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2014美赛数模题目.doc

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2014美赛数模题目.doc

TeamsStudentorAdvisorarenowrequiredtosubmitanelectroniccopysummarysheetandsolutionoftheirsolutionpaperbyemailtoosolutionscomap.comasaWordorPDFattachment.YouremailMUSTbereceivedatCOMAPbythesubmissiondeadlineof800PMEST,February10,2014.Noteyouwillnotreceiveanautoreponse.SubjectlineCOMAPyourcontrolnumberExampleCOMAP11111ClickheretodownloadaPDFofthecompletecontestinstructions.ClickheretodownloadacopyoftheSummarySheetinMicrosoftWordformat.Besuretochangethecontrolnumberandproblemselectbeforeprintingoutthepage.TeamsarefreetochoosebetweenMCMProblemA,MCMProblemBorICMProblemC.COMAPMirrorSiteFormoreinhttp//www.comap.com/undergraduate/contests/mcm/MCMTheMathematicalContestinModelingICMTheInterdisciplinaryContestinModeling2014ContestProblemsMCMPROBLEMSPROBLEMATheKeepRightExceptToPassRuleIncountrieswheredrivingautomobilesontherightistherulethatis,USA,ChinaandmostothercountriesexceptforGreatBritain,Australia,andsomeformerBritishcolonies,multilanefreewaysoftenemployarulethatrequiresdriverstodriveintherightmostlaneunlesstheyarepassinganothervehicle,inwhichcasetheymoveonelanetotheleft,pass,andreturntotheirformertravellane.Buildandanalyzeamathematicalmodeltoanalyzetheperformanceofthisruleinlightandheavytraffic.Youmaywishtoexaminetradeoffsbetweentrafficflowandsafety,theroleofunderoroverpostedspeedlimitsthatis,speedlimitsthataretoolowortoohigh,and/orotherfactorsthatmaynotbeexplicitlycalledoutinthisproblemstatement.IsthisruleeffectiveinpromotingbettertrafficflowIfnot,suggestandanalyzealternativestoincludepossiblynoruleofthiskindatallthatmightpromotegreatertrafficflow,safety,and/orotherfactorsthatyoudeemimportant.Incountrieswheredrivingautomobilesontheleftisthenorm,arguewhetherornotyoursolutioncanbecarriedoverwithasimplechangeoforientation,orwouldadditionalrequirementsbeneeded.Lastly,theruleasstatedabovereliesuponhumanjudgmentforcompliance.Ifvehicletransportationonthesameroadwaywasfullyunderthecontrolofanintelligentsystem–eitherpartoftheroadnetworkorimbeddedinthedesignofallvehiclesusingtheroadway–towhatextentwouldthischangetheresultsofyourearlieranalysisPROBLEMBCollegeCoachingLegendsSportsIllustrated,amagazineforsportsenthusiasts,islookingforthebestalltimecollegecoachmaleorfemaleforthepreviouscentury.Buildamathematicalmodeltochoosethebestcollegecoachorcoachespastorpresentfromamongeithermaleorfemalecoachesinsuchsportsascollegehockeyorfieldhockey,football,baseballorsoftball,basketball,orsoccer.Doesitmakeadifferencewhichtimelinehorizonthatyouuseinyouranalysis,i.e.,doescoachingin1913differfromcoachingin2013Clearlyarticulateyourmetricsforassessment.Discusshowyourmodelcanbeappliedingeneralacrossbothgendersandallpossiblesports.Presentyourmodelstop5coachesineachof3differentsports.InadditiontotheMCMformatandrequirements,preparea12pagearticleforSportsIllustratedthatexplainsyourresultsandincludesanontechnicalexplanationofyourmathematicalmodelthatsportsfanswillunderstand.ICMPROBLEMPROBLEMCUsingNetworkstoMeasureInfluenceandImpactClickthetitlebelowtodownloadaPDFofthe2014ICMProblem.YourICMsubmissionshouldconsistofa1pageSummarySheetandyoursolutioncannotexceed20pagesforamaximumof21pages.UsingNetworkstoMeasureInfluenceandImpact2014ICMProblemUsingNetworkstoMeasureInfluenceandImpactOneofthetechniquestodetermineinfluenceofacademicresearchistobuildandmeasurepropertiesofcitationorcoauthornetworks.Coauthoringamanuscriptusuallyconnotesastronginfluentialconnectionbetweenresearchers.Oneofthemostfamousacademiccoauthorswasthe20thcenturymathematicianPaulErdöswhohadover500coauthorsandpublishedover1400technicalresearchpapers.Itisironic,orperhapsnot,thatErdösisalsooneoftheinfluencersinbuildingthefoundationfortheemerginginterdisciplinaryscienceofnetworks,particularly,throughhispublicationwithAlfredRényiofthepaperOnRandomGraphsin1959.ErdössroleasacollaboratorwassosignificantinthefieldofmathematicsthatmathematiciansoftenmeasuretheirclosenesstoErdösthroughanalysisofErdössamazinglylargeandrobustcoauthornetworkseethewebsitehttp//www.oakland.edu/enp/.TheunusualandfascinatingstoryofPaulErdösasagiftedmathematician,talentedproblemsolver,andmastercollaboratorisprovidedinmanybooksandonlinewebsitese.g.http//wwwhistory.mcs.stand.ac.uk/Biographies/Erdos.html.Perhapshisitinerantlifestyle,frequentlystayingwithorresidingwithhiscollaborators,andgivingmuchofhismoneytostudentsasprizesforsolvingproblems,enabledhiscoauthorshipstoflourishandhelpedbuildhisastoundingnetworkofinfluenceinseveralareasofmathematics.InordertomeasuresuchinfluenceasErdösproduced,therearenetworkbasedevaluationtoolsthatusecoauthorandcitationdatatodetermineimpactfactorofresearchers,publications,andjournals.SomeoftheseareScienceCitationIndex,Hfactor,Impactfactor,Eigenfactor,etc.GoogleScholarisalsoagooddatatooltousefornetworkinfluenceorimpactdatacollectionandanalysis.YourteamsgoalforICM2014istoanalyzeinfluenceandimpactinresearchnetworksandotherareasofsociety.Yourtaskstodothisinclude1BuildthecoauthornetworkoftheErdos1authorsyoucanusethefilefromthewebsitehttps//files.oakland.edu/users/grossman/enp/Erdos1.htmlortheoneweincludeatErdos1.htm.Youshouldbuildacoauthornetworkoftheapproximately510researchersfromthefileErdos1,whocoauthoredapaperwithErdös,butdonotincludeErdös.ThiswilltakesomeskilleddataextractionandmodelingeffortstoobtainthecorrectsetofnodestheErdöscoauthorsandtheirlinksconnectionswithoneanotherascoauthors.Thereareover18,000linesofrawdatainErdos1file,butmanyofthemwillnotbeusedsincetheyarelinkstopeopleoutsidetheErdos1network.Ifnecessary,youcanlimitthesizeofyournetworktoanalyzeinordertocalibrateyourinfluencemeasurementalgorithm.Oncebuilt,analyzethepropertiesofthisnetwork.Again,donotincludeErdösheisthemostinfluentialandwouldbeconnectedtoallnodesinthenetwork.Inthiscase,itscoauthorshipwithhimthatbuildsthenetwork,butheisnotpartofthenetworkortheanalysis.1)建立erdos1作者里面的合著者网络(你可以用https//files.oakland.edu/users/grossman/enp/erdos1.htmlor这个网站上的文件或者我们包括在Erdos1.htm中的文件)。你应该从文件erdos1(与Erdös合著一篇论文的人)里建立一个大约510的研究人员的合著网络(但不包括Erdös),这将需要提取一些技术数据和建模的努力来获得节点(Erdös的合著者)的正确设置以及他们之间的链接(与另一个合著者的连接)。在erdos1文件有超过18000的原始数据线,但他们中的许多人不会被使用,因为他们联系了erdos1网络以外的人。如果有必要,你可以限制您的网络大小去分析,来校准你的影响的测量算法。建成网络之后,分析这个网络的性能。(再次,不包括Erdös他是最有影响力的也将被连接到所有节点网络。在这种情况下,它是共同作者和他建立的网络,但他不是网络或分析的一部分。)