Network structure of multivariate time series

A Gentle Introduction and Application of Feature-Based Clustering with Psychological Time Series

Psychological researchers and practitioners collect increasingly complex time series data aimed at identifying differences between the developments of participants or patients. Past research has proposed a number of dynamic measures that describe meaningful developmental patterns for psychological data (e.g., instability, inertia, linear trend). Yet, commonly used clustering approaches are often not able to include these meaningful measures (e.g., due to model assumptions). We propose feature-based time series clustering as a flexible, transparent, and well-grounded approach that clusters participants based on the dynamic measures directly using common clustering algorithms. We introduce the approach and illustrate the utility of the method with real-world empirical data that highlight common ESM challenges of multivariate conceptualizations, structural missingness, and non-stationary trends. We use the data to showcase the main steps of input selection, feature extraction, feature reduction, feature clustering, and cluster evaluation. We also provide practical algorithm overviews and readily available code for data preparation, analysis, and interpretation.

Visibility Graph Investigation of the Shallow Seismicity of Lai Chau Area (Vietnam)

In this study, the topological properties of the shallow seismicity occurring in the area around the Lai Chau hydropower plant (Vietnam) are investigated by using visibility graph (VG) analysis, a well-known method to convert time series into networks or graphs. The relationship between the seismicity and reservoir water level was analyzed using Interlayer Mutual Information (IMI) and the Frobenius norm, both applied to the corresponding VG networks. IMI was used to assess the correlation between the two variables, while the Frobenius norm was employed to estimate the time delay between them. The total seismicity, which resulted in an M≥0.8 with a b-value of 0.86, is characterized by a k-M slope of ≈9.1. Analyzing the variation of the seismological and topological parameters of the seismicity relative to the distance from the center of the Lai Chau reservoir revealed the following features: (1) the b-value fluctuates around a mean value of 1.21 at distances of up to 10-11 km, while, for distances larger than 25-30 km, it tends to the value of 0.86; (2) the maximum IMI between the monthly number of earthquakes and the monthly mean water level occurs at a distance of 9-11 km, showing a distance evolution similar to that of the b-value; (3) at these distances from the center of the reservoir, the time lag between the earthquake monthly counts and the monthly water level mean is 9-10 months; (4) the relationship between the b-value and the k-M slope suggests that the k-M slope depends on the number of earthquakes within a 22 km radius from the center of the dam. Our study's findings offer new insights into the complex dynamics of seismicity occurring around reservoirs.

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

BACKGROUND

A 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).

METHODS

Ten 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.

RESULTS

Results 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).

CONCLUSIONS

These 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.

From physiological complexity to data interactions-A case study of recordings from exercise monitoring

The popularity of nonlinear analysis has been growing simultaneously with the technology of effort monitoring. Therefore, considering the simple methods of physiological data collection and the approaches from the information domain, we proposed integrating univariate and bivariate analysis for the rest and effort comparison. Two sessions separated by an intensive training program were studied. Nine subjects participated in the first session (S1) and seven in the second session (S2). The protocol included baseline (BAS), exercise, and recovery phase. During all phases, electrocardiogram (ECG) was recorded. For the analysis, we selected corresponding data lengths of BAS and exercise usually lasting less than 5 min. We found the utility of the differences between original data and their surrogates for sample entropy Sdiff and Kullback-Leibler divergence KLDdiff. Sdiff of heart rate variability was negative in BAS and exercise but its sensitivity for phases discrimination was not satisfactory. We studied the bivariate analysis of RR intervals and corresponding QT peaks by Interlayer Mutual Information (IMI) and average edge overlap (AVO) markers. While the IMI parameter decreases in exercise conditions, AVO increased in effort compared to BAS. These findings conclude that researchers should consider a bivariate analysis of extracted RR intervals and corresponding QT datasets, when only ECG is recorded during tests.

Simplicial complex entropy for time series analysis

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts.

Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators

Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators. We show that the normalized persistent entropy (NPE) allows us to characterize the effective coupling between pairs of oscillators because it tends to increase with the coupling strength and to decrease with the distance between the oscillators. We also observed that pairs of oscillators that have similar degrees and are nearest neighbors tend to have higher NPE values than pairs with different degrees. However, large variability is found in the NPE values. Comparing the NPE behavior with that of the phase-locking value (PLV, commonly used to evaluate the synchronization of phase oscillators), we find that for large enough coupling, PLV only displays a monotonic increase, while NPE shows a richer behavior that captures variations in the behavior of the oscillators. This is due to the fact that PLV only captures coupling-induced phase changes, while NPE also captures amplitude changes. Moreover, when we consider the same network but with Kuramoto phase oscillators, we also find that NPE captures the transition to synchronization (as it increases with the coupling strength), and it also decreases with the distance between the oscillators. Therefore, we propose NPE as a data analysis technique to try to differentiate pairs of oscillators that have strong effective coupling because they are first or near neighbors, from those that have weaker coupling because they are distant neighbors.

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.

