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While abrupt regime shifts between different metastable states have occurred in natural systems from many areas including ecology, biology, and climate, evidence for this phenomenon in transportation systems has been rarely observed so far. This limitation might be rooted in the fact that we lack methods to identify and analyze possible multiple states that could emerge at scales of the entire traffic network. Here, using percolation approaches, we observe such a metastable regime in traffic systems. In particular, we find multiple metastable network states, corresponding to varying levels of traffic performance, which recur over different days. Based on high-resolution global positioning system (GPS) datasets of urban traffic in the megacities of Beijing and Shanghai (each with over 50,000 road segments), we find evidence supporting the existence of tipping points separating three regimes: a global functional regime and a metastable hysteresis-like regime, followed by a global collapsed regime. We can determine the intrinsic critical points where the metastable hysteresis-like regime begins and ends and show that these critical points are very similar across different days. Our findings provide a better understanding of traffic resilience patterns and could be useful for designing early warning signals for traffic resilience management and, potentially, other complex systems.

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset, Nat. Commun. 10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

Understanding, quantifying and predicting market fluctuation has become increasingly important in recent decades. Volatility and volume are the two commonly used quantities to study the market dynamics and the relationship between these two has been modeled and debated for years with several hypothesis been put forward. Using empirical data, we investigate the causality and correlation between volume and volatility and find new ways in which they interact, particularly when the levels of both are high. We find that the volume-conditional volatility distribution scales with volume as a power-law function with an exponential cutoff. We exploit the characteristics of a volume-volatility scatterplot and find a strong correlation between logarithmic volume and a quantity we define as local maximum volatility (LMV), the highest volatility observed in a given range of volume. This supports our empirical analysis, showing that volume is an effective parameter for prediction of the maximum value of volatility for both same-day and near-future time periods. The joint conditional probability of volume and volatility also indicates if we invoke both quantities, the prediction of the largest next-day volatility will be better than invoking either one alone. This approach is thus a greatly improved method of risk assessment.

We analyze the structural and functional robustness of networked critical infrastructure systems (CISs). We propose a structural and functional robustness model of a typical complex network and take into account the corresponding measuring metrics and cascading processes to assess the impact of different hazard modes on robustness. We analyze the robustness of the shanghai subway network and the central China power grid to demonstrate an application of the model. We find that both are strongly robust to random failure but extremely vulnerable to targeted attack. We identify the critical areas most likely to be attack targets and use a functional perspective to identify vulnerabilities. Our proposed method can be applied to other CISs and aid in understanding the mechanisms of network robustness.

The linkages between crude oil spot and futures markets are widely studied in previous literatures. Most of these conventional methods are static, linear and parametric. In order to overcome this difficulty, we employ the nonparametric and nonlinear symmetric thermal optimal path (TOPS) method to determine the time-dependent lead–lag relationship between two time series. Based on the daily, weekly, monthly spot and futures returns for maturities of one, two, three and four months of the West Texas Intermediate (WTI) crude oil benchmark, we apply the TOPS method together with self-consistent test to investigate the time-varying lead–lag dependences between spot and futures markets from 1987 to 2017. We find that, for total three data sets with different frequencies, the TOPS paths indicate an alternate lead–lag structure instead of a dominance between spot and futures markets in most of the time periods. For the daily data, the lead–lag relationship between the two markets exists within one day except on some specific days. Moreover, without considering the units of time, on average, the lead–lag steps between the two markets are diminishing with the increasing frequency. Roughly speaking, these periods with strong lead–lag signals coincide with major influential changes in the oil and stock markets and the geopolitics, which can reflect real economic, financial and geopolitical regime changes. All in all, the results show that the lead–lag relationship between the spot and futures oil markets exists only temporarily.

We construct the empirical information network (EIN) of traders using the order flow data of the constituent stocks of SZSE 100 Index in 2013. A statistical validation method is applied to the edges of the network to filter out noises and uncover the intrinsic interaction behaviors of traders. We investigate the correlation between topological structures and statistical properties for their largest connected components. We find that the statistical validated network shows an assortative mixing pattern while the original network exhibits a disassortative mixing pattern. We consider two definitions of edge weight for comparison but there is no significant difference in a same network. We also analyze the mutual relationships among node degree, edge weight and node strength.

The Beijing–Tianjin–Hebei (BTH) integration project in China is ambitious which offers great potential with its promotion of sustainable and inclusive development. This study investigates the impact of regional financial development on economic growth in the BTH region, with panel data collected from 2007 to 2016. Two indicators namely, CREDIT (denoted as regional financial development depth) and BRANCH (denoted as regional financial intermediaries accessibility) are used to construct an integrated regional financial development indicator through the spatial econometrics approach. The spatio-temporal distribution characteristics of regional financial development and economic growth are analyzed. Afterward, the global Moran’s I and local Getis–Ord Gi* statistics are applied to detect the presence of spatial autocorrelation. Finally, a spatial Durbin model (SDM) is utilized to examine spatial distribution and spatial association. The research findings of this study suggest that the CREDIT has a positive effect on regional economic growth, while the BRANCH has no impact on regional economic growth. Moreover, it is found that the spatial autocorrelation of CREDIT and BRANCH are statistically significant. The CREDIT of the neighboring areas has a negative spatial spillover effect on economic growth of one area, while the BRANCH in the neighboring areas has a positive effect on the one area. The results and research findings reported in this article highlight the role of regional financial development in improving the economic growth not only for Chinese policy makers but also for other countries’ researchers and practitioners in this field.

