Recurrence Networks Research Articles

Mesoscale eddy in situ observation and characterization via underwater glider and complex network theory.

Mesoscale eddies have attracted increased attention due to their central role in ocean energy and mass transport. The observations of their three-dimensional structure will facilitate the understanding of nonlinear eddy dynamics. In this paper, we propose a novel framework, the mesoscale eddy characterization from ordinal modalities recurrence networks method (MeC-OMRN), that utilizes a Petrel-II underwater glider for in situ observations and vertical structure characterization of a moving mesoscale eddy in the northern South China Sea. First, higher resolution continuous observation profile data collected throughout the traversal by the underwater glider are acquired and preprocessed. Subsequently, we analyze and compute these nonlinear data. To further amplify the hidden structural features of the mesoscale eddy, we construct ordinal modalities sequences rich in spatiotemporal characteristics based on the measured vertical density of the mesoscale eddy. Based on this, we employ ordinal modalities recurrence plots (OMRPs) to depict the vertical structure inside and outside the eddy, revealing significant differences in the OMRPs and the unevenness of density stratification within the eddy. To validate our intriguing findings from the perspective of complex network theory, we build the multivariate weighted ordinal modalities recurrence networks, through which network measures exhibit a more random distribution of vertical density stratification within the eddy, possibly due to more intense vertical convection and oscillations within the eddy's seawater micelles. These framework and intriguing findings are anticipated to be applied to more data-driven in situ observation tasks of oceanic phenomena.

Dynamical network-based evaluation for neuromuscular dysfunction in stroke-induced hemiplegia during standing

BackgroundA given movement requires precise coordination of multiple muscles under the control of center nervous system. However, detailed knowledge about the changing characteristics of neuromuscular control for multi-muscle coordination in post-stroke hemiplegic patients during standing is still lacking. This study aimed to investigate the hemiplegia-linked neuromuscular dysfunction during standing from the perspective of multi-muscle dynamical coordination by utilizing a novel network approach – weighted recurrence network (WRN).MethodsTen male hemiplegic patients with first-ever stroke and 10 age-matched healthy male adults were instructed to stand on a platform quietly for 30 s with eyes opened and eyes closed, respectively. The WRN was constructed based on the surface electromyography signals of 16 muscles from trunk, hips, thighs and calves. Relevant topological parameters, including clustering coefficient (C) and average shortest path length (L), were extracted to evaluate the dynamical coordination of multiple muscles. A measure of node centrality in network theory, degree of centrality (DC), was innovatively introduced to assess the contribution of single muscle in the multi-muscle dynamical coordination. The standing-related assessment metric, center of pressure (COP), was provided by the platform directly.ResultsResults showed that the post-stroke hemiplegic patients stood with remarkably higher similarity of muscle activation and more coupled intermuscular dynamics, characterized by higher C and lower L than the healthy subjects (p < 0.05). The DC values and rankings of back, hip and calf muscles on the affected side were significantly decreased, whereas those on the unaffected side were significantly increased in hemiplegia group compared with the healthy group (p < 0.05). Without visual feedback, subjects exhibited enhanced muscle coordination and increased muscle involvement (p < 0.05). A decrease in C and an increase in L of WRN were observed with decreased COP areas (p < 0.05).ConclusionsThese findings revealed that stroke-induced hemiplegia could significantly influence the neuromuscular control, which was manifested as more coupled intermuscular dynamics, abnormal deactivation of muscles on affected side and compensation of muscles on unaffected side from the perspective of multi-muscle coordination. Enhanced multi-muscle dynamical coordination was strongly associated with impaired postural control. This study provides a novel analytical tool for evaluation of neuromuscular dysfunction and specification of responsible muscles for impaired postural control in stroke-induced hemiplegic patients, and could be potentially applied in clinical practice.

