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Identifying Alzheimer’s disease (AD) in its early stages is a challenging task for physicians and clinicians. This paper proposes a new algorithm for diagnosing AD, which is based on analyzing spontaneous speech signals. The proposed method uses two visibility graph methods, Natural Visibility Graph (NVG) and Horizontal Visibility Graph (HVG), to derive features from speech windows. These features are then given to a deep BiLSTM-based classifier to decide about segments of the signal. The proposed approach could obtain a sensitivity of 98.33%, specificity of 99.44%, and accuracy of 99.17%. The advantage of converting speech signals into graphs using NVG and HVG is that it allows for the extraction of complex structural features that are not easily captured by traditional methods. This method is highly beneficial due to its non-invasive nature, low cost, and lack of side effects. Patients can undergo the procedure without experiencing any discomfort, while also benefiting from its affordability and accessibility. The method’s safety and practicality make it an ideal choice for those seeking a reliable and effective solution. Moreover, the proposed algorithm has a high accuracy in detecting the early stage of AD, which makes it a promising tool to evaluate Alzheimer’s disease diagnosis in its pre-clinical stage. [ABSTRACT FROM AUTHOR]

This paper adopts the visibility graph (VG) methodology to analyze the dynamic behavior of West Texas Intermediate (WTI), Brent and Shanghai (SC) crude oil futures during the COVID-19 pandemic and Russia–Ukraine conflict. Utilizing daily and high-frequency data, our study reveals a clear power-law decay in VG degree distributions and highlights pronounced clustering tendencies within crude oil futures VGs. We also uncover an inverse correlation between clustering coefficients and node degrees, further identifying that all VGs adhere not only to the small-world property but also exhibit intricate assortative mixing. Through the time-varying characteristics of VGs, we observe that WTI and Brent demonstrate aligned behaviors, while the SC market, with its unique trading mechanisms, deviates. Notably, the five-minute assortativity coefficient provides deep insights into the markets reactions to these global challenges, underscoring the distinct sensitivity of each market. [ABSTRACT FROM AUTHOR]

Accurately classifying and deinterleaving overlapping radar signals presents a significant challenge in complex environments, such as electronic warfare. Traditional methods, such as spectrogram-based analysis, often struggle to differentiate radar signals with similar scan patterns, particularly under low signal-to-noise ratio (SNR) conditions. To address these limitations, we propose a novel two-stage classification framework that combines amplitude pattern (AMP) analysis and visibility graphs to enhance the accuracy and efficiency of radar signal classification. In the first stage, AMP analysis groups radar reception signals into broad categories, which reduces noise and isolates signal features. In the second stage, a visibility graph technique is applied to refine these classifications, enabling the practical separation of radar signals with overlapping or similar amplitude features. The proposed method is particularly effective in handling complex scans, such as the Palmer series, which blends search and tracking patterns. Deep learning models, including GoogLeNet and ResNet, are integrated within this framework to improve classification performance further, demonstrating robustness in low-SNR and multi-signal environments. This approach offers significant improvements over conventional methods, providing enhanced performance in differentiating radar signals across various scanning patterns in challenging multi-signal environments. [ABSTRACT FROM AUTHOR]

This paper outlined the advantages of the k-visibility algorithm proposed in [1,2] compared to traditional time series clustering algorithms, highlighting enhanced computational efficiency and comparable clustering quality. This method leveraged visibility graphs, transforming time series into graph structures where data points were represented as nodes, and edges are established based on visibility criteria. It employed the traditional k-means clustering method to cluster the time series. This approach was particularly efficient for long time series and demonstrated superior performance compared to existing clustering methods. The structural properties of visibility graphs provided a robust foundation for clustering, effectively capturing both local and global patterns within the data. In this paper, we have compared the k-visibility algorithm with 4 algorithms frequently used in time series clustering and compared the results in terms of accuracy and computational time. To validate the results, we have selected 15 datasets from the prestigious UCR (University of California, Riverside) archive in order to make a homogeneous validation. The result of this comparison concluded that k-visibility was always the fastest algorithm and that it was one of the most accurate in matching the clustering proposed by the UCR archive. [ABSTRACT FROM AUTHOR]

This paper outlined the advantages of the k-visibility algorithm proposed in [1,2] compared to traditional time series clustering algorithms, highlighting enhanced computational efficiency and comparable clustering quality. This method leveraged visibility graphs, transforming time series into graph structures where data points were represented as nodes, and edges are established based on visibility criteria. It employed the traditional k-means clustering method to cluster the time series. This approach was particularly efficient for long time series and demonstrated superior performance compared to existing clustering methods. The structural properties of visibility graphs provided a robust foundation for clustering, effectively capturing both local and global patterns within the data. In this paper, we have compared the k-visibility algorithm with 4 algorithms frequently used in time series clustering and compared the results in terms of accuracy and computational time. To validate the results, we have selected 15 datasets from the prestigious UCR (University of California, Riverside) archive in order to make a homogeneous validation. The result of this comparison concluded that k-visibility was always the fastest algorithm and that it was one of the most accurate in matching the clustering proposed by the UCR archive.