We use isonymic distance to measure the dissimilarity in surname structure between populations of Chinese provinces, and we employ the minimum spanning tree (MST) and the single linkage cluster analysis (SLCA) to investigate the hierarchical structure of Chinese provinces and present its corresponding geographical features. We find diverse discrepancies in the averaged isonymic distance among provinces that are attributed to the heterogeneous surname distributions. The MST displays a core–fringe structure with Henan, Anhui, and Hubei making up the core, and several border provinces on the fringe. The degree centrality list in the MST reveals some “local centers” that act as regional economic centers. On the other hand, the geographical layout of MST reflects the historical “Rush to Northeast” mass migration, as well as the blocking effect of the Qinling–Huaihe line that separates north and south China. The clustering results derived from the SLCA show nine groups of provinces in which each group is geographically continuous.

We use a heterogeneous agent-based two-state sociophysics model to simulate financial markets. Focusing on stock market trader dynamics, we propose a model with two kinds of individual – the contrarian agent and the noise trader – in which the dynamics of buying and selling investors are governed by local and global interactions. We define an antiferromagnetic coupling that relates the option of contrarian agents to global magnetization and a ferromagnetic interaction that connects noise traders to their local neighborhood. Our model presents such stylized facts of real financial markets as clustered volatility, power-law distributed returns, and the long-time correlation of the absolute returns with exponential decay. We also observe that the distribution of logarithmic returns can be fitted by the Student’s t distribution in which its degree of freedom changes with the percentage of contrarian agents in the market.

Examining the venture capital market as a representative case, we made the first empirical study about timing and rhythm in organizational behavior. We analyze inter-event time intervals and find that the fat-tailed property of organizational behavior is similar that found in individual behavior, but that its lower scaling exponent indicates it is more heterogeneous than individual behavior. We quantify the observable burst and memory effect in organizational behavior. The burst effect occurs when organizations make frequent business deals during a short time period. This is a potential factor affecting economic cycles and market turbulence. The memory effect occurs when future organizational behavior correlates with past behavior, which potentially allows the prediction of future behavior. We find fewer bursts and a stronger memory effect in organizational behavior than in individual behavior. This difference may be related to resource constraint, business routine, and market competition. These findings shed light on the changeable features of organizational behavior and economic system. We drew a necessity to extend study on human dynamics to organization dynamics by exploring real organizational data in a wide range and proposing a mechanism to better modeling organizational behaviors. Understanding the temporal characteristics of organizational behavior is essential to understanding economic complexities.

Using the theoretical framework of spatial econometrics, we estimate the impact of capital markets, i.e., stock markets, medium-and-long term bond markets, and medium-and-long term loan markets, on industrial structure upgrading (ISU) across 31 provinces in China from 1998 to 2015. We apply an explanatory spatial data analysis (ESDA) to detect the presence of spatial dependence and use a spatial Durbin model (SDM) to examine spatial distribution and spatial association. Although our overall estimation results from the 31 provinces indicate a degree of correlation between capital markets and industrial structure upgrading, the magnitude of spatial spillover effects in three sub-markets on ISU differ. We divide the 31 provinces into four economic zones, and explore the impact of three sub-markets on ISU in the eastern zone, central zone, western zone, and northeastern zone. Using our results, we provide policy suggestions that better facilitate ISU in China.

Water is a fascinating material. Its composition is simple—one oxygen andtwo hydrogen atoms—but its chemistry and physics are extremely complex andexhibit 75 documented anomalies. Although these anomalies and theirmolecular origin are not completely understood, we know that hydrogen bondsplay key roles in all of the phases of water. Moreover, there isexperimental evidence that the polymorphism of the ice structure extendsinto the liquid phase and is associated with a liquid-liquid coexistenceline. This is currently a topic of great interest in water research becausethere are indications that the end point of the coexistence line correspondsto a second critical point inside the supercooled liquid regime. We examinethe recent progress in understanding water anomalies and the liquid-liquidphase transition hypothesis, including the results of recent experimentalwork and molecular simulations of both bulk and confined water. We examineexperimental results that test whether the behavior of liquid water isconsistent with the textquotedblleft liquid polymorphismtextquotedblrighthypothesis that liquid water can exist in two distinct phases of differingdensities. We also examine recent research on the anomalies of nanoconfinedwater and, in particular, on water in biological environments. We find thatthe concept of liquid polymorphism can also describe the properties of otherliquids that have two characteristic length scales.