Recurrence analysis of 3D point clouds for the detection of surface anomalies in advanced manufacturing

Due to tool wear, machine malfunction, and other internal and external factors, surface anomalies are widely observed in diverse manufacturing processes, such as machining, stamping, and additive manufacturing. The detection of surface anomalies remains an important challenge for assuring the quality and reliability of manufacturing products. Conventional image-based approaches lack the ability to fully capture the 3-dimensional (3D) morphologies of surface defects, which hinder their applications in defect identification, characterization, and diagnosis. The emerging 3D sensing technologies, such as laser or structured-light scanning, enable the collection of point clouds, which embodies a comprehensive representation of defect-altered surface morphologies in 3D space. However, scanned point cloud data are unstructured and oftentimes contain large numbers of points, which pose significant challenges for the recognition of defective surface patterns. To address the challenges, this study develops a recurrence-based approach for the representation learning of 3D point clouds to detect surface defects in manufactured products. Specifically, with a scanned point cloud, key points are first extracted using a voxel-based sampling strategy, and each key point and its neighboring points form a localized sub-region. Then, a recurrence network is generated through a tailored approach, which considers both the morphology similarity and spatial closeness of sub-regions. For anomaly detection, a tensor-based one-class classification model is further deployed to distinguish abnormal surface patterns from normal ones. The developed methodology is experimentally evaluated through simulation and real-world case studies. Experimental results have demonstrated that the developed methodology outperforms benchmarks, highlighting its efficacy in the detection of surface anomalies.

Characteristics of Air Traffic Flow in Terminal Airspace: A Multiplex Recurrence Network Analysis

Characteristics of Air Traffic Flow in Terminal Airspace: A Multiplex Recurrence Network Analysis

Identification of climatic tipping points and transitions in Chinese loess grain-size records utilizing nonlinear time series analysis

As one of the most important terrestrial sediments, Chinese loess provides valuable information on regional and global climatic and environmental changes and holds great potential for studying on nonlinear behaviors of the East Asian monsoon system. Utilizing objective and quantitative methods to identify tipping points and climate transitions in paleoclimatic records can help us understand the climatic change in the Chinese Loess Plateau (CLP). This study explores critical tipping points and nonlinear climate transitions within the CLP using the Chiloparts record, a comprehensive 2600-ka paleoclimate dataset. We pinpointed potential tipping points using recurrence quantification analysis and the augmented Kolmogorov-Smirnov test, ultimately leading to 15 critical tipping points. We argued that these 15 tipping points represent some of the most significant climatic changes recorded in the Chinese loess paleoclimate record. Employing recurrence quantification analysis, recurrence networks, and visibility graphs, we also identified several climate transitions and provided some nonlinear information, including the Mid-Pleistocene Transition (MPT) as well as the Mid-Brunhes Transition (MBT). We particularly highlight a significant climatic regime transition around 500 ka that may reflect a nonlinear response to variations in the Atlantic Meridional Overturning Circulation (AMOC). Our research also contributes to the understanding of the complex interplay between loess deposition, environmental change, and tectonic activity, emphasizing the need for further investigations to elucidate the mechanisms driving these transitions.

Machine learning approach to detect dynamical states from recurrence measures.

We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms: Logistic Regression, Random Forest, and Support Vector Machine for this study. The input features are derived from the recurrence quantification of nonlinear time series and characteristic measures of the corresponding recurrence networks. For training and testing, we generate synthetic data from standard nonlinear dynamical systems and evaluate the efficiency and performance of the machine learning algorithms in classifying time series into periodic, chaotic, hyperchaotic, or noisy categories. Additionally, we explore the significance of input features in the classification scheme and find that the features quantifying the density of recurrence points are the most relevant. Furthermore, we illustrate how the trained algorithms can successfully predict the dynamical states of two variable stars, SX Her and AC Her, from the data of their light curves. We also indicate how the algorithms can be trained to classify data from discrete systems.

