research article agent based simulation of group emotions...

Research ArticleAgent Based Simulation of Group Emotions Evolution andStrategy Intervention in Extreme Events

Bo Li Duoyong Sun Shuquan Guo and Zihan Lin

College of Information System and Management National University of Defense Technology Changsha 410072 China

Correspondence should be addressed to Bo Li libonudtgmailcom

Received 5 November 2014 Accepted 4 December 2014 Published 28 December 2014

Academic Editor Francisco Solis

Copyright copy 2014 Bo Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Agent based simulation method has become a prominent approach in computational modeling and analysis of public emergencymanagement in social science research The group emotions evolution information diffusion and collective behavior selectionmake extreme incidents studies a complex system problem which requires new methods for incidents management and strategyevaluation This paper studies the group emotion evolution and intervention strategy effectiveness using agent based simulationmethod By employing a computational experimentation methodology we construct the group emotion evolution as a complexsystemand test the effects of three strategies In addition the events-chainmodel is proposed tomodel the accumulation influence ofthe temporal successive events Each strategy is examined through three simulation experiments including twomake-up scenariosand a real case studyWe show how various strategies could impact the group emotion evolution in terms of the complex emergenceand emotion accumulation influence in extreme events This paper also provides an effective method of how to use agent-basedsimulation for the study of complex collective behavior evolution problem in extreme incidents emergency and security studydomains

1 Introduction

Understanding how the group emotion develops in extremeevents is a critical issue in emergency management Publicemergency always occurs with rumors propagating mali-cious incitement and emotion infection which cause groupemotion changing or even extreme behavior [1 2] As apublic security incident extreme group incident is differentfrom general mass incidents in the information propagationmanners [3] in which the violence activity information isspreading on the relation network in a relatively private waysuch as in the Urumqi incident (Xinjiang China 2009) [4] Itis difficult to obtain realistic investigation data of the extremeincidents for the government or researchers due to theprivacy and interaction covertness as well as the complexityof the individual interaction On the other hand the groupbehavior and extreme emotion are hard to detect whichmakes it difficult for the strategy formulation and evaluationThus the covert information spreading and related groupemotion evolution modeling and analysis become important

for incident process understanding and intervention strategyevaluation

Empirical and theoretical methods both have been usedto study the collective behavior evolution process in groupincidents [5ndash9] The results of empirical studies are differentaccording to each specific event but they are useful forfinding inherent evolution pattern in the incidents [6 9]Theoretical studies try to analyze the collective behavior withmathematical methods and it is effective in understandingthe evolution process from macro perspective [10] Howeverboth methods have limitations on modeling the complicatedsystem emergence produced by the individual interactionAgent based SimulationModeling (ABSABM) provides aneffective way to understand the complicated system evolutionproblem [11 12] It includesmodels of behaviorwhich observethe collective effects of agent behaviors and interactions [13]As a simulationmethod ABS is usually used along with othermethods according to the problem such as social network[14 15] and system dynamics [16] The autonomous agentscan be used with the heterogeneity and network structure for

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2014 Article ID 464190 17 pageshttpdxdoiorg1011552014464190

2 Discrete Dynamics in Nature and Society

researching the diversity of the agent behaviors as well asthe system complexity from the micro level Social networkis widely used to describe the relation structure betweenthe agents and the ldquonetwork agentsrdquo is an effective tool tostudy the collective behavior evolution of agents with relationnetwork [17] Based on the ABS method strategies evalua-tion with computational models is widely used for strategyeffectiveness analysis [18] One of the advantages is that thismethod provides a way to analyze the strategy effectivenesswith repeated experiments which is impossible for moststrategies in real world Simultaneously the influence factoranalysis can be carried out to understand inherent process ofevolution

In this paper we construct the ABS models for studyingthe group emotions evolution process and examine theimpacts of three strategies used in incidents interventionspeakers controlling interaction probability and commu-nication intervention The paper is organized as followsProblem description and research framework are given inSection 2 It is described as mathematical forms and theresearch framework gives an overview of this paper Themodels used in this research are given in detail in Sec-tion 3 including the relation network model the events-chain model the information model and the agent modelSection 4 gives three intervention strategies as well as eval-uation criteria based on the simulation method Simulationexperiments are performed and the results are shown inSection 5 including two virtual scenarios and a real casestudy Section 6 concludes the paper

2 Problem Description andResearch Framework

21 Problem Description and Definition Emotion and recog-nition constitute a central element of the human repertoireand the study of their functioning is a prerequisite forthe understanding of individual and collective behaviors[19] The computational modeling (such as ABS) provides apowerful tool to study the individual or collective behaviorsas a complex system This technology has been widely usedin emergency management counterterrorism and nationalsecurity This paper focuses on the group extreme incidentswhich are caused by human or organization planning Thereare some characteristics of this type of events so we makethree reasonable assumptions for the events description andcomputational experiments

The first assumption is that the events in the incidentswould not occur at the same timeThis means that the eventsare discrete in the simulation experiments Although theemotion evolution process may last for a period of timethe events (including related behaviors such as attributeschangings) are independent

The second assumption is that at any given moment allactors act conditionally independently of each other Such anassumption was already proposed in many studies [20] as abasis for ABS research

The third assumption is that the strategies are performedcompletely and ideally Although the strategy definition

and construction depend on the real possibility and fea-sibility we assume that there is no case of failure in theexperiment

The general principle of these assumptions is tomodel theprocess in a formal framework Based on the assumptionswe can treat the problem as a behavior evolution processon the network The individuals can be represented as thenodes of the network and the individual actions are the agentbehaviors based on the relation of the network

The underlying network structure is the basic structure ofthe diffusion processes which consisted of agents (individu-als) and relationships between them We use the definitionof dynamic network in [20] The set 119873 is a set of socialactors (individuals or agents) the relation on 119873 is definedmathematically as a subset of the 119873 times 119873 and the relation isrepresented by the 119899 times 119899 adjacency matrix 119883 = (119883

119894119895) The

119883119894119895

= 0 1 respectively represents that there is no link orthere is a tie between agents 119894 and 119895 (119894 119895 = 1 119899)The agentattributes are assumed to be discrete with a preset intervalof values and 119885

ℎ119894denotes the value of agent 119894 on the ℎth

attributeThe time dependence is indicated by denoting119885ℎ=

119885ℎ(119905) where 119905 denotes time and 119885

ℎis the column containing

the 119885ℎ119894values

This paper presents models andmethods for studying thedynamic evolution process of (119885

1(119905) 119885

119867(119905)) Virtually

the adjacency of the relation matrix 119883 should be includedin the dynamic analysis as well but we here assume thatthe network remained changeless in a short period (eg anevent) which is proposed by previous research [21] In con-trast to the individual attributes 119885

ℎ we are more interested

in the collective state for example the statistics result of theagentsrsquo attributes which describe the characteristics of thewhole collective behaviors and states and they are also calledcovariates [20]

Suppose that the observations on (1198851(119905) 119885

119867(119905))

are available for discrete observation time 1199051

lt 1199052

lt

sdot sdot sdot lt 119905119872 The collective attributes could be represented as

(1198651(119905) 119865

119871(119905)) and 119865

119897(119905) = 119891

119897(1198851(119905) 119885

119867(119905)) in which

1 le 119897 le 119871 For simplifying the processes (1198851(119905) 119885

119867(119905))

and (1198651(119905) 119865

119871(119905)) could be represented by the symbol

119884(119905) and the totality of available data is represented by119910(1199051) 119910(119905

119872)

The interventions strategies are defined as a series offunctions acting on the agents set 119873 the relation set 119883 andthe attributes set 119885 We use the symbol 119878 to represent thestrategy set and 119878 = (119878

1 119878

119870) where the constant 119870 is

the number of the strategies For each strategy there is aformulation of 119878

119896= 119891119896(119873119883 119885

1(119905) 119885

119867(119905) 119905) The 119905 in the

formulation means the time on which the strategy performsBased on the definition we could now describe the

problem as follows the initial data include the agentsset 119873 the relation set 119883 the attributes matrix of theagents (119885