Due to previous technical challenges with the collection of data on riding behaviors, there have only been a few studies focusing on patterns and regularities of biking traffic, which are crucial to understand to help achieve a greener and more sustainable future urban development. Recently, with the booming of the sharing economy, and the development of the Internet of Things (IoT) and mobile payment technology, dockless bike-sharing systems that record information for every trip provide us with a unique opportunity to study the patterns of biking traffic within cities. We first reveal a spatial scaling relation between the cumulative volume of riding activities and the corresponding distance to the city center, and a power law distribution on the volume of biking flows between fine-grained locations in both Beijing and Shanghai. We validate the effectiveness of the general gravity model on predicting biking traffic at fine spatial resolutions, where population-related parameters are less than unity, indicating that smaller populations are relatively more important per capita in generating biking traffic. We then further study the impacts of spatial scale on the gravity model and reveal that the distance-related parameter grows in a similar way as population-related parameters when the spatial scale of the locations increases. In addition, the flow patterns of some special locations (sources and sinks) that cannot be fully explained by the gravity model are studied.

The dynamics of opinion formation in a society is a complex phenomenon where many variables play essential roles. Recently, the influence of algorithms to filter which content is fed to social networks users has come under scrutiny. Supposedly, the algorithms promote marketing strategies, but can also facilitate the formation of filters bubbles in which a user is most likely exposed to opinions that conform to their own. In the two-state majority-vote model, an individual adopts an opinion contrary to the majority of its neighbors with probability q , defined as the noise parameter. Here, we introduce a visibility parameter V in the dynamics of the majority-vote model, which equals the probability of an individual ignoring the opinion of each one of its neighbors. For V = 0 . 5 each individual will, on average, ignore the opinion of half of its neighboring nodes. We employ Monte Carlo simulations to calculate the critical noise parameter as a function of the visibility q c ( V ) and obtain the phase diagram of the model. We find that the critical noise is an increasing function of the visibility parameter, such that a lower value of V favors dissensus. Via finite-size scaling analysis we obtain the critical exponents of the model, which are visibility-independent, and show that the model belongs to the Ising universality class. We compare our results to the case of a network submitted to a static site dilution and find that the limited visibility model is a more subtle way of inducing opinion polarization in a social network.

Departure delays are a major cause of economic loss and inefficiency in the growing industry of passenger flights. A departure delay of a current flight is inevitably affected by the late arrival of the flight immediately preceding it with the same aircraft. We seek to understand the mechanisms of such propagated delays, and to obtain universal metrics by which to evaluate an airline’s operational effectiveness in delay alleviation. Here we use big data collected by the American Bureau of Transportation Statistics to design models of flight delays. Offering two dynamic models of delay propagation, we divided all carriers into two groups exhibiting a shifted power law or an exponentially truncated shifted power law delay distribution, revealing two universal delay propagation classes. Three model parameters, extracted directly from dual data mining, help characterize each airline’s operational efficiency in delay mitigation. Therefore, our modeling framework provides the crucially lacking evaluation indicators for airlines, potentially contributing to the mitigation of future departure delays.

In real paramagnets, there is always a subtle many-body contribution to the system's energy, which can be regarded as a small effective local magnetic field $B_{loc}$. Usually, it is neglected, since it is very small when compared with thermal fluctuations and/or external magnetic fields $B$. Nevertheless, as both the temperature $T \rightarrow$ 0K and $B \rightarrow$ 0T, such many-body contributions become ubiquitous. Here, employing the magnetic Gr\"uneisen parameter $\Gamma_{mag}$ and entropy arguments, we report on the pivotal role played by the mutual interactions in the regime of ultra-low-$T$ and vanishing $B$. Our key results are: $i$) absence of a genuine zero-field quantum phase transition due to the presence of $B_{loc}$; $ii$) connection between the canonical definition of temperature and $\Gamma_{mag}$; and $iii$) possibility of performing adiabatic magnetization by only manipulating the mutual interactions. Our findings unveil unprecedented aspects emerging from the mutual interactions., Comment: 21 pages, 8 figures

The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, study of the connections between different percolation transitions is still lacking. Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks. The model evolves in generations with the result of the present percolation depending on the previous state, and thus is history-dependent. Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation. We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications, such as detecting the abnormal structures of human brain networks., We propose a unified framework for studying the origin of the discontinuous transitions of the percolation process on interacting networks,whichalsohas wide practical applications in network science.

In this paper, we study the robustness of interdependent networks with multiple-dependence (MD) relation which is defined that a node is interdependent on several nodes on another layer, and this node will fail if any of these dependent nodes are failed. We propose a two-layered asymmetric interdependent network (AIN) model to address this problem, where the asymmetric feature is that nodes in one layer may be dependent on more than one node in the other layer with MD relation, while nodes in the other layer are dependent on exactly one node in this layer. We show that in this model the layer where nodes are allowed to have MD relation exhibits different types of phase transitions (discontinuous and hybrid), while the other layer only presents discontinuous phase transition. A heuristic theory based on message-passing approach is developed to understand the structural feature of interdependent networks and an intuitive picture for the emergence of a tricritical point is provided. Moreover, we study the correlation between the intralayer degree and interlayer degree of the nodes and find that this correlation has prominent impact to the continuous phase transition but has feeble effect on the discontinuous phase transition. Furthermore, we extend the two-layered AIN model to general multilayered AIN, and the percolation behaviors and properties of relevant phase transitions are elaborated. Ministry of Education (MOE) Published version This work was supported in part by the National Natural Science Foundation of China under Grants No. 11835003, No.11975099, and No. 11872182, in part by the Natural Science Foundation of Shanghai under Grants No. 17ZR1444800 and No. 18ZR1412200, and in part by the Ministry of Education,Singapore, under Contract No. MOE2016-T2-1-119.

