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Complex networked systems, which range from biological systems in the natural world to infrastructure systems in the human-made world, can exhibit spontaneous recovery after a failure; for example, a brain may spontaneously return to normal after a seizure, and traffic flow can become smooth again after a jam. Previous studies on the spontaneous recovery of dynamical networks have been limited to undirected networks. However, most real-world networks are directed. To fill this gap, we build a model in which nodes may alternately fail and recover, and we develop a theoretical tool to analyze the recovery properties of directed dynamical networks. We find that the tool can accurately predict the final fraction of active nodes, and the prediction accuracy decreases as the fraction of bidirectional links in the network increases, which emphasizes the importance of directionality in network dynamics. Due to different initial states, directed dynamical networks may show alternative stable states under the same control parameter, exhibiting hysteresis behavior. In addition, for networks with finite sizes, the fraction of active nodes may jump back and forth between high and low states, mimicking repetitive failure-recovery processes. These findings could help clarify the system recovery mechanism and enable better design of networked systems with high resilience.

Abstract Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data.

Abstract Currently, the global situation of COVID-19 is aggravating, pressingly calling for efficient control and prevention measures. Understanding the spreading pattern of COVID-19 has been widely recognized as a vital step for implementing non-pharmaceutical measures. Previous studies explained the differences in contagion rates due to the urban socio-political measures, while fine-grained geographic urban spreading pattern still remains an open issue. Here, we fill this gap by leveraging the trajectory data of 197,808 smartphone users (including 17,808 anonymous confirmed cases) in nine cities in China. We find a general spreading pattern in all cities: the spatial distribution of confirmed cases follows a power-law-like model and the spreading centroid human mobility is time-invariant. Moreover, we reveal that long average traveling distance results in a high growth rate of spreading radius and wide spatial diffusion of confirmed cases in the fine-grained geographic model. With such insight, we adopt the Kendall model to simulate the urban spreading of COVID-19 which can well fit the real spreading process. Our results unveil the underlying mechanism behind the spatial-temporal urban evolution of COVID-19, and can be used to evaluate the performance of mobility restriction policies implemented by many governments and to estimate the evolving spreading situation of COVID-19.

Abstract In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

Research on clustering spatio-temporal data to extract mobility patterns requires further development, as most existing studies do not simultaneously integrate data along both spatial dimensions and temporal dimensions but instead focus on only one dimension or separate the dimensions in analyses and applications, which could lead to discoveries that are not representative of the overall data or are dificult to interpret. To simultaneously reveal the spatial and temporal patterns of urban mobility datasets, we propose an analytical framework that is based on co-clustering and enables mobility behaviors to be distinguished in spatial and temporal dimensions. We use one month of taxi GPS data from the Manhattan area to explore spatio-temporal co-occurrence patterns. The spatial and temporal dimensions of taxi trip data were co-clustered by using the Bregman Block Average co-clustering algorithm with I-divergence (BBAC_I). We performed this process on weekdays and holidays and compared the mobility differences between these two periods. The experimental results demonstrated the effectiveness of this analytical framework, with which we can reveal the spatial patterns and their temporal dynamics as well as temporal patterns and their spatial dynamics in mobility data.

Cities are centers for the integration of capital and incubators of inventions. Attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and prosperous future. Yet we still lack a quantitative understanding of the relationship between urban characteristics and VC activities. In this paper, we find a clear nonlinear scaling relationship between VC activities and the urban population of Chinese cities. In such nonlinear systems, the widely applied linear per capita indicators would be either biased to larger cities or smaller cities depends on whether it is superlinear or sublinear, while the residual of cities relative to the prediction of scaling law is a more objective and scale-invariant metric. Such a metric can distinguish the effects of local dynamics and scaled growth induced by the change of population size. The spatiotemporal evolution of such metrics on VC activities reveals three distinct groups of cities, two of which stand out with increasing and decreasing trends, respectively. The taxonomy results together with spatial analysis also signify different development modes between large urban agglomeration regions. Besides, we notice the evolution of scaling exponents on VC activities are of much larger fluctuations than on socioeconomic output of cities, and a conceptual model that focuses on the growth dynamics of different sized cities can well explain it, which we assume would be general to other scenarios.