The researchers have presented a spatial database model for geometric path planning suitable for facilitating disaster management activities. The spatial queries executed using the proposed approach can reduce the computational time needed to find an optimal collision free path for network analysis. The framework is applicable to 2-dimensional and 3-dimensional workspaces. The strategy used decouples the motion planning problem into small tractable problems, which are solved using know path planning algorithm.

Abstract We employ Kuramoto model to assess the presence of synchronization in individuals who fulfill a cooperation task. Our input data is a couple of signals obtained from functional Near-Infrared Spectroscopy Data Acquisition and Pre-processing technology that is used to capture the brain activity of an individual by measuring the oxyhemoglobin (HbO) level. We consider 1 min signal for individuals in three distinct states: (i) rest; (ii) before a disturb happens; (iii) after the disturbance. We estimate global and local order parameters synchronization with the purpose to compare the conditions of reaching a synchronous state in the networks corresponding to different states for distinct individuals and hemispheres of the prefrontal cortices of same individual. Experimental results confirmed once more that coherent state is reached not for same conditions in both individuals and hemispheres of the prefrontal cortices. Furthermore, condition changes even for different events. The computation of the effective frequencies for each degree class indicates clearly the network difference in rest, before and after disturb. Finally, we investigate the dynamic connectivity matrix and consider the similarity between distinct prefrontal cortices over time.

Fossil fuels remain indispensable energy resources despite their non-renewable nature. Understanding the patterns of global fossil fuel consumption is essential for energy security and policy-making. This study employs complex network theory and fractal time series analysis to explore the underlying dynamics and patterns of fossil fuel consumption globally, with a focus on coal, oil, and gas consumption.The study applies the Hurst index to raw fossil fuel consumption data to identify fractal characteristics. Additionally, the visibility graph method is used to convert time series data into complex networks, allowing further analysis of consumption patterns. The study examines fossil fuel consumption in 38 countries to assess global trends and differences. The analysis reveals that global fossil fuel consumption follows a fractal time series pattern, with Hurst index values exceeding 0.9, indicating long-term memory characteristics. The application of the visibility graph method demonstrates variations in the Hurst index of degree distribution, enabling the differentiation of consumption patterns across regions. The method also uncovers distinct features of coal, oil, and gas consumption when viewed from a network perspective. The findings suggest that fossil fuel consumption has predictable long-term patterns, which are crucial for assessing future energy demands. The study highlights the importance of legislative measures to safeguard fossil fuel resources, especially for countries like China, where energy security and international competitiveness are paramount. Understanding these consumption patterns could guide future energy policies aimed at managing non-renewable resources more effectively. [ABSTRACT FROM AUTHOR]

Introduction: As 5G networks become widespread and their application scenarios expand, massive amounts of traffic data are continuously generated. Properly analyzing this data is crucial for enhancing 5G services. Methods: This paper uses the visibility graph method to convert 5G traffic data into a visibility graph network, conducting a feature analysis of the 5G traffic data. Using the AfreecaTV dataset as the research object, this paper constructs visibility networks at different scales and observes the evolution of degree distribution with varying data volumes. The paper employs the Hurst index to evaluate the 5G traffic network and uses community detection to study the networks converted from 5G traffic data of different applications. Results: Experimental results reveal significant differences in node degree distribution and topological structures of 5G traffic data across different application scenarios, such as star structures and multiple subnetwork structures. It is found that the node degree distribution of 5G traffic networks exhibits heterogeneity, reflecting the uneven growth of node degrees during network expansion. The Hurst index analysis discovers that the 5G traffic network retains the long-term dependence and trends of the original data. Through community detection, it is observed that networks converted from 5G traffic data of different applications exhibit diverse community structures, such as high centrality nodes, star-like community structures, modularity, and multilayer characteristics. Discussion: These findings indicate that 5G traffic networks in different application scenarios exhibit complex and diverse characteristics. The heterogeneity of node degree distribution and differences in topological structures reflect the imbalance in node connection methods during network expansion. The results of the Hurst index show that the 5G traffic network inherits the long-term dependence of the original data, providing a basis for analyzing the dynamic characteristics of the network. The diverse community structures reveal the inherent modularity and hierarchy of the network, which helps to understand the performance and optimization directions of 5G networks in different applications. [ABSTRACT FROM AUTHOR]