Early warning signals for stock market crashes: empirical and analytical insights utilizing nonlinear methods

This study introduces a comprehensive framework grounded in recurrence analysis, a tool of nonlinear dynamics, to detect potential early warning signals (EWS) for imminent phase transitions in financial systems, with the primary goal of anticipating severe financial crashes. We first conduct a simulation experiment to demonstrate that the indicators based on multiplex recurrence networks (MRNs), namely the average mutual information and the average edge overlap, can indicate state transitions in complex systems. Subsequently, we consider the constituent stocks of the China’s and the U.S. stock markets as empirical subjects, and establish MRNs based on multidimensional returns to monitor the nonlinear dynamics of market through the corresponding the indicators and topological structures. Empirical findings indicate that the primary indicators of MRNs offer valuable insights into significant financial events or periods of extreme instability. Notably, average mutual information demonstrates promise as an effective EWS for forecasting forthcoming financial crashes. An in-depth discussion and elucidation of the theoretical underpinnings for employing indicators of MRNs as EWS, the differences in indicator effectiveness, and the possible reasons for variations in the performance of the EWS across the two markets are provided. This paper contributes to the ongoing discourse on early warning extreme market volatility, emphasizing the applicability of recurrence analysis in predicting financial crashes.

Carbon price interval prediction method based on probability density recurrence network and interval multi-layer perceptron

Low-carbon development is an inevitable choice under global climate change, and carbon markets have emerged accordingly. Carbon price forecasting is a crucial aspect of research on carbon-reduction strategies. Traditional forecasting methods are mostly focused on point-valued time series and contain limited information, which causes point forecasting to lose volatility information. Such limitations highlight the importance of proposing a precise interval-valued time series prediction system. To address this issue, we propose a carbon price interval forecasting framework based on a probability density recurrence network and interval multi-layer perceptron (MLPI) from the perspective of uncertainty in the presence of carbon price fluctuations. First, we convert the original data into a probability density sequence using kernel density estimation and then build the network. To extract valid information and exclude abnormal data in the carbon price sample data, we clean the data using network topology and link prediction theory; then, the MLPI model is used for interval forecasting. To verify the forecasting performance of this method, we conduct an empirical analysis using real interval-valued carbon futures price data from the EU carbon market and compare its forecasting precision with other models under the same conditions. The results show that the proposed carbon price interval prediction framework is superior to traditional methods in terms of forecasting precision.

Clinical significance of dynamical network indices of surface electromyography for reticular neuromuscular control assessment

BackgroundThere is currently no objective and accurate clinical assessment of reticular neuromuscular control in healthy subjects or patients with upper motor neuron injury. As a result, clinical dysfunctions of neuromuscular control could just be semi-quantified, efficacies and mechanisms of various therapies for neuromuscular control improving are difficult to verify.MethodsFourteen healthy participants were required to maintain standing balance in the kinetostatics model of Gusu Constraint Standing Training (GCST). A backward and upward constraint force was applied to their trunk at 0°, 20° and 25°, respectively. The multiplex recurrence network (MRN) was applied to analyze the surface electromyography signals of 16 muscles of bilateral lower limbs during the tests. Different levels of MRN network indices were utilized to assess reticular neuromuscular control.ResultsCompared with the 0° test, the MRN indices related to muscle coordination of bilateral lower limbs, of unilateral lower limb and of inter limbs showed significant increase when participants stood in 20° and 25° tests (P < 0.05). The indices related to muscle contribution of gluteal, anterior thigh and calf muscles significantly increased when participants stood in 20° and 25° tests (P < 0.05).ConclusionsThis study applied the dynamical network indices of MRN to analyze the changes of neuromuscular control of lower limbs of healthy participants in the kinetostatics model of GCST. Results showed that the overall coordination of lower limb muscles would be significantly enhanced during performing GCST, partly by the enhancement of neuromuscular control of single lower limb, and partly by the enhancement of joint control across lower limbs. In particular, the muscles in buttocks, anterior thighs and calves played a more important role in the overall coordination, and their involvement was significantly increased. The MRN could provide details of control at the bilateral lower limbs, unilateral lower limb, inter limbs, and single muscle levels, and has the potential to be a new tool for assessing the reticular neuromuscular control.Trial registration ChiCTR2100055090

Directed recurrence networks.

