key: cord-0761631-cyzie5jr authors: nan title: A Lightweight Social Computing Approach to Emergency Management Policy Selection date: 2015-10-26 journal: IEEE Trans Syst Man Cybern Syst DOI: 10.1109/tsmc.2015.2484281 sha: 9b1d6584d465b86320d3f5034e5b55669e0795ee doc_id: 761631 cord_uid: cyzie5jr In order to select effective policies for emergency management in a timely manner, this paper proposes an agile and lightweight social computing approach to facilitating policy selection, evaluation, and adjustment relative to emergency management in both quantitative and qualitative ways. The approach consists of three components represented as PZE: 1) (P) emergency management policy selecting; 2) (Z) modeling artificial societies with the zombie-city model (a general and formal artificial society model); and 3) (E) policy evaluation. The formal specification of the zombie-city model and rigorous expressions of scenarios enable rigorous description and formal reasoning of an artificial society. A feedback loop of this approach supports the iterative adjustment of emergency management policies and the creation of more effective policies. This approach is verified by applying it to a case of an infectious disease transmission with quantitative evaluations, qualitative reasoning and analysis, and iterative adjustments. Results indicate effective emergency management policies can be established with the approach in an iterative way. In contrast with existing research, our proposed approach offers the benefits of being simple, general, rapidly adaptive to changes, and low cost. C URRENTLY, new technologies make people interact on a global basis and data dispatch instantly and rapidly. These conveniences come with potentially negative impacts. For example, an infectious disease can be easily spread in a society and a computer virus can quickly infect computers on the Internet. An emergency as an event or situation [1] may induce the emergence (e.g., an emergence as outbreak of an infectious disease) for local nonlinear interactions among people [2] . This emergence can affect people's health, Manuscript life, property, and even social stability. Emergencies demand effective policies to reduce impacts and limit their spread. Emergency management experts can make several policies to control the emergencies. Policies enacted in the absence of suitable evaluation can cause great damage and loss to society. Thus, how to select appropriate emergency management policies is a meaningful work, but there are great challenges, as follows. 1) Ever-increasing human interactions through diverse realtime communication channels may cause an exponential increase in negative impacts during an emergency. An emergency that is complex, has potential derivative hazards, and presents with inadequate precursors, is called an unconventional emergency [3] . It then becomes increasingly difficult to formulate useful management responses using traditional approaches. 2) Experimental management responses cannot be applied in a real society because they may result in a great loss of life and property. When combined with computing and information technologies, and the theories and methods of sociology, social computing [4] as a novel pattern can assist in solving these challenging problems in effective emergency management. Because social computing makes experiments of social sciences possible to apply virtual models in the computer world, social computing is originally considered as creating or recreating social conventions, social behaviors, and social contexts through software and technologies such as microblogs and emails, which could be interpreted as social software [5] . Meanwhile, another meaning of social computing focuses on supporting computations of social sciences, and it has been used for predicting markets, population dynamics, and so forth. The latter sense of social computing is the focus of this paper and used to effectively assist emergency management. Two primary modes facilitate emergency management: "prediction-response" and "scenario-response" [6] , [7] . Both of them could be supported and conducted by social computing. In the former mode, mathematical methods or human intuition are usually used to conduct management. However, the former mode may not accurately predict the development of an unconventional emergency's evolution with these methods, and the prepared emergency management policies may have no impacts. The latter one inherits advantages and overcomes shortcomings of the prediction-response mode. This mode can not only be used to predict the development of an emergency through scenario evolution, but also respond to unconventional emergencies in real time to reduce impacts and losses. Therefore, the scenario-response