Narrow Results

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.

Oil and natural gas are indispensable energy commodities. Investigating the evolution and transformation of energy market dynamics represented by oil and natural gas holds significant implications for global energy governance, as well as political and economic development. We have employed the visibility graph algorithm to transform the most intuitive and readily available time series data of oil and natural gas prices into complex networks. Then, three network embedding algorithms based on machine learning are utilized to embed the network into multidimensional vector spaces, enabling us to identify market state changes in both energy products through the sequential clustering method. We find that the visibility graph algorithm and network embedding methods effectively preserve internal structural characteristics of data, capture similarities between price change rate nodes across different trading days in the oil and gas markets, while also identifying the memorability of price volatility trends. Beyond simple price trends, critical market fluctuations such as those induced by events like the COVID-19 or Russia–Ukraine conflict can be discerned from similarity matrix partitions of network node representation vectors. Furthermore, the sequential clustering algorithm accurately identifies transition points in the oil and gas markets’ states. Unlike conventional time series analysis methods, this innovative combination of visibility graph and network embedding algorithms allows for a multi-faceted exploration of market state changes at various levels; thereby facilitating deeper insights into underlying logic behind price time series.

Autism Spectrum Disorder (ASD) is presented with significant challenges in diagnosis and intervention due to its multifaceted nature, varied symptomatology, and the high cost and time demands of behavior-based assessments. Traditional behavior-based tests, while effective, have been noted for being time-consuming and expensive. This study investigates an Electroencephalography (EEG)-based approach as a cost-effective, non-invasive alternative, utilizing minimal EEG channels to capture ASD-related abnormalities in brain oscillations with high temporal resolution. To enhance diagnostic accuracy, channel selection and feature extraction were optimized using filtering methods and particle swarm optimization. EEG data from individuals with ASD and control groups were analyzed, employing various visibility graph types and machine learning classifiers to assess coherence, causality, and time lag metrics. Results show that visibility graphs effectively capture brain connectivity differences in ASD, and machine learning classifiers trained on these features achieve higher classification accuracy compared to traditional methods. The efficacy of different visibility graph types and machine learning classifiers in ASD classification was analyzed, focusing on coherence, causality, and time lag methods. It is widely accepted that EEG signal patterns reliably reflect ASD-related abnormalities and that visibility graphs effectively represent brain connectivity. Limitations include the variability in EEG signal quality and the need for larger, more diverse datasets for validation. Comparative analysis has highlighted the pros and cons of other available methods, such as MRI and behavior-based assessments, emphasizing the superior cost-efficiency and accessibility of EEG approaches. The proposed method has been shown to outperform the existing methodologies quantitatively, achieving higher classification accuracy and performance by integrating horizontal and natural visibility graphs with machine learning classifiers. This study is presented as a significant step forward in ASD diagnosis and intervention, underscoring the potential of EEG-based technologies to revolutionize clinical practices and improve outcomes for individuals with ASD.

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.

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

There are numerous existing works on investigating the dynamics of particle production process in ultrarelativistic nuclear collision. In the past, fluctuation of spatial pattern has been analyzed in terms of the scaling behavior of voids. But analysis of the scaling behavior of the void in fractal scenario has not been explored yet. In this work, we have analyzed the fractality of void probability distribution with a completely different and rigorous method called visibility graph analysis, analyzing the void-data produced out of fluctuation of pions in ${}^{32}$S–AgBr interaction at 200 GeV in pseudo-rapidity $(\eta )$ and azimuthal angle $(\varphi )$ space. The power of scale-freeness of visibility graph denoted by PSVG is a measure of fractality, which can be used as a quantitative parameter for the assessment of the state of chaotic system. As the behavior of particle production process depends on the target excitation, we can dwell down the void probability distribution in the event-wise fluctuation resulted out of the high energy interaction for different degree of target excitation, with respect to the fractal scenario and analyze the scaling behavior of the voids. From the analysis of the PSVG parameter, we have observed that scaling behavior of void probability distribution in multipion production changes with increasing target excitation. Since visibility graph method is a classic method of complex network analysis, has been applied over fractional Brownian motion (fBm) and fractional Gaussian noises (fGn) to measure the fractality and long-range dependence of a time series successfully, we can quantitatively confirm that fractal behavior of the void probability distribution in particle production process depends on the target excitation.