1(1199051) 119885

119867(1199051)) and the covariates set (119865

1(1199051)

119865119871(1199051)) the agents will take actions (interaction) during each

time step which makes the values of 119885 and 119865 changingthe purpose of this paper is to understand the dynamicevolution process of the collective emotions 119865 and to observethe effectiveness of different intervention strategies in theevolution process

Discrete Dynamics in Nature and Society 3

The intervention strategies (S)

Model intervention (data)

Models for simulation

The events-chain model (E)

The social network model (N X)

The information model

The interaction model

Strategies analysis

Process intervention

System evolution driven

The group structure

Collective emotion driven

Interaction rules

drivenEvents

Relation

The agentmodel

Diffusion

Interaction protocol

The agent basedartificial social

simulationframework

Statisticalresults

The strategies evaluation

Comparative analysis

Simulation results analysis

Evolution characteristics analysis

Characteristicsextracting

Intervention effectiveness (F)

Covariatescalculating

Collective emotion evolution (Z)

Figure 1 The research framework of collective emotion simulation and strategy evaluation

22 Research Framework Based on the problem definitionmentioned above the research framework can be constructedfor the sake of emotion evolution process analysis andintervention strategy evaluation As shown in Figure 1 thiswork consists of the following four components (1) Theagent based artificial social simulation framework involvingfrequent interactions between individuals within the groupand the resulting changes of collective emotion state duringthe extreme emotion diffusion (2) Models for simulationincluding four models used in the simulation experimentsthe events-chain model as system evolution driven the socialnetworkmodel as the group structure (agent interaction envi-ronment) the information model as the collective emotiondriven and the interaction model as the interaction rulesin the agent based simulation (ABS) method (3) Simulationexperiments results analysis providing the statistical resultsof the collective emotion evolution (119885) the covariates resultsfor the intervention effectiveness (119865) and the characteristicsanalysis of the evolution process (4) The intervention strate-gies and evaluation including the strategies constructionwith mathematical forms and the effectiveness evaluation

The core module of the method is the ABS structurewhich is used to model the complex interaction behav-ior between the individuals and to observe the collectiveemotion emergence The models for simulation are builtto describe the specific environment and behavior in thecorresponding scenarios of the extreme events such asthe successive terrorism events the information diffusionprocess and the individual interaction With simulationtime going on the statistical results are changing with theindividualsrsquo behaviors and the collective emotion criteriacapture the evolution dynamics from the macro perspectiveThus the simulation results analysis is a dynamic processdescribing the macro collective emotion state The strategieseffectiveness is analyzed by the covariates calculating and theevolution characteristics analysis which provides results for

strategies evaluation The strategies make influence in twoways the model intervention (data aspect) and the processintervention (interaction aspect)

3 Model Description

31 The Relationship Network Model In extreme events forcovertness information spreading is always invisible and actsin relatively covert ways instead of public channels suchas email instant messaging or even mouth-to-mouth wayDuring the process the personal relation plays an importantrole in the communication object selection In this methodthe BA network model [22] is used as the relation structurewhich can be seen as the interaction environment rather thanthe behavior model given it can format the rules of agentselection in interaction During the period of an event thenetwork structure can be treated as a static state [21]

32 The Events-Chain Model In order to simulate the tem-poral successive events two structures are proposed theldquoevents-chainrdquo structure and ldquometa-eventrdquo structure Theldquometa-eventrdquo structure is a unit of single event or can be calledepisode which is the component unit of the events-chain Forexample it can be rumors spreading process or an action ofan organization It also includes the following related groupresponse activities The ldquoevents-chainrdquo structure consists ofseries of temporal ldquometa-eventsrdquo and the structure makesit capable of describing the complex event process for thesimulation The accumulated emotion of events is expressedthrough the agent model which makes it possible to analyzethe events related collective emotion and behavior evolutionin a computational experimentation way

Figure 2 illustrates the events-chain model of temporalseries events In the model the nodes represent the meta-events which are ordered by the temporal relations and


Meta-eventTime t1 t2 tk

Events-chain E1 E2 middot middot middot Ek

The agent model

Figure 2 The events-chain model of temporal successive events

denoted as 119864119896 The attributes of the event can be noted as

119864119896119897 which includes the event criticality (119864

1198961) and the start

time (1198641198962) The criticality represents the event ldquoimportancerdquo

level to the individuals When the criticality value is highthe group response will be violent and when it is lowthe collective behavior will be peaceful Thus the successiveevents can be modeled as a set 119864 = 119864

1 1198642 119864

119870 and

the criticality set 119868 = 11986411 11986421 119864

1198701 and start time set

119879 = 11986412 11986422 119864

1198702 The accumulated effects of events

militate through the agent attributes and behavior which willbe described in the agent model

33The InformationModel The events usually occur accom-panying event information in the forms of news rumorsor extreme activity information Information transferringbetween agents makes agent attributes and behavior chang-ing The information spreading process of meta-event issimilar to the rumor spreading process but the differenceis that the impact can be accumulated during the period ofevent influence time According to the event information seteach agent has an event information set of 119885119868

119894= 119885119864

1 1198851198642

119885119864119870 and 119885119864

119896= 0 1

We assume that after the individual receives the infor-mation it will be transmitted which is different from theclassic rumor propagation model [5] Agent will randomlyselect another agent who connects with it to send themessageand exchange opinion rather than treating the informationas several statuses This is because we have found that theextremists or radicals will send the violent activity informa-tion over and over again even though the object has got theinformation [4]

34 The Agent Model The agent model describes theattributes and behavior rules in the simulation Asmentionedbefore the attributes are the values of 119885 and the agentbehavior can be modeled as a series of functions on 119885

341 Agent Attributes

Autonomy Autonomy is an important variable when con-sidering the information propagation in agent based sim-ulation [23] The autonomy of an agent will influence theacceptable level of the external information which expressesthe impact on the behavior of the individual [8] It deter-mines the extreme emotion level after the individual receives

the information and the impact of environment by the otherindividuals denoted as 119885

1

Extreme Emotion There are many researches on the emotionmodel and emotion agent [24 25] however it is difficult tobuild a uniform model to describe the emotion changingprocess due to the complexity of emotion and its influencefactors Based on the KISS rule (keep it simple and stupid)[26] we define three variables to model the extreme emotionin this specific application scenario the individual self-generated emotion 119885

2 environmental influence emotion 119885

3

and individual extreme emotion 1198854 Self-generated emotion

describes the individualrsquos own level of radicalization and theenvironmental influence emotion describes the conformitydegree of an agent to the others

Emotion Decay Rate For individuals there is a process ofmood self-adjustment so extreme emotion has a decayprocess If there is no external information within a periodof time individual mood will gradually calm down This isanother factor that affects the extreme emotion evolution andis denoted as 119885

5 Meanwhile after receiving the information

for a certain period of time the emotions are hardly affectedby other external individuals which means 119885

3will be zero

after a time threshold labeled as 120590

342 Personal Interaction Model

Self-Generated Emotion After an agent receives the eventinformation the self-generated emotion will be generated bythe agent itself and it can be modeled as a function of theindividual autonomy and the event criticality 119864

1198961 which can

be shown as follows

1198852119894

= 119891 (1198851119894 1198641198961) = 1198851119894times 1198641198961 (1)

Actually the individual self-generated emotion is relatedwithmany factors such as the content of events individualityand other related social attributes These factors involvemore complex questions and event classification issues ofindividual emotional tendencies which are out of scope ofthis paper Considering the simulation scenario we use amultiplication rule

Environmental Emotion The extreme emotion contagionprocess occurs among the individuals through the relationnetwork thus the emotion of agent will be affected bythe others connecting with it Assume the number of theagents who connect with agent 119894 and have received the eventinformation is119889 then the environmental emotion of an agentcan be expressed as