Complex network approaches have attracted a growing interest in the analysis of nonlinear time series. Among other reconstruction methods, it has been shown that the recurrence plot can be used as the adjacency matrix for recurrence networks, expanding the applications of the already successful recurrence analysis. We study here the potential benefits of a directed formulation of recurrence networks through a simple modification of the recurrence plot. As it is directly related to the recurrence analysis field, this approach takes advantage of the progresses regarding the creation and treatment of the recurrence plot. It appears that directed recurrence networks provide more robust results than their undirected counterpart for transitions detection as well as temporal patterns discovery and clustering. New applications for network cleaning and data modeling are also demonstrated.

The geometry of synchronization: quantifying the coupling direction of physiological signals of stress between individuals using inter-system recurrence networks.

In the study of synchronization dynamics between interacting systems, several techniques are available to estimate coupling strength and coupling direction. Currently, there is no general 'best' method that will perform well in most contexts. Inter-system recurrence networks (IRN) combine auto-recurrence and cross-recurrence matrices to create a graph that represents interacting networks. The method is appealing because it is based on cross-recurrence quantification analysis, a well-developed method for studying synchronization between 2 systems, which can be expanded in the IRN framework to include N > 2 interacting networks. In this study we examine whether IRN can be used to analyze coupling dynamics between physiological variables (acceleration, blood volume pressure, electrodermal activity, heart rate and skin temperature) observed in a client in residential care with severe to profound intellectual disabilities (SPID) and their professional caregiver. Based on the cross-clustering coefficients of the IRN conclusions about the coupling direction (client or caregiver drives the interaction) can be drawn, however, deciding between bi-directional coupling or no coupling remains a challenge. Constructing the full IRN, based on the multivariate time series of five coupled processes, reveals the existence of potential feedback loops. Further study is needed to be able to determine dynamics of coupling between the different layers.

Weighted Dynamic Time Warping for Time Series

Recurrence network is a typical time series analysis method. However, irregular sampling may overshadow the dynamic features characterized by traditional recurrence network method, which makes the method ineffective. This paper introduces dynamic time warping method to determine the distance between time series segments. The method can match the features of time series segments and reduce the distortion of distances caused by irregular sampling. For points in sparse sampling area, many characteristics may not be collected and thus the matching results are unreliable. To overcome this problem, we further propose weighted dynamic time warping method which assigns small weights to matching points with sparse local sampling so as to reduce their influence on distance. A recurrence network constructed by weighted dynamic time warping method can effectively capture underlying nonlinear and nonstationary system dynamics from irregular sampling time series. The effectiveness of the proposed method is illustrated by two case studies: the discrimination of different dynamic behaviors and detection of system parameter perturbation from time series of Rössler system.

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.

Identifying dominant flow features from very-sparse Lagrangian data: a multiscale recurrence network-based approach

Realistic fluid flow problems often require that Lagrangian tracers are deployed in a sparse or very-sparse manner, such as for oceanic and atmospheric flows where large-scale motion needs characterisation. Data sparsity represents a significant issue in Lagrangian analysis, especially for data-driven methods that rely heavily on large datasets. We propose a multiscale spatial recurrence network (MSRN) methodology for characterising very-sparse Lagrangian data, which exploits individual tracks and a spatial recurrence criterion to identify the spatio-temporal complexity of tracer trajectories. The MSRN is an unsupervised modelling framework that does not require a priori parameter setting, and—through the quantification of persistent link activation at specific trajectory intervals—can reveal the presence of dominant looping scales in a variety of salient fluid flows. This new paradigm is shown to be successful for the study of Lagrangian tracers seeded in complex (realistic) flows, including unsteady and advection-dominated problems. This makes MSRNs an effective and versatile tool to characterise sensor trajectories in key problems such as environmental processes critical to understanding and mitigating climate change.Graphic abstract

