美赛校内论文.docx
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美赛校内论文.docx
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美赛校内论文
SpreadofInternetRumours
QiangPuChen
YuZhang
LiYePan
ChongqingUniversity
Summer
Introduction
CurrentestimatesrevealthatroughlytwobillionpeopleareusingeverydaytheInternetanditsnumerousservices,likeE-mail,theWorldWideWeb,andsocialnetworks.Especiallynetworksprovidenewandeasilyaccessiblewaysforinteractionandcommunicationamongindividuals,thusmakingtheInternetanidealenvironmentforthespreadofallkindsofinformation.Thedynamicsofsuchinformationspreadingprocessesconstituteanimportanttopicinmanydisciplines.Butsometimesrumorsontheinternetareawful.Rumorsareanimportantformofsocialcommunications,andtheirspreadingplaysasignificantroleinavarietyofhumanaffairs.Thespreadofrumorscanshapethepublicopinioninacountry,greatlyimpactfinancialmarketsandcausepanicinasocietyduringwarsandepidemicsoutbreaks.
Analyticformulation
WiththedevelopmentofInternetcommunicationtechnology,spreadofrumoursisnotonlyfromonepersontoanotherbutrelyonInternet.Soboththescopeandspeedofrumours'spreadhasbeenexpandedandraised.Inrecentyears,increasingnumbersofInternetrumourshasbecomeabigreasonwhichaffectssocialstability.TheanalysisfocusedonthefollowingissuesaboutInternetrumorsspread.
·ModelthespreadofInternetrumours.
·Analyzehowtocontrolthenegativeimpactofrumorsbasedonfirstissue.
·Verifythemodelabove.
·SuggestionforpreventionandcontrolofInternetrumours.
Assumptions
SymbolDefinitions
Table1.SymbolandDefinitions
Symbol
Definitions
为不知道谣言的人遇到传播者而被感染的概率,
为传播者遇到不传谣的人而变为不传谣者的概率
Modeldevelopment
Part1Thenetworkrumorsspreadmodel
1.1Background
Rumorsspreadaroundpoliticalactivitiesandmilitarystruggleanditisgenerallyunfoundedorseriousdeviationfromtheactual.[4]WiththedevelopmentofInternetcommunicationtechnology,spreadofrumorsisnotonlyfromonepersontoanotherbutrelyonInternet.Thenetworkrumorunlikegeneralmodelofthespreadofthevirusandalsodifferentfromthegeneralformof"wordofmouth"communication.Ithastwoimportantfeatures:
(1)Internetrumorsspreadisatwo-waycommunicationprocess,Itisnotonlytheprocessofinformationdiffusionbutalsothesenderandreceiver’sconfrontationintheinformationfieldandcognitivedomains.Hereisasimplespreadschematicdiagram.
(2)Inthecomplexnetworksrumorsspread,mostpeopledonotknoweachother.
Soforthetwoquestionsabove,Wefirstlyestablishasmall-worldnetworkmodeltotoensurethatthespreadofrumorsisatwo-wayprocess.Atthesametime,wesettheclusteringcoefficienttoexcluderelationshipbetweeneachother.
1.2Modeloverview
In1998,WattsandStrogatzproposedtheconceptofsmall-worldnetworksandestablishedtheWSmodel.Experimentalresultsshowthatthemostrealnetworkshavesmall-worldcharacteristics(smallershortestpath)andclusteringfeatures(largeclusteringcoefficient).WSsmall-worldnetworkmodelhavesmall-worldcharacteristicsandclusteringfeaturesatthesametime,it’sgoodtorepresentrealnetwork.
1.3
1.3.1TheconstructionprocessofSmall-worldmodel
a)Startfromtherulesfigure:
ConsideranearestneighborcouplingnetworkthatcontainingNpointsandthepointssurroundedbyaring.WhereineachnodeadjacenttotheleftandrightwithiteachofK/2nodesconnected,Kisanevennumber.
b)Randomizedreconnection:
re-connectionofeachsideofthenetworkWithprobabilityprandomly.Inordertomaintainasimplegraphnatureintheprocessofrandomizedreconnection,westipulatethatcanhaveatmostoneedgebetweenanytwodifferentpredeterminednode.Andeverynodecannothaveasideconnectedwithitself.