Daylight Saving Time transitions and Cardiovascular Disease in Andalusia: Time Series Modeling and Analysis Using Visibility Graphs

The present study aimed to determine whether transitions both to and from daylight saving time (DST) led to an increase in the incidence of hospital admissions for major acute cardiovascular events (MACE). To support the analysis, natural visibility graphs (NVGs) were used with data from Andalusian public hospitals between 2009 and 2019. We calculated the incidence rates of hospital admissions for MACE, and specifically acute myocardial infarction and ischemic stroke during the 2 weeks leading up to, and 2 weeks after, the DST transition. NVG were applied to identify dynamic patterns. The study included 157 221 patients diagnosed with MACE, 71 992 with AMI (42 975 ST-elevation myocardial infarction (STEMI) and 26 752 non-ST-elevation myocardial infarction (NSTEMI)), and 51 420 with ischemic stroke. Observed/expected ratios shown an increased risk of AMI (1.06; 95% CI (1.00-1.11); P = .044), NSTEMI (1.12; 95% CI (1.02-1.22); P = .013), and acute coronary syndrome (1.05; 95% CI (1.00-1.10); P = .04) around the autumn DST. The NVG showed slight variations in the daily pattern of pre-DST and post-DST hospitalization admissions for all pathologies, but indicated that the increase in the incidence of hospital admissions after the DST is not sufficient to change the normal pattern significantly.

Environmental pollution in North-Eastern Italy and its influence on chronic obstructive pulmonary disease: time series modelling and analysis using visibility graphs

The impact on human health from environmental pollution is receiving increasing attention. In the case of respiratory diseases such as chronic obstructive pulmonary disease (COPD), the relationship is now well documented. However, few studies have been carried out in areas with low population density and low industrial production, such as the province of Belluno (North-Eastern Italy). The aim of the study was to analyze the effect of exposure to certain pollutants on the temporal dynamics of hospital admissions for COPD in the province of Belluno. Daily air pollution concentration, humidity, precipitations, and temperature were collected from the air monitoring stations in Belluno. Generalized additive mixed models (GAMM) and visibility graphs were used to determine the effects of the short-term exposure to environmental agents on hospital admissions associated to COPD. In the case of the city of Belluno, the GAMM showed that hospital admissions were associated with NO₂, PM₁₀, date, and temperature, while for the city of Feltre, GAMM produced no associated variables. Several visibility graph indices (average edge overlap and interlayer mutual information) showed a significant overlap between environmental agents and hospital admission for both cities. Our study has shown that visibility graphs can be useful in establishing associations between environmental agents and COPD hospitalization in sparsely populated areas.

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.

Hierarchical deposition and scale-free networks: A visibility algorithm approach

The growth of an interface formed by the hierarchical deposition of particles of unequal size is studied in the framework of a dynamical network generated by a horizontal visibility algorithm. For a deterministic model of the deposition process, the resulting network is scale free with dominant degree exponent γ_{e}=ln3/ln2 and transient exponent γ_{o}=1. An exact calculation of the network diameter and clustering coefficient reveals that the network is scale invariant and inherits the modular hierarchical nature of the deposition process. For the random process, the network remains scale free, where the degree exponent asymptotically converges to γ=3, independent of the system parameters. This result shows that the model is in the class of fractional Gaussian noise through the relation between the degree exponent and the series' Hurst exponent H. Finally, we show through the degree-dependent clustering coefficient C(k) that the modularity remains present in the system.

Visibility graph for time series prediction and image classification: a review

The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

Dynamic Linkages among Carbon, Energy and Financial Markets: Multiplex Recurrence Network Approach

It has become a hot issue to integrate the carbon market, energy market, and financial market into one system and explore the relationship among them. Considering that the carbon market, energy market, and financial market all have chaotic characteristics to varying degrees, this paper proposes a theoretical framework to study the linkage relationship among the three markets on the basis of the method of the Multiplex recurrence network. Firstly, we built a multiplex recurrence network of carbon-energy-financial market. Then, based on the connection relationship among nodes of the recurrence network of each market, the degree distribution of nodes of each market, and the information entropy theory, we put forward several metric indicators to explore the correlativity and mutual guidance relation among carbon market, energy market and financial market from micro and macro perspectives. Using the data generated by the deterministic system, the effectiveness of the defined index was confirmed by numerical simulation. The empirical analysis of the carbon market, energy market, and financial market revealed the evolution process of the increasingly close connection between the three markets, and we found that the carbon market plays an increasingly important role in the world capital market system. Based on the research results, we propose some suggestions for market decision-makers, enterprises, and investors.

Early Warning Signals in Phase Space: Geometric Resilience Loss Indicators From Multiplex Cumulative Recurrence Networks

The detection of Early Warning Signals (EWS) of imminent phase transitions, such as sudden changes in symptom severity could be an important innovation in the treatment or prevention of disease or psychopathology. Recurrence-based analyses are known for their ability to detect differences in behavioral modes and order transitions in extremely noisy data. As a proof of principle, the present paper provides an example of a recurrence network based analysis strategy which can be implemented in a clinical setting in which data from an individual is continuously monitored for the purpose of making decisions about diagnosis and intervention. Specifically, it is demonstrated that measures based on the geometry of the phase space can serve as Early Warning Signals of imminent phase transitions. A publicly available multivariate time series is analyzed using so-called cumulative Recurrence Networks (cRN), which are recurrence networks with edges weighted by recurrence time and directed towards previously observed data points. The results are compared to previous analyses of the same data set, benefits, limitations and future directions of the analysis approach are discussed.