In this study, we examined how the nonlinearity  α  of the Langevin equation influences the behavior of extremes in a generated time series. The extremes, defined according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the influence of the nonlinearity  α  on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main finding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly influenced by the nonlinearity, which decreases with with an increase in  α. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity. [ABSTRACT FROM AUTHOR]

Mobile robots' efficient path planning has long been a challenging task due to the complexity and dynamism of environments. If an occupancy grid map is used in path planning, the number of grids is determined by grid resolution and the size of the actual environment. Excessively high resolution increases the number of traversed grid nodes and thus prolongs path planning time. To address this challenge, this paper proposes an efficient path planning algorithm based on laser SLAM and an optimized visibility graph for mobile robots, which achieves faster computation of the shortest path using the optimized visibility graph. Firstly, the laser SLAM algorithm is used to acquire the undistorted LiDAR point cloud data, which are converted into a visibility graph. Secondly, a bidirectional A* path search algorithm is combined with the Minimal Construct algorithm, enabling the robot to only compute heuristic paths to the target node during path planning in order to reduce search time. Thirdly, a filtering method based on edge length and the number of vertices of obstacles is proposed to reduce redundant vertices and edges in the visibility graph. Additionally, the bidirectional A* search method is implemented for pathfinding in the efficient path planning algorithm proposed in this paper to reduce unnecessary space searches. Finally, simulation and field tests are conducted to validate the algorithm and compare its performance with classic algorithms. The test results indicate that the method proposed in this paper exhibits superior performance in terms of path search time, navigation time, and distance compared to D* Lite, FAR, and FPS algorithms. [ABSTRACT FROM AUTHOR]

Gearbox failures have a detrimental effect on the machine performance that affects the production capacity and economic benefits of a manufacturing industry in an adverse manner. Early detection of faults in gears helps to prevent sudden machine failures. Previously, many signal processing and artificial intelligence techniques have been successfully applied to diagnose gear faults by analyzing the machine vibrations. These techniques have repeatedly emphasized on the need to extract quality features from gear vibration signals and using artificial intelligence techniques that can identify multiple types of faults simultaneously. As such, in this article, new features called as visibility graph features based on complex network theory have been proposed to extract fault information from vibration signals. In addition, a new artificial intelligence framework for multifault classification known as error-correcting output codes-multiclass support vector machine is proposed to detect gear faults. To the best of authors' knowledge, these features along with the error-correcting output codes-artificial intelligence framework have been rarely utilized for fault diagnosis purpose. The proposed approach has been applied on experimental gear vibration data to validate its effectiveness. First, the vibration signals are transformed to graphs, and various graph properties are computed to serve as fault features. Then, the fault features are supplied to train the error-correcting output codes-multiclass support vector machine model and learn the fault patterns. Finally, the gear fault classification accuracies are determined for various gear test conditions and compared with those of existing methods. It is observed that the proposed approach provides an average improvement of 4.22%, 9.93% and 11.8% over the time-domain features, time–frequency domain features and voting-based multiclass support vector machine classifier, respectively, for different operating conditions. Furthermore, the suggested technique augments the classification accuracies by 10%, 7.5% and 6.7%, respectively, as compared with the deep-learning models, namely standard stacked sparse autoencoder, deep neural network and convolution neural network. [ABSTRACT FROM AUTHOR]

Fossil fuels remain indispensable energy resources despite their non-renewable nature. Understanding the patterns of global fossil fuel consumption is essential for energy security and policy-making. This study employs complex network theory and fractal time series analysis to explore the underlying dynamics and patterns of fossil fuel consumption globally, with a focus on coal, oil, and gas consumption.The study applies the Hurst index to raw fossil fuel consumption data to identify fractal characteristics. Additionally, the visibility graph method is used to convert time series data into complex networks, allowing further analysis of consumption patterns. The study examines fossil fuel consumption in 38 countries to assess global trends and differences. The analysis reveals that global fossil fuel consumption follows a fractal time series pattern, with Hurst index values exceeding 0.9, indicating long-term memory characteristics. The application of the visibility graph method demonstrates variations in the Hurst index of degree distribution, enabling the differentiation of consumption patterns across regions. The method also uncovers distinct features of coal, oil, and gas consumption when viewed from a network perspective. The findings suggest that fossil fuel consumption has predictable long-term patterns, which are crucial for assessing future energy demands. The study highlights the importance of legislative measures to safeguard fossil fuel resources, especially for countries like China, where energy security and international competitiveness are paramount. Understanding these consumption patterns could guide future energy policies aimed at managing non-renewable resources more effectively.

