美赛数学建模优秀论文

WhyCrimeDoesn’tPay:LocatingCriminalsThroughGeographicProfilingControlNumber:#7272February22,2010AbstractGeographicprofiling,theapplicationofmathematicstocriminology,hasgreatlyimprovedpoliceeffortstocatchserialcriminalsbyfir,manygeographicprofileseithergenerateanextremelylargeareaforpolicetocoverorgeneratesose,formulate,andtesttheGaussianRossmooth(GRS)Method,whichtakesthestrongestelementsfrommultultsshowthattheGRSMethodaccuratelypredictsthelocationofthekiller’onally,theGRSMethodismorestablewithrespecttointernalparelforpredictingthelocationofthenextcriludethattheGRSMethodisarobustandstablemodelforcreatingastrongandeffectivemodel.1Controlnumber:#72722Contents1Introduction2PlanofAttack3Defi4.3Rossmo’5Assumptions6GaussianRossmooth6..6.3.1RossmoothMethod.6.44455688GaussianRossmoothinAction7..7.2YorkshireRipper:.219BoundaryMethodinAction10Limitations11ExecutiveSummary11.1OutlineofOurModel.11.2242525252Controlnumber:#72723ListofFigures1TheeffCrimesscenesthatarelocimage,thespatialmeanislocatedatthesamepointasoneofthecrimescenesat(1,1)..ThesummandinRossmo’sformula(2B=6).Notethatthefunctionisessentially0atallpointsexceptforthesceneofthecrimeandatthebufferzoneandisundefinedatthosepoints..ThesummandinsmoothedRossmo’sformula(2B=6,φ=0.5,andEPSILON=0.5).NotethatthereisnowaregionaroundthebuffGRSoutputfortheYorkshireRippercase(B=2.846).GRSmethodrunonYorkshireRipperdata(B=2).NotethatthemajordifferencebetweenthismodelandFigure7isthatthehotzonesinthisfiGRSmethodrunonYorkshireRipperdata(B=4).NotethatthemajordifferencebetweenthismodelandFigure7isthatthehotzonesinthisfiatboundaryregioncoversmanyofthecrimescommittedbytheSutcliffe..............................GRSMethodonfirstelevenmurdersintheYorkshireRipperCaseGRSMethodonfirsttwelvemurdersintheYorkshireRipperCase6273948189191Controlnumber:#727241IntroductionCatchingserialcriminalsisadauntingproblemforlawenforcementoffinehand,alimitedamour,acquiringmoredataequatestowaitingforanothercrimetobecommitted,whichisanunacceptabletrade-off.Inthispaper,wepresentarobustandstablegeographicprofiletoprediceldrawselementsfrommultipleexistingmodelsandsynthesizesthemintoaunifiedmodelthatmakesbetteruseofcertainempiricalfactsofcriminology.2PlanofAttackOurobjectiveistocreateageographicprofilingmodelthataccuratelydescribestheresrtogenerateusefulresults,ourmodelmustincorporatetwodiff-tionally,wemustincludeassumptionsandlimitationsofthemodelinordertoensurethatitisusedformaximumeffevethisobjective,wewillproceedasfollows:fineTerms-ThisensuresthatthereaderunderstandswhatwearetalkinganEonally,bePropertiesofaGoodModel-Thisclarifiisunderlyingframework,wewillpresentourmodel,testitwithexistingdata,andcompareitagainstothermodels.3DefilMean-Givenasetofpoints,S,rdDistance-Thelowingtermswillbeusedthroughoutthepaper:4Controlnumber:#er-AserceDecay-Anempiricalphenomenonwherecriminaldon’fferArea-Aregionaroundthecriminal’sresidenceorworkplacewhereheorshedoesnotcommitcrimes.[1]Thereissomedisputeastowhetherthisregionexists.[2]Inourmodel,weassumethatthebufferareaexistsandwemeasureitinthesametanDistance-Givenpointsa=(x1,y1)andb=(x2,y2),theManhattandistancefromatobis|x1−x2|+|y1−y2|.Thisisalsoknownasthe1−tNeighborDistance-GivenasetofpointsS,thenearestneighbordistanceforapointx∈Siss∈S−{x}min|x−s|ne-Aregionwhereapredictivemodelscoresexceptionallylow.4ExistingMethodsCurrentlythereareseveralexistingmethodsforinterpolatingthepositionofacriminalgiventhelocationofthecrimes.4.1GreatCircleMethodInthegreatcirclemethod,thedista,pointofthisgreatcircleisthentheassumedlocationofthecriminal’sresiddeliscomputationallyinexpensiveandeasytounderstand.[3]Moreover,itiseasytouseandrequiresverylittletraininginordertomasterthetechnique.[2]However,mple,theareagivenbythismethodisoftenverylargeandotherstudieshaveshownthatasmallerareasuffices.[4]Additionally,afewoutlierscangenerateanevenlargersearcharea,therebyfurtherslowingthepoliceeffort.5Controlnumber:#727264.2CentrographyIncentrography,crimesareassignedxandycoordinatesandthe“centerofmass”iscomputedasfollows:xcenter=n