Assistant Professor
Rensselaer Polytechnic Institute, Department of Computer Science and Center for Network Science and Technology
I am an assistant professor at the Department of Computer Science and Center for Network Science and Technology at Rensselaer Polytechnic Institute (RPI). Prior to joining the Department of Computer Science at RPI, I was a Research Assistant Professor at the Center for Complex Network Research at Northeastern University from 2012, working with Prof. Albert-László Barabási. I got my Ph. D. degree in the Department of Automation at Shanghai Jiao Tong University from 2008 to 2012.
During my Ph.D. from 2009 to 2012 I visited Prof. H. Eugene. Stanley in Physics department at Boston University, as well as Prof. Shlomo Havlin in Physics department at Bar-IlanUniversity in 2012.
My major contribution includes the theory for robustness of networks of networks and resilience of complex networks. Since 2010, I has published over 20 papers on journals, such as Nature, Nature Physics, Nature Communications, Proceedings of the National Academy of Sciences, Physical Review Letters and more, with over 1,400 citations on Google Scholar. I have been selected as the Editor board of Nature Scientific Reports, distinguished referee of EPL (2014-2016) and Elsevier (2016), and referee of Science, PNAS, PRL, PRX and more. His publications were reported over 20 times by international public and professional media.
Rensselaer Polytechnic Institute, Department of Computer Science and Center for Network Science and Technology
Northeastern University, Center for Complex Network Research
Northeastern University, Center for Complex Network Research
Bar-Ilan University, Department of Physics
Boston University, Department of Physics
Shanghai Jiao Tong University, Intelligent Information Control Lab
Ph.D. in Control Theory and Control Engineering
Shanghai Jiao Tong University, Shanghai, China
Master of Control Theory and Control Engineering
Shanghai Jiao Tong University, Shanghai, China
Bachelor of Science in Process Equipment and Control
Dalian University of Technology, Dalian, China
Network Resilience - Resilience, a system’s ability to adjust its activity to retain its basic functionality under errors, failures and environmental changes, is a defining property of many complex systems. Despite widespread consequences for human health, economy and the environment, events leading to loss of resilience, from cascading failures in technological systems to mass extinctions in ecological networks, are rarely predictable and are often irreversible. These limitations are rooted in a theoretical gap: the current analytical framework of resilience uses low dimensional models of a few interacting components to characterize multi-dimensional systems consisting of a large number of components that interact through a complex network. Here I discuss the results that bridge this theoretical gap. To do we develop a set of analytical tools to identify the natural control and state parameters of a multi-dimensional complex system, helping us derive an effective one dimensional dynamics that accurately predicts the system’s resilience. The proposed analytical framework allows us to systematically separate the role of the system’s dynamics and topology, collapsing the behavior of different networks onto a single universal resilience function. The analytical results unveil the network characteristics that can enhance or diminish resilience, offering avenues to prevent the collapse of ecological, biological or economic systems, and guiding the design of technological systems that are resilient to external perturbations and environmental changes alike.
Network Robustness - The interdisciplinary field of network science has attracted a remarkable degree of attention in recent years. I have developed a general theoretical framework for analyzing the robustness of and cascading failures in network of networks (NONs). The results of NONs have been surprisingly rich, and they differ so greatly from those of single networks that they present a new paradigm. Increasing evidence shows that diverse critical infrastructures interact with each other, such as water and food supply, communications, fuel, financial transactions and power stations. For example, the electric power network provides power for pumping and for controlling the systems of the water network; the water network provides water for the cooling and emissions reduction of the power network; the fuel network provides fuel for generators in the electric power network; the electric power network provides power to pump oil in the fuel network, etc. The interdependence between networks can dramatically increase the vulnerability of the system, since the failure of nodes in one network may lead to the failure of dependent nodes in other networks, and this may happen recursively and lead to a cascade of failures and system collapse. For example, electrical blackouts that affect large regions are usually the result of cascading failures between interdependent communication network and the power grid.