1198853119894

=

(sum119883119894119895=1

1198854119895)

119889

(2)

where 119894 = 119895 1 le 119894 119895 le 119899 thus the agent extreme emotion canbe calculated as follows

1198854119894

= 1198851119894times 1198852119894+ (1 minus 119885

1119894) times 1198853119894 (3)


where the 1198851119894

is used as a weight between self-generatedemotion and environmental emotion The extreme emotionof agent 119894 on the event 119896 at time 119905 can be represented as119885119896

4119894(119905)

Extreme Emotion Evolution Individual extreme emotion is aprocess of accumulation and it can reach a high value enoughfor people to take extreme actions On the other hand theextreme emotion has a period of decay As suggested in [25]the emotion decreases with the time but it does not go awayinstantaneously so the decay process is represented via anexponential functionWe assume that only the self-generatedemotion decays and the environmental emotion dependson the emotions of the connected agents Given the initialemotion 119885

2119894(1199050) the current time 119905 and the decay rate 119885

5119894

the decay function is given by

1198852119894 (119905) = 119885

2119894(1199050) times 119890minus1198855119894times(119905minus1199050) (4)

The accumulation effect of the extreme emotion comesfrom the successive events influence For each event everyagent has an event emotion according to the information Attime 119905 the extreme emotion of agent 119894 should be calculated asfollows

1198856119894 (119905) =

119870

sum

119896=1

119885119896

4119894(119905) (5)

4 Intervention Strategies

The purpose of this study is to understand the evolutionprocess of the collective emotion In addition we are moreinterested in how to intervene in the extreme emotion spread-ing We call the intervention method used in the spreadingprocess as intervention strategies in this paper Valentesurveys four strategies on network intervention which areindividuals segmentation induction and alteration [27]Based on the formal description mentioned before we givethe details of the three strategies examined in this method

41 Speakers Controlling Speakers controlling strategyinvolves eliminating speakers of the network who are thesource of the events information which may also be takenas leader-focused strategy [18] The speakers here refer tothe people that spread the information and emotion atthe first time such as the schemer of the event the leaderof the group and a member of the terrorist organizationThis strategy is commonly referred to as capturing targetsjust as key players in social network mentioned in [28]The motivation of this strategy is to intervene in eventinformation spreading and emotion diffusion from thesource so as to control or prevent the event occurrencewith the understanding that eliminating the speakers in thenetwork should have the heaviest influence on the collectiveextreme emotion evolution process

Formally we note speakers controlling strategy as 1198781

thus removing the speakers could be treated as a functiontransformation from the node set 119873 and the link 119883 to thesets 119873

1and 119883

1 Let 119873

1015840

1denote the speakers set so 119873

1=

119873minus1198731015840

1 Here we use1198831015840

1to denote the link subset of119883 which

includes all the links related with the agents in 1198731015840

1 that is

1198831015840

1= 119883119894| 119894 isin 119873

1015840

1 and119883

1= 119883 minus 119883

1015840

1 In addition the agents

in 1198731015840

1will be inaccessible for any other agent once they are

removed

42 Interaction Probability The emotion contagion needscontinuous interaction between the individuals [29] Thisstrategy is based on the understanding that if the agents inter-act with lower probability the extreme emotion would gen-erate slower and less people would be affected This strategyusually associates with event popularity and high popularitywillmake people exchange the opinion and informationmorefrequently Empirical studies based on online social mediahave provided the evidence of topics intervention [30] whichis known as public opinion guidance

The probability in this strategy means the contact fre-quency in a fixed time period and its interval is [0 1] We use119875in to represent the interaction probability between each pairof agents Generally it should be a probability distributionand the probability is generated in each time step We use 119878

2

to represent this strategy thus 1198782is a probability matrix of

the link set 119864 which generates the link active probabilities ineach time step corresponding to the probability distributionTo simplify the simulation it is used as a given value in thismethod

43 Communication Intervention In contrast to interactionprobability strategy communication intervention strategytakes actions of deleting the interaction pathways betweenagents with the idea that fewer links will mitigate theinformation diffusion and emotion cognation process [31]The communication in this strategy refers to the ways thatagents keep in touch with each other such as telephoneemail instant messenger and website The motivation of thisstrategy is to reduce the communication channels betweenindividuals so as to intervene in the process of emotionevolution and even the collective behavior

This strategy is different from the two previous strategiesfrom the structural perspective Firstly the communicationstrategy interdicts the links between the agents which are stillin the network and the speaker control strategy removes theagents and the related links of the agents secondly all theagentsrsquo links may be affected by the communication strategyand only speakersrsquo links in the speaker strategy thirdlythe interaction probability strategy reduces the frequency ofinteraction and the links still exist in the network whichwould be removed in communication strategy This methodis not usually taken because it needs to interrupt the dailycommunication device and related network which mayinvolve the security department

This strategy is denoted as 1198783 Consequently removing

the links could be seen as a transformation of 119883 rarr 1198833 We

assume the obstructed link set is11988310158403 so119883

3= 119883minus119883

1015840

3The key

problem is how to get the link set11988310158403 that is how to determine

the links to be removed As the communication strategy isnot a target-focused method here we use a probability 119875re torepresent the probability of each link to be removed


44 Strategy Effectiveness Evaluation To evaluate effective-ness of the strategies the criteria should be proposed Thebasic principle of artificial society simulation is to observe thecomplex emergence results of simple agent interaction [32]and one of the effective approaches is to evaluate the statisticalcharacteristics of the group attributes As mentioned abovethe effectiveness evaluation should be a series of observationswith the time using the notation (119865

1(119905) 119865

119871(119905)) Besides

the statistical variables the characteristics of the statisticalresults curves are also important to evaluate the effectivenessof the strategies For distinction analysis the characteristics ofthe dynamic results curves are noted as (119879

1 119879

119872) In this

study nine statistical criteria are used as follows

(i) The maximum number of extreme group agentsduring event (119865

1) To specify the agentsrsquo emotion

level the distinction threshold is used to determinewhether the agent belongs to the group Specificallyin our model the extreme emotion needs to reach acertain threshold 120591

1at which the agent can be seen

with ldquoextreme emotionrdquo(ii) The maximum number of agitated group agents

during event (1198652) The distinction method of agitated

agents is similar to the extreme group with thethreshold 120591

2 The agent that belongs to this group is

between the states ldquoextremerdquo and ldquogentlerdquo who maybe incited to the state ldquoextremerdquo or calm down to thestate ldquogentlerdquo

(iii) Themaximum value of average emotion during event(1198653) The average emotion is a measurement of the

total group emotion state and it is also a symbol ofthe collective behavior

(iv) The duration of event (the time from the eventstarting to the ending denoted as 119879

1)

(v) The duration when average emotion value is above athreshold (120591

3) This duration can be seen as the ldquorisk

periodrdquo of the incident (1198792)

(vi) The length of time between the event starting andthe time when the number of extreme group agentsreaches the peak value (119879

3)

(vii) The length of time between the timewhen the numberof extreme group agents reaches the peak value andevent ending (119879

4)

(viii) The length of time between the event starting andthe time when the number of agitated group agentsreaches the peak value (119879

5)

(ix) The length of time between the timewhen the numberof agitated group agents reaches the peak value andevent ending (119879

6)

5 Simulation Experiments andResults Analysis

In the previous sections we have specified the mathematicaldescription of the problem the research framework of thisstudy the emotional dynamics of agents the models used

for simulation and the intervention strategies with ninespecific criteria for effectiveness evaluation To numericallyinvestigate themethod proposed we need to specify the setupin terms of the network the initial conditions of agents andthe parameters for experiments which are all described inthis section Simultaneously the simulation experiments aregiven as well as the results analysis and validation includinga real case study

51 Simulation Scenarios Setting The procedures of thesimulation experiments are as follows

(1) The initial social network was generated by BA net-work model as the local relation structure of agents