IntroductionAs 5G networks become widespread and their application scenarios expand, massive amounts of traffic data are continuously generated. Properly analyzing this data is crucial for enhancing 5G services.MethodsThis paper uses the visibility graph method to convert 5G traffic data into a visibility graph network, conducting a feature analysis of the 5G traffic data. Using the AfreecaTV dataset as the research object, this paper constructs visibility networks at different scales and observes the evolution of degree distribution with varying data volumes. The paper employs the Hurst index to evaluate the 5G traffic network and uses community detection to study the networks converted from 5G traffic data of different applications.ResultsExperimental results reveal significant differences in node degree distribution and topological structures of 5G traffic data across different application scenarios, such as star structures and multiple subnetwork structures. It is found that the node degree distribution of 5G traffic networks exhibits heterogeneity, reflecting the uneven growth of node degrees during network expansion. The Hurst index analysis discovers that the 5G traffic network retains the long-term dependence and trends of the original data. Through community detection, it is observed that networks converted from 5G traffic data of different applications exhibit diverse community structures, such as high centrality nodes, star-like community structures, modularity, and multilayer characteristics.DiscussionThese findings indicate that 5G traffic networks in different application scenarios exhibit complex and diverse characteristics. The heterogeneity of node degree distribution and differences in topological structures reflect the imbalance in node connection methods during network expansion. The results of the Hurst index show that the 5G traffic network inherits the long-term dependence of the original data, providing a basis for analyzing the dynamic characteristics of the network. The diverse community structures reveal the inherent modularity and hierarchy of the network, which helps to understand the performance and optimization directions of 5G networks in different applications.

Recently, graph theory has become a promising tool for biomedical signal analysis, wherein the signals are transformed into a graph network and represented as either adjacency or Laplacian matrices. However, as the size of the time series increases, the dimensions of transformed matrices also expand, leading to a significant rise in computational demand for analysis. Therefore, there is a critical need for efficient feature extraction methods demanding low computational time. This paper introduces a new feature extraction technique based on the Gershgorin Circle theorem applied to biomedical signals, termed Gershgorin Circle Feature Extraction (GCFE). The study makes use of two publicly available datasets: one including synthetic neural recordings, and the other consisting of EEG seizure data. In addition, the efficacy of GCFE is compared with two distinct visibility graphs and tested against seven other feature extraction methods. In the GCFE method, the features are extracted from a special modified weighted Laplacian matrix from the visibility graphs. This method was applied to classify three different types of neural spikes from one dataset, and to distinguish between seizure and non-seizure events in another. The application of GCFE resulted in superior performance when compared to seven other algorithms, achieving a positive average accuracy difference of 2.67% across all experimental datasets. This indicates that GCFE consistently outperformed the other methods in terms of accuracy. Furthermore, the GCFE method was more computationally-efficient than the other feature extraction techniques. The GCFE method can also be employed in real-time biomedical signal classification where the visibility graphs are utilized such as EKG signal classification. [ABSTRACT FROM AUTHOR]

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

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

Network softwarization, which shifts hardware-centric functions to software implementations, is essential for enhancing the agility of cellular and non-cellular wireless networks. This change, while raising reliability concerns, also improves system monitoring through digital twins. One example is the Digital Twin Edge Networks (DITEN), which enhances real-time analysis and quick anomaly response in the unpredictable last-mile wireless edge network environment. Positioned close to the physical infrastructure, DITEN is effective in rapidly detecting and addressing network irregularities. This study presents an advanced anomaly detection method for DITEN, employing time-series data conversion to Visibility Graph (VG) and utilising Graph Neural Network (GNN), with a focus on addressing disruptions at the network’s physical layer. Our proposed method outperforms the State-of-the-art (SOTA) time series Deep Learning (DL) classification architecture by 13 percentage points and achieves ≈110 times higher computational efficiency. Furthermore, our method surpasses the classical Machine Learning (ML) model Hive-Cote2 by 2.2 percentage points while maintaining ≈5.9 times better computational efficiency. The model also outperforms the current best SOTA imaging model by up to 6 percentage points and the leading graph-based method by up to 10 percentage points, both with significantly lower Computational Complexity (CC) of ≈210-times and ≈4-times, respectively. Additionally, we show that when 1000 concurrent requests arrive, the proposed method achieves a mean response latency of less than or equal to 60 seconds across three setups. Finally, we demonstrate that the combination of Natural Visibility Graph (NVG) and the proposed GNN model provides interpretable insights by observing gradient changes.