Recurrence Network-Based 3D Geometry Representation Learning for Quality Control in Additive Manufacturing of Metamaterials

Abstract Metamaterials are designed with intricate geometries to deliver unique properties, and recent years have witnessed an upsurge in leveraging additive manufacturing (AM) to produce metamaterials. However, the frequent occurrence of geometric defects in AM poses a critical obstacle to realizing the desired properties of fabricated metamaterials. Advances in three-dimensional (3D) scanning technologies enable the capture of fine-grained 3D geometric patterns, thereby providing a great opportunity for detecting geometric defects in fabricated metamaterials for property-oriented quality assurance. Realizing the full potential of 3D scanning-based quality control hinges largely on devising effective approaches to process scanned point clouds and extract geometric-pertinent information. In this study, a novel framework is developed to integrate recurrence network-based 3D geometry profiling with deep one-class learning for geometric defect detection in AM of metamaterials. First, we extend existing recurrence network models that focus on image data to represent 3D point clouds, by designing a new mechanism that characterizes points’ geometric pattern affinities and spatial proximities. Then, a one-class graph neural network (GNN) approach is tailored to uncover topological variations of the recurrence network and detect anomalies associated with geometric defects in the fabricated metamaterial. The developed methodology is evaluated through comprehensive simulated and real-world case studies. Experimental results have highlighted the efficacy of the developed methodology in identifying both global and local geometric defects in AM-fabricated metamaterials.

Recurrence Network Analysis of Histopathological Images for the Detection of Invasive Ductal Carcinoma in Breast Cancer.

The histopathological image analysis is one of the most crucial diagnostic procedures to identify Invasive ductal carcinoma (IDC) in breast cancers. However, this diagnosis process is currently time-consuming and heavily dependent on human expertise. Prior research has shown that different degrees of tumors present various microstructures in the histopathological images. However, very little has been done to utilize spatial recurrence features of microstructures for identifying IDC. This paper presents a novel recurrence analysis methodology for automatic image-guided IDC detection. We first utilize wavelet decomposition to delineate the subtle information in the images. Then, we model the patches with a weighted recurrence network approach to characterize the recurrence patterns of the histopathological images. Finally, we develop automated IDC detection models leveraging machine learning methods with spatial recurrence features extracted. The developed recurrence analysis models successfully characterize the complex microstructures of histopathological images and achieve the IDC detection performances of at least AUC = 0.96. This research developed a spatial recurrence analysis methodology to effectively identify IDC regions in histopathological images for BC. It shows a high potential to assist physicians in the decision-making process. The proposed methodology can further be applicable to image processing for other medical or biological applications.

A Proposal to Analyze Muscle Dynamics Under Fatiguing Contractions Using Surface Electromyography Signals and Fuzzy Recurrence Network Features

The analysis of surface electromyography (sEMG) signals is significant in the detection of muscle fatigue. These signals exhibit a great degree of complexity, nonlinearity, and chaos. Also, presence of high degree of fluctuations in the signal makes its analysis a difficult task. This study aims to analyze the nonlinear dynamics of muscle fatigue conditions using Fuzzy recurrence networks (FRN). Dynamic sEMG signals are measured from biceps brachii muscle of 45 normal subjects referenced to 50% of maximal voluntary contractions (MVC) for this. Recorded signals are then pre-processed and divided into ten equal parts. FRNs are transformed from the signals. The network features, namely average weighted degree (AWD) and Closeness centrality (CC) are extracted to analyze the muscle dynamics during fatiguing conditions. The decrease in these features during fatigue indicates a reduction in signal complexity and an increase in complex network stiffness. Both AWD and CC features are statistically significant with [Formula: see text]. Further, these features are classified using Naïve Bayes (NB), k nearest neighbor (kNN) and random forest (RF) algorithms. Maximum accuracy of 96.90% is achieved using kNN classifier for combined FRN features. Thus, the proposed features provide high-quality inputs to the neural networks that may be helpful in analyzing the complexity and stiffness of neuromuscular system under various myoneural conditions.