We perform short-time Monte Carlo simulations to study the criticality of the isotropic two-state majority-vote model on cubic lattices of volume N = L 3 , with L up to 2048. We obtain the precise location of the critical point by examining the scaling properties of a new auxiliary function Ψ . We perform finite-time scaling analysis to accurately calculate the whole set of critical exponents, including the dynamical critical exponent z = 2 . 027 ( 9 ) , and the initial slip exponent θ = 0 . 1081 ( 1 ) . Our results indicate that the majority-vote model in three dimensions belongs to the same universality class of the three-dimensional Ising model.

Research on dynamical processes in interconnected spatial networks has expanded in recent years, but there has been little focus on social contagions. Using a general social contagion model, we numerically study how an interconnected spatial system composed of two interconnected planar lattices influences social contagion dynamics. When information is transmitted and allows for a probability of behavior adoption, strongly interconnected lattices stimulate the contagion process and significantly increase the final density of adopted individuals. We perform a finite-size analysis and confirm that the dependency of prevalence on the transmission rate is continuous regardless of the adoption probability. The prevalence grows discontinuously with the adoption probability even when the transmission rate is low. Although a high transmission rate or a high adoption probability increases the final adopted density in weak interconnected lattices, the prevalence always grows continuously in these networks. These findings help us understand social contagion dynamics in interconnected lattices.

In this paper, we give a methodological framework to analyze vulnerability of interdependent infrastructure systems under deliberate attacks. Meanwhile, the intelligence of attackers is considered and a method of critical attack area identification according to community detection is proposed as well. The Interdependent power and gas system in Wuhan, China is taken as the example. We determine the vulnerabilities of different critical areas in both independent and interdependent scenarios. In the meantime, percolation theory are utilized and different coupling strengths are considered to further analyze the vulnerabilities. It is found that the disruption of only a few vertices may lead to complete collapsing for some critical areas and the vulnerabilities increase when systems become interdependent. Therefore, greater protection should be given to critical areas of a network in order to reduce the vulnerabilities when deliberate attacks occur. The proposed method could help decision makers develop mitigation techniques and optimal protection strategies.

As socioeconomic systems continue to develop, their critical infrastructure systems become more intricate and the interdependencies among systems more intensive. This cascading effect on critical infrastructure systems significantly impacts system performance. We develop an approach to quantitatively assess the complex cascading effect on critical infrastructure systems under four different types of attack: (i) random, (ii) malicious, (iii) shell-based and local, and (iv) orientated and local. In the context of these four we study three types of cascading effect – non-cascading, inner-system cascading, and inter-system cascading – in both independent systems and interdependent systems. We model both logical and geographical interdependency. We apply this approach to the Chinese road and railway system and find that (i) the damage done by different types of attack on critical infrastructures systems varies significantly, (ii) under the same type of attack the damage caused by cascading effects on different critical infrastructure systems varies significantly, and (iii) different cascading effects contribute to damage in critical infrastructure systems. These findings indicate that more theoretical and practical research on cascading effects in infrastructure systems under different attacks is needed, especially when the attacks are local and oriented.

The algorithm of limited penetrable horizontal visibility graphs (LPHVGs) including the limited penetrable horizontal visibility graph [LPHVG( ρ )], the directed limited penetrable horizontal visibility graph [DLPHVG( ρ )] and the image limited penetrable horizontal visibility graph [ILPHVG n ( ρ ) )] are used to map time series (or matrices) on graphs and are powerful tools for analyzing time series. We derive the degree distributions of LPHVGs using an iterative LPHVGs construction process. We propose a more intuitive method of reproducing the construction process of limited penetrable horizontal visibility graphs that is simple to calculate. We find that the results confirm the analytical results from previous methods. We then introduce the concept of sequential LPHVG( ρ ) motifs and present a theoretical way of computing the exact motif profiles associated with unrelated random series. We perform several numerical simulations to further check the accuracy of our theoretical results. Finally we use the analytical results of LPHVG( ρ ) motif profiles to distinguish among random, periodic, and chaotic signals and find that the frequency of the type-I motif captures sufficient information to easily distinguish among different processes.

