There are intensive debates about whether heterogeneous networks promote prosocial behaviors such as fairness and cooperation. Theoretical models predict that network heterogeneity plays a positive role, but this prediction has not been validated by experiments. We reconcile this debate by conducting experiments with two-stage ultimatum games on networks. In the first stage, we identify responders with strong fairness preferences, referred to as leaders. In the second stage, when leaders occupy high-degree nodes in a heterogeneous network, their ability to motivate fairness among neighboring proposers is amplified, and collective fairness is facilitated. We propose an evolutionary game model and an agent-based simulation framework that capture the microscopic mechanisms underlying the networked experiments. Our experiments, model, and simulations suggest that network reciprocity is achievable but requires coordinated interactions between different prosocial inclinations of individuals and social network structures.

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.

As one of the most widespread social dynamics, cooperative behavior is among the most fascinating collective phenomena. Several animal species, from social insects to human beings, feature social groups altruistically working for a common benefit. This collaborative conduct pervades the actions and opinions of individuals, yielding strategic decision-making between political, religious, ethnic, and economic social puzzles. Here, we explore how cooperative behavior phenomena impact collective opinion dynamics and entropy generation in social groups. We select a random fraction f of community members as collaborative individuals and model the opinion dynamics using a social temperature parameter q that functions as a social anxiety noise. With probability q, regular individuals oppose their companions about a social decision, assuming group dissent. Collaborative agents experience a reduced effective social noise μq, where 0<μ<1 is the social anxiety noise sensibility parameter that enhances social validation. We perform numerical simulations and mean-field analysis and find the system undergoes nonequilibrium order–disorder phase transitions with expressive social entropy production. Our results highlight the effects of a social anxiety attenuation level in improving group consensus and the emergence of cooperative dynamics as a natural maximization of entropy production in noisy social groups, thus inducing exuberant collective phenomena in complex systems.

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.

Venture capital (VC) is a relatively newly emergent industry that is still subject to large uncertainties in China. Therefore, building a robust social network with other VC institutions is a good way to share information, various resources, and benefit from skill and knowledge complementarity to against risks. Strong evidences indicate that better networked VC institutions are of a better financial performance, however, most of previous works overlook the evolution of VC institutions and only focus on some simple topology indicators of the static syndication network, which also neglects higher-order network structure and cannot give a comprehensive evaluation. In this paper, based on VC investment records in the Chinese market, we construct temporal syndication networks between VC institutions year by year. As k-shell decomposition considers higher-order connection patterns, we employ k-shell as an evaluation of the influence of VC institutions in syndication networks. By clustering time series of k-shell values, the VC institutions in China fall into five groups that are quite different from each other on financial performances and investment behaviors. This, in turn, proves the power of our method that only based on proper sequential network properties, we can reveal their financial investment performance. Compared to other network centrality measurements, k-shell is a better indicator that is indicated by a smaller intra-group distance and a larger inter-group distance.

Network, direct and indirect reciprocity are three widely recognized mechanisms driving and sustaining cooperation, and each one of them is well understood when acting alone. However, these forms of reciprocity are barely found to be isolated from one another in the real circumstances, and it is still unclear which is the specific role played by each form of reciprocity works when they take action in parallel. With a unique data set from online societies, we find that direct and indirect reciprocity are actually moderated by network reciprocity. On the one hand, the cooperation boosting effect of direct and indirect reciprocity is stronger when subjects have more social connections, indicating that network reciprocity facilitates the formation of direct and indirect reciprocal interactions. On the other hand, this effect declines dramatically for upstream indirect reciprocity (also known as generalized reciprocity) and completely disappears for downstream indirect reciprocity (regarding reputation) when social connections are absent, indicating that social links is a pivotal factor in transmitting gratitude and building reputation. Our study deepens, therefore, the understanding of simultaneous effects of different mechanisms on the evolution of cooperation, and provides a fresh framework for empirically disentangling the factors of cooperative actions in real-world networks.