(2) The simulation step was 200 steps for single eventand 250 for two correlated events The time step wasupdated as follows as the system time increases thetime step is updated and each agent selects one of theagents to interact

(3) At the time the event occurred the event informationwas given to a designated start node (speaker) Thedefault node was the node with maximum degree inthe network

(4) At each time step after the incident the agentrsquos self-generated emotion in the event was in attenuationwith the decay rate and the environmental emotionupdated based on the other agentsrsquo emotions

(5) When an agent received new information it wouldonly be affected by the agents who had also receivedthe latest information and no longer affected by thepast events

(6) After an agent received information for a time thresh-old (120590) the agent was no longer affected by theemotions of other agents about the event

Before starting the simulation experiments the settings ofthe initial parameters were fixed at default values (see Table 1)

52 Collective Emotion Evolution of Single Events We firstinvestigated the main effect of different strategies taken onsingle event In each run the strategy was taken once at thesame simulation time step (step 25 5 steps after the eventstarting) Figure 3 shows the group emotion evolution processunder different strategiesThenumerical results are presentedin Table 2

As in the figure the curves of speakers controlling strat-egy and the curves without strategy are almost overlappingThe results indicate that if the speakers controlling strategyis taken after the event start time it is almost invalid This isbecause the event information has already been propagatedand the extreme emotion of the agents will also be generatedwithout the speakers This is an interesting result becauseremoving the key nodes is usually considered as a very usefulstrategy in counterterrorism strategy and it has little effecton collective emotion As expected reducing the interactionprobability between the agents not only effectively reduces thenumber of agents in each group but also slows the growth of


Table 1 The initial parameters settings found

Simulation parameters Notation Range Default Object of parameterAutonomy 119885

1[0 100] Random Agent (person)

Self-generated emotion 1198852

[0 500] 0 Agent (person)Environmental emotion 119885


Extreme emotion 1198854

[0 500] 0 Agent (person)Decay rate 119885


Influence time 120590 [1 100] 50 Agent (person)Criticality 119864

1198961[1 5] (int) Given Event

Events start time 1198641198962

mdash 20 EventAgent number 119873 mdash 10000 NetworkgroupBA node link number mdash [1 100] 6 NetworkgroupExtreme group threshold 120591

1[0 500] 400 Agent emotion

Agitated group threshold 1205912

[0 500] 200 Agent emotionAverage emotion threshold 120591

3[0 500] 100 Group average emotion

Interaction probability 119875in [0 1] 05 Interaction probability strategyRemoving probability 119875re [0 1] 03 Communication intervention strategyStrategy execution time mdash mdash 25 Strategy

Table 2 Strategy effectiveness results of single event

Criteria Without strategy Speakers controlling Interaction probability Communication intervention1198651

541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)

emotion as well as the information diffusion process Thismay be because the information transfer process betweenagents has been delayed (Figure 3(d)) The communicationstrategy (removing part of the links) reduces the maximumof both groups and the average emotion but it only slowsthe information diffusion process to some extent Both thetime period of groups and the average emotion have littledifference

Table 2 presents the numerical results of strategies effec-tiveness on single event The values in the parenthesis arethe difference rates As expected the interaction probabilitystrategy is the most effective method in reducing the numberof each grouprsquos agents and the average emotion The speak-ers controlling strategy makes nearly no difference as theevent information has been propagated The communicationintervention strategy will reduce the number of agents andaverage emotion to some extent From time aspect the effectof speakers controlling strategy has no obvious differenceso is the communication strategyThe interaction probabilitysignificantly affects the ldquorise phaserdquo of collective emotion (119879

3

and 1198795) and the ldquofall phaserdquo (about 20) All the strategies

have no obvious effect on the length of ldquorisk periodrdquo (1198792)

Furthermore Figure 4 shows the collective emotiondistribution of different strategies at the peak points As inFigure 4(a) the interaction probability strategy reduces themean value of the emotion and also the number of agentswithhigh emotion value The speakers controlling and commu-nication strategies also have little effect In Figures 4(c) and4(d) the agents with emotion zero are those who have notreceived the event information The self-generated emotionis approximately uniformly distributed (Figure 4(c)) givenit is only determined by the autonomy of the agents thedecay rate and the event criticality On the contrary theenvironmental influence emotion approximately follows anormal distribution (Figure 4(d)) This is an interestingresult and it indicates that at the collective emotion peakpoint the environmental influence emotion plays a dominantrole for an agent to be an extreme agent Moreover in thescatter diagram of 2-dimension distribution (Figure 4(b))more points are above the symmetry line (red line) and thisalso indicates that the environmental emotion is higher thanthe self-generated emotion for most agents This interestingresult means that the environmental emotion is the maincause for an agent to become extreme


0

100

200

300

400

500

600

0 50 100 150 200Simulation time step

Without strategySpeakers controlling

Interaction probabilityCommunication

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)

Figure 3 Collective emotion evolution curves of single event (a) the number curves of extreme group agents (b) the number curves ofagitated group agents (c) average emotion value evolution curves and (d) the information spreading process curves

53 Group Emotion Evolution of Events-Chain Model Wethen discuss the results of experiments under different strate-gies with events-chain model Because of the accumulationeffect the emotion evolution will be different from that insingle event Figure 5 shows the results of two correlatedevents under different strategiesThe two events start respec-tively at time steps 20 and 60 and both with criticality of 5All the other parameters are set as default values in Table 1The curves of the two events are obviously different from

the single event especially the curves of the second eventThe numbers of extreme group agents are much higher in thesecond event than in the first one (Figure 5(a)) This is dueto the emotion accumulation influence as the start time ofthe second event is in the influence time of the first eventIn contrast the numbers of the agitated group agents reducebecause of the constant total number of agents (Figure 5(b))According to the results the speakers controlling strategy isthe most effective method to reduce the collective extreme


25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500

Self-generated emotions

Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200

Environmental influence emotions

Age

nts n

umbe

r

(d)

Figure 4 Emotion components distribution at the peak points (a) emotion distribution of agents in different strategies (b) scatter diagramof 2-dimension emotion distribution (without strategy) (c) self-generated emotion distribution (without strategy) and (d) environmentalemotion distribution (without strategy)

value because the information of the second event cannotbe transferred (Figure 5(d)) since the speakers have beenremoved from the network

As in single event the same nine criteria are used forstrategy effectiveness analysis Unlike the single event weare more interested in the accumulation influence on thesecond eventThus in this experiment all the time indicatorsdescribe the characteristics of the second event (except1198792) and the numerical results are shown in Table 3 The

percentage in the column of ldquowithout strategyrdquo is calculatedbased on the single event (column 2) and the others arecalculated based on the accumulation events (column 3without strategy)

Firstly the difference between the single event and accu-mulation event is obvious especially the number of extremegroup agents (+108190) On the contrary the numberof the agitated group agents decreases due to the constanttotal agents Another difference is that the time indicatorsall increase especially the ldquofall phaserdquo of the two groupsIt is interesting that although the maximum number ofthe agitated groups has decreased (119865

2 minus2476) the time

length still increases (1198796 +4865) Secondly the speakers

controlling is themost effective strategy for correlated eventsthis is because removing the speakers from the networkdirectly prevents the second event from taking place (asanalysis of Figure 5) Thirdly the effectiveness of interaction


0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000

Simulation time step

The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)

0 50 100 150 200 250Simulation time step



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)

Figure 5 Group emotion evolution curves of successive events (a) the number of extreme group agents (b) the number of agitated groupagents (c) average emotion value evolution curves (d) the information diffusion curves (the second event)

probability strategy on the collective emotion has no obviousdifference as in single event but the time indicators changea lot The duration of event shortens a little (119879

1 minus157)

as well as the ldquofall phaserdquo of the two groups (resp minus3065of extreme group and minus970 of agitated group) Lastly theeffectiveness of communication strategy becomes weakersuch as the duration of the event time (119879

1) the ldquofall phaserdquo

of the extreme and the agitated groups (1198794and 119879

6) In

sum accumulation influence makes the collective emotionstronger and it will weaken the strategy effectiveness exceptthe speakers controlling strategy