Feature Extraction of the Brain's Dynamic Complex Network Based on EEG and a Framework for Discrimination of Pediatric Epilepsy

Most of the current complex network studies about epilepsy used the electroencephalogram (EEG) to directly construct the static complex network for analysis and discarded the dynamic characteristics. This study constructed the dynamic complex network on EEG from pediatric epilepsy and pediatric control when they were asleep by the sliding window method. Dynamic features were extracted and incorporated into various machine learning classifiers to explore their classification performances. We compared these performances between the static and dynamic complex network. In the univariate analysis, the initially insignificant topological characteristics in the static complex network can be transformed to be significant in the dynamic complex network. Under most connectivity calculation methods between leads, the accuracy of using dynamic complex network features for discrimination was higher than that of static complex network features. Particularly in the imaginary part of the coherency function (iCOH) method under the full-frequency band, the discrimination accuracies of most machine learning classifiers were higher than 95%, and the discrimination accuracies in the higher-frequency band (beta-frequency band) and the full-frequency band were higher than that of the lower-frequency bands. Our proposed method and framework could efficiently summarize more time-varying features in the EEG and improve the accuracies of the discrimination of the machine learning classifiers more than using static complex network features.

Network Analysis of Time Series: Novel Approaches to Network Neuroscience

In the last two decades, there has been an explosion of interest in modeling the brain as a network, where nodes correspond variously to brain regions or neurons, and edges correspond to structural or statistical dependencies between them. This kind of network construction, which preserves spatial, or structural, information while collapsing across time, has become broadly known as "network neuroscience." In this work, we provide an alternative application of network science to neural data: network-based analysis of non-linear time series and review applications of these methods to neural data. Instead of preserving spatial information and collapsing across time, network analysis of time series does the reverse: it collapses spatial information, instead preserving temporally extended dynamics, typically corresponding to evolution through some kind of phase/state-space. This allows researchers to infer a, possibly low-dimensional, "intrinsic manifold" from empirical brain data. We will discuss three methods of constructing networks from nonlinear time series, and how to interpret them in the context of neural data: recurrence networks, visibility networks, and ordinal partition networks. By capturing typically continuous, non-linear dynamics in the form of discrete networks, we show how techniques from network science, non-linear dynamics, and information theory can extract meaningful information distinct from what is normally accessible in standard network neuroscience approaches.

Automated sleep state classification of wide-field calcium imaging data via multiplex visibility graphs and deep learning

BACKGROUND

Wide-field calcium imaging (WFCI) allows for monitoring of cortex-wide neural dynamics in mice. When applied to the study of sleep, WFCI data are manually scored into the sleep states of wakefulness, non-REM (NREM) and REM by use of adjunct EEG and EMG recordings. However, this process is time-consuming and often suffers from low inter- and intra-rater reliability and invasiveness. Therefore, an automated sleep state classification method that operates on WFCI data alone is needed.

NEW METHOD

A hybrid, two-step method is proposed. In the first step, spatial-temporal WFCI data is mapped to multiplex visibility graphs (MVGs). Subsequently, a two-dimensional convolutional neural network (2D CNN) is employed on the MVGs to be classified as wakefulness, NREM and REM.

RESULTS

Sleep states were classified with an accuracy of 84% and Cohen's κ of 0.67. The method was also effectively applied on a binary classification of wakefulness/sleep (accuracy=0.82, κ = 0.62) and a four-class wakefulness/sleep/anesthesia/movement classification (accuracy=0.74, κ = 0.66). Gradient-weighted class activation maps revealed that the CNN focused on short- and long-term temporal connections of MVGs in a sleep state-specific manner. Sleep state classification performance when using individual brain regions was highest for the posterior area of the cortex and when cortex-wide activity was considered.

COMPARISON WITH EXISTING METHOD

On a 3-hour WFCI recording, the MVG-CNN achieved a κ of 0.65, comparable to a κ of 0.60 corresponding to the human EEG/EMG-based scoring.

CONCLUSIONS

The hybrid MVG-CNN method accurately classifies sleep states from WFCI data and will enable future sleep-focused studies with WFCI.

Assessment of time irreversibility in a time series using visibility graphs

In this paper, we studied the time-domain irreversibility of time series, which is a fundamental property of systems in a nonequilibrium state. We analyzed a subgroup of the databases provided by University of Rochester, namely from the THEW Project. Our data consists of LQTS (Long QT Syndrome) patients and healthy persons. LQTS may be associated with an increased risk of sudden cardiac death (SCD), which is still a big clinical problem. ECG-based artificial intelligence methods can identify sudden cardiac death with a high accuracy. It follows that heart rate variability contains information about the possibility of SCD, which may be extracted, provided that appropriate methods are developed for this purpose. Our aim was to assess the complexity of both groups using visibility graph (VG) methods. Multivariate analysis of connection patterns of graphs built from time series was performed using multiplex visibility graph methods. For univariate time series, time irreversibility of the ECG interval QT of patients with LQTS was lower than for the healthy. However, we did not observe statistically significant difference in the comparison of RR intervals time series of the two groups studied. The connection patterns retrieved from multiplex VGs have more similarity with each other in the case of LQTS patients. This observation may be used to develop better methods for SCD risk stratification.