One of the most interesting challenges in network science is to understand the relation between network structure and dynamics on it, and many topological properties, including degree distribution, community strength and clustering coefficient, have been proposed in the last decade. Prominent in this context is the centrality measures, which aim at quantifying the relative importance of individual nodes in the overall topology with regard to network organization and function. However, most of the previous centrality measures have been proposed based on different concepts and each of them focuses on a specific structural feature of networks. Thus, the straightforward and standard methods may lead to some bias against node importance measure. In this paper, we introduce two physical processes with potential complementarity between them. Then we propose to combine them as an elegant integration with the classic eigenvector centrality framework to improve the accuracy of node ranking. To test the produced power iteration ranking (PIRank) algorithm, we apply it to the selection of attack targets in network optimal attack problem. Extensive experimental results on synthetic networks and real-world networks suggest that the proposed centrality performs better than other well-known measures. Moreover, comparing with the eigenvector centrality, the PIRank algorithm can achieve about thirty percent performance improvement while keeping similar running time. Our experiment on random networks also shows that PIRank algorithm can avoid the localization phenomenon of eigenvector centrality, in particular for the networks with high-degree hubs.

Being able to theoretically predict the outbreak threshold of an epidemic is essential in disease control. Real-world correlated networks are ubiquitous and their topological structure strongly affects the prediction accuracy of present-day theoretical methods. Quantifying their accuracy and fitness in predicting outbreak thresholds of correlated networks is thus essential. We use a susceptible–infected–removed (SIR) model to examine four widely-used theoretical methods – the heterogeneous mean-field ( H M F ), quenched mean-field ( Q M F ), dynamical message passing ( D M P ), and connectivity matrix ( C M ) methods – to predict the outbreak threshold of a correlated network. The potential topological structure of correlated network impacts on prediction accuracy of these four methods. We emphasize that the quantitative changes of degree correlation, degree distribution exponent and network size strongly affect the outbreak of SIR spreading dynamics, and compare the simulation results with the theoretical ones obtained from these four methods. The extensive experiments in synthetic networks show that (a) the increasing degree correlation coefficients reduce outbreak threshold and suppress outbreak size; (b) the increasing degree distribution exponents raise outbreak threshold but suppress outbreak size; (c) the increasing network sizes decrease outbreak threshold but do not affect outbreak size; (d) as for four theoretical methods, C M and D M P are more likely to precisely predict outbreak threshold because they to some extent incorporate network topology with dynamical correlations. The experimental results in 50 real-world networks also prove the above conclusions.

Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a global process, it is commonly believed that measuring the influence of nodes inevitably requires the knowledge of the entire network. Employing percolation theory, we show that the spreading process displays a nucleation behavior: once a piece of information spread from the seeds to more than a small characteristic number of nodes, it reaches a point of no return and will quickly reach the percolation cluster, regardless of the entire network structure, otherwise the spreading will be contained locally. Thus, we find that, without the knowledge of entire network, any nodes' global influence can be accurately measured using this characteristic number, which is independent of the network size. This motivates an efficient algorithm with constant time complexity on the long standing problem of best seed spreaders selection, with performance remarkably close to the true optimum., 6 pages, 5 figures, Proceedings of the National Academy of Sciences of the United States of America (PNAS), July 3, 2018

Detecting and characterizing community structure plays a crucial role in the study of networked systems. However, there is still a lack of understanding of how community structure affects the systems' resilience and stability. Here, we develop a framework to study the resilience of networks with community structure based on percolation theory. We find both analytically and numerically that the interlinks (connections between the communities) affect the percolation phase transition in a manner similar to an external field in a ferromagnetic-paramagnetic spin system. We also study the universality class by defining the analogous critical exponents $\delta$ and $\gamma$, and find that their values for various models and in real-world co-authors networks follow fundamental scaling relations as in physical phase transitions. The methodology and results presented here not only facilitate the study of resilience of networks but also brings a fresh perspective to the understanding of phase transitions under external fields., Comment: 15 pages,4 figures

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series., Comment: 23 pages, 12 figures

It is proposed that the core–periphery structure of complex networks can be simulated by h -cores and fingerprint curves. While the features of core structure are characterized by h -core, the features of periphery structure are visualized by rose or spiral curve as the fingerprint curve linking to entire-network parameters. It is suggested that a complex network can be approached by h -core and rose curves as the first-order Fourier-approach, where the core–periphery structure is characterized by five parameters: network h-index, network radius, degree power, network density and average clustering coefficient. The simulation looks Fourier-like analysis.

To investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events, we use a Potts dynamic system to construct a random financial time series model of the attitudes of market traders. We use multiscale multifractal detrended cross-correlation analysis (MM-DCCA) and Lempel–Ziv complexity (LZC) perform numerical research of the return intervals for two significant China’s stock market indices and for the proposed model. The new MM-DCCA method is based on the Hurst surface and provides more interpretable cross-correlations of the dynamic mechanism between different return interval series. We scale the LZC method with different exponents to illustrate the complexity of return intervals in different scales. Empirical studies indicate that the proposed return intervals from the Potts system and the real stock market indices hold similar statistical properties.