Network Control - We will know that we understand the dynamics of complex networks when we reach the point that we can control them and determine the conditions under which the dynamics of a network can be driven from any initial state to any desired final state within a finite amount of time. In engineered systems (e.g. the auto-pilot system of an airplane) full control is essential, but the massive size and complexity of many biological, technological, and social systems make their full control neither feasible nor necessary. In these cases it is more realistic to achieve target control, i.e. to control the subset or subsystem of target nodes that enable a system to carry out its designated task. I have developed an alternative ``k-walk'' theory for directed tree networks, and have rigorously proven that one node can control a set of target nodes if the path length to each target node is unique. I have also proposed a novel "greedy'' algorithm for approximating the minimum set of driver nodes sufficient for target control. By applying the greedy algorithm to a wide range of real-world networks including gene regulatory, trust, power grid, metabolic, electronic circuits, neuronal, and food webs, I found that degree heterogeneous networks are target controllable with a higher efficiency than degree homogeneous networks. I also found that the structure of the power grid is not optimized for local target control compared with neuronal networks. Finally, I validate my algorithm on 4 gene regulatory networks, 2 trust networks, 4 food webs, 1 power grid, 3 metabolic networks, 3 electronic networks and 2 neuronal networks.
Here you will be able to sort and find all of my publications, including journal papers, chinese papers, books & book chapters, invited talks & conference talks.
Almost all real-world social networks are dynamic and evolving with time, where new links may form and old links may drop, largely determined by the homophily of social actors (i.e., nodes in the network). Meanwhile, (latent) properties of social actors, such as their opinions, are changing along the time, partially due to social influence received from the network, which will in turn affect the network structure. Social network evolution and node property migration are usually treated as two orthogonal problems, and have been studied separately. In this paper, we propose a co-evolution model that closes the loop by modeling the two phenomena together, which contains two major components: (1) a network generative model when the node property is known; and (2) a property migration model when the social network structure is known. Simulation shows that our model has several nice properties: (1) it can model a broad range of phenomena such as opinion convergence (i.e., herding) and community-based opinion divergence; and (2) it allows us control the evolution via a set of factors such as social influence scope, opinion leader, and noise level. Finally, the usefulness of our model is demonstrated by an application of co-sponsorship prediction for legislative bills in Congress, which outperforms several state-of-the-art baselines.
When controlling a complex networked system it is not feasible to control the full network because many networks, including biological, technological, and social systems, are massive in size and complexity. But neither is it necessary to control the full network. In complex networks, the giant connected components provide the essential information about the entire system. How to control these giant connected components of a network remains an open question. We derive the mathematical expression of the degree distributions for four types of giant connected components and develop an analytic tool for studying the controllability of these giant connected components. We find that for both Erdős-Rényi (ER) networks and scale-free (SF) networks with p fraction of remaining nodes, the minimum driver node density to control the giant component first increases and then decreases as p increases from zero to one, showing a peak at a critical point p = p_m. We find that, for ER networks, the peak value of the driver node density remains the same regardless of its average degree ⟨k⟩ and that it is determined by p_m⟨k⟩. In addition, we find that for SF networks the minimum driver node densities needed to control the giant components of networks decrease as the degree distribution exponents increase. Comparing the controllability of the giant components of ER networks and SF networks, we find that when the fraction of remaining nodes p is low, the giant in-connected, out-connected, and strong-connected components in ER networks have lower controllability than those in SF networks.