Brain functional networks analysis of five fingers grasping in virtual reality environment

This study investigated the effects of different center of mass (COM) of the grasping device and visual time-delay on the information interaction between brain regions during five-finger grasping process. Nine healthy right-handed subjects used five fingers to grasp a special device in a virtual reality (VR) environment. Two independent variables were set in the experiment: the COM of the grasping device and the visual delay time. Place a 50 g mass randomly at five different directions of the grasping device base. The three levels of visual delay time appear randomly. The kinematics and dynamics and electroencephalogram (EEG) signals were recorded during the experiment. The brain network was constructed based on multiplex horizontal visibility graph (MHVG). Interlayer mutual information (MI) and phase locking value (PLV) were calculated to quantify the network, while clustering coefficient (C), shortest path length (L) and overall network efficiency (E) are selected to quantify the network characteristic. Statistical results show that when the mass is located in the radial side, during the load phase of grasping, the C and E is significantly higher than that in the proximal, ulnar and medial side, and L was significantly lower than that in the proximal and radial side. This shows that when grasping an object with a COM bias on the radial side, the process of brain feedforward control has higher level of information interaction and ability and it can build stronger sensorimotor memory. It is also found that the brain network features of theta, beta and gamma bands of EEG are positively correlated, especially between beta and gamma bands, which suggests there is a coupling relationship between different bands in information processing and transmission.Clinical Relevance- This study explains the neural mechanism of grasping control from the topological structure of the whole brain network level and the informatics.

Artificial Intelligence Based Body Sensor Network Framework-Narrative Review: Proposing an End-to-End Framework using Wearable Sensors, Real-Time Location Systems and Artificial Intelligence/Machine Learning Algorithms for Data Collection, Data Mining and Knowledge Discovery in Sports and Healthcare

With the rising amount of data in the sports and health sectors, a plethora of applications using big data mining have become possible. Multiple frameworks have been proposed to mine, store, preprocess, and analyze physiological vitals data using artificial intelligence and machine learning algorithms. Comparatively, less research has been done to collect potentially high volume, high-quality 'big data' in an organized, time-synchronized, and holistic manner to solve similar problems in multiple fields. Although a large number of data collection devices exist in the form of sensors. They are either highly specialized, univariate and fragmented in nature or exist in a lab setting. The current study aims to propose artificial intelligence-based body sensor network framework (AIBSNF), a framework for strategic use of body sensor networks (BSN), which combines with real-time location system (RTLS) and wearable biosensors to collect multivariate, low noise, and high-fidelity data. This facilitates gathering of time-synchronized location and physiological vitals data, which allows artificial intelligence and machine learning (AI/ML)-based time series analysis. The study gives a brief overview of wearable sensor technology, RTLS, and provides use cases of AI/ML algorithms in the field of sensor fusion. The study also elaborates sample scenarios using a specific sensor network consisting of pressure sensors (insoles), accelerometers, gyroscopes, ECG, EMG, and RTLS position detectors for particular applications in the field of health care and sports. The AIBSNF may provide a solid blueprint for conducting research and development, forming a smooth end-to-end pipeline from data collection using BSN, RTLS and final stage analytics based on AI/ML algorithms.

Multiplex Recurrence Network Analysis of Inter-Muscular Coordination During Sustained Grip and Pinch Contractions at Different Force Levels

Production of functional forces by human motor systems require coordination across multiple muscles. Grip and pinch are two prototypes for grasping force production. Each grasp plays a role in a range of hand functions and can provide an excellent paradigm for studying fine motor control. Despite previous investigations that have characterized muscle synergies during general force production, it is still unclear how intermuscular coordination differs between grip and pinch and across different force outputs. Traditional muscle synergy analyses, such as non-negative matrix factorization or principal component analysis, utilize dimensional reduction without consideration of nonlinear characteristics of muscle co-activations. In this study, we investigated the novel method of multiplex recurrence networks (MRN) to assess the inter-muscular coordination for both grip and pinch at different force levels. Unlike traditional methods, the MRN can leverage intrinsic similarities in muscle contraction dynamics and project its layers to the corresponding weighted network (WN) to better model muscle interactions. Twenty-four healthy volunteers were instructed to grip and pinch an apparatus with force production at 30%, 50%, and 70% of their respective maximal voluntary contraction (MVC). The surface electromyography (sEMG) signals were recorded from eight muscles, including intrinsic and extrinsic muscles spanning the hand and forearm. The sEMG signals were then analyzed using MRNs and WNs. Interlayer mutual information ( I ) and average edge overlap ( ω ) of MRNs and average shortest path length ( L ) of WNs were computed and compared across groups for grasp types (grip vs. pinch) and force levels (30%, 50% and 70% MVC). Results showed that the extrinsic, rather than the intrinsic muscles, had significant differences in network parameters between both grasp types ( ), and force levels ( ), and especially at higher force levels. Furthermore, I and ω were strengthened over time ( ) except with pinch at 30% MVC. Results suggest that the central nervous system (CNS) actively increases cortical oscillations over time in response to increasing force levels and changes in force production with different sustained grasping types. Muscle coupling in extrinsic muscles was higher than in intrinsic muscles for both grip and pinch. The MRNs may be a valuable tool to provide greater insights into inter-muscular coordination patterns of clinical populations, assess neuromuscular function, or stabilize force control in prosthetic hands.