Using the detrended cross-correlation analysis (DCCA) coefficient and the detrended partial cross-correlation analysis (DPCCA) coefficient, we investigate cross-correlations and net cross-correlations among five major world gold markets (London, New York, Shanghai, Tokyo, and Mumbai) at different time scales. We propose multiscale influence measures for examining the influence of individual markets on other markets and on the entire system. We find (i) that the cross-correlations, net cross-correlations, and net influences among the five gold markets vary across time scales, (ii) that the cross-market correlation between London and New York at each time scale is intense and inherent, meaning that the influence of other gold markets on the London–New York market is negligible, (iii) that the remaining cross-market correlations (i.e., those other than London–New York) are greatly affected by other gold markets, and (iv) that the London gold market significantly affects the other four gold markets and dominates the world-wide gold market. Our multiscale findings give market participants and market regulators new information on cross-market linkages in the world-wide gold market.

We examine how real-world individuals and companies can either reach an agreement or fail to reach an agreement after several stages of negotiation. We use a modified prisoner’s dilemma game with two-sided players who can either cooperate or not cooperate with their neighbors. We find that the presence of even a small number of these two-sided players substantially promotes the cooperation because, unlike the rock–paper–scissors scenario, when the cooperators change to the non-cooperators to gain a payoff, they can turn to the two-sided players and continue negotiating. We find that the network structure influences the spread of strategies. Lattice and regular-random (RR) networks benefit the spread of both non-cooperation and two-sided strategies, but scale-free (SF) networks stop both strategies. We also find that the Erdos–R e nyi (ER) network promotes the two-sided strategy and blocks the spread of non-cooperation. As the ER network density decreases, and the network degree is lowered the lifetime of non-cooperators increases. Our results expand our understanding of the role played by the two-sided strategy in the growth of the cooperative behavior in networks.

We study stochastic resonance (SR) in an oscillator with nonlinear noise, fractional-order external damping, and fractional-order intrinsic damping. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are non-monotonic. Using numerical simulations we verify the accuracy of this analytical result. We find (i) that nonlinear noise plays a key role in system behavior and that the resonance of the output amplitude is diverse when there is nonlinear noise, (ii) that the order of the fractional-order damping strongly impacts resonant intensity and that the impact on resonant intensity of fractional-order external damping is opposite that of fractional-order intrinsic damping, and (iii) that the evolution of the output amplitude versus the frequency of the external periodic force exhibits three behaviors: a resonance with one peak, a resonance with one peak and one valley, and a resonance with one valley.

Cascading failures in the internet have attracted recent attention due to their unpredictability and destructive consequences. Exploring the failure behavior patterns is necessary because they can provide effective intervention approaches to prevent huge network disasters. To analyze internet flow behaviors during cascading failures (chain reactions in router and link failures), we characterize the internet as two coupled networks, the router network and the flow network. Here the flow network is an abstract representation of data correlations obtained from the router network. We use this coupled network to build a cascading failure model for studying flow transmission and competition, which is reflected in bandwidth competition given by limited link capacity. We first study the dependency between routers and flows to explore the flow transmission efficiency when a failure event occurs. Moreover, we find that rerouting enables flow competition area (the number of flows with which one flow has a competitive relationship) to initially remain stable during a failure episode, but that it then quickly drops due to poor physical network connectivity. Additionally, in the early stage after the failure event, the degree of flow competition sharply increases because of the growing number of the flows and congestion. Subsequently, the flow competition decreases due to the failure of flow transmission.

Interdependent networks as an important structure of the real system not only include one-to-one dependency relationship but also include more realistic undirected multiple interdependent relationship. The study on interdependent networks plays an important role in designing more resilient real systems. Here, we mainly focus on the case of interdependent networks with a multiple-to-multiple correspondence of interdependent nodes by generalizing feedback and nonfeedback conditions. We develop a new mathematical framework and study numerically and analytically the percolation of interdependent networks with partial multiple-to-multiple dependency links by using percolation theory. By analyzing the process of cascading failure, the size of the giant component and the critical threshold are analytically obtained and testified by simulation results for couple Erdos-R e˙nyi and scale-free networks. The results imply that the system shows a discontinuous phase transition for different coupling strengths. We find that the system becomes more resilient and easy to defend by increasing the coupling strength and the connectivity density. Our model has the potential to shed light on designing more resilient real-world dependent systems.

The hidden nature of causality is a puzzling, yet critical notion for effective decision-making. Financial markets are characterized by fluctuating interdependencies which seldom give rise to emergent phenomena such as bubbles or crashes. In this paper, we propose a method based on symbolic dynamics, which probes beneath the surface of abstract causality and unveils the nature of causal interactions. Our method allows distinction between positive and negative interdependencies as well as a hybrid form that we refer to as “dark causality.” We propose an algorithm which is validated by models of a priori defined causal interaction. Then, we test our method on asset pairs and on a network of sovereign credit default swaps (CDS). Our findings suggest that dark causality dominates the sovereign CDS network, indicating interdependencies which require caution from an investor’s perspective.