Resilience, a system’s ability to adjust its activity to retain its basic functionality when errors, failures and environmental changes occur, is a defining property of many complex systems1. Despite widespread consequences for human health2, the economy3 and the environment4, events leading to loss of resilience—from cascading failures in technological systems5 to mass extinctions in ecological networks6—are rarely predictable and are often irreversible. These limitations are rooted in a theoretical gap: the current analytical framework of resilience is designed to treat low-dimensional models with a few interacting components7, and is unsuitable for multi-dimensional systems consisting of a large number of components that interact through a complex network. Here we bridge this theoretical gap by developing a set of analytical tools with which to identify the natural control and state parameters of a multi-dimensional complex system, helping us derive effective one-dimensional dynamics that accurately predict the system’s resilience. The proposed analytical framework allows us systematically to separate the roles of the system’s dynamics and topology, collapsing the behaviour of different networks onto a single universal resilience function. The analytical results unveil the network characteristics that can enhance or diminish resilience, offering ways to prevent the collapse of ecological, biological or economic systems, and guiding the design of technological systems resilient to both internal failures and environmental changes.
Increasing evidence shows that real-world systems interact with one another via dependency connectivities. Failing connectivities are the mechanism behind the breakdown of interacting complex systems, e.g., blackouts caused by the interdependence of power grids and communication networks. Previous research analyzing the robustness of interdependent networks has been limited to undirected networks. However, most real-world networks are directed, their in-degrees and out-degrees may be correlated, and they are often coupled to one another as interdependent directed networks. To understand the breakdown and robustness of interdependent directed networks, we develop a theoretical framework based on generating functions and percolation theory. We find that for interdependent Erdős–Rényi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions. We also find that the percolation behavior of interdependent directed scale-free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness: the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correlations, confirming our theoretical analysis.
In a cyber war game where a network is fully distributed and characterized by resource constraints and high dynamics, attackers or defenders often face a situation that may require optimal strategies to win the game with minimum effort. Given the system goal states of attackers and defenders, we study what strategies attackers or defenders can take to reach their respective system goal state (i.e., winning system state) with minimum resource consumption. However, due to the dynamics of a network caused by a node’s mobility, failure or its resource depletion over time or action(s), this optimization problem becomes NP-complete. We propose two heuristic strategies in a greedy manner based on a node’s two characteristics: resource level and influence based on k-hop reachability. We analyze complexity and optimality of each algorithm compared to optimal solutions for a small-scale static network. Further, we conduct a comprehensive experimental study for a large-scale temporal network to investigate best strategies, given a different environmental setting of network temporality and density. We demonstrate the performance of each strategy under various scenarios of attacker/defender strategies in terms of win probability, resource consumption, and system vulnerability.
Many complex systems in the real world can be modeled as complex networks, which has captured in recent years enormous attention from researchers of diverse fields ranging from natural sciences to engineering. The extinction of species in ecosystems and the blackouts of power girds in engineering exhibit the vulnerability of complex networks, investigated by empirical data and analyzed by theoretical models. For studying the resilience of complex networks, three main factors should be focused on: the network structure, the network dynamics and the failure mechanism. In this review, we will introduce recent progress on the resilience of complex networks based on these three aspects. For the network structure, increasing evidence shows that biological and ecological networks are coupled with each other and that diverse critical infrastructures interact with each other, triggering a new research hotspot of “networks of networks” (NON), where a network is formed by interdependent or interconnected networks. The resilience of complex networks is deeply influenced by its interdependence with other networks, which can be analyzed and predicted by percolation theory. This review paper shows that the analytic framework for NON yields novel percolation laws for n interdependent networks and also shows that the percolation theory of a single network studied extensively in physics and mathematics in the last 60 years is a specific limited case of the more general case of n interacting networks. Due to spatial constraints inherent in critical infrastructures, including the power gird, we also review the progress on the study of spatially-embedded interdependent networks, exhibiting extreme vulnerabilities compared to their non-embedded counterparts, especially in the case of localized attack. For the network dynamics, we illustrate the percolation framework and methods using an example of a real transportation system, where the analysis based on network dynamics is significantly different from the structural static analysis. For the failure mechanism, we here review recent progress on the spontaneous recovery after network collapse. These findings can help us to understand, realize and hopefully mitigate the increasing risk in the resilience of complex networks.
