-range correlations, which has been widely neglected in previous studies. Furthermore, a combination of de-trended fluctuation analysis and diffusion entropy analysis demonstrated that the sentence series was generated by a fractional Brownian motion.

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.