The concept of resilience can be realized in natural and engineering systems, representing the ability of system to adapt and recover from various disturbances. Although resilience is a critical property needed for understanding and managing the risks and collapses of transportation system, an accepted and useful definition of resilience for urban traffic as well as its statistical property under perturbations is still missing. Here we define city traffic resilience based on the spatio-temporal clusters of congestion in real traffic, and find that the resilience follows a scale free distribution in two-dimensional city road networks and one-dimensional highways, with different exponents, but similar exponents in different days and different cities. The traffic resilience is also revealed to have a novel scaling relation between the cluster size of the spatio-temporal jam and its recovery duration, independent of microscopic details. Our findings of universal traffic resilience can provide indication towards better understanding and designing these complex engineering systems under internal and external disturbances., Comment: 6 pages, 4 figures

Cooperation is key to the survival of all biological systems. The spatial structure of a system constrains who interacts with whom (interaction partner) and who acquires new traits from whom (role model). Understanding when and to what degree a spatial structure affects the evolution of cooperation is an important and challenging topic. Here, we provide an analytical formula to predict when natural selection favours cooperation where the effects of a spatial structure are described by a single parameter. We find that a spatial structure promotes cooperation (spatial reciprocity) when interaction partners overlap role models. When they do not, spatial structure inhibits cooperation even without cooperation dilemmas. Furthermore, a spatial structure in which individuals interact with their role models more often shows stronger reciprocity. Thus, imitating individuals with frequent interactions facilitates cooperation. Our findings are applicable to both pairwise and group interactions and show that strong social ties might hinder, while asymmetric spatial structures for interaction and trait dispersal could promote cooperation.

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

We thoroughly study the robustness of partially interdependent networks when suffering attack combinations of random, targeted, and localized attacks. We compare analytically and numerically the robustness of partially interdependent networks with a broad range of parameters including coupling strength, attack strength, and network type. We observe the first and second order phase transition and accurately characterize the critical points for each combined attack. Generally, combined attacks show more efficient damage to interdependent networks. Besides, we find that, when robustness is measured by the critical removing ratio and the critical coupling strength, the conclusion drawn for a combined attack is not always consistent.

In this review article we present some of achievements of econophysics and sociophysics which appear to us the most significant. We briefly explain what their roles are in building of econo- and sociophysics research fields. We point to milestones of econophysics and sociophysics facing to challenges and open problems.

In this work, three models of the motion of charged particles in three-dimensional semiconductors governed by a stochastic differential equation driven by a magnetic field and an intrinsic fractional Gaussian noise have been introduced. Based on the general expansion theorem for the Laplace transform, the expressions of the average position and the average velocity of a charged particle have been obtained. The expressions of the complex susceptibilities, the spectral amplification, the stationary form of current density, as well as power absorption also have been obtained. It is worthy to note that the cyclotron resonance, stochastic dynamics of a charged particle could be induced by fractional noise. Furthermore, the expressions of variances and the generalized Fokker–Planck equation (GFPE) for the non-Markovian dynamics also have been investigated.

We study stochastic resonance (SR) phenomenon in the fractional oscillator with time delay and damping fluctuation, analyze the impact of time delay and fractional damping as two memory ingredients on SR, and put forward firstly the concept of the robustness of GSR. By moment method, we obtain the analytical expression of the output amplitude gain and find that fluctuations in the output amplitude gain are non-monotonic. Using numerical simulations we verify the accuracy of the analytical results. We find (i) that the length of time delay and system order are parameters related to memory; (ii) that the output amplitude gain could attain a maximum by increasing driving frequency close to system frequency, and small time delay and system order contribute to enhance the resonance intensity; (iii) that the evolution of the output amplitude gain versus the noise intensity exhibits one-peak resonance, and small time delay can enhance the resonance intensity and the robustness of SR regarding to driving frequency and system frequency; (iv) that the evolution of the output amplitude gain versus the noise correlation rate presents one-peak resonance in the presence of small time delay, critical time delay is bigger with the increasing system order when noise intensity is fixed and critical time delay is smaller with the increasing noise intensity when system order is fixed.

We construct a Pearson correlation-based network and a partial correlation-based network, i.e., two minimum spanning trees (MST-Pearson and MST-Partial), to analyze the correlation structure and evolution of world stock markets. We propose a new method for constructing the MST-Partial. We use daily price indices of 57 stock markets from 2005 to 2014 and find (i) that the distributions of the Pearson correlation coefficient and the partial correlation coefficient differ completely, which implies that the correlation between pairs of stock markets is greatly affected by other markets, and (ii) that both MSTs are scale-free networks and that the MST-Pearson network is more compact than the MST-Partial. Depending on the geographical locations of the stock markets, two large clusters (i.e., European and Asia-Pacific) are formed in the MST-Pearson, but in the MST-Partial the European cluster splits into two subgroups bridged by the American cluster with the USA at its center. We also find (iii) that the centrality structure indicates that outcomes obtained from the MST-Partial are more reasonable and useful than those from the MST-Pearson, e.g., in the MST-Partial, markets of the USA, Germany, and Japan clearly serve as hubs or connectors in world stock markets, (iv) that during the 2008 financial crisis the time-varying topological measures of the two MSTs formed a valley, implying that during a crisis stock markets are tightly correlated and information (e.g., about price fluctuations) is transmitted quickly, and (v) that the presence of multi-step survival ratios indicates that network stability decreases as step length increases. From these findings we conclude that the MST-Partial is an effective new tool for use by international investors and hedge-fund operators.

