2014美赛数模题目.doc

Teams(StudentorAdvisor)arenowrequiredtosubmitanelectroniccopy(summarysheetandsolution)asaWordorPDFattachment.YouremailMUSTbereceivedatCOMAPbythesubmissiondeadlineof8:00PMEST,February10,2014.Noteyouwillnotreceiveanautoreponse.SubjectlineCOMAPyourcontrolnumberExample:COMAP11111ClickheretodownloadaPDFofthecompletecontestinstructions.ClickheretodownloadacopyoftheSummarySheetinMicrosoftWordformat.*Besuretochangethecontrolnumberandproblemselectbeforeprintingoutthepage.TeamsarefreetochoosebetweenMCMProblemA,MCMProblemBorICMProblemC.COMAPMirrorSite:Formorein:/undergraduate/contests/mcm/MCM:TheMathematicalContestinModelingICM:TheInterdisciplinaryContestinModeling2014ContestProblemsMCMPROBLEMSPROBLEMA:TheKeep-Right-Except-To-PassRuleIncountrieswheredrivingautomobilesontherightistherule(thatis,USA,ChinaandmostothercountriesexceptforGreatBritain,Australia,andsomeformerBritishcolonies),multi-lanefreewaysoftenemployarulethatrequiresdriverstodriveintheright-mostlaneunlesstheyarepassinganothervehicle,inwhichcasetheymoveonelanetotheleft,pass,andreturntotheirformertravellane.Buildandanalyzeamathematicalmodeltoanalyzetheperformanceofthisruleinlightandheavytraffic.Youmaywishtoexaminetradeoffsbetweentrafficflowandsafety,theroleofunder-orover-postedspeedlimits(thatis,speedlimitsthataretoolowortoohigh),and/orotherfactorsthatmaynotbeexplicitlycalledoutinthisproblemstatement.Isthisruleeffectiveinpromotingbettertrafficflow?Ifnot,suggestandanalyzealternatives(toincludepossiblynoruleofthiskindatall)thatmightpromotegreatertrafficflow,safety,and/orotherfactorsthatyoudeemimportant.Incountrieswheredrivingautomobilesontheleftisthenorm,arguewhetherornotyoursolutioncanbecarriedoverwithasimplechangeoforientation,orwouldadditionalrequirementsbeneeded.Lastly,theruleasstatedabovereliesuponhumanjudgmentforcompliance.Ifvehicletransportationonthesameroadwaywasfullyunderthecontrolofanintelligentsystemeitherpartoftheroadnetworkorimbeddedinthedesignofallvehiclesusingtheroadwaytowhatextentwouldthischangetheresultsofyourearlieranalysis?PROBLEMB:CollegeCoachingLegendsSportsIllustrated,amagazineforsportsenthusiasts,islookingforthe“bestalltimecollegecoach”maleorfemaleforthepreviouscentury.Buildamathematicalmodeltochoosethebestcollegecoachorcoaches(pastorpresent)fromamongeithermaleorfemalecoachesinsuchsportsascollegehockeyorfieldhockey,football,baseballorsoftball,basketball,orsoccer.Doesitmakeadifferencewhichtimelinehorizonthatyouuseinyouranalysis,i.e.,doescoachingin1913differfromcoachingin2013?Clearlyarticulateyourmetricsforassessment.Discusshowyourmodelcanbeappliedingeneralacrossbothgendersandallpossiblesports.Presentyourmodelstop5coachesineachof3differentsports.InadditiontotheMCMformatandrequirements,preparea1-2pagearticleforSportsIllustratedthatexplainsyourresultsandincludesanon-technicalexplanationofyourmathematicalmodelthatsportsfanswillunderstand.ICMPROBLEMPROBLEMC:UsingNetworkstoMeasureInfluenceandImpactClickthetitlebelowtodownloadaPDFofthe2014ICMProblem.YourICMsubmissionshouldconsistofa1pageSummarySheetandyoursolutioncannotexceed20pagesforamaximumof21pages.UsingNetworkstoMeasureInfluenceandImpact2014ICMProblemUsingNetworkstoMeasureInfluenceandImpactOneofthetechniquestodetermineinfluenceofacademicresearchistobuildandmeasurepropertiesofcitationorco-authornetworks.Co-authoringamanuscriptusuallyconnotesastronginfluentialconnectionbetweenresearchers.Oneofthemostfamousacademicco-authorswasthe20thcenturymathematicianPaulErdswhohadover500co-authorsandpublishedover1400technicalresearchpapers.Itisironic,orperhapsnot,thatErdsisalsooneoftheinfluencersinbuildingthefoundationfortheemerginginterdisciplinaryscienceofnetworks,particularly,throughhispublicationwithAlfredRnyiofthepaper“OnRandomGraphs”in1959.ErdssroleasacollaboratorwassosignificantinthefieldofmathematicsthatmathematiciansoftenmeasuretheirclosenesstoErdsthroughanalysisofErdssamazinglylargeandrobustco-authornetwork(seethewebsite/enp/).TheunusualandfascinatingstoryofPaulErdsasagiftedmathematician,talentedproblemsolver,andmastercollaboratorisprovidedinmanybooksandon-linewebsites(e.g.http:/www-history.mcs.st-and.ac.uk/Biographies/Erdos.html).Perhapshisitinerantlifestyle,frequentlystayingwithorresidingwithhiscollaborators,andgivingmuchofhismoneytostudentsasprizesforsolvingproblems,enabledhisco-authorshipstoflourishandhelpedbuildhisastoundingnetworkofinfluenceinseveralareasofmathematics.InordertomeasuresuchinfluenceasErdsproduced,therearenetwork-basedevaluationtoolsthatuseco-authorandcitationdatatodetermineimpactfactorofresearchers,publications,andjournals.SomeoftheseareScienceCitationIndex,Hfactor,Impactfactor,Eigenfactor,etc.GoogleScholarisalsoagooddatatooltousefornetworkinfluenceorimpactdatacollectionandanalysis.YourteamsgoalforICM2014istoanalyzeinfluenceandimpactinresearchnetworksandotherareasofsociety.Yourtaskstodothisinclude:1)Buildtheco-authornetworkoftheErdos1authors(youcanusethefilefromthewebsite/users/grossman/enp/Erdos1.htmlortheoneweincludeatErdos1.htm).Youshouldbuildaco-authornetworkoftheapproximately510researchersfromthefileErdos1,whocoauthoredapaperwithErds,butdonotincludeErds.Thiswilltakesomeskilleddataextractionandmodelingeffortstoobtainthecorrectsetofnodes(theErdscoauthors)andtheirlinks(connectionswithoneanotherascoauthors).Thereareover18,000linesofrawdatainErdos1file,butmanyofthemwillnotbeusedsincetheyarelinkstopeopleoutsidetheErdos1network.Ifnecessary,youcanlimitthesizeofyournetworktoanalyzeinordertocalibrateyourinfluencemeasurementalgorithm.Oncebuilt,analyzethepropertiesofthisnetwork.(Again,donotincludeErds-heisthemostinfluentialandwouldbeconnectedtoallnodesinthenetwork.Inthiscase,itsco-authorshipwithhimthatbuildsthenetwork,butheisnotpartofthenetworkortheanalysis.)1）建立erdos1作者里面的合著者网络（你可以用/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Erds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Erds），这将需要提取一些技术数据和建模的努力来获得节点（Erds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Erds-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。）2)Developinfluencemeasure(s)todeterminewhointhisErdos1networkhassignificantinfluencewithinthenetwork.ConsiderwhohaspublishedimportantworksorconnectsimportantresearcherswithinErdos1.Again,assumeErdsisnottheretoplaytheseroles.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Erds没有发挥这些作用。3)Anothertypeofinfluencemeasuremightbetocomparethesignificanceofaresearchpaperbyanalyzingtheimportantworksthatfollowfromitspublication.Choosesomesetoffoundationalpapersintheemergingfieldofnetworkscienceeitherfromtheattachedlist(NetSciFoundation.pdf)orpapersyoudiscover.Usethesepaperstoanalyzeanddevelopamodeltodeterminetheirrelativeinfluence.Buildtheinfluence(coauthororcitation)networksandcalculateappropriatemeasuresforyouranalysis.Whichofthepapersinyoursetdoyouconsideristhemostinfluentialinnetworkscienceandwhy?Isthereasimilarwaytodeterminetheroleorinfluencemeasureofanindividualnetworkresearcher?Considerhowyouwouldmeasuretherole,influence,orimpactofaspecificuniversity,department,orajournalinnetworkscience?Discussmethodologytodevelopsuchmeasuresandthedatathatwouldneedtobecollected.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。4)Implementyouralgorithmonacompletelydifferentsetofnetworkinfluencedata-forinstance,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。5)Finally,discussthescience,understandingandutilityofmodelinginfluenceandimpactwithinnetworks.Couldindividuals,organizations,nations,andsocietyuseinfluencemethodologytoimproverelationships,conductbusiness,andmakewisedecisions?Forinstance,attheindividuallevel,describehowyoucoulduseyourmeasuresandalgorithmstochoosewhototrytoco-authorwithinordertoboostyourmathematicalinflue