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.

Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data

A key challenge to gaining insight into complex systems is inferring nonlinear causal directional relations from observational time-series data. Specifically, estimating causal relationships between interacting components in large systems with only short recordings over few temporal observations remains an important, yet unresolved problem. Here, we introduce large-scale nonlinear Granger causality (lsNGC) which facilitates conditional Granger causality between two multivariate time series conditioned on a large number of confounding time series with a small number of observations. By modeling interactions with nonlinear state-space transformations from limited observational data, lsNGC identifies casual relations with no explicit a priori assumptions on functional interdependence between component time series in a computationally efficient manner. Additionally, our method provides a mathematical formulation revealing statistical significance of inferred causal relations. We extensively study the ability of lsNGC in inferring directed relations from two-node to thirty-four node chaotic time-series systems. Our results suggest that lsNGC captures meaningful interactions from limited observational data, where it performs favorably when compared to traditionally used methods. Finally, we demonstrate the applicability of lsNGC to estimating causality in large, real-world systems by inferring directional nonlinear, causal relationships among a large number of relatively short time series acquired from functional Magnetic Resonance Imaging (fMRI) data of the human brain.

A multiplex visibility graph motif‐based convolutional neural network for characterizing sleep stages using EEG signals

Sleep is an essential integrant in everyone’s daily life; therefore, it is an important but challenging problem to characterize sleep stages from electroencephalogram (EEG) signals. The network motif has been developed as a useful tool to investigate complex networks. In this study, we developed a multiplex visibility graph motif‐based convolutional neural network (CNN) for characterizing sleep stages using EEG signals and then introduced the multiplex motif entropy as the quantitative index to distinguish the six sleep stages. The independent samples t‐test shows that the multiplex motif entropy values have significant differences among the six sleep stages. Furthermore, we developed a CNN model and employed the multiplex motif sequence as the input of the model to classify the six sleep stages. Notably, the classification accuracy of the six‐state stage detection was 85.27%. Results demonstrated the effectiveness of the multiplex motif in characterizing the dynamic features underlying different sleep stages, whereby they further provide an essential strategy for future sleep‐stage detection research.

Multiplex recurrence networks from multi-lead ECG data

We present an integrated approach to analyze the multi-lead electrocardiogram (ECG) data using the framework of multiplex recurrence networks (MRNs). We explore how their intralayer and interlayer topological features can capture the subtle variations in the recurrence patterns of the underlying spatio-temporal dynamics of the cardiac system. We find that MRNs from ECG data of healthy cases are significantly more coherent with high mutual information and less divergence between respective degree distributions. In cases of diseases, significant differences in specific measures of similarity between layers are seen. The coherence is affected most in the cases of diseases associated with localized abnormality such as bundle branch block. We note that it is important to do a comprehensive analysis using all the measures to arrive at disease-specific patterns. Our approach is very general and as such can be applied in any other domain where multivariate or multi-channel data are available from highly complex systems.

Construction of Multiplex Muscle Network for Precision Pinch Force Control

Muscle synergy is a fundamental mechanism of motor control. Despite a number of studies focusing on muscle synergy during power grip and pinch at high-level force, relatively less is known about the functional interactions between muscles within low-level force production during precision pinch. Traditional analytical tools such as nonnegative matrix factorization or principal component analysis have limitations in processing nonlinear dynamic electromyographic signals and have confined sensitivity particularly for the low-level force production. In this study, we developed a novel method - multiplex muscle networks, to investigate the dynamical coordination of muscle activities at low-level force production during precision pinch. The multiplex muscle network was constructed based on multiplex limited penetrable horizontal visibility graph (MLPHVG). Seven forearm and hand muscles, including brachioradialis (BR), flexor carpi ulnaris (FCU), flexor carpi radialis (FCR), flexor digitorum superficialis (FDS), extensor digitorum communis (EDC), abductor pollicis brevis (APB) and first dorsal interosseous (FDI), were examined using surface electromyography (sEMG). Eight healthy subjects were instructed to perform a visuomotor force tracking task by producing higher (10% MVC) and lower (1% MVC) precision pinch. Interlayer mutual information I, average edge overlap ω weighted clustering coefficient C^W, weighted characteristic path length L^W were selected as network metrics. We assessed the undirected weighted network generated from multiplex muscle network after taking the I between paired muscle network layers as edge. There are significant differences between higher and lower force level with higher I, ω, C^W and lower L^W at higher force level. Advanced efficiency of information processing in the regional and global perspective indicated dynamical alterations when human faces the higher force tracking task. It suggested that ω may be an important characteristic to classify different force control states with the average classification accuracy of 82.21%. These findings reveal related alterations of functional interactions between muscles involved in precision pinch. The novel method for constructing multiplex muscle network may provide insights into muscle synergies during precision pinch force control.

