2016美赛原版奖-优秀已打2016d

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TeamControlProblemD

ForofficeuseonlyAbridgetheDistancebetweenHuman—ResearchonSocialInformationInformationcirculationnetworkisascomplicatedasthehumanbrain,whilebrainwithwisdomseekstoexplorethemysteriesoftheinformationcirculationnetwork.,weestablishamodelofinformationcirculationnetwork(ICP).Thenweestablishfivenetworktopologygraphsandqualitativelyyzeevolutionoffiveperiods.Basedonclassicalepidemicmodel,weintroducethesuper-spreader,whichcaneffectivelyacceleratethecirculationofinformationasthecentralnode.Thedifferentialequationsandtheirresultsgiveusreasonablecirculationlaws:thedensityofthespreaderandthesuper-spreaderrapidlyincreaseatthebeginning,thentheyreachakanddeclinerapidly;theignorantdensityshowsarapiddownwardtrendwhiletheimmunedensitygenerallyincreases.Webuildthefuzzycomprehensiveevaluationmodel(NF)tofilterwhatqualifiesasnews.Weproposeaudienceawarenessindex(AAI)toindicatetheinherentvalueofinformation.Thenweusefourgivenexamplestotestthemodel.Undoubtedly,theassassinationofAbrahamLincolnwasqualifiedasnews;andsodoestheimportant’sassassinationtoday.AsforinformationofTaylor’sstyletransition,it esnewstoday,butitmightnotbenewsin1860.Thenweusetheneuralnetworkpredictionmodel(ICNP)topredictthenetworks’relationshipsandcapacities.WegetthenodenumberandthenodedegreeviapreviousdatafromthreestatesinUSA.AndtheresultsofICNPmodelare:inthefifthperiod,nodenumberofNewYorkis22535000,anditsrelativeerroris15.32%;inthefifthperiod,nodedegreeis13533000,anditsrelativeerroris20.58%.SoitvalidatesthereliabilityofICPmodel.Inaround2050,nodenumberofNewYorkis34885000andnodedegreeis23766000.Finally,webuildourmodel(PIINI)consideringtheinterestattenuationmechanismandsocialstrengtheningmechanism.Takingtheinteractionofinformationcirculationnetworkandpublicinterestsintoaccount,weestablishdifferentialequationssimilarly.Anditcomestointeractionlaws:thedensityofthespreaderandnodesinconnectionstaterapidlyincreaseatthebeginning,theyreachapeakandthendeclinerapidly.Theignorantdensityshowsarapiddownwardtrendwhiletheimmunedensitygenerallyincreases. Keyword:InformationCirculationNetwork EpidemicModel BPNeuralNetworksAbridgetheDistancebetweenHuman—ResearchonSocialInformationRestatementofthe JustificationofOur Symbol The Informationcirculationnetworkmodel Themodel Tosolvethe Newsfiltermodel Influentialfactorsofaudience’sawareness Themodel Theprocesstotestthe Informationcirculationnetworkpredictionmodel Influential Themodel Tosolvethe Publicinterestandinformationnetworkinteractionmodel Themodel Tosolvethe Sensitivity Strengthsand