Abstract Recent studies have shown that online users tend to select information that adheres to their system of beliefs, ignore information that does not, and join groups that share a common narrative. This information environment can elicit tribalism instead of informed debate, especially when issues are controversial. Algorithmic solutions, fact-checking initiatives, and many other approaches have shown limitations in dealing with this phenomenon, and heated debate and polarization still play a pivotal role in online social dynamics (e.g. traditional vs. anti-establishment polarization). To understand the effect of different communication strategies able to smooth polarization, in this paper, together with Corriere della Sera, a major Italian news outlet, we measure the social response of users to different types of news framing. We analyse users’ reactions to 113 ad-hoc articles published on the newspaper’s Facebook page and the corresponding news articles on the topic of migration, published from March to December 2018. We examine different journalistic techniques and content types by analyzing their impact on user comments in terms of toxicity, criticism of the newspaper, and stance concerning migration. We find that visual pieces and factual news reports elicit the highest level of trust in the media source, while opinion pieces and editorials are more likely to be criticized. We also notice that data-driven pieces elicit an extremely low level of trust in the news source. Furthermore, coherently with the echo chambers behaviour, we find social conformity strongly affecting the commenting behaviour of users on Facebook.

We investigate via numerical simulations of the TIP4P/Ice model the isothermal decompression of high density amorphous ice (HDA) mirroring the experimental protocol followed by recent experiments [H. K. Kim, et al., Science 370, 978, 2020]. Taking advantage of the recent determination of the TIP4P/Ice liquid-liquid critical point, we decompress our samples at temperatures both below and above the critical temperature. We follow the crossover between high and low density, complementing the time evolution of the structure factor with the time evolution of microscopic descriptors. Our results support the interpretation of the experimental pathway as a structural change from high to low density states through a first-order transition line. In the simulation study we do not observe nucleation events, but rather a spinodal-like non-equilibrium transformation, which offers an explanation on why the decompression process even at sub-critical temperatures may result in a continuous time evolution of the density and of the microscopic descriptors.

Abstract We use the recently-proposed compressible cell Ising-like model to estimate the ratio between thermal expansivity and specific heat (the Grüneisen parameter Γ s ) in supercooled water. Near the critical pressure and temperature, Γ s becomes significantly sensitive to thermal fluctuations of the order-parameter, a characteristic behavior of pressure-induced critical points. Such enhancement of Γ s indicates that two energy scales are governing the system, namely the coexistence of high- and low-density liquids, which become indistinguishable at the critical point in the supercooled phase. The temperature dependence of the compressibility, sound velocity and pseudo-Grüneisen parameter Γ w are also reported. Our findings support the proposed liquid-liquid critical point in supercooled water in the No-Man’s Land regime, and indicates possible applications of this model to other systems. In particular, an application of the model to the qualitative behavior of the Ising-like nematic phase in Fe-based superconductors is also presented.

How does a scientist’s tendency to explore a variety of topics affect their career? Here, the authors analyze scientific publication data to understand how often scientists switch topics, how topic switching has changed over time, and how it relates to research productivity.

The spread of flood-induced failures in critical infrastructure systems is understudied. Here the authors apply the CaMa-Flood global river flood simulation model to estimate the flood-induced failures and their spread in China and the US and find that the number of flood-induced total failures is in-between that of random and localized damage given the same intensity.

The shipping market, a major component of the global economy, is characterized by high risk and volatility. The Baltic dry index is an influential indicator in the world shipping market and international trade. Several studies have used a variety of techniques to generate Baltic dry index predictions. The most prominent techniques utilize either econometric or artificial intelligence computing. We compare the forecasting accuracy of two typical univariant econometric models and three artificial neural networks (ANNs)-based algorithms. We find that when using daily data, econometric forecasting models produce better one-step-ahead predictions than ANN-based algorithms. When forecasting weekly and monthly data, ANN-based algorithms produce fewer errors and a higher direction matching rate than econometric models. We also compare the predictive power of a number of different models when applied to the 2008 financial crisis and find that the generalized autoregressive conditional heteroskedasticity model and the back propagation neural network algorithm produce the best one-step-ahead and seven-steps ahead predictions, respectively.