A graph approach to time series data provides a new perspective for analyzing and comprehending the characteristics of the data. One common method of converting time series into a graph is through visibility graph analysis. This technique has been developed and refined in various iterations over time. Moreover, visibility graph analysis has gained significant attention in recent years, with more than 88% of related articles published since 2016. Its applications span across multiple fields, including medicine, economy, geology, weather, architecture, and industrial processes. Accordingly, to conduct this research, a comprehensive collection of all articles in this field was obtained by searching the title, abstract, and keywords from Science Direct and Google Scholar databases. Finally, 249 related articles were gathered. These articles were then analyzed based on their publication year, field of application, network type, journal source, university affiliation, and other relevant factors. Through this examination process, unexplored areas with potential for future exploration were identified. Specifically, analyzing visibility graphs in security and service fields presents promising avenues for further investigation. Consequently, the study of visibility graph analysis offers valuable insights into time series data analysis. By understanding its applications across various disciplines and identifying untapped areas for research, we can expand our knowledge and contribute to advancements in this field.

With the integration of multiple energy sources into the power grid makes power quality disturbances (PQDs) more complex. Dealing with power quality problems requires automatic classification of PQDs. This paper proposes a novel semi-supervised Graph Convolutional Network (GCN) framework based on Temporal Ensembling for PQDs classification. Considering both short-term and long-term features of PQDs, a Visibility Graph (VG) based graph theory model was adopted to process PQDs to highlight features. In the proposed semi-supervised framework, Graph Convolutional Network was designed to extract features from massive PQDs and classify PQDs automatically. Due to the fact that GCN belongs to supervised learning, it is necessary to label the data in advance. However, labeling is costly and easily lead to human mistake. Therefore, this article introduces the Temporal Ensembling algorithm which provides pseudo labels to reduce the amount of labeled data and has tolerance to incorrect labels. Simulation results prove that the proposed method is capable of noise resistance, tolerates incorrect labels, and has high classification performance in both single and composite PQDs.

Recently, graph theory has become a promising tool for biomedical signal analysis, wherein the signals are transformed into a graph network and represented as either adjacency or Laplacian matrices. However, as the size of the time series increases, the dimensions of transformed matrices also expand, leading to a significant rise in computational demand for analysis. Therefore, there is a critical need for efficient feature extraction methods demanding low computational time. This paper introduces a new feature extraction technique based on the Gershgorin Circle theorem applied to biomedical signals, termed Gershgorin Circle Feature Extraction (GCFE). The study makes use of two publicly available datasets: one including synthetic neural recordings, and the other consisting of EEG seizure data. In addition, the efficacy of GCFE is compared with two distinct visibility graphs and tested against seven other feature extraction methods. In the GCFE method, the features are extracted from a special modified weighted Laplacian matrix from the visibility graphs. This method was applied to classify three different types of neural spikes from one dataset, and to distinguish between seizure and non-seizure events in another. The application of GCFE resulted in superior performance when compared to seven other algorithms, achieving a positive average accuracy difference of 2.67% across all experimental datasets. This indicates that GCFE consistently outperformed the other methods in terms of accuracy. Furthermore, the GCFE method was more computationally-efficient than the other feature extraction techniques. The GCFE method can also be employed in real-time biomedical signal classification where the visibility graphs are utilized such as EKG signal classification.

In the face of escalating frequency and severity of hot extreme (HE) events worldwide, understanding their spatio-temporal characteristics and hazard patterns has become crucial. This study employs a complex network (CN) approach, specifically using visibility graph and similarity network analysis, to investigate HEs. According to the HE network, we have successfully identified anomalous years, divided stages of change, selected representative cities, and zoned spatial hazard patterns of HE. Results reveal that 85% of cities in China experienced varying degrees of increasing HEs, with the highest increase observed as 63 times. The HE networks in China exhibit small-world characteristics, allowing the classification of HE changes into 5–8 stages and 10 types. Hefei emerges as the most representative city in this context. Additionally, the hazard of HE in China can be divided into four grades, with a gradual increase from north to south. This study sheds light on the intensifying hot extreme events in China and establishes a connection between CN and HE analysis, offering innovative ideas and methods for studying climate extremes. [ABSTRACT FROM AUTHOR]