mode could be widely and effectively applied in emergency management. In order to support the scenario-response mode for emergency management policy selecting, we must resolve some issues: 1) what constitutes a scenario and how can it be expressed in a rigorous way; 2) how do we rapidly construct general and formal artificial society models according to emergency scenarios; and 3) how can we establish a simple, systematic process of evaluation and adjustment for selecting more effective emergency management policies. To support the scenario-response mode, we consider the existing systematic and integrated social computing technique known as the ACP approach: (A) artificial society for modeling, (C) computation experiments for analysis, and (P) parallel execution for control. It is a methodology mainly used to solve the issues of complex socioeconomic systems and urban development (such as transportation systems) [8] , [9] . The practice in the domain of emergency management is its extended application. The ACP approach is a general methodology, but this approach is complicated and highly expensive. For modeling an artificial society, various researchers build different artificial societies or systems [10] according to a set of specifications. Although some work aims at providing a standardized and accepted method for modeling artificial societies [11] , there is still none for the ACP approach. Moreover, in the ACP approach, real-world and artificial societies run in parallel, requiring expensive runtime environments such as supercomputers. If a policy without suitable evaluations is adopted both in the artificial society and in the real world, the decisionmakers may take significant risks in the real world. A policy database with evaluations should be established. The ACP approach is not suitable for this paper due to its complexity and high cost. Therefore, it is necessary to consider a lightweight approach to emergency management policy selection, evaluation, and adjustment. This can also assist in the rapid production of a lightweight policy database. This paper concentrates on proposing a lightweight social computing method to effectively settle these scientific issues. It comprises (PZE) three main components: 1) (P) emergency management policy selecting; 2) (Z) zombie-city model for constructing artificial societies; and 3) (E) evaluation of emergency management policies. The major contributions offered in this paper include the following. 1) Systematic scenario expressions, thus allowing for scenario-based policy-making and selecting. Additionally, scenarios can reduce the gap between the individual level and the system level. 2) The provision of both quantitative and qualitative evaluation methods (the formal analysis and reasoning) for evaluating policy effectiveness. 3) Finally, the provision of a feedback loop for iterative policy adjustment, borrowing the idea of iterative and agile development from the software engineering domain. The remainder of this paper is organized as follows. Section II describes related works. Section III analyzes the requirements of the novel approach, introduces the PZE approach, and then specifies the concept of scenario to describe runtime conditions of an artificial society. Section IV illustrates the usability and effectiveness of this approach through a comprehensive case study, and discusses possible future work. Section V discusses additional practical applications of this approach, and then compares this paper with other related works. Section VI summarizes current efforts. In the past, based on mathematical equations, especially differential equations, mathematical methods have been successfully used to describe macro dynamics of infectious disease spread [12] , population dynamics [13] , etc. Meanwhile, mathematical methods have also been applied in a predictionresponse mode, which consists of two processes: 1) calculating a result using a prediction algorithm or mathematical method and 2) making decisions to preprepare for emergency management according to this result. In an emergency arising from complex uncertain circumstances, this mode cannot accurately predict the event's evolution and the prepared emergency management policies may have no positive impacts. For example, the 7.9 M W (moment magnitude) earthquake striking Sichuan province in Southwest China on May 12, 2008, had not been accurately predicted. The event caused significant casualties and property loss. A new mode-scenario-response has been proposed to effectively support decision-making during an uncertain and unconventional emergency. Scenarios reflect the macro behaviors and properties of a system. Policymakers could analyze various scenarios and then quickly establish emergency management