54 Model Validation Validation is a critical issue for anymodeling approach applied to any system especially whenusing ABS to model complex adaptive systems (CAS) [3334] We validate the proposed simulation with the methodmentioned in [35] This part presents the operational valida-tion of the simulation and the empirical validation will beperformed in the real case study

541 Statistical Tests of Randomness Effects In order to exam-ine the extent to which the randomness affects the simulationresults experiment was repeated ten times The results are


Table 3 Strategy effectiveness results of successive events

Criteria Without strategy(single event) Without strategy Speakers controlling Interaction probability Communication intervention

1198651 547 6465 (+108190) 0 (minus100) 3236 (minus4995) 5460 (minus1555)

1198652 8220 6185 (minus2476) 0 (minus100) 5474 (minus1150) 5918 (minus432)



1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)


Table 4 Statistical significance for the three strategies

Criteria Speakerscontrolling

Interactionprobability

Communicationintervention

1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872

shown in Figure 6 and the statistical significance results areshown in Table 4 (119875 lt 001) From Figure 6 we couldfind that the randomness extent is changing with the rate ofvariables changing and this is due to the speed of informationspreading From the entire period the randomness has nosignificance effect on the evolution process From the resultsin Table 4 we could find that the interaction probabilitystrategy significantly affects all the outcomes and speakerscontrolling strategy has little effect on the single eventCommunication strategy works well on the statistical groupemotion but not on the event time except the rise time periodof agitated group

542 Sensitivity Analysis We then examined the effective-ness difference under different parameter values for sen-sitivity analysis and the results are shown in Figure 7As described in Sections 52 and 53 the effectiveness ofspeakers controlling strategy only depends on the executiontime while the other two depend on the probabilities Thusin this examination we focus on the intervention strategyprobability that is the interaction probability and linkremoving probability corresponding to the two strategiesFrom Figure 7 we could find that the probabilities havea significance effect on the effectiveness of the strategiesBesides the closer the probability is to the critical value(119875in rarr 0 119875re rarr 1) the more significant the effect is

55 A Case Study The computational model mentionedabove was applied to the Urumqi incident in Xinjiangprovince (China) The incident took place on July 5 2009when approximately 20000 people had ever received theviolence activity information through all kinds of channelsand almost 5000 people attended the activities The incidentstarted as the information spreading of Shaoguan (Guang-dong China) incident among the population of Xinjiang bythe terrorists organization Hizb ut-Tahrir [36] with extremeviolence emotion instigation More details of the incidentscan be found in [4] Based on the research method proposedthe effectiveness of intervention strategies was tested throughthe simulation experiments

To simulate the incident the events-chain model wasconstructed based on the events time during the incidentand meta-events are presented in Table 5 According tothe incident evolution information the meta-events weremodeled as related information diffusion events during theprocess The time of the events was translated into thesimulation steps as events attributes The criticalities of theevents were given manually based on the instigation degreeof the information which were also mentioned in [4] Theagent number was 20000 and the other parameters were setas default values in Table 1

Figure 8 shows the average emotion evolution resultsduring the incident and derivative events are marked onthe figure according to the event time The blue events arethe meta-events used in the events-chain model and thered events are the derivative violence activities during theincident It is easy to find that the derivative events usuallyoccurred at the peak points of the collective emotions and hadthe highest participation at these points Another interestingresult is that the meta-events usually occurred at the concavepoints of the curve which means that the violence activitiesinformation is propagated at the low points of the collectiveemotion curves

The emotion evolution results and the collective deriva-tive events (events 6 7 8) show good consistency in Figure 8This indicates the validity of proposed method from themacro tendency perspective As the detailed individual datais impossible to obtain the macro emergent results provedthat ABS provides a feasible way to study the collectiveemotion evolution in this type of incidents Furthermore the


20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)

Figure 6 Randomness influence on the results (without strategy single event)

Table 5 Meta-events of the case incident

Event number Event time Simulation step Criticality Event1 June 25 125 1 The Shaoguan incident2 June 27 175 3 The statement of Shaoguan3 June 30 250 4 Violence activity information4 July 2 300 2 Activity information5 July 5 375 5 Violence activity instigation

consistency between the events and group emotion can beused in events forecasting which is also an important issuein emergency management

To compare the simulation results with the real events formodel validation the derivative events are listed in Table 6The time of derivative events is translated into simulationstep The start time of derivative violence events is obtainedas the time at peak points The number of extreme peopleis the number of extreme groups at the peak points As

a complex system simulation the macro evolution tendencyis much more important for understanding the emergentcharacteristics of the systemThe consistency of the derivativeevents and simulation results also shows the validity ofproposed method

Figure 9 shows the influences of different strategieson the collective emotion evolution The tendency ofcurves is similar to the results in Section 53 whichindicates that the effectiveness of the strategies has no


0 50 100 150 200Simulation step

0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)

Figure 7 Parameters difference influence on the strategies effectiveness (a) (c) (e) and (g) interaction probability strategy (b) (d) (f) and(h) Communication intervention strategy

Table 6 Derivative events in the case incident

Number Date Simulation step Experiments results Extreme people (estimated) Experiments results6 June 28 200 193 50 547 July 1 280 267 1800 16348 July 7 400 392 5000 5277

Table 7 Strategy effectiveness results of the case incident

Criteria Without strategy Speakers controlling Interaction probability Communication1198651

5277 30 (minus9943) 3144 (minus4042) 4629 (minus1228)1198652



122 25 (minus7951) 133 (+902) 123 (+082)

obvious difference under different events simulation sce-narios The speakers controlling strategy is still the mosteffective method for reducing the emotion of successiveevents and the interaction probability strategy can slowthe emotion spread speed and reduce the number of groupagents

Table 7 shows experiment results of the incident simu-lation In this experiment since there is a series of eventsthe time characteristics of single event are the focus exceptthe ldquorisk periodrdquo indicator (119879

2) Based on the ldquorise and

fallrdquo pattern of collective emotion [6] 1198792presents the total

accumulation time when the average emotion is above

the threshold of 1205913 As the strategies were taken after the

second event occurred (step 200) the speakers controllingstrategy is still the most effective method for successive vio-lence events The interaction probability strategy is effectivein reducing both group agents and average emotion valueThe communication intervention strategy also has slighteffect on the collective emotion evolution

This case study simulates the group emotion evolutionin the Urumqi incident and examines the effectiveness ofthe three strategies The consistency shows that the proposedmethod is useful to describe the evolution process of this typeof incidents and themethod of strategies evaluation provides


0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5

Event 1 The Shaoguan incident

Event 3 Violence activity informationEvent 4 Activity informationEvent 5 Violence activity instigationEvent 6 Individual violence activitiesEvent 7 Group violence activitiesEvent 8 Large-scale violence activities

Event 2 The statement of Shaoguan

Figure 8 Group emotion evolution and events in the case incident

a convenient tool for the strategy formulation to intervene inthe incidents

6 Conclusion

This paper studied the dynamics of the group emotionevolution and effectiveness of intervention strategies withABSmethod in extreme events Modeling and simulating theprocess of information spreading and emotion evolution pro-vide some insight into potentially useful strategies Throughthe use of ABS the complexities of the collective emotionevolution and group behavior can be better understoodThe strategies can be tested in simulation environmentthat behave similarly to real world situation To furtherunderstand the accumulation influence of successive eventsthe events-chain model is proposed to model the continuousrelevant events using simulation experiments In this modelthe continuous events are expressed as a series of meta-events and information spreading processesThe informationdiffusion between individuals is the driving power of emotionand behavior changing In order to evaluate strategiesrsquo effec-tiveness three strategies are modeled based on mathematicaldefinitions Nine criteria are defined from the statistical andtemporal perspectives which measure the collective motiondynamics with statistical properties and evolution curvecharacteristics Based on the constructed simulation systemthree experiments are performed as well as model validationThe simulation results allow us to derive several conclusionseither on the collective emotion evolution or on the strategieseffectiveness