The increasing complexity and dynamics of the stock trading market are major challenges for the financial industry and are primary dilemmas for all countries nowadays. In addition, the stock trading market has a considerable impact on the global economy, and its importance is self-evident. To cope with the complexity and dynamics of a stock trading market, this paper applies complex network theory and model to explore the topology of the global stock trading network. First, this paper collects stock trading data from 74 countries from 1999 to 2020. It converts the collected stock trading data of these countries into a complex network using a type of algorithm based on the time series visibility graph (VG) algorithm. Then, the data are analyzed by a complex network model, and six analytical metrics are obtained. Finally, the six metrics are analyzed by the entropy weight method to identify the key nodes in the network and to obtain the ranking of each country's stock trading data. This paper is an effective application of complex network and entropy weight method in stock trend analysis, which mainly includes two contributions. First, the VG algorithm provides a novel research perspective for modeling the global stock trading trend. Second, key nodes in the network are analyzed and identified based on the entropy weight method, and the ranking of key nodes in the stock trading network is obtained, which provides a new method for further research on the stock trading trend, investment portfolio, and stock return forecasting. [ABSTRACT FROM AUTHOR]

The human heartbeat reflects one of the most crucial types of complex physiologic fluctuations. The purpose of this study is to study and evaluate the complexity of heart rate time series to capture its intrinsic multiscale dynamics based on the concept of fractality and complexity. The visibility graph (VG) of the heart rate series is proposed as a quantitative method to differentiate subjects in rest and meditation periods of two techniques: Chi meditation and Kundalini Yoga meditation. Differential complexities between the two mentioned states are quantified using the power of scale-freeness (PS) and the graph index complexity (GIC) in VG. The model is applied to available heart rate signals in the PhysioBank. The results reveal the promising ability of PS and GIC to assess the distinction between the two states. However, in both meditation techniques, the complexities of heart rate signals are increased during meditation. The results also show all heart rate series have visibility graphs with a power-law topology, and fractality in the heart rate series is dictated by a mechanism associated with the chaotic nature of the biological signals that could be useful to evaluate heart rate signals during meditation.

Heatwaves are increasingly frequent and severe, prompting international research concerns. This study utilized the Visibility Graph to construct complex networks (CNs) of heatwaves in China. From a CN perspective, we analyzed the spatial and temporal variability and hazard patterns of heatwaves, with a focus on their reliability and advantages. Our findings indicate that heatwaves in China have exhibited a consistent overall increasing trend since 1961, with a more significant rise observed in the past 30 years. Notably, there are substantial variations in the changes and severity of heatwaves experienced in different regions and decades, with southern China experiencing higher heatwaves hazards compared to central China where they are relatively lower. The utilization of CNs has demonstrated remarkable advantages in anomaly detection, change phase delineation, analysis of connections between meteorological stations, and selection of representative values. And, CNs enable the incorporation of both heatwave changes and severity in hazard zoning. The results of this study provide new methods and perspectives for researching climate extremes, and they establish a solid foundation for more comprehensive and accurate heatwave hazard prevention in China.

In the past two decades, network-based analysis has garnered considerable attention for analyzing time series data across various fields. Time series data can be transformed into graphs or networks using different methods, with the visibility graph (VG) being a widely utilized approach. The VG holds extensive applications in comprehending, identifying, and predicting specific characteristics of time series data. Its practicality extends to domains such as medicine, economics, meteorology, tourism, and others. This research presents a scoping review of scholarly articles published in reputable English-language journals and conferences, focusing on VG-based analysis methods related to brain disorders. The aim is to provide a foundation for further and future research endeavors, beginning with an introduction to the VG and its various types. To achieve this, a systematic search and refinement of relevant articles were conducted in two prominent scientific databases: Google Scholar and Scopus. A total of 51 eligible articles were selected for a comprehensive analysis of the topic. These articles categorized based on publication year, type of VG used, rationale for utilization, machine learning algorithms employed, frequently occurring keywords, top authors and universities, evaluation metrics, applied network properties, and brain disorders examined, such as Epilepsy, Alzheimer's disease, Autism, Alcoholism, Sleep disorders, Fatigue, Depression, and other related conditions. Moreover, there are recommendations for future advancements in research, which involve utilizing cutting-edge techniques like graph machine learning and deep learning. Additionally, the exploration of understudied medical conditions such as attention deficit hyperactivity disorder and Parkinson's disease is also suggested. [ABSTRACT FROM AUTHOR]

We prove that, given a polyhedron P in R 3 , every point in R 3 that does not see any vertex of P must see eight or more edges of P , and this bound is tight. More generally, this remains true if P is any finite arrangement of internally disjoint polygons in R 3 . We also prove that every point in R 3 can see six or more edges of P (possibly only the endpoints of some these edges) and every point in the interior of P can see a positive portion of at least six edges of P . These bounds are also tight. [ABSTRACT FROM AUTHOR]