Dynamic Analysis of Muscle Coordination at Different Force Levels during Grip and Pinch with Multiplex Recurrence Network

Muscle synergistic contraction to produce force has been recognized as an important neurophysiological mechanism in neuromuscular system. Despite a range of approaches, such as nonnegative matrix factorization or principal component analysis that have been widely used, limitations still exist in analysis of dynamic coordination of multiple muscles. In addition, it is still less studied about the potential difference of muscle dynamic coordination at different force levels during grip and pinch within the same framework. With this aim, this study analyzed the dynamic coordination of multiple upper-limb muscles at low, medium and high force levels during pinch and grip with multiplex recurrence network (MRN). Twenty-four healthy subjects participated in the experiment. Subjects were instructed to grip an apparatus to match the target force as stably as they could for 10 s. Surface electromyographic (sEMG) signals were recorded from 8 upper-limb muscles and analyzed by the MRN. The interlayer mutual information (I) and the average edge overlap (ω) of MRNs were calculated to quantify muscle correlation and muscle synchronization, respectively. Results showed that I and ω values of extrinsic muscles' MRNs during grip were significantly higher than that during grip at medium and high force. Furthermore, the I and ω values of extrinsic muscle networks during grip increased with augmented force levels. No significant changes were found for the intrinsic muscles with force output levels. These findings indicate that the muscles coordination patterns between grip and pinch were different and higher co-contraction of extrinsic muscles is favorable to synergistic force production. With the force output increased, muscles' coordination was augmented in extrinsic muscles, but no change in intrinsic muscles because of independent and complicated control of fingers. This study provides an analytical tool for dynamic muscles coordination and provides insights into the mechanisms of synergistic control of muscle contractions for force production.Clinical Relevance-This study provides a novel analytical tool for muscle coordination during force production, which may facilitate the evaluation of neuromuscular function or serve as indicators for neuromuscular disorders.

Improving graph-based detection of singular events for photochemical smog agents

Recently, a set of graph-based tools have been introduced for the identification of singular events of O₃, NO₂ and temperature time series, as well as description of their dynamics. These are based on the use of the Visibility Graphs (VG). In this work, an improvement of the original approach is proposed, being called Upside-Down Visibility Graph (UDVG). It adds the possibility of investigating the singular lowest episodes, instead of the highest. Results confirm the applicability of the new method for describing the multifractal nature of the underlying O₃, NO₂, and temperature. Asymmetries in the NO₂ degree distribution are observed, possibly due to the interaction with different chemicals. Furthermore, a comparison of VG and UDVG has been performed and the outcomes show that they describe opposite subsets of the time series (low and high values) as expected. The combination of the results from the two networks is proposed and evaluated, with the aim of obtaining all the information at once. It turns out to be a more complete tool for singularity detection in photochemical time series, which could be a valuable asset for future research.

Estimation of Dynamic Bivariate Correlation Using a Weighted Graph Algorithm

Dynamic correlation is the correlation between two time series across time. Two approaches that currently exist in neuroscience literature for dynamic correlation estimation are the sliding window method and dynamic conditional correlation. In this paper, we first show the limitations of these two methods especially in the presence of extreme values. We present an alternate approach for dynamic correlation estimation based on a weighted graph and show using simulations and real data analyses the advantages of the new approach over the existing ones. We also provide some theoretical justifications and present a framework for quantifying uncertainty and testing hypotheses.

On fractality of functional near-infrared spectroscopy signals: analysis and applications

Significance: The human brain is a highly complex system with nonlinear, dynamic behavior. A majority of brain imaging studies employing functional near-infrared spectroscopy (fNIRS), however, have considered only the spatial domain and have ignored the temporal properties of fNIRS recordings. Methods capable of revealing nonlinearities in fNIRS recordings can provide new insights about how the brain functions. Aim: The temporal characteristics of fNIRS signals are explored by comprehensively investigating their fractal properties. Approach: Fractality of fNIRS signals is analyzed using scaled windowed variance (SWV), as well as using visibility graph (VG), a method which converts a given time series into a graph. Additionally, the fractality of fNIRS signals obtained under resting-state and task-based conditions is compared, and the application of fractality in differentiating brain states is demonstrated for the first time via various classification approaches. Results: Results from SWV analysis show the existence of high fractality in fNIRS recordings. It is shown that differences in the temporal characteristics of fNIRS signals related to task-based and resting-state conditions can be revealed via the VGs constructed for each case. Conclusions: fNIRS recordings, regardless of the experimental conditions, exhibit high fractality. Furthermore, VG-based metrics can be employed to differentiate rest and task-execution brain states.

Visibility Graphs for Image Processing

The family of image visibility graphs (IVG/IHVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such\an operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibility graphs encapsulates relevant information on the structure of the images and we explore their potential as image filters. We introduce several graph features, including the novel concept of Visibility Patches, and show through several examples that these features are highly informative, computationally efficient and universally applicable for general pattern recognition and image classification tasks.

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.

Multiscale Horizontal Visibility Graph Analysis of Higher-Order Moments for Estimating Statistical Dependency

The horizontal visibility graph is not only a powerful tool for the analysis of complex systems, but also a promising way to analyze time series. In this paper, we present an approach to measure the nonlinear interactions between a non-stationary time series based on the horizontal visibility graph. We describe how a horizontal visibility graph may be calculated based on second-order and third-order statistical moments. We compare the new methods with the first-order measure, and then give examples including stock markets and aero-engine performance parameters. These analyses suggest that measures derived from the horizontal visibility graph may be of particular relevance to the growing interest in quantifying the information exchange between time series.

Can complex networks describe the urban and rural tropospheric O3 dynamics?