Appendix(dataanddataTeam# Page1ofRestatementoftheInformationspreadquicklyintoday’stech-connectedcommunicationsnetwork;sometimesitisduetotheinherentvalueoftheinformationitself,andothertimesitisduetotheinformationfindingitswaytoinfluentialorcentralnetworknodesthataccelerateitsspreadthroughsocialmedia.ExploretheflowofinformationandfilterorfindwhatqualifiesasPredictthecommunicationnetworks’relationshipsandcapacitiesaroundtheyearExplorehowpublicinterestandopinioncanbechangedthroughinformationnetworksintoday’sconnectedworld.Determinehowinformationvalue,people’sinitialopinionandbias,formofthemessageoritssource,andthetopologyorstrengthoftheinformationnetworkinaregion,country,orworldwidecouldbeusedtospreadinformationandinfluencepublicopinion.InterpretationoftheseWeshouldbuildamodeltoindicatehowinformationcirculateinsocialWeshouldfigureoutanimprovedmodeltofilterwhatqualifiesasnewsbasedonmodel.Weshouldpredictpresentnetwork’srelationshipandcapacitytovalidatemodelbyusingourmodel’spredictionability,andpredictfuturenetwork’srelationshipandcapacityinaround2050.Weshouldbuildanothermodeltoexploretheinteractionofpublicinterestandinformationnetwork.Socialinformationcirculationnetworkisaveryactiveresearcharea.Buildingthesocialinformationcirculationnetworkisthehotareaofcomplexnetworkresearch.ThatresearchhasveryimportantvalueforunderstandingthedynamicbehaviorofthePreviousInpreviousysis,mostofmodelsarebasedontheclassicalepidemicmodelSI,SISandSIR,etc.[1,2]TheICmodel[3,4]proposedbyJacobGoldenbergandtheLTmodel[5]proposedbyMarkGranovetterismostwidelystudiedcurrently.AndJaewon迈思数模2018美赛课程表及报名安排 VIP学员无报名费（强制80（建议参加）；点评联系辅助报名：750元模拟赛学员：700联系门班课程元；三科398元【限时特惠168-268-368】赛前冲刺20法班课程赛前冲刺课程更新时间为：1116共计20节课赛前冲刺20VIP（入门班课程【限时特568-668-768拟赛+辅助报名（100支付后，请联系下VIP（算法班课程拟赛+辅助报名（100拟赛+辅助报名（100群（比提醒：VIP班学员强制参加模拟赛，其他学员建议参与模拟赛，因为根据国赛模拟赛结果来看，参与模拟赛的学员几乎都了国奖，未参加模拟赛的学员国奖的比例远没有参加模拟赛国奖的比例高！！！联 andotherresearchersproposedalinearinfluencemodel[6]bytheysisof’susers’behaviors.Fromtheaspectofsocialpsychology,themassinformationcirculationprocessisplacedinaenvironmentaffectedbyavarietyofsocialforcesandpsychologicalfactors.Massadescribedtheysisandpredictionofperceiveduserbehaviorbasedontrustframework[7].Jamaliandotherresearchers[8]useTrustWalkermodeltopredictbehaviors’ofusers.JosangA[9]buildausertrustpredictionsystemtodescribethedevelopmentoftrustbetweendifferentusers.Table1 WedonottaketimedelayduringinformationcirculationtwonodesintoICNWethinkthepublicinterestisWedonottakesocialstrengtheningintoWedonotconsiderthedifferencebetweendifferentWethinktheinfluencebetweentwonodeswillnotaffectourNF WethinktheaudienceawarenessistheonlyindicatorofinterestandICNPWedonotconsidersecondaryWethinkthenetworkisuniversalaroundthePIINI WedonotconsidersecondaryJustificationofOurICNDynamicsofepidemicdiseasecaneffectivelyportrayonthecirculationcharacteristicsofcomplexnetwork,whichisanimportantbasisforthecurrentnetworkcirculationdynamics.Super-spreaderplaysanimportantroleintheinformationcirculationnetwork.Onthebasisofclassicalepidemicmodelweintroduceofthesuper-spreaderandestablishdifferentialequationswhichcaneffectivelyportrayinformationcirculationnetwork’scharacteristics.NFNewsisobjectivereportofwhataudiencesareconcernedabout.Theconceptofaudienceawarenessisvague,butwecanqualitativelyyzeaudienceawarenessindexhasapositiveinfluenceoninherentvalueofinformation.Thefuzzycomprehensiveevaluationmodelcancharacterizethetransitionstatebetweennewsandinformation.Therefore,itisappropriatetouseNFmodeltofilterwhatqualifiesasnews.ICNPmodelInformationcirculationnetworkisacomplexandrandomsystem,influencedbymanyfactors.UsingthestatisticalforecastingmodeltopredictmighthavedefectsespeciallywhenthesampledataarenotenoughandwhenhistoricaldataareAndweuseBPneuralnetworktobuildICNPmodel,whichcan