policies. At the same time, we can reconstruct these scenarios with a computer-based artificial society model. This would allow emergency policies to evolve with experimental simulations through a process of observation, evaluation, and adjustment. As a result, more effective policies are applied to the management of real emergencies. Attempts also have been made to support group decision-making for emergency management [14] . These works focus on how to provide mechanisms, means, or platforms for policy-making as a component of emergency management. Advancements in computer and information technologies have allowed social computing to deeply influence problem solution in society [15] , [16] , i.e., solutions based on real-time and repeatable simulation experiments. Hence, emergency management can also utilize social computing to select, evaluate, and adjust policy. The ACP approach could effectively support the scenario-response mode. This method could help emergency management in the paradigm of scenarioresponse under unconventional emergencies. However, such an approach: 1) lacks a general artificial society model (there is no standardized and accepted model or method for modeling an artificial society [17] , and the ACP approach lacks a general artificial society model or standards of modeling); 2) is cumbersome (the ACP approach has several complex norms); 3) is complex and high cost (the artificial society runs in parallel with the real society); and 4) lacks descriptions of emergences and scenarios. Emergencies may rapidly evolve and change, thus emergency management faces serious challenges. A lightweight social computing approach should be proposed to aid in emergency management to adapt to the evolutions and changes of emergencies. Such an approach is easily and rapidly mastered by policy-makers with limited practice. Timely emergency management policies should conduct direct actions intended to reduce negative impacts and suppress a possible damaging emergence. Social computing should concentrate on emergency management policy selection. Based on the analysis of related works, this section proposes a lightweight social computing method-the PZE approach to support emergency management, including policy selection, evaluation, and adjustment. As shown in Fig. 1 , the PZE approach includes three parts: 1) (P) emergency management policy selecting; 2) (Z) artificial society modeling with the zombie-city model; and 3) (E) the quantitative evaluation of emergency management policies through simulation experiments and comparisons, and the qualitative evaluation of policies through formal reasoning and analysis. This approach is a lightweight method borrowing research results from the software engineering domain [18] . The PZE approach supports emergency management policy-making (i.e., selecting appropriate policies) through iterative adjustments. Compared with the ACP approach, this approach has a general artificial society model, and it has relatively few easily followed norms. With only limited practices, policymakers could easily model an artificial society, make policies, and evaluate and adjust these policies based on this approach. Initially, experts make an emergency policy. Then, based on the zombie-city model, this policy could be transformed into rules in the zombie-city model, and policy-makers could construct their instances of the zombie-city model. The constructed zombie-city instances should be translated into simulation codes (e.g., Netlogo codes and Repast codes), and policy-makers could conduct simulation experiments based on these codes. Lastly, the experts could evaluate and adjust these policies according to the simulation experiments. If a policy does not have an obvious effect on the emergency management, then the experts could adjust the policy and transform the policy into the rules in the zombie-city model, and then simulate again to quantitatively evaluate the adjusted policy. Meanwhile, experts could qualitatively evaluate the policy through formal reasoning and analysis with the formalizations of zombie-city model. According to an emergency scenario, emergency management experts may create several policies in their minds. However, not all these policies can be applied to managing and controlling the emergency. Policy selection is to select some policies for further evaluations and adjustments. The PZE approach forms a feedback loop for evaluating and adjusting selected emergency management policies. In self-organization systems, a policy is a means to dynamically regulate the behavior of system components to acquire an emergence at the system level [19] . Emergence is the global properties, behaviors, structures, or patterns of a complex system arising from localized, individual