The thermodynamic properties of commonly used water pair-potentials (ST2, TIP4P, and SPC/E) are calculated from molecular dynamics simulations. In particular, the properties of supercooled and stretched states are found, yielding a determination of the equation of state (EOS) in this region for the metastable liquid. The ability of these models to reproduce the unique thermodynamic properties of water is confirmed. The calculated EOS does not exhibit a re-entrant liquid spinodal and also predicts that the line of density maxima in the phase diagram has a maximum in temperature T as a function of pressure P. In addition, an unexpected feature appears at lower T, in the form of an inflection in the liquid phase isotherms of P versus density ρ, suggesting that a critical point occurs in the liquid state phase diagram at low T. This critical point may be the end-point of a line of first-order phase transitions, separating two liquid phases of different density. We propose to relate these two liquid phases to the low and high density amorphous ices.

Optimal and efficient immunization of large networks remains a challenging task. Many theories and approaches have been suggested, however most of them require complete knowledge of the underlying network structure. Here, we study a targeted immunization strategy that incorporates the fact that there is often limited knowledge on the network structure. Previous work has suggested ‘acquaintance’ immunization, where rather than selecting a random individual to immunize, an individual is selected and then one of their acquaintances is immunized. Here, we generalize acquaintance immunization to the case where rather than selecting a random acquaintance, we examine the degrees of n acquaintances and immunize the one with the highest degree. We develop and solve an analytic framework for this model and verify our model with extensive numerical simulations. We determine the critical percolation threshold p c and the size of the giant component, P ∞ , for arbitrary degree distributions. We also consider our immunization strategy on real-world networks and determine the variation of p c with increasing n . We find that our new approach improves on both acquaintance immunization and random immunization using limited knowledge.

Wildfires, suspended soil and other particulates, and industrial emissions combine to raise the urgency of air quality as a planetary threat. This paper introduces Prometheus, a proactive decision-making framework for managing environmental and health risks associated with air pollution and climate change. The framework integrates causality analyses with data-driven methods, enabling the anticipation of consequences and proactive countermeasures for a variety of threats. The framework thus improves resilience to potential disasters and improves societal wellbeing by including scientific expertise and causality-driven analytics into policy making processes. A case demonstration with air pollution of Beijing, China, illustrates the features of the framework to address non-obvious and complex interactions of factors for a mega-region.

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.

The Social Internet of Things (SIoT), integration of the Internet of Things and Social Networks paradigms, has been introduced to build a network of smart nodes that are capable of establishing social links. In order to deal with misbehaving service provider nodes, service requestor nodes must evaluate their trustworthiness levels. In this paper, we propose a novel trust management mechanism in the SIoT to predict the most reliable service providers for each service requestor, which leads to reduce the risk of being exposed to malicious nodes. We model the SIoT with a flexible bipartite graph (containing two sets of nodes: service providers and service requestors), then build a social network among the service requestor nodes, using the Hellinger distance. Afterward, we develop a social trust model using nodes' centrality and similarity measures to extract trust behaviors among the social network nodes. Finally, a matrix factorization technique is designed to extract latent features of SIoT nodes, find trustworthy nodes, and mitigate the data sparsity and cold start problems. We analyze the effect of parameters in the proposed trust prediction mechanism on prediction accuracy. The results indicate that feedbacks from the neighboring nodes of a specific service requestor with high Hellinger similarity in our mechanism outperforms the best existing methods. We also show that utilizing the social trust model, which only considers a similarity measure, significantly improves the accuracy of the prediction mechanism. Furthermore, we evaluate the effectiveness of the proposed trust management system through a real-world SIoT use case. Our results demonstrate that the proposed mechanism is resilient to different types of network attacks, and it can accurately find the most proper and trustworthy service provider.