Collective motions of animals that move towards the same direction is a conspicuous feature in nature. Such groups of animals are called a self-propelled agent (SPA) systems. Many studies have been focused on the synchronization of isolated SPA systems. In real scenarios, different SPA systems are coupled with each other forming a network of SPA systems. For example, a flock of birds and a school of fish show predator-prey relationships and different groups of birds may compete for food. In this work, we propose a general framework to study the collective motion of coupled self-propelled agent systems. Especially, we study how three different connections between SPA systems: symbiosis, predator-prey, and competition influence the synchronization of the network of SPA systems. We find that a network of SPA systems coupled with symbiosis relationship arrive at a complete synchronization as all its subsystems showing a complete synchronization; a network of SPA systems coupled by predator-prey relationship can not reach a complete synchronization and its subsystems converges to different synchronized directions; and the competitive relationship between SPA systems could increase the synchronization of each SPA systems, while the network of SPA systems coupled by competitive relationships shows an optimal synchronization for small coupling strength, indicating that small competition promotes the synchronization of the entire system.
Network science is a highly interdisciplinary field ranging from natural science to engineering technology and it has been applied to model complex systems and used to explain their behaviors. Most previous studies have been focus on isolated networks, but many real-world networks do in fact interact with and depend on other networks via dependency connectivities, forming “networks of networks” (NON). The interdependence between networks has been found to largely increase the vulnerability of interacting systems, when a node in one network fails, it usually causes dependent nodes in other networks to fail, which, in turn, may cause further damage on the first network and result in a cascade of failures with sometimes catastrophic consequences, e.g., electrical blackouts caused by the interdependence of power grids and communication networks. The vulnerability of a NON can be analyzed by percolation theory that can be used to predict the critical threshold where a NON collapses. We review here the analytic framework for analyzing the vulnerability of NON, which yields novel percolation laws for n-interdependent networks and also shows that percolation theory of a single network studied extensively in physics and mathematics in the last 50 years is a specific limited case of the more general case of n interacting networks. Understanding the mechanism behind the cascading failure in NON enables us finding methods to decrease the vulnerability of the natural systems and design of more robust infrastructure systems. By examining the vulnerability of NON under targeted attack and studying the real interdependent systems, we find two methods to decrease the systems vulnerability: (1) protect the high-degree nodes, and (2) increase the degree correlation between networks. Furthermore, the ultimate proof of our understanding of natural and technological systems is reflected in our ability to control them. We also review the recent studies and challenges on the controllability of networks and temporal networks.
Complex networks appear in almost every aspect of science and technology. Previous work in network theory has focused primarily on analyzing single networks that do not interact with other networks, despite the fact that many real-world networks interact with and depend on each other. Very recently an analytical framework for studying the percolation properties of interacting networks has been introduced. Here we review the analytical framework and the results for percolation laws for a network of networks (NON) formed by nn interdependent random networks. The percolation properties of a network of networks differ greatly from those of single isolated networks. In particular, although networks with broad degree distributions, e.g., scale-free networks, are robust when analyzed as single networks, they become vulnerable in a NON. Moreover, because the constituent networks of a NON are connected by node dependencies, a NON is subject to cascading failure. When there is strong interdependent coupling between networks, the percolation transition is discontinuous (is a first-order transition), unlike the well-known continuous second-order transition in single isolated networks. We also review some possible real-world applications of NON theory.