ethisPIINIStrengtheningsocialmechanismisanimportantdistinctionbetweentheinformationcirculationandthespreadofdisease.Socialinterestattenuationmechanismisalsosignificantininformationcirculationnetwork.ProposedPIINImodeltakessocialinterestattenuationandsocialstrengtheningintoaccount,soitcanbeeffectivelyandreasonablyreveallawsintheinformationcirculationnetwork.SymbolTherearesomemajorsymbolsappearinthemodel,asshown k kk-1 kk-inodeiandneighborsineighbors.EistheedgesC ClusteringcoefficientrepresentprobabilityofanytwonodesD NNNetworkdensityisasymptomnetwork’s aNkiNNkTheaverageofallnodedegreestheNodedegreeaveragejjNNkiaija.Ni matrixAThedegreeofnodesisthenumberconnectednodes.AndgiveNode connectedanddisconnectedNotes:wewillexplainothersymbolswhenweuseTheInformationcirculationnetworkmodelSocialnetworkisacomplexnetwork,whichiscomposedofsocialindividualsaswellasthesocialrelationshipsbetweenindividualmembers.[10]Intherelatednetworkresearch,researchersusedG（V,E,W）graphtobuildmodel.Visthesetofnetworknodes;EVVisthesetofrelationshipsbetweensocialindividuals;WistheweightofsocialTopologicalpropertiesofnetworkareirrelevantwithsize,location,shandfunctionofnodes.However,theyareonlyrelevantwithnumberofnodesandtheconnectionfeaturesbetweenconnectednodes.Intheresearchofsocialnetworks,directedgraphhasabetterexpressiveabilityandapplicability,soweuseadirectedgraphtocharacterizesocialnetworks.Andbasedonthis,resentthefollowingindices.ThemodelTherearelotsofclassicalepidemicmodels,suchasSI,SIS,SIR,ICandLT.Wetakeintoaccountthecentralnode(suchastheInternet)hashigherspreadingfunctionthanordinaryspreader.Wethenintroducesuper-spreaderstoournetworktoimprovetheSIRmodel.Wedividetheuserintofourparts:ignorant,spreader,super-spreaderandimmune.Andthedefinitionoftheseareasfollows[11]:Table3FourtypeofTypesofTheignoranthasnotreceivedanyinformationfromThespreaderreceivesinformation,thespreaderwillprobablyspreadtheinformationtoneighbors.TheimmunewillnotspreadtheinformationafterreceivingtheThesuper-spreaderisabletoquicklydeliverinformationtomoreγβδSuper-TheγβδSuper-αFig1thepropagationrulesoftheTherulesofinformationcirculationareshownabove.Wecanconcludetherulesasfollows:Ifignorantconnectstoaspreader,theywillturnintospreaderwithaprobabilityβ.Forpublicityandotherreasons,somespreaderswillturnintosuper-spreaderwithaprobabilityα.Aftercontactingwithotherspreaders,thesuper-spreaderwillturnintotheimmunewithprobabilityδ.Aftercontactingwithotherspreaders,immunesorsuper-spreaders,thespreaderwillturnintotheimmunewithaprobabilityγ.TheinformationcirculationnetworkinfiveOnthebasisoftheestablishmentofinformationcirculationnetworkmodel,consideringthecharacteristicsofmodesinformationcirculationinfiveperiods,welistthenetworkcirculationinformationmodelinfiveperiodsasfollows:Table4theinformationcirculationgraphand