2DevelopinfluencemeasurestodeterminewhointhisErdos1networkhassignificantinfluencewithinthenetwork.ConsiderwhohaspublishedimportantworksorconnectsimportantresearcherswithinErdos1.Again,assumeErdösisnottheretoplaytheseroles.2)改进影响的方法来判定谁在erdos1网络中有最重要的影响。考虑谁发表了重要的工作或和在erdos1网络中重要的研究者联系。再次,假定Erdös没有发挥这些作用。3Anothertypeofinfluencemeasuremightbetocomparethesignificanceofaresearchpaperbyanalyzingtheimportantworksthatfollowfromitspublication.ChoosesomesetoffoundationalpapersintheemergingfieldofnetworkscienceeitherfromtheattachedlistNetSciFoundation.pdforpapersyoudiscover.Usethesepaperstoanalyzeanddevelopamodeltodeterminetheirrelativeinfluence.Buildtheinfluencecoauthororcitationnetworksandcalculateappropriatemeasuresforyouranalysis.WhichofthepapersinyoursetdoyouconsideristhemostinfluentialinnetworkscienceandwhyIsthereasimilarwaytodeterminetheroleorinfluencemeasureofanindividualnetworkresearcherConsiderhowyouwouldmeasuretherole,influence,orimpactofaspecificuniversity,department,orajournalinnetworkscienceDiscussmethodologytodevelopsuchmeasuresandthedatathatwouldneedtobecollected.3)另一种类型的影响的方法可能是通过分析随着它的出版而产生的重要作品来比较一篇研究论文的重要性,。从所附清单(NetSciFoundation.pdf)中选择一套在网络科学的新领域的基础性文件或你自己找的文件。用这些文件来分析和建立一个模型来确定它们的相对影响。建立影响(合著者或引用)的网络和为你的分析计划合适的方法。在你的论文中,你认为哪一个在网络科学最有影响力,为什么是否存在一个类似的方法来确定地作用或影响一个人的网络测量研究考虑你如何开发这样的度量法和需要收集的数据。4Implementyouralgorithmonacompletelydifferentsetofnetworkinfluencedataforinstance,influentialsongwriters,musicbands,performers,movieactors,directors,movies,TVshows,columnists,journalists,newspapers,magazines,novelists,novels,bloggers,tweeters,oranydatasetyoucaretoanalyze.Youmaywishtorestrictthenetworktoaspecificgenreorgeographiclocationorpredeterminedsize.4)在一个完全不同的网络影响数据中实现你的算法例如,有影响力的作曲家,音乐的乐队,表演,电影演员,导演,电影,电视,报纸,杂志的专栏作家,记者,小说家,小说,博客,高音喇叭,或任何你想分析的数据集。你可以限制网络到一个特定的风格或地理位置或预定尺寸。5Finally,discussthescience,understandingandutilityofmodelinginfluenceandimpactwithinnetworks.Couldindividuals,organizations,nations,andsocietyuseinfluencemethodologytoimproverelationships,conductbusiness,andmakewisedecisionsForinstance,attheindividuallevel,describehowyoucoulduseyourmeasuresandalgorithmstochoosewhototrytocoauthorwithinordertoboostyourmathematicalinfluenceasrapidlyaspossible.Orhowcanyouuseyourmodelsandresultstohelpdecideonagraduateschoolorthesisadvisortoselectforyourfutureacademicwork5)最后,理解建立网络中的影响模型的作用,讨论模型的科学性。个人,组织,国家和社会,可以用影响的方法来改善关系,开展业务,并使明智的决定吗例如,在个人层面上,为了尽可能迅速地提高你的数学的影响,应该怎样用你的措施和算法来选择和谁一起合著论文。或者您可以如何利用你的模型和结果可以为你未来的学术工作选择一个研究生学校或研究生导师6Writeareportexplainingyourmodelingmethodology,yournetworkbasedinfluenceandimpactmeasures,andyourprogressandresultsforthepreviousfivetasks.Thereportmustnotexceed20pagesnotincludingyoursummarysheetandshouldpresentsolidanalysisofyournetworkdatastrengths,weaknesses,andsensitivityofyourmethodologyandthepowerofmodelingthesephenomenausingnetworkscience.6)写一份报告,说明你的建模方法,你的网络的影响的措施,和你之前五项任务的进展和结果。本报告不得超过20页(不包括你的总结表),并且应该使用网络科学对你做的网络的数据、优势、弱点、方法的灵敏度、建模的能力这些方面进行具体分析。©2014COMAP,TheConsortiumforMathematicsandItsApplicationsMaybereproducedforacademic/researchpurposesForMoreinformationonCOMAPandthisprojectvisithttp//www.comap.com

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