Different from numerical attributes, measuring the similarity between categorical attributes is more complex due to their non-inherently ordered characteristic, especially in an unsupervised scheme. This work, therefore, presents a new method, Heterogeneous Graph-based Similarity measure (HGS), to measure the similarity between categorical data for unsupervised learning. In order to capture the possible complex relationships hidden among attributes, a heterogeneous weighted graph is creatively constructed by extracting the information from categorical data. Both objects and attribute values are represented as nodes and their occurrence and co-occurrence relationships are shown as edges. Based on a derived node-pair graph, three rules are used to iteratively update the similarity scores between object pairs and attribute-value pairs until the scores converge. We also analyze its complexities and validate the metric properties and convergence. In experiment validation, five state-of-the-art measures are compared with HGS based on 20 UCI datasets and 6 high-dimensional datasets in the medical domain in both k-modes and spectral clustering and similarity search experiments. The results show although no measure can outperform all other measures on all datasets, HGS can perform better in both clustering and similarity search tasks on the whole. Finally, six studies further discuss the convergence, time cost, and parameter sensitivity of the HGS, explore its application to imbalanced class distribution, and compare it with its variants by different initialization and graph construction.

Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics of market returns also exhibit calendar anomalies such as day-of-the-week effects. We apply multifractal detrended fluctuation analysis (MF-DFA) to the daily returns of market indices worldwide for each day of the week. Our results indicate that distinct multifractal properties characterize individual days of the week. Monday returns tend to exhibit more persistent behavior and richer multifractal structures than other day-resolved returns. Shuffling the series reveals that multifractality arises from a broad probability density function and long-term correlations. The time-dependent multifractal analysis shows that the Monday returns’ multifractal spectra are much wider than those of other days. This behavior is especially persistent during financial crises. The presence of day-of-the-week effects in multifractal dynamics of market returns motivates further research on calendar anomalies for distinct market regimes.

Abstract Determining the core structure of complex network systems allows us to simplify them. Using h-bridge and h-strength measurements in a weighted network, we extract the h-backbone core structure. We find that focusing on the h-backbone in a network allows greater simplification because it has fewer edges and thus fewer adjacent nodes. We examine three practical applications: the co-citation network in an information system, the open flight network in a social system, and coauthorship in network science publications.

Abstract Research on social contagion dynamics has not yet included a theoretical analysis of the ubiquitous local trend imitation (LTI) characteristic. We propose a social contagion model with a tent-like adoption probability to investigate the effect of this LTI characteristic on behavior spreading. We also propose a generalized edge-based compartmental theory to describe the proposed model. Through extensive numerical simulations and theoretical analyses, we find a crossover in the phase transition: when the LTI capacity is strong, the growth of the final adoption size exhibits a second-order phase transition. When the LTI capacity is weak, we see a first-order phase transition. For a given behavioral information transmission probability, there is an optimal LTI capacity that maximizes the final adoption size. Finally we find that the above phenomena are not qualitatively affected by the heterogeneous degree distribution. Our suggested theoretical predictions agree with the simulation results.

Cities can be treated as dynamic complex systems being controlled by the interactions among people, whilst the detail remains largely unknown. Li et al. use spatial attraction together with matching growth to unify population, roads, and socioeconomic interactions crossing ten representative cities.

Abstract Understanding the spreading mechanisms of social contagions in complex network systems has attracted much attention in the physics community. Here we propose a generalized threshold model to describe social contagions. Using extensive numerical simulations and theoretical analyses, we find that a hysteresis loop emerges in the system. Specifically, the steady state of the system is sensitive to the initial conditions of the dynamics of the system. In the steady state, the adoption size increases discontinuously with the transmission probability of information about social contagions, and trial size exhibits a non-monotonic pattern, i.e., it first increases discontinuously then decreases continuously. Finally we study social contagions on heterogeneous networks and find that network topology does not qualitatively affect our results.

Systems composed of many interacting dynamic networks exhibit complicated collective dynamics. Here, the authors study failure, damage spread and recovery in two interacting networks, constructing the phase diagram and revealing the role of triple points for optimal damage repair.