Tropospheric ozone (O₃) time series have been converted into complex networks through the recent so-called Visibility Graph (VG), using the data from air quality stations located in the western part of Andalusia (Spain). The aim is to apply this novel method to differentiate the behavior between rural and urban regions when it comes to the ozone dynamics. To do so, some centrality parameters of the resulting complex networks have been investigated: the degree, betweenness and shortest path. Some of them are expected to corroborate previous works in order to support the use of this technique; while others to supply new information. Results coincide when describing the difference that tropospheric ozone exhibits seasonally and geographically. It is seen that ozone behavior is fractal, in accordance to previous works. Also, it has been demonstrated that this methodology is able to characterize the divergence encountered between measurements in urban environments and countryside. In addition to that, the promising outcomes of this technique support the use of complex networks for the study of air pollutants dynamics. Particularly, new nuances are offered such as the identification and description of singularities in the signal.

Characterization of SSMVEP-based EEG signals using multiplex limited penetrable horizontal visibility graph

The steady state motion visual evoked potential (SSMVEP)-based brain computer interface (BCI), which incorporates the motion perception capabilities of the human visual system to alleviate the negative effects caused by strong visual stimulation from steady-state VEP, has attracted a great deal of attention. In this paper, we design a SSMVEP-based experiment by Newton's ring paradigm. Then, we use the canonical correlation analysis and Support Vector Machines to classify SSMVEP signals for the SSMVEP-based electroencephalography (EEG) signal detection. We find that the classification accuracy of different subjects under fatigue state is much lower than that in the normal state. To probe into this, we develop a multiplex limited penetrable horizontal visibility graph method, which enables to infer a brain network from 62-channel EEG signals. Subsequently, we analyze the variation of the average weighted clustering coefficient and the weighted global efficiency corresponding to these two brain states and find that both network measures are lower under fatigue state. The results suggest that the associations and information transfer efficiency among different brain regions become weaker when the brain state changes from normal to fatigue, which provide new insights into the explanations for the reduced classification accuracy. The promising classification results and the findings render the proposed methods particularly useful for analyzing EEG recordings from SSMVEP-based BCI system.

Multiplex Limited Penetrable Horizontal Visibility Graph from EEG Signals for Driver Fatigue Detection

Driver fatigue is an important contributor to road accidents, and driver fatigue detection has attracted a great deal of attention on account of its significant importance. Numerous methods have been proposed to fulfill this challenging task, though, the characterization of the fatigue mechanism still, to a large extent, remains to be investigated. To address this problem, we, in this work, develop a novel Multiplex Limited Penetrable Horizontal Visibility Graph (Multiplex LPHVG) method, which allows in not only detecting fatigue driving but also probing into the brain fatigue behavior. Importantly, we use the method to construct brain networks from EEG signals recorded from different subjects performing simulated driving tasks under alert and fatigue driving states. We then employ clustering coefficient, global efficiency and characteristic path length to characterize the topological structure of the networks generated from different brain states. In addition, we combine average edge overlap with the network measures to distinguish alert and mental fatigue states. The high-accurate classification results clearly demonstrate and validate the efficacy of our multiplex LPHVG method for the fatigue detection from EEG signals. Furthermore, our findings show a significant increase of the clustering coefficient as the brain evolves from alert state to mental fatigue state, which yields novel insights into the brain behavior associated with fatigue driving.

Visibility graphs of ground-level ozone time series: A multifractal analysis

A recent method based on the concurrence of complex networks and multifractal analyses is applied for the first time to explore ground-level ozone behavior. Ozone time series are converted into complex networks for their posterior analysis. The searched purpose is to check the suitability of this transformation and to see whether some features of these complex networks could constitute a preliminary analysis before the more thorough multifractal formalism. Results show effectively that the exposed transformation stores the original information about the ozone dynamics and gives meaningful knowledge about the time series. Based on these results, the multifractal analysis of the complex networks is performed. Looking at the physical meaning of the multifractal properties (such as fractal dimensions and singularity spectrum), a relationship between those and the degree distribution of the complex networks is found. In addition to all the promising results, this novel connection between time series and complex networks can deal with both stationary and non-stationary time series, overcoming one of the main limitations of multifractal analysis. Therefore, this technique can be regarded as an alternative to give supplementary information within the study of complex signals.

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.

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

The limited penetrable horizontal visibility algorithm is an analysis tool that maps time series into complex networks and is a further development of the horizontal visibility algorithm. This paper presents exact results on the topological properties of the limited penetrable horizontal visibility graph associated with independent and identically distributed (i:i:d:) random series. We show that the i.i.d: random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution, independent of the probability distribution from which the series was generated. We deduce the exact expressions of mean degree and clustering coefficient, demonstrate the long distance visibility property of the graph and perform numerical simulations to test the accuracy of our theoretical results. We then use the algorithm in several deterministic chaotic series, such as the logistic map, H´enon map, Lorenz system, energy price chaotic system and the real crude oil price. Our results show that the limited penetrable horizontal visibility algorithm is efficient to discriminate chaos from uncorrelated randomness and is able to measure the global evolution characteristics of the real time series.