Our main conclusions are summarized as follows

(i) The group extreme emotion evolution process is thecollective response dynamics of events accompany-ing information diffusion The dynamics generatewave pattern with the increase of time which can beregarded as pulses of events

(ii) The environmental influence emotion is the maincause that makes individualrsquos emotion become ex-tremeThe extreme emotion infection between agentsgenerates centralized emotion distribution whichshows convergence in collective emotion dynamics

(iii) For single event interaction probability is the mosteffective strategy either in reducing the number ofgroup agents or in slowing the evolutionary processCommunication can only reduce the peak value ofthe group agents and speakers controlling has littleeffectiveness if it is taken after the event starts

(iv) For successive events because of the accumulationinfluence the speakers controlling is the most use-ful strategy for preventing the derivative events asit removes the information source of the eventsThe interaction probability strategy displays similarresults in single event as well as the communicationintervention strategy

(v) The sensitive analysis indicates that the probabilitiesare the deterministic factor that determines the effec-tiveness of speakers controlling and communicationintervention strategies Meanwhile the statistical testof randomness effects proves that the model is robustand valid

Moreover the real case study shows consistency betweenthe group emotion dynamics and the collective behavior(violence activities events) This makes it possible to predictgroup emotion evolution tendency and test effectiveness ofvarious strategies The predictive value would be significantfor government in managing and preventing extreme inci-dents

In conclusion the presented agent based simulationsgive a new insight into group extreme emotion dynamicsin extreme events It can be used to test variety of simula-tion experiments for understanding the emotion dynamicsassociated with other models Meanwhile based on thesimulation framework other intervention strategies can beevaluated through corresponding models Hence despite itsmathematical complexity our method provides a laboratoryfor further experiments on the group emotional behaviorof agents (eg under different driving conditions variedagent behaviors and parameters values) and for comparativeanalysis of intervention strategies A future development ofthe research would be to apply more models of sophisti-cated events including events classification (distinguishingdifferent types of events and agentsrsquo response to them) andevents impact model (how the events influence the agentsrsquobehavior) Furthermore heterogeneity of agents also shouldbe considered in the simulation




0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e



0 100 200 300 400 500 600Simulation time step

(c)

Figure 9 Group emotion evolution of the case incident (a) the number curves of extreme group agents (b) the number curves of agitatedgroup agent and (c) average emotion value evolution curves (The strategies were taken at simulation step 200)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (Grant no 71473263) and the Special-ized Research Fund for the Doctoral Program of HigherEducation of China (Grant no 20134307110020)

References

[1] I J Roseman M S Spindel and P E Jose ldquoAppraisals ofemotion-eliciting events testing a theory of discrete emotionsrdquoJournal of Personality and Social Psychology vol 59 no 5 pp899ndash915 1990

[2] D Bar-Tal E Halperin and J de Rivera ldquoCollective emotions inconflict situations societal implicationsrdquo Journal of Social Issuesvol 63 no 2 pp 441ndash460 2007

[3] A Wedeman ldquoEnemies of the state mass incidents and sub-version in Chinardquo in Proceedings of the Annual Meeting of theAmerican Political Seience Association Toronto Canada 2009


[4] WebPage httpenwikipediaorgwikiJuly 2009 Urumqi riots[5] M Nekovee Y Moreno G Bianconi and M Marsili ldquoTheory

of rumour spreading in complex social networksrdquo Physica AStatisticalMechanics and Its Applications vol 374 no 1 pp 457ndash470 2007

[6] Y Matsubara Y Sakurai B A Prakash L Li and C FaloutsosldquoRise and fall patterns of information diffusion model andimplicationsrdquo in Proceedings of the 18th ACM SIGKDD Inter-national Conference on Knowledge Discovery and Data Mining(KDD rsquo12) pp 6ndash14 Beijing China August 2012

[7] T Bosse M Hoogendoorn M C A Klein J Treur C N vander Wal and A van Wissen ldquoModelling collective decisionmaking in groups and crowds integrating social contagionand interacting emotions beliefs and intentionsrdquo AutonomousAgents and Multi-Agent Systems vol 27 no 1 pp 52ndash84 2013

[8] R L Goldstone and M A Janssen ldquoComputational models ofcollective behaviorrdquo Trends in Cognitive Sciences vol 9 no 9pp 424ndash430 2005

[9] Y Sano K Yamada H Watanabe H Takayasu and MTakayasu ldquoEmpirical analysis of collective human behavior forextraordinary events in the blogosphererdquo Physical Review E vol87 no 1 Article ID 012805 2013

[10] T Bosse M Hoogendoorn M Klein et al ldquoAgent-basedmodelling of social emotional decision making in emergencysituationsrdquo in Co-Evolution of Intelligent Socio-Technical Sys-tems pp 79ndash117 Springer Berlin Germany 2013

[11] J Duffy ldquoAgent-basedmodels and human subject experimentsrdquoin Handbook of Computational Economics L Tesfatsion and KL Judd Eds pp 950ndash1011 Elsevier 2006

[12] J H Miller and S E Page Somplex Adaptive Systems AnIntroduction to Computational Models of Social Life PrincetonUniversity Press 2009

[13] C M MacAl and M J North ldquoTutorial on agent-basedmodelling and simulationrdquo Journal of Simulation vol 4 no 3pp 151ndash162 2010

[14] S J Alam and A Geller ldquoNetworks in agent-based socialsimulationrdquo in Agent-Based Models of Geographical Systems AJ Heppenstall Ed Springer Science+BusinessMedia BV 2012

[15] I-C Moon and K M Carley ldquoModeling and simulatingterrorist networks in social and geospatial dimensionsrdquo IEEEIntelligent Systems vol 22 no 5 pp 40ndash49 2007

[16] R Colbaugh and K Glass ldquoEarly warning analysis for socialdiffusion eventsrdquo Security Informatics vol 1 no 18 pp 1ndash262012

[17] F Bergenti E Franchi and A Poggi ldquoAgent-based interpreta-tions of classic networkmodelsrdquoComputational andMathemat-ical Organization Theory vol 19 no 2 pp 105ndash127 2013

[18] J P Keller K C Desouza and Y Lin ldquoDismantling terroristnetworks evaluating strategic options using agent-based mod-elingrdquo Technological Forecasting amp Social Change vol 77 no 7pp 1014ndash1036 2010

[19] DMMackie T Devos and E R Smith ldquoIntergroup emotionsexplaining offensive action tendencies in an intergroup contextrdquoJournal of Personality and Social Psychology vol 79 no 4 pp602ndash616 2000

[20] T A B Snijders C E G Steglich and M SchweinbergerldquoModeling the co-evolution of networks and behaviorrdquo inLongitudinal Models in the Behavioral and Related Sciences KV Montfort J Oud and A Satorra Eds pp 41ndash71 ErlbaumAssociates Publishers 2007

[21] A Apolloni K Channakeshava L Durbeck et al ldquoA study ofinformation diffusion over a realistic social network modelrdquo inProceedings of the IEEE International Conference on Computa-tional Science and Engineering (CSE rsquo09) vol 4 pp 675ndash682Vancouver Canada August 2009

[22] A L Barabasi and R Albert ldquoEmergence of scaling in randomnetworksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[23] S Field ldquoSelf-determination instructional strategies for youthwith learning disabilitiesrdquo Journal of Learning Disabilities vol29 no 1 pp 40ndash52 1996

[24] K A Maria and R A Zitar ldquoEmotional agents a modeling andan applicationrdquo Information and Software Technology vol 49no 7 pp 695ndash716 2007

[25] G Marreiros R Santos C Ramos and J Neves ldquoContext-aware emotion-based model for group decision makingrdquo IEEEIntelligent Systems vol 25 no 2 pp 31ndash39 2010

[26] R AxelrodTheComplexity of Cooperation Agent-BasedModelsof Competition and Collaboration Princeton University PressPrinceton NJ USA 1997