Theinformationcirculation

Thenumberofnode,thedegreeofnode,internetdensityandclusteringcoefficientare"Newsproffice"nodeisregardedassuper-spreadersandplaysanimportantroleintheinformationnetwork.Theclosenessofinformationcirculationispoor.Regionallinksbetweenusersarestrong.(4)SpreadingflowissmallandspreadingspeedisSametotheperiod,thenumberofnode,thedegreeofnode,internetdensityandclusteringcoefficientaresmall."Radio"nodeisregardedassuper-spreadersandplaysanimportantroleintheinformationnetwork.(3)Theclosenessofinformationcirculationispoor.Regionallinksbetweenusersdecrease.(4)Comparedwith period,thespreadingflowandspreadingspeedincreasesignally.

Thenumberofnode,andinternetdensityarelarge,whilethedegreeofnodeandtheclusteringcoefficientaresmall."evisionstation"nodeisregardedassuper-spreadersandplaysanimportantroleintheinformationnetwork.Theclosenessofinformationcirculationisbetter.Regionallinksbetweenusersispoor.(4)Comparedwithsecondperiod,thespreadingflowandspreadingspeedincreasesignally.ComparedComparedwiththefourthperiod,thenumberofnode,thedegreeofnode,internetdensityandclusteringcoefficientarelarger.Somenodesininternetareregardedassuper-spreadersandplayanimportantroleintheinformationnetwork.Theclosenessofinformationcirculationiswell.Regionallinksbetweenusersispoor.(4)Comparedwithfourthperiod,thespreadingflowandspreadingspeedincreasesignally.densityandclusteringcoefficientarelarge. Theclosenessofinformationcirculationiswell.Regionallinksbetweenusersispoor.(4)Comparedwiththirdperiod,thespreadingflowandspreadingspeedincreasesignally.WhichnodesdonotenterthenetworkarenotshownintheSolidcirclerepresentsthesuper-spreader,anddottedcirclerepresentstheThedifferentialequationofinformationcirculationBasedonthreecirculationprinciples,webuilddifferentialequationsasdI(t)IdS(t)S(t)I(t)S dJ J S(t)JtIntheseequations,I(t)，S(t)，J(t)andR(t)respectivelyrepresent,attimet,thedensityoftheunknown,thespreader,thesuper-spreaderandtheimmune.Thedensityoffourtypesofusersmeetstheconditionofnormalization:ItStJtRt1.When0,0,thismodelwillturnintoclassicalSIRmodel.Withtheevolutionofthesystem,whenthenumberofspreadersiszero,theprocessstopsandspreadofnetworkends.AndthenetworkwillonlycontainthosewhohavenotyetreceivedanyTosolvetheWeuse2014bsoftwaretosolvedifferentialequations.Bymeansofnumericalsimulations,thenumberofconfigurednodesis1000inthenetwork,theinitialnumberofspreadersis1.Intheinitialstage,St011000,It09991000,Jt0Rt00,andweassume0.1,0.7,0.5,0.3[17].Fig1showsgeneraltrendsoftypesofnodes’Fig2densitiesofdifferentgroupsintheAccordingtotheysisoffig2,wecanLawone:Spreader’densityrapidincreaseattheinitialstage.Afteritreachesapeak,itdeclinesrapidly,untilthespreaderentersintotheimmunestate.Lawtwo:Theevolutionarytrendofsuper-spreaderslikethatofordinaryspreaders,anditalsoexperiencesanincrease,andthendecreaseuntilitdisappears.However,thecurvechangesgently.Thepeakdensityisalsomuchsmallerthanordinaryspreaders.Thisshowsthatintheonlinesocialnetworks,super-spreadersareasmallnumberof"starnodes."Lawthree:Ignorantdensityshowsarapiddownwardtrend.Anditeventuallysettlestoanon-zerovalue.Andthatreflectstheinformationcirculation’sbreadthanddeptharelimitedanditisimpossibletocoverallusers.Lawfour:Thetrendofimmunedensityisoppositetothatoftheignorant.Itexperiencesarapidincreasestageandthengraduallystabilizestoavaluecloseto1.Rapidincreaseoftheimmunedensityismainlybecausespreadersandsuper-spreaderscontinueturningintotheimmunestate.Andtheincreasingtrendslowsbecausethereisnonewspreader.Lawfive:Itisworthnotingthat,wheninformationcirculationstops,thedensityofthespreaderandthesuper-spreaderareequaltozero,butthedensityoftheignorantandtheimmunearenotzero.Itindicatesthatthereareuserswhodoesnotreceivetheinformationinthenetwork.Thesizeofinformationcirculationhasacertainlimit,anditisimpossibleto“infect”allusers.NewsfiltermodelNewsisdefinedasareportforwhataudiencesfocus[12].Thedogsbitehumanbeingsisnormal,whilethathumanbeingsbitedogswill enews.Thereasoniswefocusmoreonhumanbeingsbitingdogs.Sointhelightofaudience’sawareness,wedefineaudience’sawarenessindex(AAI).BydeterminingthevalueofAAI,wecanfilterwhatqualifiesasnews.Influentialfactorsofaudience’sawarenessThenumberofaudiences,thepoliticalstatusofaudiencesandtheinfluenceofinformationhaveaninfluenceonAAI[13].AndtheysisofthesefactorsareasThenumberofThenumberofaudiencesisthenumberof swhoareconcernedaboutthisinformation.Themorethenumberoftheaudiencesis,thehighertheAAIis.ThepoliticalstatusofHigherpoliticalstatusofaudiences,themoreitcanarousetheaudience'sattention,soAAIwillbehigher.TheinfluenceofThehighertheinfluenceofnews,thehigherthevalueofAccordingtoforegoingysis,therearepositivecorrelationsbetweentheAAIandthesefactors.ThemodelInordertocalculate,webuildthefuzzycomprehensiveevaluationmodel.,weshoulddetermineindexweightmatrix.Thenweimprovethemaxminalgorithmandtheprincipalof ummembershipdegreeamongevaluationresults.Webuildthesetoffactors,thesetofevaluation,membershipfunctionandthesetofweight[13].Last,wecomprehensivelyevaluateAAI.Step1:DeterminethesetofevaluationP={InformationtobeStep2:BuildthesetofevaluationUu1,u2,u1,u2,u3isthenumberofaudiences,thepoliticalstatusofaudiencesandtheinfluenceofnewsrespectively.Step3:DeterminetheuniverseofevaluationBuildasetofevaluationv，eachlevelcancorrespondtoafuzzysubsetV=v1,v2,Step4:CalculateindexUsepairedcomparisonmethodand1-9comparativescaletocalculateindexweight,wehaveA=[0.4,0.3,0.3]Step5:CalculatefuzzyrelationshipmatrixEvaluateU,andthenfigureoutthemembershipdegree.FinallygetthefuzzyrelationshipmatrixR.Step6:CalculatethevectoroffuzzyevaluationresultsUsetheweightedaverageoffuzzyarithmeticoperatorsM,todetermineindexweightmatrixAandfuzzyrelationshipmatrixR,andtheformulais: bi(airij)min1,airij,j1,

