2014美賽數(shù)模題目.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作者里面的合著者網(wǎng)絡(luò)（你可以用/users/grossman/enp/erdos1.htmlor這個(gè)網(wǎng)站上的文件或者我們包括在Erdos1.htm中的文件）。你應(yīng)該從文件erdos1（與Erds合著一篇論文的人）里建立一個(gè)大約510的研究人員的合著網(wǎng)絡(luò)（但不包括Erds），這將需要提取一些技術(shù)數(shù)據(jù)和建模的努力來(lái)獲得節(jié)點(diǎn)（Erds的合著者）的正確設(shè)置以及他們之間的鏈接（與另一個(gè)合著者的連接）。在erdos1文件有超過(guò)18000的原始數(shù)據(jù)線，但他們中的許多人不會(huì)被使用，因?yàn)樗麄兟?lián)系了erdos1網(wǎng)絡(luò)以外的人。如果有必要，你可以限制您的網(wǎng)絡(luò)大小去分析，來(lái)校準(zhǔn)你的影響的測(cè)量算法。建成網(wǎng)絡(luò)之后，分析這個(gè)網(wǎng)絡(luò)的性能。（再次，不包括Erds-他是最有影響力的也將被連接到所有節(jié)點(diǎn)網(wǎng)絡(luò)。在這種情況下，它是共同作者和他建立的網(wǎng)絡(luò)，但他不是網(wǎng)絡(luò)或分析的一部分。）2)Developinfluencemeasure(s)todeterminewhointhisErdos1networkhassignificantinfluencewithinthenetwork.ConsiderwhohaspublishedimportantworksorconnectsimportantresearcherswithinErdos1.Again,assumeErdsisnottheretoplaytheseroles.2）改進(jìn)影響的方法來(lái)判定誰(shuí)在erdos1網(wǎng)絡(luò)中有最重要的影響?？紤]誰(shuí)發(fā)表了重要的工作或和在erdos1網(wǎng)絡(luò)中重要的研究者聯(lián)系。再次，假定Erds沒(méi)有發(fā)揮這些作用。3)Anothertypeofinfluencemeasuremightbetocomparethesignificanceofaresearchpaperbyanalyzingtheimportantworksthatfollowfromitspublication.Choosesomesetoffoundationalpapersintheemergingfieldofnetworkscienceeitherfromtheattachedlist(NetSciFoundation.pdf)orpapersyoudiscover.Usethesepaperstoanalyzeanddevelopamodeltodeterminetheirrelativeinfluence.Buildtheinfluence(coauthororcitation)networksandcalculateappropriatemeasuresforyouranalysis.Whichofthepapersinyoursetdoyouconsideristhemostinfluentialinnetworkscienceandwhy?Isthereasimilarwaytodeterminetheroleorinfluencemeasureofanindividualnetworkresearcher?Considerhowyouwouldmeasuretherole,influence,orimpactofaspecificuniversity,department,orajournalinnetworkscience?Discussmethodologytodevelopsuchmeasuresandthedatathatwouldneedtobecollected.3）另一種類型的影響的方法可能是通過(guò)分析隨著它的出版而產(chǎn)生的重要作品來(lái)比較一篇研究論文的重要性，。從所附清單（NetSciFoundation.pdf）中選擇一套在網(wǎng)絡(luò)科學(xué)的新領(lǐng)域的基礎(chǔ)性文件或你自己找的文件。用這些文件來(lái)分析和建立一個(gè)模型來(lái)確定它們的相對(duì)影響。建立影響（合著者或引用）的網(wǎng)絡(luò)和為你的分析計(jì)劃合適的方法。在你的論文中，你認(rèn)為哪一個(gè)在網(wǎng)絡(luò)科學(xué)最有影響力，為什么？是否存在一個(gè)類似的方法來(lái)確定地作用或影響一個(gè)人的網(wǎng)絡(luò)測(cè)量研究？考慮你如何開(kāi)發(fā)這樣的度量法和需要收集的數(shù)據(jù)。4)Implementyouralgorithmonacompletelydifferentsetofnetworkinfluencedata-forinstance,influentialsongwriters,musicbands,performers,movieactors,directors,movies,TVshows,columnists,journalists,newspapers,magazines,novelists,novels,bloggers,tweeters,oranydatasetyoucaretoanalyze.Youmaywishtorestrictthenetworktoaspecificgenreorgeographiclocationorpredeterminedsize.4）在一個(gè)完全不同的網(wǎng)絡(luò)影響數(shù)據(jù)中實(shí)現(xiàn)你的算法-例如，有影響力的作曲家，音樂(lè)的樂(lè)隊(duì)，表演，電影演員，導(dǎo)演，電影，電視，報(bào)紙，雜志的專欄作家，記者，小說(shuō)家，小說(shuō)，博客，高音喇叭，或任何你想分析的數(shù)據(jù)集。你可以限制網(wǎng)絡(luò)到一個(gè)特定的風(fēng)格或地理位置或預(yù)定尺寸。5)Finally,discussthescience,understandingandutilityofmodelinginfluenceandimpactwithinnetworks.Couldindividuals,organizations,nations,andsocietyuseinfluencemethodologytoimproverelationships,conductbusiness,andmakewisedecisions?Forinstance,attheindividuallevel,describehowyoucoulduseyourmeasuresandalgorithmstochoosewhototrytoco-authorwithinordertoboostyourmathematicalinflue