behaviors [20] , and arises from the nonlinear interactions of local components in a system where the emergence cannot be traced back to those components [21] . These interactions may arise from the self-organization of a system. This emergence is beneficial or harmful to the system, and meets or violates the expectations of the system. For example, in a distributed computing system the emergence that all computing nodes could run in parallel with load balancing is based on some policies, and this emergence is beneficial for this distributed system. However, a policy of emergency management aims at avoiding or preventing the occurrence of an emergence such as the 2003 outbreak of severe acute respiratory syndrome (SARS). Policy selection based on emergency scenarios is the first step of the PZE approach, and is also one main focus of emergency management, where the concept of scenario will be introduced in the Appendix. Emergency management attempts to control the situation and limits its negative impacts. Emergency management policies can be viewed as a set of rules or norms that restrict the behaviors or states of people in a society. Policies specify the rights and prohibitions of people in a society and must be followed. We could identify two different kinds of policies: 1) obligation and 2) prohibition [22] . An obligation specifies an action to be performed by a person or a state that must be maintained by that person. A prohibition indicates an action not to be performed by a person or a state of affairs not to be maintained. Moreover, a policy also consists of the conditions to be satisfied and the action (state) to be performed (kept) by people. It can be formally described as follows: where the symbol "::=" means "be defined as." When a policy has been formulated, the next step is to construct an artificial society, then evaluate and adjust it according to the evaluation results in this artificial society. This PZE provides a general artificial society model to conduct artificial societies modeling. The zombie-city model is the foundation of the PZE approach. The artificial society is modeled as a multiagent organization, which consists of a number of autonomous and interacting agents sharing some common rules at the society level. Each agent in the society has specific capabilities and may be infected with some viruses through interactions. Agents inhabit an environment and have several social relationships that compose the social network. Meanwhile, agents could play different roles to adapt to various changes of environments, social networks, or their own states. Fig. 2 presents the meta-model of the zombiecity model. The symbols between two concepts denote the numerical relation between these two concepts. For example, "1" (agent) to "1 . . . * " (role) means an agent can dynamically play one or more roles. Through establishing a formal model to accurately define and specify an artificial society, it becomes possible for formal reasoning and qualitative evaluation of a policy. Hence, the formalization of the zombie-city is important to qualitatively evaluate policies. A zombie-city model could be described by a five-tuple, as zombie-city ::= . AG = {a 1 , a 2 , . . . , a n }, for any a i (1 ≤ i ≤ n), a i is an agent, and AG is a set of agents, where n means the number of agents in the artificial society. SN = {l k |1 ≤ k ≤ n * (n − 1)}, l k is a link of the social network, SN is a set of links, and a social network is constructed by links between agents. an atomic environment unit for an agent to inhabit, where l denotes the number of girds in the environment of the artificial society. EN is a set of grids. where m indicates the number of roles that agents can play. RO is a set of roles. RU is a set of rules, where k means the number of rules in the artificial society. This set could be divided into four subsets: R A , R S , R E , and R R that are finite rule sets for agents, the social network, the environment, and roles. To support qualitative analysis of an emergency management policy, the other detailed formalizations of the zombiecity model are presented in the Appendix. The main purpose of the PZE approach is to facilitate the selection of emergency management policies. In fact, the key task of selecting effective policies is to evaluate then adjust these policies according to evaluation results. The PZE approach provides both quantitative evaluation and qualitative analysis methods for emergency management policies. After policy-makers make policies, these policies will be transformed into rules of the zombie-city model. When the artificial society has been built, it will be translated into various simulation codes according to the platform on which the artificial society model