SynthesizingtheAandRwillgetthevectoroffuzzyevaluationresultsB.Accordingtothedefinition,ifBs>Bt,thevalueofinformationsishigherthanthatofinformationt.ThevalueofvectorBisAAI.Step7:CalculatethevalueofiWeuseCAAI=(B'[3,2,1])3toindicatethevalueofiTheprocesstotesttheWeusethegivenfourexamplestotestourInformationa:country-turned-popsingerTaylorSwift’spossibleengagementInformationb:country-turned-popsingerTaylorSwift’spossibleengagementinInformationc:an wasassassinatedInformationd:assassinationofUSAbrahamLincolninDuetospacelimitations,thesolutionprocessomitssteps1-4.Andaccordingtostep5,wegettheevaluationmatrixes: R=

，R

0.1 0.1 0.4 a

b 0.1 0.4

R= c

，Rd

0.1 0 Wecalculatetheresultofevaluationvector,andweBa[0.30,0.54Thenaccordingtostep7,we

Bb[0.10,0.46,0.44]Bd[0.89,0.07,CAAIa=0.71，CAAIb=0.55，CAAIc=0.87，CAAIdAccordingtopreviousysis,thegreatervalueofCAAI,thegreaternumberofaudienceswillbeconcernedaboutgiveninformation.Sotherearemorereasonstoexplainwhythisinformationisqualifiedasnews.Inthisfourexamples,thattheUSwasassassinatedundoubtedlybecamenews;andsodoestheimportantoccurredtoday.AsforinformationofTaylortransitionstyle,itisstillisanewstoday,butifithappened1870,perhapsitwillnotbeconcernedabout.InformationcirculationnetworkpredictionmodelInformationcirculationnetworkisacomplexandrandomsystem,influencedbymanyfactors.Usingthestatisticalforecastingmodeltopredictmighthavedefectsespeciallywhenthesampledataarenotenoughandwhenhistoricaldataarevolatile.Therefore,weimprovetheICNmodelbyaddingBPneuralnetworkpredictionmodeltopreviousmodeltopredictinformationcirculationnetwork’snodenumberandnodeInfluentialComprehensiveysisoffactorsthatinfluencethespreadofinformationnetworksisaprerequisitetoimproveICNmodelbyusingitsabilityofprediction.Basedontherealityofsociallifeandthecomplexityoffindingdata,wewillselectthefollowingmainfactors:LevelofregionaleconomicThelevelofregionaleconomicdevelopmentismeasuredbyregionalGDP.Thehigherthelevel,themorebeneficialtoinformationcirculation.LevelofregionalcommunicationThelevelofregionalcommunicationdevelopmentismeasuredbyinformationcommunicationtechnologydevelopmentindex(IDI)[15].ThelargertheIDI,themorebeneficialtoinformationcirculation.LevelofregionaleducationThelevelofregionaleducationdevelopmentismeasuredbyeducationindexThelargertheEI,themorebeneficialtoinformationThemodelAccordingtotheforegoingICNmodel,wewillbuildICNPmodeltopredictthenumberofnodeandthedegreeofnode.Thenumberofnodedeterminethesizeofnetwork,andthedegreeofnodedeterminethecapacityoftheSimilartoteralneuralnetworkmodel,ourICNPmodel’spredictionprocessisasfollows:Fig3ICNPmodel’spredictionDataInthisp r,dataarenormalizedbyusing umandminimumnormalizationmethod.Thedatanormalizedformulais:X XX