A rectangle visibility graph (RVG) is represented by assigning to each vertex a rectangle in the plane with horizontal and vertical sides in such a way that edges in the graph correspond to unobstructed horizontal and vertical lines of sight between their corresponding rectangles. To discretize, we consider only rectangles whose corners have integer coordinates. For any given RVG, we seek a representation with smallest bounding box as measured by its area, perimeter, height, or width (height is assumed not to exceed width). We derive a number of results regarding these parameters. Using these results, we show that these four measures are distinct, in the sense that there exist graphs G 1 and G 2 with area (G 1) < area (G 2) but perim (G 2) < perim (G 1) , and analogously for all other pairs of these parameters. We further show that there exists a graph G 3 with representations S 1 and S 2 such that area (G 3) = area (S 1) < area (S 2) but perim (G 3) = perim (S 2) < perim (S 1) . In other words, G 3 requires distinct representations to minimize area and perimeter. Similarly, such graphs exist to demonstrate the independence of all other pairs of these parameters. Among graphs with n ≤ 6 vertices, the empty graph E n requires largest area. But for graphs with n = 7 and n = 8 vertices, we show that the complete graphs K 7 and K 8 require larger area than E 7 and E 8 , respectively. Using this, we show that for all n ≥ 8 , the empty graph E n does not have largest area, perimeter, height, or width among all RVGs on n vertices. [ABSTRACT FROM AUTHOR]

El Niño-Southern Oscillation (ENSO) is a complex climate phenomenon that results from ocean–atmosphere interactions and exhibits nonlinearity in both spatial and temporal evolution. The directed horizontal visibility graph (DHVG) and Kullback–Leibler divergence (KLD) efficiently characterize the nonlinearity of complex systems without requiring additional symbolization processes. Our study utilizes this method to quantify sea surface temperature (SST) irreversibility across multiple El Niño events and identified similar fluctuation patterns. Subsequently, we map the irreversibility series into visibility graphs and analyze multiple topological properties to investigate the fluctuation structure of SST irreversibility. The irreversibility fluctuation structure effectively explains the periodic changes of El Niño and its nonlinear evolution over time. Results show that KLD exhibits a sharp increase during the strengthening and ending phases of El Niño events and remains in a lower value after the peak month of Niño events; the visibility graph of SST irreversibility exhibits scale-free and small-world properties, indicating that the KLD series has scale invariance and self-similarity, and its fluctuations are not random but correlated; Hurst exponent analysis revealed long-range anti-persistence and mean reversion characteristics in the KLD series. This study utilizes complex network and information theory to investigate the fluctuation pattern and structure of SST irreversibility during El Niño events, providing novel insights into the evolution of ENSO over time scales. [ABSTRACT FROM AUTHOR]

The features of numerical sequences and time series have been studied by using entropies and graphs. In this article, two sequences derived from the divisors of natural numbers are investigated. These sequences are obtained either directly from the divisor function or by recursively applying the divisor function. For comparison purposes, analogous sequences formed from the divisors of happy numbers are also examined. Firstly, the informational entropy of these four sequences is numerically determined. Then, each sequence is mapped into graphs by employing two visibility algorithms. For each graph, the average degree, the average shortest-path length, the average clustering coefficient, and the degree distribution are calculated. Also, the links in these graphs are quantified in terms of the parity of the numbers that these links connect. These computer experiments suggest that the four analyzed sequences exhibit characteristics of quasi-random sequences.

In this paper, we propose a textural information-based analysis of scalogram image obtained from continuous wavelet transform of heart rate variability (HRV) signal to study its dynamics during meditation. In addition to features from scalogram image, visibility graph-based complexity measures and multiscale permutation entropies (MPEs) from HRV signal are used to elucidate the modulation in autonomic activity of heart during meditative and non-meditative state. Significant changes in the probability distribution of pixel intensities of scalogram image and undiminished permutation entropy at higher scales are observed during the meditative state. From the extracted features, we have selected the top-ranked features based on ReliefF algorithm and minimum threshold weight of importance set at 0.04. Considering the small sample size (12 subjects) of meditation dataset, we have employed a novel data augmentation technique based on averaging of feature sets to overcome the issue of overfitting. To examine the efficacy of the proposed technique, both the non-augmented and augmented data are applied to four different classifiers, namely k-nearest neighbor, support vector machine (SVM), logistic regression and random forest classifiers. Experimental results demonstrate that performance of classifiers in distinguishing meditative and pre-meditative state are much superior with the augmented data as compared to that with regular non-augmented data. Out of these classifiers, radial basis function (RBF)-based SVM classifier results in the best performance with an average accuracy of 96.67%, sensitivity of 95.83% and specificity of 97.5%.