is executed and results are quantitatively assessed. Therefore, experts could receive feedback to improve or adjust their policies, and iteratively conduct simulations to acquire an ideal policy. This process is similar to the iterative and agile software development in the domain of software engineering to deal with the dynamic and changing software requirements, as shown in Fig. 3 . An emergency scenario is the input of this development process. The evaluated and effective emergency management policies are the output, which will be stored in the policy database. While a similar emergency scenario appears in a real-world society, these corresponding policies could be applied directly in responding to this emergency. Simulation is a powerful way to predict the emergence and evaluate the effect of an emergency management policy. We can extract macro data and properties of the simulation at the micro-level to quantitatively assess the effectiveness of the policy with numerical evaluations, as shown in Fig. 4 . These parameters and evaluation methods are related to specific applications. Specifying the observed states of an artificial society is an important challenge in evaluating the effectiveness of an emergency management policy. The scenario is an appropriate choice, which could not only describe the system behaviors and properties but also assist decision-makers in selecting emergency management policies according to scenarios. A scenario [23] is a runtime situation of a system to be observed and describes the global properties, behaviors, structures, etc. An emergence could be described by a scenario of the system, and this special scenario is called the specification of the emergence, which is written as Specification Emergence . At any moment, a system is in a scenario, i.e., written as Implementation System . At moment t, the scenario of the system satisfies the scenario of the emergence, i.e., the emergence appears at moment t, and this situation could be formally depicted as Implementation System ∝ t Specification Emergence . The process of an emergence is from quantitative change to qualitative change. This process could be described by scenarios. An emergence of a system could be detected by sensors. These may be hardware sensors, soft sensors, or humanbeings. The runtime status of a system can be abstracted into scenarios at different moments. While at t moment the scenario of the system satisfies the specification of the emergence, we could say that the emergence appears and at this moment the scenario is the emergence scenario. The PZE approach also provides a qualitative method for evaluating policies. As shown in Fig. 5 , we should input a policy into the artificial society based on the zombie-city model, and then formally specify the artificial society. Scenarios could be formally specified (as seen in the Appendix), which are used to describe rules in the artificial society. Meanwhile, the policy is transformed into rules. There could be also several lemmas. Based on these lemmas and rules formal reasoning and analysis can be carried out. We should find out whether there are some scenarios that may bring out the emergence. If there is a scenario that could result in the emergence with a high probability, we should adjust the policy. With a more effective policy, there are no scenarios that may result in the emergence or there are some scenarios that may hardly cause the emergence with a low probability. The PZE approach can be definitely reused by others. This approach is a general-purpose and application-independent method for emergency management policies selection. Fig. 6 presents how to use the PZE approach to select emergency policies. This approach could effectively facilitate policy-makers in selecting, evaluating, and refining policies after an artificial society is constructed. In 2009, the infectious disease H1N1 spread in more than 180 countries, and infected about 1 million people, which caused over 18 000 deaths [24] . Thus, an increasing number of researchers have focused on controlling the spread of infectious diseases, and some accepted works have successfully been applied in the analysis of the spread of infectious diseases, e.g., infectious diseases transmission models. For the H1N1 infectious disease, the Susceptible (S), Exposed (E), Infected (I), and Recovered (R) (SEIR) [25] model could accurately describe the process of H1N1 infectious disease diffusion. The following equation depicts the mathematical model of SEIR: (1) Equation (1) defines four permitted states: 1) susceptible (S); 2) exposed (E); 3) infected and ill (I); and 4) healthy and unsusceptible or dead (R), and each individual is in one of these states. The states of individuals evolve in time and depend on their previous states. The probabilities of transitions between these states are described as follows: ω denotes the probability that a susceptible individual (S) will be infected to become exposed (E) by an infected and ill individual (I); μ indicates the probability that an exposed individual (E) becomes infected and ill (I); and λ denotes the probability that an infected and ill individual (I) will recover, or die (R). In this section, we aim at modeling the H1N1 infectious disease transmission case by the zombie-city model. Several policies will be made, evaluated, and iteratively adjusted in order to manage the emergency. The zombie-city model of the case is defined as follows. 