Complex networks appear in almost every aspect of science and technology. Previous work in network theory has focused primarily on analyzing single networks that do not interact with other networks, despite the fact that many real-world networks interact with and depend on each other. Very recently an analytical framework for studying the percolation properties of interacting networks has been introduced. Here we review the analytical framework and the results for percolation laws for a Network Of Networks (NONs) formed by n interdependent random networks. The percolation properties of a network of networks differ greatly from those of single isolated networks. In particular, because the constituent networks of a NON are connected by node dependencies, a NON is subject to cascading failure. When there is strong interdependent coupling between networks, the percolation transition is discontinuous (first-order) phase transition, unlike the well-known continuous second-order transition in single isolated networks. Moreover, although networks with broader degree distributions, e.g., scale-free networks, are more robust when analyzed as single networks, they become more vulnerable in a NON. We also review the effect of space embedding on network vulnerability. It is shown that for spatially embedded networks any finite fraction of dependency nodes will lead to abrupt transition.
Controlling large natural and technological networks is an outstanding challenge. It is typically neither feasible nor necessary to control the entire network, prompting us to explore target control: the efficient control of a preselected subset of nodes. We show that the structural controllability approach used for full control overestimates the minimum number of driver nodes needed for target control. Here we develop an alternate ‘k-walk’ theory for directed tree networks, and we rigorously prove that one node can control a set of target nodes if the path length to each target node is unique. For more general cases, we develop a greedy algorithm to approximate the minimum set of driver nodes sufficient for target control. We find that degree heterogeneous networks are target controllable with higher efficiency than homogeneous networks and that the structure of many real-world networks are suitable for efficient target control.
Network science has attracted much attention in recent years due to its interdisciplinary applications. We witnessed the revolution of network science in 1998 and 1999 started with small-world and scale-free networks having now thousands of high-profile publications, and it seems that since 2010 studies of ‘network of networks’ (NON), sometimes called multilayer networks or multiplex, have attracted more and more attention. The analytic framework for NON yields a novel percolation law for n interdependent networks that shows that percolation theory of single networks studied extensively in physics and mathematics in the last 50 years is a specific limit of the rich and very different general case of n coupled networks. Since then, properties and dynamics of interdependent and interconnected networks have been studied extensively, and scientists are finding many interesting results and discovering many surprising phenomena. Because most natural and engineered systems are composed of multiple subsystems and layers of connectivity, it is important to consider these features in order to improve our understanding of such complex systems. Now the study of NON has become one of the important directions in network science. In this paper, we review recent studies on the new emerging area—NON. Due to the fast growth of this field, there are many definitions of different types of NON, such as interdependent networks, interconnected networks, multilayered networks, multiplex networks and many others. There exist many datasets that can be represented as NON, such as network of different transportation networks including flight networks, railway networks and road networks, network of ecological networks including species interacting networks and food webs, network of biological networks including gene regulation network, metabolic network and protein–protein interacting network, network of social networks and so on. Among them, many interdependent networks including critical infrastructures are embedded in space, introducing spatial constraints. Thus, we also review the progress on study of spatially embedded networks. As a result of spatial constraints, such interdependent networks exhibit extreme vulnerabilities compared with their non-embedded counterparts. Such studies help us to understand, realize and hopefully mitigate the increasing risk in NON.
Our dependence on networks – be they infrastructure, economic, social or others – leaves us prone to crises caused by the vulnerabilities of these networks. There is a great need to develop new methods to protect infrastructure networks and prevent cascade of failures (especially in cases of coupled networks). Terrorist attacks on transportation networks have traumatized modern societies. With a single blast, it has become possible to paralyze airline traffic, electric power supply, ground transportation or Internet communication. How, and at which cost can one restructure the network such that it will become more robust against malicious attacks? The gradual increase in attacks on the networks society depends on – Internet, mobile phone, transportation, air travel, banking, etc. – emphasize the need to develop new strategies to protect and defend these crucial networks of communication and infrastructure networks. One example is the threat of liquid explosives a few years ago, which completely shut down air travel for days, and has created extreme changes in regulations. Such threats and dangers warrant the need for new tools and strategies to defend critical infrastructure. In this paper we review recent advances in the theoretical understanding of the vulnerabilities of interdependent networks with and without spatial embedding, attack strategies and their affect on such networks of networks as well as recently developed strategies to optimize and repair failures caused by such attacks.
