预览加载中，请您耐心等待几秒...

备战美国数学建模竞赛与论文剖析.ppt

预览
1/10
2/10
3/10
4/10
5/10
6/10
7/10
8/10
9/10
10/10

亲，该文档总共36页，到这已经超出免费预览范围，如果喜欢就直接下载吧～

下载提示 文本预览

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

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; theotherextrapolatesthenumberoffingerprintsfromthe Shannonentropyoftheinformationthatdefinesafingerprint. 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： Introduction Wedevelopsomemodels,apatternmodel,ashapemodelandapracticalmodel,toanalyzetheuniquenessoffingerprintsandoddsofmisidentificationbyfingerprintevidence.Throughcomparison,wealsodevelopasequencemodeltoanalyzeoddsofmisidentificationbyDNAevidence. Noticingthatthereareseveralpatternsoffingerprints,andtheridgesandfurrowsinfingerprintsaredifferentfromonetoanother,weusethesecharacteristicstodevelopourmodel.Consideringtheincompletenessofthefingerprints,weanalyzetheprobabilityofmisidentificationoffingerprints. Basedono