1) Agents: The population of agents is 1000. It is assumed that the initial number of infected agents is 2. 2) Environments: The agents in the case are assumed to be situated in an environment that consists of 32×32 grids. 3) Role: Agents could play different roles, including susceptible, exposed, infected, and recovered. Susceptible means that the playing agents are healthy; exposed denotes those who carry viruses but are not confirmed infected; infected indicates those who are confirmed being infected with viruses; and recovered represents those who are recovered and acquire immunity against the virus. 4) Rules: Agents, roles, and social network should conform to rules in the artificial society. Hence, there are some rules for them. a) Rules of agents (R A ): There are rules for agents in this case: 1) agents interact with other agents with social relationships and 2) self-adaptive rule: a susceptible agent may play role exposed with a chance of ω after interacting with other infected agents. An exposed agent may play role infected with a probability of μ. An infected agent becomes recovered with a probability of λ, i.e., an infected agent may recover. The rules of agents can be formally described as [r.1]-[r.5] follows. [r.1]: ∀a 1 (∀a 2 (a 1 t a 2 ∧ a 2 = Random(Linka 1,t ))) → a 1 t a 2 . [r.2]: ∀a 1 (∀a 2 (a 1 t a 2 ∧ a 1 [r.4]: ∀a 1 (a 1 t Exposed)|[μ] → a 1 ↑ t Quit(Exposed) ∧ a 1 ↑ t Play(Infected). [r.5]: ∀a 1 (a 1 t Infected)|[λ] → a 1 ↑ t Quit(Infected) ∧ a 1 ↑ t Play(Recovered). b) Rules of the social network (R S ): It is assumed that the average degree of the social network is 10, and in each moment the selected agent should link with another nearest agent with minimum degree, which has not connected with it. This rule could be formally described as [r.6] follows. [r.6]: a 2 ), where: a) Aid is the identification of agent a; b) AT is a set of attributes of agent a; c) AC is a set of common actions agent a could do; d) N l is a set of identifications of links that agent a is participating; e) N r means a set of identifications of roles that agent a is playing. Scenarios could be described by formal expressions. Let A and B be the variables that can take ids of agents, grids, or links as their values. Let a 1 and a 2 be agents, and b be a role. Let g denotes a grid or a set of grids in an environment. S, S 1 , and S 2 indicate scenarios, respectively. The system is in a scenario when the corresponding scenario expression is true. The scenario expressions could be defined as follows. 1) A := B means that variable/cid A is assigned the value of B. 2) A = B means that the value of A is equal to that of B. 3) A = B means that the value of A is not equal to that of B. 4) A > B means that the value of A is larger than that of B. 5) A ≥ B means that the value of A is larger than or equal to that of B. 6) A ≤ B means that the value of A is less than or equal to that of B. 7) A < B means that the value of A is less than that of B. 8) a 1 ↑ t Action means that agent a 1 is doing the action Action at moment t. 9) a 1 t a 2 means that agent a 1 is interacting with agent a 2 at moment t. 10) a 1 t b means that agent a 1 is playing role b at moment t. 11) a 1 @ t g means that agent a 1 is staying on the grid g or grid set g at moment t. 12) a 1 t a 2 means that agent a 1 is connecting with agent a 2 at moment t. 13) ∀x(S) means that for any agent x, the S[x/A] is true. S[x/A] is a scenario expression obtained from S by replacing free occurrences of variable x with A. 14) ∃ [n] x(S) means that at least n agents make S[x/A] true. The default value of n is 1. 15) [n]x(S) means that just n agents make S[x/A] true. The default value of n is 1. 16) ∼ S means the system is not in the scenario S, i.e., the scenario S is not true. 17) S 1 ∨ S 2 means that the system is in either S 1 or S 2 . 18) S 1 ∧ S 2 means the system is in both scenarios S 1 and S 2 . 