Percolation theory is an approach to study the vulnerability of a system. We develop an analytical framework and analyze the percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the size of the failure, i.e., the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to an abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of n classic Erdős-Rényi (ER) networks, where each network depends on the same number m of other networks, i.e., for a random regular network (RR) formed of interdependent ER networks. The dependency between nodes of different networks is taken as one-to-one correspondence, i.e., a node in one network can depend only on one node in the other network (no-feedback condition). In contrast to a treelike NetONet in which the size of the largest connected cluster (mutual component) depends on n, the loops in the RR NetONet cause the largest connected cluster to depend only on m and the topology of each network but not on n. We also analyzed the extremely vulnerable feedback condition of coupling, where the coupling between nodes of different networks is not one-to-one correspondence. In the case of NetONet formed of ER networks, percolation only exhibits two phases, a second order phase transition and collapse, and no first order percolation transition regime is found in the case of the no-feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when the coupling strength q (fraction of interdependency links) is large and a second order phase transition when q is small. Our insight on the resilience of coupled networks might help in designing robust interdependent systems.
We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-p fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the coupling strength between the two networks q reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths q1 and q2, which separate three different regions with different behavior of the giant component as a function of p.
The robustness of a network of networks (NON) under random attack has been studied recently [Gao et al., Phys. Rev. Lett. 107, 195701 (2011)]. Understanding how robust a NON is to targeted attacks is a major challenge when designing resilient infrastructures. We address here the question how the robustness of a NON is affected by targeted attack on high- or low-degree nodes. We introduce a targeted attack probability function that is dependent upon node degree and study the robustness of two types of NON under targeted attack: (i) a tree of n fully interdependent Erdős-Rényi or scale-free networks and (ii) a starlike network of n partially interdependent Erdős-Rényi networks. For any tree of n fully interdependent Erdős-Rényi networks and scale-free networks under targeted attack, we find that the network becomes significantly more vulnerable when nodes of higher degree have higher probability to fail. When the probability that a node will fail is proportional to its degree, for a NON composed of Erdős-Rényi networks we find analytical solutions for the mutual giant component P∞ as a function of p, where 1−p is the initial fraction of failed nodes in each network. We also find analytical solutions for the critical fraction pc, which causes the fragmentation of the n interdependent networks, and for the minimum average degree k⎯⎯min below which the NON will collapse even if only a single node fails. For a starlike NON of n partially interdependent Erdős-Rényi networks under targeted attack, we find the critical coupling strength qc for different n. When q>qc, the attacked system undergoes an abrupt first order type transition. When q≤qc, the system displays a smooth second order percolation transition. We also evaluate how the central network becomes more vulnerable as the number of networks with the same coupling strength q increases. The limit of q=0 represents no dependency, and the results are consistent with the classical percolation theory of a single network under targeted attack.
Complex networks appear in almost every aspect of science and technology. Although most results in the field have been obtained by analysing isolated networks, many real-world networks do in fact interact with and depend on other networks. The set of extensive results for the limiting case of non-interacting networks holds only to the extent that ignoring the presence of other networks can be justified. Recently, an analytical framework for studying the percolation properties of interacting networks has been developed. Here we review this framework and the results obtained so far for connectivity properties of ‘networks of networks’ formed by interdependent random networks.
Many real-world networks interact with and depend upon other networks. We develop an analytical framework for studying a network formed by n fully interdependent randomly connected networks, each composed of the same number of nodes N. The dependency links connecting nodes from different networks establish a unique one-to-one correspondence between the nodes of one network and the nodes of the other network. We study the dynamics of the cascades of failures in such a network of networks (NON) caused by a random initial attack on one of the networks, after which a fraction p of its nodes survives. We find for the fully interdependent loopless NON that the final state of the NON does not depend on the dynamics of the cascades but is determined by a uniquely defined mutual giant component of the NON, which generalizes both the giant component of regular percolation of a single network (n=1) and the recently studied case of the mutual giant component of two interdependent networks (n=2).