IntheWSmodel,p=0correspondstocompletelyrulenetworkandP=1correspondstothecompletelyrandomnetwork.
wecancontrolthetransitionfromthecompletelyrulenetworktocompletelyrandomnetworkbyadjustingthe.Wewillgetthefollowinggraphicbyadjustingthedifferentp-value.wehaveestablishedatwo-waynetworkifwegetsimilargraphicsbyMatlab.
Figure1.Thenetworkdiagramchangeofadjustingthep-value
WetakethePvaluesare,,,,。
weprovidetwographicsbycalculatinganddrawing.
WefindtheoutputresultsareconsistentinFigure1.Thatmeansweensurearumorspreadonthenetworkisbi-directional.
下面我们通过设置集聚系数进一度排除在复杂网络中人之间的熟悉关系。
集聚系数是用来描述图或网络中的顶点(节点)之间结集成团的程度的系数。
具体来说,是一个点的邻接点之间相互连接的程度,因为在现实中的复杂网络是稀疏的,所以我们设置集聚系数为的,通过Matlab,得到以下图形:
说明对话框后
1.3.2基于小世界网络的谣言传播
我们把人群分成没有听过谣言的人、谣言传播者和听到谣言但并不传播谣言的人3种类型,用i(t),s(t),r(t)分别代表着3种类型在人群中的比例,在小世界模型等指数型均匀网络上建立平均场方程为:
通过matlab编程,我们得到了如下图形:
结果分析:
事实上,整个谣言传播的过程可以简单的概括如下:
首
先系统里只有少量的传播者,其它都为无知者,免疫者的数
量为0。
随着传播者开始散播谣言,无知者的数量很快减少,
传播者的数量急剧增加。
随着谣言的进一步扩散,免疫者的
数量开始增加,而传播者的数量达到一个峰值以后开始下降。
最后,传播者的数量变为了0,而网络里就只剩下免疫者和少
量的无知者,恰恰是这部分人从来没有受到过谣言的骚扰
Part2howtocontrolnegativerumorspread
现实生活中,每当有危及国计民生的谣言的时候,政府往往会出来辟谣,我
们这里把政府辟谣的言论与谣言假定为两个相互竞争的种群,借助种群竞争模型
来分析“以言辟谣”这种情况。
Step1:
summarize
Inreallife,Governmenttendstouseitspositiveinfluencetostoptherumorsspreadingwheneverrumorstounderminesocialstability.Assumethatthegovernmentspeechandrumorsfortwocompetingpopulations.Weestablishapopulationcompetitionmodeltoanalyzethiscase.
Step2:
Assumptions
·changeinvalueobeyLogisticlawwhentwokindsremarksexistindependently.
·Thespeech-orientedofGovernmentarepositive.
Stp3:
thecontrolmodel
经分析我们建立以下两个模型
Byfurtheranalysis,Weknowthatthesmall-worldnetworkmodelisuniformnetworkorindexnetwork,itsdegreedistributionofthenetworkconnectioncanbeapproximatedbyaPoissondistribution.Itsdistributionhasapeakinthedegreeofaveragevalue(k)Thenexponentiallyfastdecay.However,inrecentyears,thethecomplexnetworkstudyshowsthatmanycomplicatednetworkconnectionfunctionhastheformofapower-law.Itsnodedegreehasnotobviouscharacteristiclength,SowehavefurtheradoptedtheBAscale-freenetworkcorrectiontorevise.
Part3modelvalidation
3.1TheAnalysisoftheProblem
前两问中,我们分别建立了网络谣言的传播模型以及对谣言的消极影响的控制模型,但是由于模型自身的一些局限性可能会影响最终的结果,所以下面我们分别对上述模型进行验证。
Weestablishthenetworkrumorsspreadmodelandthenegativeimpactofrumorscontrolmodelintheprevioustwoquestions.Howeverweshouldverifythemodelduetosomelimitationsofthemodelitself.Hereisourmodelvalidation.
3.2.1Verifythenetworkrumorsspreadmodelbasedoncellularautomata
Inordertoverifythemodelaboutthenetworkrumorspreadr,weintroducedastructureofthecellularautomatontodealtheproblem.