Text characterization based on recurrence networks

Several complex systems are characterized by exhibiting intricate properties that occur at multiple scales. These multi-scale characterizations are used in various applications. In particular, texts can be characterized by a hierarchical structure, which can be approached by using multi-scale concepts and methods. Here, we adopt an extension of the multi-scale, mesoscopic approach – hereafter referred to as a recurrence network – to represent text narratives, in which only the recurrent relationships among tagged parts of speech (subject, verb and direct object) are considered to establish connections among sequential pieces of text. The characterization of the texts was then achieved by considering scale-dependent complementary methods: accessibility and symmetry. To evaluate the potential of these concepts, we approached the problem of distinguishing between meaningful and meaningless texts and different literary genres (namely, fiction and non-fiction). A set of 300 books was considered and compared by using the above approaches. The recurrence network characterization was able to discriminate to some extent between real and meaningless and between the two genres assessed. Thus, our results indicate that recurrence networks are able to capture subtleties in book plots, suggesting that a similar methodology can be used in related networked applications.

Optical Flow Reusing for High-Efficiency Space-Time Video Super Resolution

In this paper, we consider the task of space-time video super-resolution (ST-VSR), which can increase the spatial resolution and frame rate for a given video simultaneously. Despite the remarkable progress of recent methods, most of them still suffer from high computational costs and inefficient long-range information usage. To alleviate these problems, we propose a Bidirectional Recurrence Network (BRN) with the optical-flow-reuse strategy to better use temporal knowledge from long-range neighboring frames for high-efficiency reconstruction. Specifically, an efficient and memory-saving multi-frame motion utilization strategy is proposed by reusing the intermediate flow of adjacent frames, which considerably reduces the computation burden of frame alignment compared with traditional LSTM-based designs. In addition, the proposed hidden state in BRN is updated by the reused optical flow and refined by the Feature Refinement Module (FRM) for further optimization. Moreover, by utilizing intermediate flow estimation, the proposed method can inference non-linear motion and restore details better. Extensive experiments demonstrate that our optical-flow-reuse-based bidirectional recurrent network (OFR-BRN) is superior to state-of-the-art methods in accuracy and efficiency.

BCR-Net: A deep learning framework to predict breast cancer recurrence from histopathology images.

Breast cancer is the most common malignancy in women, with over 40,000 deaths annually in the United States alone. Clinicians often rely on the breast cancer recurrence score, Oncotype DX (ODX), for risk stratification of breast cancer patients, by using ODX as a guide for personalized therapy. However, ODX and similar gene assays are expensive, time-consuming, and tissue destructive. Therefore, developing an AI-based ODX prediction model that identifies patients who will benefit from chemotherapy in the same way that ODX does would give a low-cost alternative to the genomic test. To overcome this problem, we developed a deep learning framework, Breast Cancer Recurrence Network (BCR-Net), which automatically predicts ODX recurrence risk from histopathology slides. Our proposed framework has two steps. First, it intelligently samples discriminative features from whole-slide histopathology images of breast cancer patients. Then, it automatically weights all features through a multiple instance learning model to predict the recurrence score at the slide level. On a dataset of H&E and Ki67 breast cancer resection whole slides images (WSIs) from 99 anonymized patients, the proposed framework achieved an overall AUC of 0.775 (68.9% and 71.1% accuracies for low and high risk) on H&E WSIs and overall AUC of 0.811 (80.8% and 79.2% accuracies for low and high risk) on Ki67 WSIs of breast cancer patients. Our findings provide strong evidence for automatically risk-stratify patients with a high degree of confidence. Our experiments reveal that the BCR-Net outperforms the state-of-the-art WSI classification models. Moreover, BCR-Net is highly efficient with low computational needs, making it practical to deploy in limited computational settings.