Baidu search engine is the most common one adopted by Chinese Internet users, and Baidu index provides a platform to capture the behaviors of massive users on Baidu, which is one important statistical tool to mine the Internet users’ behaviors and characteristics in China. Here, we utilize the Baidu index data on greenhouse gas from January 1, 2011 to November 29, 2019, to perform the related statistical analyses at first. Then, on the basis of Baidu index time series data, the corresponding network is constructed by use of the visibility graph method. Finally, the topology of the generated network is analyzed from different perspectives. Our results indicate that people’s attention to greenhouse gases obeys the power-law distribution, and we can identify the significant nodes and find some outliers in time series data by use of the topological properties of networks. Taking together, the current model offers a novel means to represent and depict the time series data of Baidu index through the complex network analysis.

Complex network is now widely used in a series of disciplines such as biology, physics, mathematics, sociology and so on. In this paper, we construct the stock price trend network based on the knowledge of complex network, and then propose a method based on information entropy to divide the stock network into some communities, that is, a gathering study of stock price trend. We construct time series networks for each stock in Chinese A-share market based on time series network model, and then use these networks to divide the stock market into communities. We find that the average trend of stocks in the same community is the same as the trend of market value weighting, but the average trend of stocks in different communities is quite different and the sequence correlation is low. This conclusion shows that stocks in the same community share the same price trend, while the stock trend in different communities varies. This paper is a successful application of complex network and information entropy in stock trend analysis, which mainly includes two contributions. First, the success of the visibility graph algorithm provides a new perspective for enriching stock price trend modeling. Second, our conclusion proves that the clustering based on information entropy theory is effective, which provides a new method for further research on stock price trend, portfolio construction and stock return prediction.

In this paper, we investigate signatures of variation in the behavior of correlated time series by analyzing changes in the topological properties of the corresponding visibility graph. Variations in six different network measures: assortativity, average path length, clustering, transitivity, density, and the average of the mean link length, are explored. We construct visibility graphs from the original and the magnitude and sign of its increment series. Both the horizontal and the natural visibility graphs are studied. Through extensive numerical studies on the time series of fractional Brownian motion (fBm), we first identify network measures that can reflect the changes in correlations in the time series. The efficacy of these markers is examined to identify the transitions in two systems, a two-dimensional (2D) Ising spin system and EEG data with seizures. While all the identified network measures capture the change in the thermal equilibrium correlations for the Ising spin system, they have limited success in the case of the time-dependent fluctuations in the EEG data. We identify some markers relevant to detecting seizures in the EEG data set.

Path planning is an essential and inevitable problem in robotics. Trapping in local minima and discontinuities often exist in local path planning. To overcome these drawbacks, this paper presents a smooth path planning algorithm based on modified visibility graph. This algorithm consists of three steps: (1) polygons are generated from detected obstacles; (2) a collision-free path is found by simultaneous visibility graph construction and path search by A${}^{\ast }$ (SVGA); (3) the path is smoothed by B-spline curves and particle swarm optimization (PSO). Simulation experiment results show the effectiveness of this algorithm, and a smooth path can be found fleetly.

The refugee problem is one of the most important issues facing the international community today. It not only troubles the countries where refugees are generated but also has a great impact on the countries where refugees are influx. With the continuous development of globalization, the refugee problem is no longer a problem of a country or a region, but a global problem faced by the international community. To cope with the global refugee problem, this paper analyzes the number of refugees in 156 countries from 1990 to 2020 and transforms the refugee population data of these countries into a complex network through a time series visibility graph (VG) method. First, we categorize the income level of 156 countries and analyze the impact of income level on the increase of refugee numbers. Then, the evaluation index of the number of refugees is obtained through the VG method. Finally, a TOPSIS comprehensive evaluation method based on the entropy weight approach is employed to analyze the data. This paper includes two main contributions. First, the application of the VG method provides a new perspective for enriching the modeling of the global refugee population growth trend. Second, this paper shows that the TOPSIS evaluation method based on the entropy weight method is effective, which provides a new method for further research on the global refugee population growth trend.

As a basic industry in the country’s development, the transportation industry has a significant relationship to its normal operation for developing and constructing the national economy. The increase in carbon emissions from transport is an increasingly growing problem, and countries worldwide are also taking measures to reduce emissions. Using time series data over the period from 1990 to 2016, this paper applies the visibility graph approach to transform it into a complex network and excavate some information about the data, then evaluates all countries based on the TOPSIS method. We find that the development of transportation is an important symbol to measure the degree of modernization of a country’s transportation, and low-income countries have lower carbon emissions due to slower transportation development. The results of transportation carbon emissions are especially encouraging for the Chinese government given its long-term and sustained efforts to expand railway and waterway infrastructure, and provide a new perspective for further research on the development trend of global transportation carbon emissions. Meanwhile, it is urgent to speed up the development and use of clean energy for economically developed countries.