Cellularautomataarediscrete-timedynamicalsystemscomprisingfinite-stateunits,calledcells,whosestatesevolveintimeasaresultoftheinteractionswithothercells.SincetheirintroductionnearlyfivedecadesagobyvonNeumann[1],cellularautomatahaveacquiredanevermoreprominentstatusasamodelingtoolinseveralresearchareasandhaveevencometoberegardedbysomeasacentralabstractioninthemodelingofnature’sfundamentalprocesses[4].
现假设参与事件的整个群体是一个L×L规模的二维网格,其中每一个个体占据其中一个格子。
格子中的个体即为一个元胞,每个元胞都具有自己的观点S,S可以为正观点(+1)负观点(-1)和保留意见(0)其中的一种。
每个个体都具有8个相邻的邻居个体,这些邻居个体和当前个体之间的位置关系如图1所示。
ItisassumedthattheentiregroupparticipatingintheeventisaL×Lscaletwo-dimensionalgrid,eachindividualtooccupyoneofthelattice.individualshallbeacellintheLatticeandeachcellhasitsownpointofviewS.Scanbeapositivepointofvieworanegativepointoraqualifiedopinion.EachindividualhavingeightadjacentandthepositionalrelationshipbetweenneighborsindividualandcurrentindividualhaveshowninFigure1byAutoCAD.
Figure2.Thecellularautomataneighborsmodel
上面是我们对元胞模型的基本陈述,在本题中,我们根据对影响网络谣言传播发展及变化趋势的分析,将元胞的情感的变化作为主要因素,,进而对谣言的发展趋势进行仿真。
Theaboveisabasicstatementofourcellularmodel.Inthetitle,wetakecellularemotionalchangesasmajorfactorsbasedontheanalysisoftheimpactofthedevelopmentandchangesofthenetworkrumorspreadtrends.Thenwemakeatrendofthedevelopmentsimulationofrumors.
将元胞自动机二维网络中元胞抽象为用网络谣言传播系统中的个体。
每个元胞存在3种可能状态:
格子为0,表示该格子上的人对谣言的传播不做贡献;为1,表示该格子上的人对谣言持支持意见;为一1,表示该格子上的人持反对意见。
首先在个体观点的初始分布采用均匀分布的情况下,随机生成了一个
的网格,每个格子随机分配
的值,并进行整值化,(蓝色表示该元胞持支持态度,红色表示反对态度,空白表示保留意见)。
仿真中的初始分布情况如图2。
Assumecellularwhichintwo-dimensionalnetworkastheindividualinthenetworkrumorspreadsystem.Eachcellhavethreekindsofpossiblestates:
Plaidto0,indicatingthatthepeopleonthelatticehavenocontributiontothespreadofrumors.To1,indicatingthatthepeoplehavethesupportivecommentsonrumors.To1,indicatingthatthepeoplehavetheoppositecommentsonrumors.
Firstinthecasethatindividualviewpointssatisfyuniformlydistributed,generatinga
gridrandomly.Eachgridisrandomlyassignedavalueof
androunded.
(BluemeanstheCellulartakesupportiveattitude,redtakeoppositeattitude,Blankexpressedtakereservations)SimulationoftheinitialdistributionisshowninFigure2.
Figure3.Theinitialdistributiondiagram
由于初始状态观点概率呈均匀分布,在对谣言的发展趋势无引导策略时呈现自然演进状态,所以可以看出图中分布杂乱无章。
Sincetheinitialstateprobabilityisuniformlydistributed,thedevelopmenttrendoftherumorsinanaturalevolutionofthestate.wecanseethatthedistributionisscattered.
进一步我们通过设置相关的系数值,仿真得到在谣言传播中期和末期的分布情况,如图:
intermediatestateFinalstate
Figure4.Networkrumorsystemevolutionofsimulation
结果分析:
由上图可以看出,在观点均匀分布的初始状态下,随着邻居元胞和时间的影响,谣言的发展变化趋于几乎正观点和负观点相均衡的状态,一种观点很难最终占据整个群体的结果。
另一方面由于从众现象的影响,系统中谣言的发展最终趋于群聚的现象,即一定区域内人员的观点趋于一致。
由最终结果可以看出,随着谣言的传播,系统中谣言免疫者逐渐增加,并且最后越来越多。
和ws小世界模型最后得到的结果吻合,即可验证其正确性。
BAmodelisproposedtoexplaint
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