19) S 1 ∝ t S 2 means that at moment t, the system is in scenario S 2 if the system is in scenario S 1 , i.e., S 1 is satisfying S 2 at moment t. For example, we could define a scenario that at moment t each agent is connecting with not less than 2. Hence, we could formally describe this scenario as: S 2 = ∃ [2] x(∀y(x y)). If S 1 = ∃ [m] x(∀y(x y))∧m ≥ 2, then we could see that S 1 ∝ t S 2 . C. Other Formal Aspects of Zombie-City Model 1) Environment: From the definitions in Section B, a@ t g means that agent a lives in the environment g at this moment t, and the environment g may be an atomic grid or a set of grids. AGENT g,t denotes the set of agents living in g at moment t, i.e., AGENT g,t = {a|a@ t g} and AGENT g,t ⊆ AG. Distance(a 1 , a 2 ) is a function to return the distance between agents a 1 and a 2 . The primitive Move() means that an agent a moves from the current place to the destination. 1) Distance(a 1 , a 2 ): An abstract and general function for computing the distance between agents a 1 and a 2 . In different applications, the meanings of this function may be diverse. 2) Move(g 1 , g 2 ): An agent a will move from g 1 to g 2 . a @ t g 1 and g 1 = g 2 , AGENT g1,t+1 = AGENT g1,t \{a}, and AGENT g2,t+1 = AGENT g2,t ∪ {a}. 2) Social Network: For an undirected graph, a 1 t a 2 (a 1 , a 2 ∈ AG) means that agent a 1 links with agent a 2 at moment t, which is equivalent to a 2 t a 1 . LINK a1,t denotes the set of agents to which agent a 1 connects at moment t, i.e., LINK a1,t = {a 2 |a 1 t a 2 ∧ a 2 ∈ AG}. For a directed graph, let a 1 t a 2 (a 1 , a 2 ∈ AG) denotes that agent a 1 links to a 2 , and agent a 1 is the source of this link. LINK S a1,t denotes the set of agents, to which agent a 1 links, and agent a 1 is the source of these links, i.e., LINK S a1,t = {a 2 |a 1 t a 2 ∧ a 2 ∈ AG}. Let LINK T a1,t indicates the set of agents that link to agent a 1 at moment t and agent a 1 is the target of these links, i.e., LINK T a1,t = {a 2 |a 2 t a 1 ∧ a 2 ∈ AG}. Therefore, the set of agents that link to agent a 1 at moment t contains the agents which agent a 1 links to and the agents that link to agent a 1 , i.e., LINK a1,t = LINK S a1,t ∪ LINK T a1,t . For describing the initialization process of a static social network and the varying and growing process of a dynamic social network, we have defined two primitives: Create() and Delete(), to depict the action of creating and deleting a social relationship between two agents, respectively. SN t denotes the set of social links in an artificial society at moment t. 1) Create(a i , a j ): To create a link (social relationship) from agent a i to agent a j . For the undirected graph, a i t a j , i.e., a j / ∈ LINK ai,t and a i / ∈ LINK aj,t , then LINK ai,t+1 = LINK ai,t ∪{a j } and LINK aj,t+1 = LINK aj,t ∪{a i }; for the directed graph, a i t a j , then LINK S ai,t+1 = LINK S ai,t ∪ {a j } and LINK T ai,t+1 = LINK T ai,t , and LINK S aj,t+1 = LINK S aj,t and LINK T aj,t+1 = LINK T aj,t ∪ {a i }. For both two graphs, the link l = (a i , a j ) and SN t+1 = SN t ∪ {l}. 2) Delete(a i , a j ): To delete the link (social relationship) from agent a i to agent a j . For the undirected graph, a j ∈ LINK ai,t and a i ∈ LINK aj,t , and LINK ai,t+1 = LINK ai,t \{a j } and LINK aj,t+1 = LINK aj,t \{a i }; for the directed graph, a j ∈ LINK S ai,t and a i ∈ LINK T aj,t , LINK S ai,t+1 = LINK S ai,t \{a j } and LINK S aj,t+1 = LINK S aj,t , and LINK T ai,t+1 = LINK T ai,t and LINK T aj,t+1 = LINK T aj,t \{a i }. For both graphs, the link l = (a i , a j ) and SN t+1 = SN t \{l}. All agents have the capability of self-adaption through dynamically playing roles. We use ROLE a,t to denote the set of roles that agent a plays at moment t, i.e., ROLE a,t = {b|a t b, b ∈ RO} and ROLE a,t ⊆ RO. As the mechanism of dynamically playing roles describe, let ROLE A a,t indicates the set of active roles that agent a plays at moment t, and ROLE I a,t denotes the set of inactive roles. Therefore, the set of roles that agent a plays at moment t includes active roles and inactive role, i.e., ROLE a,t = ROLE A a,t ∪ ROLE I a,t . 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Guessoum in Lip6, University Pierre et Marie Curie, and M. Brewes for proofing and editing this paper. He was a Visiting Scholar with the Lip6, Université Pierre and Marie Curie, Paris, France, from 2012 to 2013. He has published over ten research papers and one book chapter. His current research interests include social computing, complex system, multiagent system, and agent technology. He is a Full Professor and a Ph.D. Supervisor with the College of Computer, NUDT. He was a Visiting Scholar with the Department of Computer Science, University of Toronto, Toronto, ON, Canada. He has published over 100 research papers and two books. His current research interests include agent-oriented software engineering, autonomous robot software, and self-adaptive and autonomic software technologies.