We study a system composed of two partially interdependent networks; when nodes in one network fail, they cause dependent nodes in the other network to also fail. In this paper, the percolation of partially interdependent networks under targeted attack is analyzed. We apply a general technique that maps a targeted-attack problem in interdependent networks to a random-attack problem in a transformed pair of interdependent networks. We illustrate our analytical solutions for two examples: (i) the probability for each node to fail is proportional to its degree, and (ii) each node has the same probability to fail in the initial time. We find the following: (i) For any targeted-attack problem, for the case of weak coupling, the system shows a second order phase transition, and for the strong coupling, the system shows a first order phase transition. (ii) For any coupling strength, when the high degree nodes have higher probability to fail, the system becomes more vulnerable. (iii) There exists a critical coupling strength, and when the coupling strength is greater than the critical coupling strength, the system shows a first order transition; otherwise, the system shows a second order transition.
Network research has been focused on studying the properties of a single isolated network, which rarely exists. We develop a general analytical framework for studying percolation of n interdependent networks. We illustrate our analytical solutions for three examples: (i) For any tree of n fully dependent Erdős-Rényi (ER) networks, each of average degree k⎯⎯, we find that the giant component is P∞=p[1−exp(−k⎯⎯P∞)]n where 1−p is the initial fraction of removed nodes. This general result coincides for n=1 with the known second-order phase transition for a single network. For any n>1 cascading failures occur and the percolation becomes an abrupt first-order transition. (ii) For a starlike network of n partially interdependent ER networks, P∞ depends also on the topology—in contrast to case (i). (iii) For a looplike network formed by n partially dependent ER networks, P∞ is independent of n.
When an initial failure of nodes occurs in interdependent networks, a cascade of failure between the networks occurs. Earlier studies focused on random initial failures. Here we study the robustness of interdependent networks under targeted attack on high or low degree nodes. We introduce a general technique which maps the targeted-attack problem in interdependent networks to the random-attack problem in a transformed pair of interdependent networks. We find that when the highly connected nodes are protected and have lower probability to fail, in contrast to single scale-free (SF) networks where the percolation threshold pc=0, coupled SF networks are significantly more vulnerable with pc significantly larger than zero. The result implies that interdependent networks are difficult to defend by strategies such as protecting the high degree nodes that have been found useful to significantly improve robustness of single networks.
Understanding the synchronization process of self-propelled objects is of great interest in science and technology. We propose a synchronization model for a self-propelled objects system in which we restrict the maximal angle change of each object to θR. At each time step, each object moves and changes its direction according to the average direction of all of its neighbors (including itself). If the angle change is greater than a cutoff angle θR, the change is replaced by θR. We find that (i) counterintuitively, the synchronization improves significantly when θR decreases, (ii) there exists a critical restricted angle θRc at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude η, the synchronization as a function of θR shows a maximum value, indicating the existence of an optimal θR that yields the best synchronization for every η.
We investigate an evolutionary prisoner’s dilemma game among self-driven agents, where collective motion of biological flocks is imitated through averaging directions of neighbors. Depending on the temptation to defect and the velocity at which agents move, we find that cooperation can not only be maintained in such a system but there exists an optimal size of interaction neighborhood, which can induce the maximum cooperation level. When compared with the case that all agents do not move, cooperation can even be enhanced by the mobility of individuals, provided that the velocity and the size of neighborhood are not too large. Besides, we find that the system exhibits aggregation behavior, and cooperators may coexist with defectors at equilibrium.
We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius R. Adopting the the prisoner’s dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of R, and for modest values of R, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of R or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.