A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

We explore a combinatorial framework which efficiently quantifies the asymmetries between minima and maxima in local fluctuations of time series. We first showcase its performance by applying it to a battery of synthetic cases. We find rigorous results on some canonical dynamical models (stochastic processes with and without correlations, chaotic processes) complemented by extensive numerical simulations for a range of processes which indicate that the methodology correctly distinguishes different complex dynamics and outperforms state of the art metrics in several cases. Subsequently, we apply this methodology to real-world problems emerging across several disciplines including cases in neurobiology, finance and climate science. We conclude that differences between the statistics of local maxima and local minima in time series are highly informative of the complex underlying dynamics and a graph-theoretic extraction procedure allows to use these features for statistical learning purposes.

Multiplex recurrence networks

We have introduced a multiplex recurrence network approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on coupled map lattices and a typical example from palaeobotany research. In both examples, topological changes in the multiplex recurrence networks allow for the detection of regime changes in their dynamics. The method goes beyond classical interpretation of pollen records by considering the vegetation as a whole and using the intrinsic similarity in the dynamics of the different regional vegetation elements. We find that the different vegetation types behave more similarly when one environmental factor acts as the dominant driving force.

Multiscale network representation of physiological time series for early prediction of sepsis

Objective and Approach: Sepsis, a dysregulated immune-mediated host response to infection, is the leading cause of morbidity and mortality in critically ill patients. Indices of heart rate variability and complexity (such as entropy) have been proposed as surrogate markers of neuro-immune system dysregulation with diseases such as sepsis. However, these indices only provide an average, one dimensional description of complex neuro-physiological interactions. We propose a novel multiscale network construction and analysis method for multivariate physiological time series, and demonstrate its utility for early prediction of sepsis.

MAIN RESULTS

We show that features derived from a multiscale heart rate and blood pressure time series network provide approximately 20% improvement in the area under the receiver operating characteristic (AUROC) for four-hour advance prediction of sepsis over traditional indices of heart rate entropy ([Formula: see text] versus [Formula: see text]). Our results indicate that this improvement is attributable to both the improved network construction method proposed here, as well as the information embedded in the higher order interaction of heart rate and blood pressure time series dynamics. Our final model, which included the most commonly available clinical measurements in patients' electronic medical records and multiscale entropy features, as well as the proposed network-based features, achieved an AUROC of [Formula: see text].

SIGNIFICANCE

Prediction of the onset of sepsis prior to clinical recognition will allow for meaningful earlier interventions (e.g. antibiotic and fluid administration), which have the potential to decrease sepsis-related morbidity, mortality and healthcare costs.

Visibility graphs for fMRI data: Multiplex temporal graphs and their modulations across resting-state networks

Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a) this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b) this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach.

A multiplex network approach for the analysis of intracranial pressure and heart rate data in traumatic brain injured patients

BACKGROUND

We present a multiplex network model for the analysis of Intracranial Pressure (ICP) and Heart Rate (HR) behaviour after severe brain traumatic injuries in pediatric patients. The ICP monitoring is of vital importance for checking life threathening conditions, and understanding the behaviour of these parameters is crucial for a successful intervention of the clinician. Our own observations, exhibit cross-talks interaction events happening between HR and ICP, i.e. transients in which both the ICP and the HR showed an increase of 20% with respect to their baseline value in the window considered. We used a complex event processing methodology, to investigate the relationship between HR and ICP, after traumatic brain injuries (TBI). In particular our goal has been to analyse events of simultaneous increase by HR and ICP (i.e. cross-talks), modelling the two time series as a unique multiplex network system (Lacasa et al., Sci Rep 5:15508-15508, 2014).

METHODS AND DATA

We used a complex network approach based on visibility graphs (Lacasa et al., Sci Rep 5:15508-15508, 2014) to model and study the behaviour of our system and to investigate how and if network topological measures can give information on the possible detection of crosstalks events taking place in the system. Each time series was converted as a layer in a multiplex network. We therefore studied the network structure, focusing on the behaviour of the two time series in the cross-talks events windows detected. We used a dataset of 27 TBI pediatric patients, admitted to Addenbrooke's Hospital, Cambridge, Pediatric Intensive Care Unit (PICU) between August 2012 and December 2014.

RESULTS

Following a preliminary statistical exploration of the two time series of ICP and HR, we analysed the multiplex network proposed, focusing on two standard topological network metrics: the mutual interaction, and the average edge overlap (Lacasa et al., Sci Rep 5:15508-15508, 2014). We compared results obtained for these two indicators, considering windows in which a cross talks event between HR and ICP was detected with windows in which cross talks events were not present. The analysis of such metrics gave us interesting insights on the time series behaviour. More specifically we observed an increase in the value of the mutual interaction in the case of cross talk as compared to non cross talk. This seems to suggest that mutual interaction could be a potentially interesting "marker" for cross talks events.

Visibility graphs of random scalar fields and spatial data

We extend the family of visibility algorithms to map scalar fields of arbitrary dimension into graphs, enabling the analysis of spatially extended data structures as networks. We introduce several possible extensions and provide analytical results on the topological properties of the graphs associated to different types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension. This result holds independently of the field's marginal distribution and it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatiotemporal chaos. The range of potential applications of this combinatorial framework includes image processing in engineering, the description of surface growth in material science, soft matter or medicine, and the characterization of potential energy surfaces in chemistry, disordered systems, and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed.

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.