Identifying influential nodes in networks is important for the understanding of their structure and function, but there are several so far unrelated measures to assess this. Here, the authors unfold relations among knows criteria and construct a family of indices that interpolate between degree and coreness.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Most network research studying the robustness of critical infrastructure networks focuses on a particular aspect and does not take the entire system into consideration. We develop a general methodological framework for studying network robustness from multiple perspectives, i.e., Robustness assessment based on percolation theory, vulnerability analysis, and controllability analysis. Meanwhile, We use this approach to examine the Shanghai subway network in China. Specifically, (1) the topological properties of the subway network are quantitatively analyzed using network theory; (2) The phase transition process of the subway network under both random and deliberate attacks are acquired (3) Critical dense areas that are most likely to be the target of terrorist attacks are identified, vulnerability values of these critical areas are obtained; (4) The minimum number of driver nodes for controlling the whole network is calculated. Results show that the subway network exhibits characteristics similar to a scale-free network with low robustness to deliberate attacks. Meanwhile, we identify the critical area within which disruptions produce large performance losses. Our proposed method can be applied to other infrastructure networks and can help decision makers develop optimal protection strategies.

In complex systems, statistical dependencies between individual components are often considered one of the key mechanisms which drive the system dynamics observed on a macroscopic level. In this paper, we study cross-sectional time-lagged dependencies in financial markets, quantified by nonparametric measures from information theory, and estimate directed temporal dependency networks in financial markets. We examine the emergence of strongly connected feedback components in the estimated networks, and hypothesize that the existence of information feedback in financial networks induces strong spatiotemporal spillover effects and thus indicates systemic risk. We obtain empirical results by applying our methodology on stock market and real estate data, and demonstrate that the estimated networks exhibit strongly connected components around periods of high volatility in the markets. To further study this phenomenon, we construct a systemic risk indicator based on the proposed approach, and show that it can be used to predict future market distress. Results from both the stock market and real estate data suggest that our approach can be useful in obtaining early-warning signals for crashes in financial markets.

Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics schemes, especially the continuous-time quantum walk. Difficulty exists, however, in producing closed-form solutions with controllable accuracy against the complexity of memory kernels. Here, we introduce a new multiple-scale perturbation method that works on integro-differential equations for general study of memory effects in dynamical systems. We propose an open-system model in which a continuous-time quantum walk is enclosed in a non-Markovian reservoir, that naturally corresponds to an error correction algorithm scheme. By applying the multiple-scale method we show how emergence of different timescales is related to transition of system dynamics into the non-Markovian regime. We find that up to two long-term modes and two short-term modes exist in regular networks, limited by their intrinsic symmetries. In addition to the effective approximation by our perturbation method on general forms of reservoirs, the speed-up of quantum walks assisted by non-Markovianity is also confirmed, revealing the advantage of reservoir engineering in designing time-sensitive quantum algorithms.

We study the annual growth rates of six macroeconomic variables: public debt, public health expenditures, exports of goods, government consumption expenditures, total exports of goods and services, and total imports of goods and services. For each variable, we find (i) that the distribution of the growth rate residuals approximately follows a double exponential (Laplace) distribution and (ii) that the standard deviation of growth rate residuals scales according to the size of the variable as a power law, with a scaling exponent similar to the scaling exponent found for GDP [Economics Letters 60, 335 (1998)]. We hypothesise that the volatility scaling we find for these GDP constituents causes the volatility scaling found in GDP data.

We analyze the daily returns of stock market indices and currencies of 56 countries over the period of 2002–2012. We build a network model consisting of two layers, one being the stock market indices and the other the foreign exchange markets. Synchronous and lagged correlations are used as measures of connectivity and causality among different parts of the global economic system for two different time intervals: non-crisis (2002–2006) and crisis (2007–2012) periods. We study community formations within the network to understand the influences and vulnerabilities of specific countries or groups of countries. We observe different behavior of the cross correlations and communities for crisis vs. non-crisis periods. For example, the overall correlation of stock markets increases during crisis while the overall correlation in the foreign exchange market and the correlation between stock and foreign exchange markets decrease, which leads to different community structures. We observe that the euro, while being central during the relatively calm period, loses its dominant role during crisis. Furthermore we discover that the troubled Eurozone countries, Portugal, Italy, Greece and Spain, form their own cluster during the crisis period.