This paper is concerned with the robust H∞ filter problem for networked environments, which are subject to both transmission delay and packet dropouts randomly. By employing random series which have Bernoulli distributions taking value of 0 or 1, the data transmission model is obtained. Based on state augmentation and stochastic theory, the sufficient condition for robust stability with H∞ constraints is derived for the filtering error system. The robust filter is designed in terms of feasibility of one certain linear matrix inequality (LMI), which is formed by adopting matrix congruence transformations. A numerical example is given to show the effectiveness of the proposed filtering method.
We investigate a weighted self-propelled agent system, wherein each agent’s direction is determined by its spatial neighbors’ directions with exponential weights according to the neighbor numbers. In order to describe the fact that some agents with more neighbors might have larger influence on its neighbors, we introduce a scaling exponent of the neighbor number between 0 and ∞. When the exponent is equal to 1, the convergence efficiency is enhanced in our simulation. Furthermore, as the exponent increases, i.e., the effect of weight becomes stronger, the network of agents becomes easier to achieve direction consensus.
Lectures: Tue & Fri 2pm - 3:50pm, MRC 334
Office Hours: Tue 4pm - 5pm, Thu 10:30am - 11:30am, MRC 304
This course is an interdisciplinary introduction to network resilience and its applications in both science and engineering. Classes will interchangeably present the chapters from these textbooks with emphasis on the current active research related to network resilience, robustness, stability, and control. Topics to be covered include the network theory, dynamical systems, data analysis, and applications to biology, ecology, sociology, technology, and other fields. Students will learn about the ongoing research in the field, and ultimately apply their knowledge to conduct their own analysis of a real network data set of their choosing as part of the final project.
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This is a web page for the class which contains the basic information about the course, lecture notes, This page will also contain the corrections and general news about the course.
Course Content includes:(i)Basic conception of single networks; (ii) From single networks to networks of networks;Robustness of networks of networks; (iii) Dynamical systems; (iv) Multi-agent systems; (v) Network stability; (vi) Network control.
Class 1: Introduction and overview
Class 2: Basic conception of single networks: Graph Theory
Class 3: Basic conception of single networks: Random Networks
Class 4: Basic conception of single networks: Scale-Free Property
Boston University - ”Network Science (PY895)” with H. E. Stanley.
Boston University - ”Network Science (PY895)” with H. E. Stanley. The students were from Department of Physics, Department of Chemistry, Department of Electrical & Computer Engineering, and Department of Psychology. I taught half of class, including four chapters (Network Robustness, Degree Correlations, Evolving Networks, and Spreading Phenomena), front research in Network Science (Network controllability, Network of networks, and Network resilience), and software for computation and data visualization. I also designed the homework and guided the research project of each group.
Intelligent Information Control Lab, Shanghai Jiao Tong University. Supervise undergraduate and graduate students on their research with Yunze Cai.
Baosteel Company - Matlab training to 13 employees of Baosteel Company
Continuing Education School, Shanghai Jiao Tong University “Computer Graph” and “Operating System”. The students were from Department of Computer Science.
Published videos regarding some of my work.
The Co-Evolution Model for Social Network Evolving and Opinion Migration
The world is a complicated place. Our planet is made up of millions of networks from microscopic ecosystems to global migration. How can we ever hope to understand and predict the complexity of our mulit-networked world? New research may have the answer…
The extreme vulnerability of network of networks by Jianxi Gao
If you would like to talk about my research or work with me I would be happy to hear from you.
You can find me at my office located at MRC 304, 110 8th Street, Troy, NY
I am at my office Monday through Friday from 9:00am until 6:00pm, but you may contact me to fix an appointment.
You can find me at my office located at MRC 304, 110 8th Street, Troy, NY
I am at my office Monday through Friday from 9:00 until 6:00pm, but you may contact me to fix an appointment.
You can find me at my office located atMRC 304, 110 8th Street, Troy, NY
I am at my office Monday through Friday from 9:00 until 6:00pm, but you may contact me to fix an appointment.