Since the outbreak of the coronavirus disease 2019 (COVID-19) pandemic, the international medical device trade has received extensive attention. To maintain the domestic supply of medical devices, some countries have sought multilateral trade cooperation or simply implemented export restrictions, which has exacerbated the instability and fragility of the global medical device market. It is crucial for government policymakers to identify the most influential countries in the international medical device trade and nip exports in the bud. However, few efforts have been made in previous studies to explore various countries' influence on the international medical device trade in light of their intricate trade relationships. To fill these research gaps, this study constructs a global medical device trade network (GMDTN) and explores the criticality of various countries from a network-based perspective. The evolution patterns and geographical distribution of influence among countries in the GMDTN are revealed. Details on the ways in which the influence of some crucial countries has formed are provided. The results show that the global medical device trade market is export oriented. The formation of some countries' strong influence may be due to their large number of trading partners or the deep dependence of some of those trading partners on that country (namely, breadth- or depth-based patterns). It is worth noting that the US has a dominant position in the international medical device trade in terms of both breadth and depth. In addition, some countries play a critical role as intermediate points in the influence formation process of other countries, although these countries are not critical direct trading partners. The findings of this study provide implications for policymakers seeking to understand the influence of countries on the international medical device trade and to proactively prepare responses to unexpected changes in this trade.

Swarm intelligence occurs when the collective behavior of low-level individuals and their local interactions form an overall pattern of uniform function. Incorporating swarm intelligence allows us to disregard global models when we explore collective cooperation systems that lack any central control. Blockchain is a key technology in the functioning of Bitcoin and combines network and cryptographic algorithms. A group of agents agrees on a particular status and records the protocol without controlling it. Blockchain and other distributed systems, such as ant colony systems, allow the building of “ants” that are more secure, flexible, and successful. We use the principle of blockchain technology and carry out ant colony research to solve three urgent problems. We use new security protocols, system implementations, and business models to generate ant swarm system scenarios. Finally we combine these two technologies to solve the problems of limitation and reduced future potential. Our work opens the door to new business models and approaches that allow ant colony technologies to be applied to a wide range of market applications.

We investigate the financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize the individuals in a financial market by their trading strategy, namely noise traders and fundamentalists. The opinion of a local majority compels the market exchanging behavior of noise traders, whereas the global behavior of the market influences the fundamentalist agents' decisions. We introduce a noise parameter $q$ to represent a level of anxiety and perceived uncertainty regarding the market behavior, enabling the possibility for an adrift financial action. We place the individuals as nodes in an Erd\"os-R\'enyi random graph, where the links represent their social interaction. At a given time, they assume one of two possible opinion states $\pm 1$ regarding buying or selling an asset. The model exhibits such fundamental qualitative and quantitative real-world market features as the distribution of logarithmic returns with fat-tails, clustered volatility, and long-term correlation of returns. We use Student's t distributions to fit the histograms of logarithmic returns, showing the gradual shift from a leptokurtic to a mesokurtic regime, depending on the fraction of fundamentalist agents. We also compare our results with the distribution of logarithmic returns of several real-world financial indices.

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 [Formula: see text], as well as the standard critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] 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.

The number of available control sources is a limiting factor to many network control tasks. A lack of input sources can result in compromised controllability and/or sub-optimal network performance, as noted in engineering applications such as the smart grids. The mechanism can be explained by a linear time-invariant model, where structural controllability sets a lower bound on the number of required sources. Inspired by the ubiquity of time-varying topologies in the real world, we propose the strategy of spatiotemporal input control to overcome the source-related limit by exploiting temporal variation of the network topology. We theoretically prove that under this regime, the required number of sources can always be reduced to 2. It is further shown that the cost of control depends on two hyperparameters, the numbers of sources and intervals, in a trade-off fashion. As a demonstration, we achieve controllability over a complex network resembling the nervous system of Caenorhabditis elegans using as few as 6% of the sources predicted by a static control model. This example underlines the potential of utilizing topological variation in complex network control problems.

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a tipping point, such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.

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.

The Special Issue comes out in the increasing accumulation of negative global tensions in many areas [...].

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.