XmaxXiDeterminetheinputnumberofAccordingtoHurvich’sstudy,whensampledataisless,ifusingACIcriteria,therewillbegreatestimationbias.So,basedonACIcriteria,HurvichproposedAICCcriteriaspecificallyapplicabletosmallsamples.Andtheformulais:Amongthe

AICC(m)NlnE NNm

N N20~m

~N,N40~

lnN,N100~TosolvetheCollectWecollectfrominternet,andcollectdatainthreestates:California(CA),Texas(TX)andNewYork(NY)inUSA.AndthesethreestateshavetopthreelargestpopulationamongfiftystatesinUSA.Thereasonwechoosethesethreestatesarebecausethesedataareeasiertofindandthesedatasamplesarelarger.ThedataanddatasourceareshownintheWeusedataexcludingthedatafromNewYorkatfifthperiod.AndthenweusetheICNPmodeltopredictthedatainNewYorkatfifthperiodandcomparethesedatawithpresentdatatovalidateourICNmodel.Table5duringthesampleperiodFromICNFrompredictRelativeerrorNumbernode(Degree Predictfuturenetwork’srelationshipsandcapacitiesinTable6duringthesampleperiodICNPNumberof)Degreeof PublicinterestandinformationnetworkinteractionmodelIntheprocessofsocialinformationcirculationnetworks,thecirculationofinformationaffectsindividuals’preferences.Wealsothinkthatindividuals’differentpreferencesaffectsinformationcirculationnetworks.Thatissameaswhatquestionsaidthatpublicinterestcanbechangedthroughinformationnetworks.Intheme informationvalue,people’sinitialopinionandbias,formofthemessageoritssource,andthetopologyorstrengthoftheinformationnetworkinaregion,country,orworldwidecouldinfluencepublicopinion.ThemodelInformationcirculationisintrinsicallydifferentfromthecharacteristicsofthespreadofdisease[17].Anditscharacteristicsshouldconsideravarietyoffactors.Weconsideronlyconsidertwofactors:publicinterestdecayandsocialstrengtheningeffectBasedonthesetwofactors,webuildPIINImodeltorevealtheinteractionofpublicinterestandinformationnetwork.PublicinterestattenuationThepublicinterestdecaymechanismreferstothepublicinterestdecreaseswhenthetimesofreceivingsameinformationincrease[18].Ifusersrepeatedlyreceivedthesameinformationfromneighboringnodes,userswillacquiesceininformationbeingwidelydisseminated.Thenthereexistsattenuationcoefficient[19]whichindicatesuserswillgraduallydecreasetheirbehaviorofcirculatinginformation.Therefore,weintroduceasaturationfunctiontorepresentpublicinterestattenuationcoefficient:(m)a Andaisthe umattenuationrate,bistheadjustablecoefficient,theispublicinterestattenuationcoefficientandmisthenumberofconnectedusers.Thesaturationisanon-linearincreasingfunction.Whenthe umattenuationratea=1,b=1adjustablecoefficient,asmincreasesandnonlineargrowth,indicatingthatthelossofinterestandforwardedintoaconnectedstatemoreandmoreusers.Whena=1,b=1,whenmandincreases,thenumberofuserslosinginterestincreases.Asshowninfig4.Fig4themechanismofinterestSocialstrengtheningSocialstrengtheninghavenonlinearcumulativeeffectwhichhaveasignificanteffectonpublicinterest[20].Becauseofthismechanism,anindividual,userswillbeaffectedbyneighbors’cumulativeeffectsbeforetheyadoptreceivedopinions[21].Inourpr,wedefinethesocialstrengtheningmechanismas:theprobabilityofauser’sbehavior(includingtheacceptanceanddisseminationofinformation)willdecreasewhilestrengtheningfacteneratedfromneighbors’discouragement.Thelargerthestrengtheningfactor,thelowertheprobabilityofauser’sbehavior(includingtheacceptanceanddisseminationofinformation).Weusethefollowingnonlinearfunctiontoexplainthesocialstrengtheningmechanism.(n)