[27] T W Valente ldquoNetwork interventionsrdquo Science vol 336 no6090 pp 49ndash53 2012

[28] S P Borgatti ldquoIdentifying sets of key players in a social net-workrdquo Computational and Mathematical Organization Theoryvol 12 no 1 pp 21ndash34 2006

[29] T Bosse R Duell Z A Memon J Treur and C N van derWal ldquoA multi-agent model for mutual absorption of emotionsrdquoinProceedings of the 23rd EuropeanConference onModelling andSimulation (ECMS rsquo09) pp 212ndash218 June 2009

[30] A B Krueger and J Maleckova ldquoAttitudes and action publicopinion and the occurrence of international terrorismrdquo Sciencevol 325 no 5947 pp 1534ndash1536 2009

[31] D Kempe J Kleinberg and E Tardos ldquoInfluential nodes in adiffusion model for social networksrdquo in Automata Languagesand Programming vol 3580 of Lecture Notes in ComputerScience pp 1127ndash1138 Springer Berlin Germany 2005

[32] N Gilbert Agent Based Models Sage 2007[33] S Moss ldquoAlternative approaches to the empirical validation of

agent-based modelsrdquo Journal of Artificial Societies and SocialSimulation vol 11 no 1 p 15 2008

[34] L Yilmaz ldquoValidation and verification of social processeswithin agent-based computational organization modelsrdquo Com-putational andMathematical OrganizationTheory vol 12 no 4pp 283ndash312 2006

[35] P Windrum G Fagiolo and A Moneta ldquoEmpirical validationof agent-based models alternatives and prospectsrdquoThe Journalof Artificial Societies and Social Simulation vol 10 no 2 pp 1ndash19 2007

[36] httpenwikipediaorgwikiHizb ut-Tahrir

Submit your manuscripts athttpwwwhindawicom

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MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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OptimizationJournal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

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Stochastic AnalysisInternational Journal of


researching the diversity of the agent behaviors as well asthe system complexity from the micro level Social networkis widely used to describe the relation structure betweenthe agents and the ldquonetwork agentsrdquo is an effective tool tostudy the collective behavior evolution of agents with relationnetwork [17] Based on the ABS method strategies evalua-tion with computational models is widely used for strategyeffectiveness analysis [18] One of the advantages is that thismethod provides a way to analyze the strategy effectivenesswith repeated experiments which is impossible for moststrategies in real world Simultaneously the influence factoranalysis can be carried out to understand inherent process ofevolution

In this paper we construct the ABS models for studyingthe group emotions evolution process and examine theimpacts of three strategies used in incidents interventionspeakers controlling interaction probability and commu-nication intervention The paper is organized as followsProblem description and research framework are given inSection 2 It is described as mathematical forms and theresearch framework gives an overview of this paper Themodels used in this research are given in detail in Sec-tion 3 including the relation network model the events-chain model the information model and the agent modelSection 4 gives three intervention strategies as well as eval-uation criteria based on the simulation method Simulationexperiments are performed and the results are shown inSection 5 including two virtual scenarios and a real casestudy Section 6 concludes the paper

2 Problem Description andResearch Framework

21 Problem Description and Definition Emotion and recog-nition constitute a central element of the human repertoireand the study of their functioning is a prerequisite forthe understanding of individual and collective behaviors[19] The computational modeling (such as ABS) provides apowerful tool to study the individual or collective behaviorsas a complex system This technology has been widely usedin emergency management counterterrorism and nationalsecurity This paper focuses on the group extreme incidentswhich are caused by human or organization planning Thereare some characteristics of this type of events so we makethree reasonable assumptions for the events description andcomputational experiments

The first assumption is that the events in the incidentswould not occur at the same timeThis means that the eventsare discrete in the simulation experiments Although theemotion evolution process may last for a period of timethe events (including related behaviors such as attributeschangings) are independent

The second assumption is that at any given moment allactors act conditionally independently of each other Such anassumption was already proposed in many studies [20] as abasis for ABS research

The third assumption is that the strategies are performedcompletely and ideally Although the strategy definition

and construction depend on the real possibility and fea-sibility we assume that there is no case of failure in theexperiment

The general principle of these assumptions is tomodel theprocess in a formal framework Based on the assumptionswe can treat the problem as a behavior evolution processon the network The individuals can be represented as thenodes of the network and the individual actions are the agentbehaviors based on the relation of the network

The underlying network structure is the basic structure ofthe diffusion processes which consisted of agents (individu-als) and relationships between them We use the definitionof dynamic network in [20] The set 119873 is a set of socialactors (individuals or agents) the relation on 119873 is definedmathematically as a subset of the 119873 times 119873 and the relation isrepresented by the 119899 times 119899 adjacency matrix 119883 = (119883

119894119895) The

119883119894119895

= 0 1 respectively represents that there is no link orthere is a tie between agents 119894 and 119895 (119894 119895 = 1 119899)The agentattributes are assumed to be discrete with a preset intervalof values and 119885

ℎ119894denotes the value of agent 119894 on the ℎth

attributeThe time dependence is indicated by denoting119885ℎ=

119885ℎ(119905) where 119905 denotes time and 119885

ℎis the column containing

the 119885ℎ119894values

This paper presents models andmethods for studying thedynamic evolution process of (119885

1(119905) 119885

119867(119905)) Virtually

the adjacency of the relation matrix 119883 should be includedin the dynamic analysis as well but we here assume thatthe network remained changeless in a short period (eg anevent) which is proposed by previous research [21] In con-trast to the individual attributes 119885

ℎ we are more interested

in the collective state for example the statistics result of theagentsrsquo attributes which describe the characteristics of thewhole collective behaviors and states and they are also calledcovariates [20]

Suppose that the observations on (1198851(119905) 119885

119867(119905))

are available for discrete observation time 1199051

lt 1199052

lt

sdot sdot sdot lt 119905119872 The collective attributes could be represented as

(1198651(119905) 119865

119871(119905)) and 119865

119897(119905) = 119891

119897(1198851(119905) 119885

119867(119905)) in which

1 le 119897 le 119871 For simplifying the processes (1198851(119905) 119885

119867(119905))

and (1198651(119905) 119865

119871(119905)) could be represented by the symbol

119884(119905) and the totality of available data is represented by119910(1199051) 119910(119905

119872)

The interventions strategies are defined as a series offunctions acting on the agents set 119873 the relation set 119883 andthe attributes set 119885 We use the symbol 119878 to represent thestrategy set and 119878 = (119878

1 119878

119870) where the constant 119870 is

the number of the strategies For each strategy there is aformulation of 119878

119896= 119891119896(119873119883 119885

1(119905) 119885

119867(119905) 119905) The 119905 in the

formulation means the time on which the strategy performsBased on the definition we could now describe the

problem as follows the initial data include the agentsset 119873 the relation set 119883 the attributes matrix of theagents (119885

1(1199051) 119885

119867(1199051)) and the covariates set (119865

1(1199051)

119865119871(1199051)) the agents will take actions (interaction) during each

time step which makes the values of 119885 and 119865 changingthe purpose of this paper is to understand the dynamicevolution process of the collective emotions 119865 and to observethe effectiveness of different intervention strategies in theevolution process









Strategies analysis



The group structure


Interaction rules

drivenEvents

Relation

The agentmodel

Diffusion



simulationframework

Statisticalresults













3 Model Description







The agent model







1 1198642 119864

119870 and



119879 = 11986412 11986422 119864




119894= 119885119864

1 1198851198642

119885119864119870 and 119885119864

119896= 0 1






1



3






3will be zero




1198961 which can

be shown as follows

1198852119894

= 119891 (1198851119894 1198641198961) = 1198851119894times 1198641198961 (1)



1198853119894

=

(sum119883119894119895=1

1198854119895)

119889

(2)


1198854119894

= 1198851119894times 1198852119894+ (1 minus 119885

1119894) times 1198853119894 (3)


where the 1198851119894


4119894(119905)