A supply chain network is a typical interdependent network composed of an undirected cyber-layer network and a directed physical-layer network. To analyze the robustness of this complex interdependent supply chain network when it suffers from disruption events that can cause nodes to fail, we use a cascading failure process that focuses on load propagation. We consider load propagation via connectivity links as node failure spreads through one layer of an interdependent network, and we develop a priority redistribution strategy for failed loads subject to flow constraint. Using a giant component function and a one-to-one directed interdependence relation between nodes in a cyber-layer network and physical-layer network, we construct time-varied functional equations to quantify the dynamic process of failed loads propagation in an interdependent network. Finally, we conduct a numerical simulation for two cases, i.e., single node removal and multiple node removal at the initial disruption. The simulation results show that when we increase the number of removed nodes in an interdependent supply chain network its robustness undergoes a first-order discontinuous phase transition, and that even removing a small number of nodes will cause it to crash.

Made available in DSpace on 2020-12-12T01:16:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-09-15 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) This paper studies the effects of overconfidence and loss aversion in an artificial stock exchange. When we model only fundamentalists we find results that are consistent with homogeneous agent models. Adding 5% of chartists increases the stock return rate but also increases other variables, including volatility and kurtosis. We find that the inclusion of confidence in 5% of chartists raises the trading volume as empirical evidences corroborate and price volatility increases considerably. On the other hand, loss aversion in 5% of chartists substantially decreases the trading volume, although chartist traders now have a higher percentage of stocks in their portfolios, and a buy and hold strategy is adopted to mitigate losses. Department of Economics Sao Paulo State University (UNESP) Swiss Federal Institute of Technology in Zurich (ETH Zurich) Center for Polymer Studies Boston University Department of Economics Sao Paulo State University (UNESP) FAPESP: 2018/22562-4 CNPq: 303986/2017-4 CNPq: 428433/2018-9

The connection adaption strategy (CAS) has been proposed for the synchronization of networked mobile chaotic agents, which is considered to be a simpler scheme compared to commonly used coupling adaption strategies. However, this strategy only provides a limited range of feasible coupling strength allowing a success control. In this paper, we develop the CAS by introducing a jump process to resolve this problem. We show that the proposed approach systematically outperforms the original CAS in the whole range of the mobility and the range of feasible coupling strength is extensively expanded. In addition, we show that motion of the agents could be classified into three different regimes. The dynamical features of these motion regimes are analyzed and relevant measures are provided to characterize the controllability of the network in each regime. Ministry of Education (MOE) Published version This work was supported in part by the National Natural Science Foundation of China under Grant 11835003, in part by the Ministry of Education, Singapore, under Contract MOE2016-T2-1-119, and in part by NSF Grant PHY-1505000 and by DTRA Grant HDTRA1-14-1-0017.

This paper investigates the fractal structure of China’s stock market by calculating the multifractal singularity spectrum and comparing the scaling behavior of the bubble phase of eight abnormal volatilities with that of normal fluctuation on the timeline. We find robust evidence that the Shanghai Stock Exchange Composite Index has multifractal features in the bubble and normal fluctuation periods, where the higher multifractality is associated with a bubble and more unstable market. The short-sighted administrative policies cause over-supply of intervention, which enhances the multifractality and increases the instability of the stock market. The multifractal parameter set ( α 0 , Δ α , − B ) might be used as a quantifier to characterize the status of the stock market. A policy aimed to improve the stability of the stock market should be devoted to optimizing the parameter set.

Feedback is one of the most powerful influences in dynamical systems, performing a fundamental function in self-regulating processes. However, it is not known whether the underlying control of networked systems is associated with feedback. Here, we analyze structural feedback, defined by adding directed links from controlled nodes to driver nodes, to determine the control energy requirement of networked systems. We show that feedback systems with positive links require less energy than feedback systems with negative links, and the control energies of positive and negative perturbed feedback systems with the same amplitudes display a universal symmetry for regular graphs. Then, we describe an algorithm to construct a structural feedback system enabling the control of both synthetic and empirical networks. Our results improve the understanding of feedback in determining the control energy of dynamical systems, thus providing a potential way to devise new feedback control schemes.

We study stochastic resonance (SR) in a fractional harmonic oscillator with time delay and mass fluctuation. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are nonmonotonic. Using numerical simulations we verify the accuracy of the analytical result. We find (i) that the evolution of output amplitude versus the frequency of the external periodic force exhibits One-Peak SR and Two-Peaks SR, resonance region and resonance form largely depend on the noise correlation rate and noise intensity, (ii) that the evolution of output amplitude versus the noise intensity exhibits One-Peak SR and the increasing time delay lower the critical driving frequency, and (iii) that the evolution of output amplitude versus feedback gain performs diverse resonance forms, the increasing time delay widens the region for occurrence of SR and diversifies the resonance form.