indicatestheprobabilityofauser’sbehavior(includingtheacceptanceanddisseminationofinformation),nindicatesthenumberofconnectednode,isthestrengtheningfactor,01.Fig5thesocialstrengtheningeffectchangedwithAsfig5shows,thelargervalueof,thelargervalueofn.Intheme ,thelargervalueof,thesmallervalueof.Fig6thesocialstrengtheningeffectchangedwithAsfig6shows,whentheprobabilityisconstant,thevalueofwilldecreasewhenthevalueincreases.Itshowsthatbyincreasingtheeffectofsocialstrengthening,moreuserswillstayintheunconnectedstate.AndthereforethenumberofspreaderswillImprovetheinformationcirculationThestateofconnectiondefinedasastatethatusershavealreadyreceivedinformationbuttheyarenotsurewhethertospreadtheinformation.Andtheinformationcirculationrulesareasfollows:Ifignorantisconcernedaboutreceivedinformation,theignorantwillturnintospreaderwithaprobabilityβ;ifignorantisnotconcernedaboutreceivedinformation,thewillturnintotheimmunewithaprobabilityγ.Withtimesofcirculationincreasing,thespreaderwillgraduallyloseinterestintransferringinformationtoothersandturnintotheimmunewithaprobabilityofInterestInterestattenuationγβξζθFig7thecirculationrulesofPIINIThedifferentialequationsinPIINII(t、S(t、C(tandR(t)indicatethedensityofignorantnodesspreadernodesinconnectionstateandimmunenodeswhennodedegreeiskattimet.Theequationsareshownbelow:dI(t)IdS(t)I(t)()S(t)S(t)

S(t) dR(t)()S When0,0,0,thismodelwilldegeneratetoclassicalmodelTosolvetheWeuse2014bsoftwaretosolvedifferentialequations.Bymeansofnumericalsimulations,thenumberofconfigurednodesis1000inthenetwork,theinitialnumberofspreadersis1.AndSt011000,It09991000,Jt0Rt00and 0.1,0.7,0.5,0.3,0.3,0.15[17].Fig8showsgeneraltrendsoffourtypesofnodes’density.Fig8densitiesofdifferentgroupsintheAccordingtotheysisoffig8,wecanLawone:Spreader’densityrapidincreaseattheinitialstage.Afteritreachesapeak,itdeclinesrapidly,untilthespreaderentersintotheimmunestate.Lawtwo:Theevolutionarytrendnodesinconnectionstaikethatofordinaryspreaders,anditalsoexperiencesanincrease,andthendecreaseuntilitdisappears.However,thecurvechangesgently.Thepeakdensityisalsomuchsmallerthanordinaryspreaders.Thisindicatesthatintoday’sonlinesocialnetworknodesintheconnectionstateareasmallpartofallnodes.Andthisstateofnodewillchangequicklyintothespreadingstate.Lawthree:Ignorantdensityshowsarapiddownwardtrend.Anditeventuallysettlestoanon-zerovalue.Andthatreflectstheinformationcirculation’sbreadthanddeptharelimitedanditisimpossibletocoverallusers.Lawfour:Thetrend