Plastic deformation of DC04 steel is regarded as a nonlinear, complex, irreversible, and self-organized process. The stress–strain time series analysis provided the possibility to identify areas of (quasi-)elastic deformation, plastic deformation, and necking. The latter two regions are the most informative. The area of inelastic deformation is reflected by collective, self-organized processes that lead to the formation of pores, and finally, the development of microcracks and a general crack as the cause of sample failure. Network measures for the quantitative assessment of the structural deformations in metals are proposed. Both spectral and topological measures of network complexity were found to be especially informative. According to our results, they can be used not only to classify the stages of plastic deformation, but also, they can be applied as a precursor of the material destruction process.

Important nodes can determine the internal structure of complex networks and reveal the internal relationships of real-world systems, and identifying key nodes in complex networks is one of the important research areas of complex network science. As the king of commodities, changes in the price of gold significantly impact the economic development of various countries. Especially in the early stages of the outbreak of war between Russia and Ukraine, the price of gold futures has been greatly impacted, and the systemic risks are gradually spreading. In this paper, a gold future price series is mapped into a visibility graph (VG), the characteristics of the gold price time series and key points-in-time, have been explored from the perspective of complex network. First, according to the data structure characteristics of gold futures, this paper converts the closing prices of gold futures of the New York Mercantile Exchange into a complex network through the VG model. Then, by using the complex network model to further delve into the price of gold futures, it is found that the degree distribution of the gold futures network follows a power-law distribution, and has obvious scale-free characteristics. Finally, this paper uses the visual network node shrinking algorithm and the technique for order preference by similarity to ideal solution (TOPSIS) analysis method to identify the key nodes of the gold futures visual map to find the key time nodes in the timeline of gold futures market. Analysis of the key time nodes of this market by four methods reveals that the repetition rate of the key time nodes in the methods' top 10 ranking is as high as 82.5%, indicating that the results obtained in this paper are robust. This study introduces a new model to describe the characteristics of gold futures price series, one which can find key time nodes in gold futures prices and provide potential help for predicting gold futures prices. [ABSTRACT FROM AUTHOR]

Most solid-state drives (SSDs) adopt an on-board Dynamic Random Access Memory (DRAM) to buffer the write data, which can significantly reduce the amount of write operations committed to the flash array of SSD if data exhibits locality in write operations. This article focuses on efficiently managing the small amount of DRAM cache inside SSDs. The basic idea is to employ the visibility graph technique to unify both temporal and spatial locality of references of I/O accesses, for directing cache management in SSDs. Specifically, we propose to adaptively generate the visibility graph of cached data pages and then support batch adjustment of adjacent or nearby (hot) cached data pages by referring to the connection situations in the visibility graph. In addition, we propose to evict the buffered data pages in batches by also referring to the connection situations, to maximize the internal flushing parallelism of SSD devices without worsening I/O congestion. The tracedriven simulation experiments show that our proposal can yield improvements on cache hits by between 0.8% and 19.8%, and the overall I/O latency by 25.6% on average, compared to state-of-the-art cache management schemes inside SSDs. [ABSTRACT FROM AUTHOR]

This research proposes an integrated voyage optimization algorithm that combines quadtree graph generation, visibility graph simplification, Dijkstra's algorithm, and a 3D dynamic programming (3DDP) method. This approach enables the determination of a minimum distance initial reference route and the creation of a 2D navigational graph for efficient route optimization. We effectively store and process complex terrain information by transforming the GEBCO uniform grid into a quadtree structure. By utilizing a nearest neighbour search algorithm, edges are connected between adjacent ocean nodes, facilitating the generation of a quadtree graph. Applying Dijkstra's algorithm to the quadtree graph, we derive the shortest initial route and construct a visibility graph based on the waypoints. This results in a simplified reference route with reduced search distance, allowing for more efficient navigation. For each waypoint along the reference route, a boundary is defined angled at 90 degrees to the left and right, based on the waypoint's reference bearing. A line segment formed by the waypoint and both boundaries is defined as a navigational stage. A navigational graph is defined by connecting adjacent stages. Employing a 3DDP method on the navigational graph, and incorporating weather forecasting data, including wind, wave, and currents, we search for a route that minimizes fuel oil consumption with estimated time of arrival restrictions. Our approach is tested on several shipping routes, demonstrating a fuel consumption reduction compared to other voyage optimization routes. This integrated algorithm offers a potential solution for tackling complex voyage optimization problems in marine environments while considering various weather factors. [ABSTRACT FROM AUTHOR]