In general, visibility reconstruction problems involve determining a set of objects in the plane that exhibit a specified set of visibility constraints. In this paper, an algorithm is presented for reconstructing a set of parallel line segments from specified visibility information contained in an extended endpoint visibility graph. The algorithm runs in polynomial time and relies on simple vector arithmetic to generate a system of linear inequalities. A related problem, solvable with the same technique, is the point reconstruction problem, in which the cyclic ordering and the x-coordinates of a set of points is specified.

A second contribution is the definition of an extension of the visibility graph called the Stab Graph, which contains extra visibility information.

In this paper, we study several geometric path query problems. Given a scene of disjoint polygonal obstacles with totally n vertices in the plane, we construct efficient data structures that enable fast reporting of an "optimal" obstacle-avoiding path (or its length, cost, directions, etc) between two arbitrary query points s and t that are given in an on-line fashion. We consider geometric paths under several optimality criteria: L_m length, number of edges (called links), monotonicity with respect to a certain direction, and some combinations of length and links. Our methods are centered around the notion of gateways, a small number of easily identified points in the plane that control the paths we seek. We give efficient solutions for several special cases based upon new geometric observations. We also present solutions for the general cases based upon the computation of the minimum size visibility polygon for query points.

A new necessary condition for a graph G to be the visibility graph of a simple polygon is given: each 3-connected component of G must have a vertex ordering in which every vertex is adjacent to a previous 3-clique. This property is used to give an algorithm for the distance visibility graph problem: given an edge-weighted graph G, is it the visibility graph of a simple polygon with the given weights as Euclidean distances?

Let Γ_n denote the collection of visibility graphs of staircase polygons (orthogonal convex fans) which consist of n−1 horizontal steps of arbitrary lengths. We show that for n≥7 there are graphs in Γn which cannot be realized as the visibility graphs of staircase polygons with uniform step length.

We introduce the visibility complex (a 2-dimensional regular cell complex) of a collection of n pairwise disjoint convex obstacles in the plane. It can be considered as a subdivision of the set of free rays (i.e., rays whose origins lie in free space, the complement of the obstacles). Its cells correspond to collections of rays with the same backward and forward views. The combinatorial complexity of the visibility complex is proportional to the number k of free bitangents of the collection of obstacles. We give an O(n log n+k) time and O(k) working space algorithm for its construction. Furthermore we show how the visibility complex can be used to compute the visibility polygon from a point in O(m log n) time, where m is the size of the visibility polygon. Our method is based on the notions of pseudotriangle and pseudo-triangulation, introduced in this paper.

This paper is concerned with the problem of capturing meaningful and useful visibility information inside a simple polygon given only an inaccurate representation of the vertices of the polygon. We introduce a notion of a visibility skeleton of an inaccurate representation of a simple polygon. We show that in most cases the visibility skeleton of a representation can be computed efficiently; furthermore, the visibility skeleton can be used to plan a collision-free path inside the polygon whose length approximates the length of a shortest such path to within a constant factor (independent of the number of vertices in the polygon).

Visibility graphs (VGs), horizontal visibility graphs (HVGs) and the sandbox algorithm (SB) are applied for multifractal characterization of complex network systems that are converted from time series measurements, are used to characterize the fluctuations in pseudorapidity densities of singly charged particles produced in ${}^{16}$O–AgBr interactions at 60AGeV. The work presents the analysis of ring-like and jet-like events in terms of multifractality characterization of ${}^{16}$O–AgBr interactions at 60AGeV. We systematically compared the experimental events of both ring- and jet-like events with Monte Carlo (MC) simulated events. The investigation reveals that the multifractal spectrum for the jet-like events and ring-like events is different and can be distinguished. The ring-like events have its parameters slightly higher than that of jet-like events. Further analysis shows that the strength of the nonstatistical fluctuations is larger for ring-like events than those of jet-like events. The SB method presented here appears to be more useful than the conventional methods used for multifractal characterization.

In this paper, the network metrics are studied in a time series of the KOSPI and the KOSDAQ indices converting by the visibility graph algorithm. The degree distributions for the KOSPI and the KOSDAQ are proportional to a power law rather than the Poisson distribution. Since we mainly simulate and analyze the network metrics from the nodes and its links, our result cannot be found unambiguously to have universal and characteristic properties of statistical quantities via financial networks. Particularly, these topological properties may improve by implementing the statistical method and its technique from altered data of financial networks.