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备战美国数学建模竞赛与论文剖析.ppt

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数学建模竞赛讲座美国数学建模竞赛概况2部分MCM/ICM题目3评阅4OutstandingWinner竞赛论文剖析竞赛论文剖析Agoodexampleofaclear,conciseandthoroughsummary(2004A)Fingerprintidentificationdependsontheassumptionthataperson’sfingerprintsareunique.Weassessthetruthofthisassumptionbycalculatingthetotalnumberofdistinctfingerprints.Weassumeaccuratefingerprints(ignoringproceduralerror)aredefinedby12pointsofdetailorminutiae.Thenumberofdistinctfingerprintsdependsalsoonthenumberofpotentialpositionsoftheseminutiae.Twohistoricalmethodsandageometricanalysisestimatetheretobe1,400positions,afigureconfirmedbyouralgorithmforcountingridgesinafingerprint.Wecreatetwomodelstoestimatethenumberofuniquefingerprints:Onemodelcomputesfingerprintsasarrangementsinminutiae;theotherextrapolatesthenumberoffingerprintsfromtheShannonentropyoftheinformationthatdefinesafingerprint.Agoodexampleofaclear,conciseandthoroughsummary(2004A)Thesetwomodelsagreetowithinanorderofmagnitudethatthereare51033uniquefingerprints,acompellingvalidationofourgeneralapproach.Tohandlethelargenumberoffingerprints,weimplementanapproximationforthecalculationofprobabilities.Givenacumulativeworldpopulationof120billion,theprobabilityoftwopeopleeverhavingthesamefingerprintis1.410-6.Theprobabilityoftwohumanslivingtodaysharingafingerprintis3.510-15,whichsuggeststhatfingerprintsareatheoreticallymorereliablemethodofidentificationthanDNAanalysis,whichhasafalsepositiveprobabilityof10-9.Noneofthesecalculationstakeintoaccountproceduralerrors.竞赛论文剖析Example2：IntroductionWedevelopsomemodels,apatternmodel,ashapemodelandapracticalmodel,toanalyzetheuniquenessoffingerprintsandoddsofmisidentificationbyfingerprintevidence.Throughcomparison,wealsodevelopasequencemodeltoanalyzeoddsofmisidentificationbyDNAevidence.Noticingthatthereareseveralpatternsoffingerprints,andtheridgesandfurrowsinfingerprintsaredifferentfromonetoanother,weusethesecharacteristicstodevelopourmodel.Consideringtheincompletenessofthefingerprints,weanalyzetheprobabilityofmisidentificationoffingerprints.Basedonourlimitedknowl