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1、Team#307Page23of23ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber307 ProblemChosenAForofficeuseonlyF1________________F2________________F3________________F4________________2004MathematicalContestinModeling(MC
2、M)SummarySheetUniqueornot?Fingerprintsays“Yes!”SummeryItishardtobelievethateveryone’snameisuniquetohimself.But“areyourfingerprintsuniquetoyourself?”manypeoplewillanswer“yes”.Inordertoprovethisproblem,wecreatemodelstoexplainit.Atfirstwecreateasimpleandcomprehensible
3、modeltoquicklyandcoarselyestimatethisproblemwithfingerprintspatterns.It’seasytoseethatourfingerprintsvaryingeneralpatterns.Therearecommonly9patternsinourfingerprints.AssumethatwecandistinguishckindsoffingerprintsinacertainpatternforsampledpopulationA.Withthevariety
4、ofparametercandA,wegetaninterestingconclusionthatevenwecandistinguishahugeamountoffingerprintsinacertainpattern(c=1000billion)foralocalcity’spopulation(A=30million),theprobabilityoftwoormorepeoplehavethesamefingerprints,orsimilarexactly,isnearly100%.Toobtainanavail
5、ablemodel,wecreateanadvancedmodelmorestrictlyandprecisely.Theridgesandfurrowsinfingerprinthavesomesimilarcharacteristics.Weselect3kindsofminutiaepointsincludingtheirnumbers,positionsanddirectionsanddevelopastatisticalalgorithmtocalculatetheuniquenessoffingerprints.
6、Theansweristhatfingerprintsareunique,asexpected!Thosetwomodelsareunderaprimaryassumptionthatallcharacteristicsofagivenfingerprintcanbewellrecognized.But,ifthefingerprintsathandaremostlyincomplete,pollutedordistorted,oddsofmisidentificationwilloccur.Basedonoursecond
7、model,weanalyzehowtheincompletenessanddistortionofminutiaepointsinfluenceprecisionoffingerprintsidentification,andobtainsomeessentialrequirementsforacceptablefingerprintsidentification.InordertocompareoddsofmisidentificationbyfingerprintevidenceandthatbyDNA,wedevel
8、opamodeltoanalyzetheidentificationbyDNAevidence.Restrictedbybiochemicalknowledge,ourmodelissheerlybasedontheDNAsequencestructure,regardlessofthos