5119894


1198852119894 (119905) = 119885



1198856119894 (119905) =

119870

sum

119896=1

119885119896

4119894(119905) (5)






1and 119883

1 Let 119873

1015840


1=

119873minus1198731015840

1 Here we use1198831015840



1 that is

1198831015840

1= 119883119894| 119894 isin 119873

1015840

1 and119883

1= 119883 minus 119883

1015840


in 1198731015840


removed



2








3= 119883minus119883

1015840

3The key





1(119905) 119865

119871(119905)) Besides


1 119879

119872) In this














1)





3)


4)


5)


6)



































541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)



3





0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















Strategies analysis



The group structure


Interaction rules

drivenEvents

Relation

The agentmodel

Diffusion



simulationframework

Statisticalresults













3 Model Description







The agent model







1 1198642 119864

119870 and



119879 = 11986412 11986422 119864




119894= 119885119864

1 1198851198642

119885119864119870 and 119885119864

119896= 0 1






1



3






3will be zero




1198961 which can

be shown as follows

1198852119894

= 119891 (1198851119894 1198641198961) = 1198851119894times 1198641198961 (1)



1198853119894

=

(sum119883119894119895=1

1198854119895)

119889

(2)


1198854119894

= 1198851119894times 1198852119894+ (1 minus 119885

1119894) times 1198853119894 (3)


where the 1198851119894


4119894(119905)



5119894


1198852119894 (119905) = 119885



1198856119894 (119905) =

119870

sum

119896=1

119885119896

4119894(119905) (5)






1and 119883

1 Let 119873

1015840


1=

119873minus1198731015840

1 Here we use1198831015840



1 that is

1198831015840

1= 119883119894| 119894 isin 119873

1015840

1 and119883

1= 119883 minus 119883

1015840


in 1198731015840


removed



2








3= 119883minus119883

1015840

3The key





1(119905) 119865

119871(119905)) Besides


1 119879

119872) In this














1)





3)


4)


5)


6)



































541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)



3





0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












The agent model







1 1198642 119864

119870 and



119879 = 11986412 11986422 119864




119894= 119885119864

1 1198851198642

119885119864119870 and 119885119864

119896= 0 1






1



3






3will be zero




1198961 which can

be shown as follows

1198852119894

= 119891 (1198851119894 1198641198961) = 1198851119894times 1198641198961 (1)



1198853119894

=

(sum119883119894119895=1

1198854119895)

119889

(2)


1198854119894

= 1198851119894times 1198852119894+ (1 minus 119885

1119894) times 1198853119894 (3)


where the 1198851119894


4119894(119905)



5119894


1198852119894 (119905) = 119885



1198856119894 (119905) =

119870

sum

119896=1

119885119896

4119894(119905) (5)






1and 119883

1 Let 119873

1015840


1=

119873minus1198731015840

1 Here we use1198831015840



1 that is

1198831015840

1= 119883119894| 119894 isin 119873

1015840

1 and119883

1= 119883 minus 119883

1015840


in 1198731015840


removed



2








3= 119883minus119883

1015840

3The key





1(119905) 119865

119871(119905)) Besides


1 119879

119872) In this














1)





3)


4)


5)


6)



































541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)



3





0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










where the 1198851119894


4119894(119905)



5119894


1198852119894 (119905) = 119885



1198856119894 (119905) =

119870

sum

119896=1

119885119896

4119894(119905) (5)






1and 119883

1 Let 119873

1015840


1=

119873minus1198731015840

1 Here we use1198831015840



1 that is

1198831015840

1= 119883119894| 119894 isin 119873

1015840

1 and119883

1= 119883 minus 119883

1015840


in 1198731015840


removed



2








3= 119883minus119883

1015840

3The key





1(119905) 119865

119871(119905)) Besides


1 119879

119872) In this














1)





3)


4)


5)


6)



































541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)



3





0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1(119905) 119865

119871(119905)) Besides


1 119879

119872) In this














1)





3)


4)


5)


6)



































541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)



3





0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






























541 537 (001) 327 (minus3955) 479 (minus1146)1198652

8223 8201 (000) 6008 (minus2694) 7122 (minus1339)1198653

25094 25039 (000) 20958 (minus1648) 23022 (minus826)1198791

122 124 (+164) 158 (+2951) 122 (000)1198792

45 45 (000) 44 (minus222) 45 (000)1198793

16 17 (+625) 29 (+8125) 17 (+625)1198794

40 40 (000) 49 (+2250) 43 (+750)1198795

20 20 (000) 34 (+7000) 21 (+500)1198796

102 104 (+196) 125 (+2255) 102 (000)



3





0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

100

200

300

400

500

600




The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)





25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










25 75 125 175 225 275 325 375 425 4750

500

1000

1500

2000

2500

3000

3500

4000

4500

Emotion value

Num

ber o

f age

nts



(a)

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500


Envi

ronm

enta

l infl

uenc

e em

otio

ns(b)

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

900


Age

nts n

umbe

r

(c)

0 50 100 150 200 250 300 350 400 4500

200

400

600

800

1000

1200


Age

nts n

umbe

r

(d)










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 50 100 150 200 2500

1000

2000

3000

4000

5000

6000

7000


The n

umbe

r of e

xtre

me g

roup

agen

ts



(a)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)



1 minus157)




6) In











1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















1198792 45 84 (+8667) 46 (minus4524) 86 (+238) 86 (+238)

1198793 17 18 (+588) 0 (minus100) 33 (+8333) 18 (0)


1198795 20 25 (+2500) 0 (minus100) 38 (+5200) 25 (0)






1198651 0608 0000 0000

1198652 0221 0000 0000

1198653 0152 0000 0000

1198791 0437 0000 0818

1198792 0407 0000 0169

1198793 0340 0000 0022

1198794 0849 0000 0166

1198795 0470 0000 0003

1198796 0411 0000 0872








20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20 30 40 50 60 700

100

200

300

400

500

600

Simulation step

The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)

20 30 40 50 60 70 800

1000

2000

3000

4000

5000

6000

7000

8000

9000

Simulation step

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

20 40 60 80 1000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

(c)

20 30 40 50 60 700

2000

4000

6000

8000

10000

Simulation step

The n

umbe

r of a

gent

s hav

ing

even

t inf

orm

atio

n

(d)










0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0

100

200

300

400

500

600Th

e num

ber o

f ext

rem

e gro

up ag

ents

(a)


0

100

200

300

400

500

600

The n

umbe

r of e

xtre

me g

roup

agen

ts

(b)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(c)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(d)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e


Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(e)

0

50

100

150

200

250

Aver

age e

mot

ion

valu

e


Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(f)

Figure 7 Continued



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000ha

ving

even

t inf

orm

atio

nTh

e num

ber o

f age

nts

Pin = 01

Pin = 02

Pin = 03

Pin = 04

Pin = 05

Pin = 06

Pin = 07

Pin = 08

Pin = 09

Pin = 10

(g)


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

havi

ng ev

ent i

nfor

mat

ion

The n

umbe

r of a

gent

s

Pre = 00

Pre = 01

Pre = 02

Pre = 03

Pre = 04

Pre = 05

Pre = 06

Pre = 07

Pre = 08

Pre = 09

(h)









122 25 (minus7951) 133 (+902) 123 (+082)










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 100 200 300 400 500 6000

50

100

150

200

250

300

Simulation step

Aver

age e

mot

ion

valu

e

Event 6

Event 7 Event 8

Event 4

Event 3

Event 2

Event 1

Event 5






6 Conclusion













0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


The n

umbe

r of e

xtre

me g

roup

agen

ts

(a)



00 100 200 300 400 500 600


2000

4000

6000

8000

10000

12000

The n

umbe

r of a

gita

ted

grou

p ag

ents

(b)

0

50

100

150

200

250

300

Aver

age e

mot

ion

valu

e




(c)




Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article agent based simulation of group emotions...

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