美国大学生数学建模B题参考论文.docx

美国大学生数学建模B题参考论文.docx

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美国大学生数学建模B题参考论文

CampingalongtheBigLongRiver

Abstract:

Geographicprofileisanimportantwaytostudyserialcrime.Howtogenerategeographicprofileissophisticated.Thepaperproposesamethodtogenerateageographicprofile.ThemethodconsistsofananalogmodelandasimulationalgorithmbasedonBayesianformula.Theanalogmodelrequiresthelocationofserialcrimestomeetthe"ringhypothesis".weestimatetheoffenders’residencesbythephysicsmethodtofindtheminimumdistanceandfindtheminimumpointofthesumfunctionofthedistancebetweentheoffenders’residencesandthecrimelocations.

Themainideaofthismethodisaswhatfollows.Makingthepoint（quasi-residence）derivedbytheanalogmodelcontrolsthedirectionofsimulation,searchingthelocationsfromoutsidelayerstotheinsideones,takingthefinalsearchsequenceofquasi-residencepoints,solvingtheminimumpointofthefunctionwhichisthesumofthedistancebetweenthefinalsequenceofquasi-residencepointsearchedandthecrimesites.Theminimumpointistheresidenceoftheserialoffender.

ByBPneuralnetworkwepredictthenextpossiblecrimepoint.Finally,wetestourapproachbyserialmurdercasesofPeterSutcliffe.Wederivetheresultthatthedistancebetweenthepredictingresidencespointandtheactualresidencepointisonly9.892kilometer,whichshowsthatourapproachisfeasible.

Keywords:

ringhypothesis;geographicprofile;BPneuralnetworks;PeterSutcliffesimulation

Contents

Executivesummary..…………………………………………………………………3

1.Introduction……………………………………………………………………...5

2.Thefactorsthataffecttheserialcrimes………………………………………..5

2.1Thedistributionofthepopulationdensity………………………………5

2.2Topographicalfeatures…………………………………………………...6

2.3Thenatureofthecaseitself…………………………………...................6

2.4Factorsoftheoffendersthemselves……………………………………6

3.AnalysisofMikeO’Leary’sMethod……………………………….....................6

4.AnalogModel…………………………………………………………...................8

5.SimulationAlgorithmModel……………………………………………………..9

5.1Terms,DefinitionsandSymbols…………………………………............9

5.2Assumptions………………………………………………………………..9

5.3ThetheoryofModel……………………………………………………...10

5.4Methodology………………………………………………………………11

5.5Howtodeterminethevariabled……………………………………….13

5.6Modeltest…………………………………………………........................15

5.7AnalysisoftheResult……………………………………………………19

5.7.1SensitivityAnalysis………………………………………………...19

5.7.2Modelimprovement………………………………………………...20

6.Thecombinationoftheabovemodel…………………………………………...21

6.1modelfoundation…………………………………………………………..21

6.2SinglehiddenlayerBPneuralnetworkmodel………………………..22

6.2.1Methodology………………………………………………………...22

6.2.2Determinationthelayerofthenetwork…………………………23

6.3ModelEvaluation………………………………………………………….25

7.Conclusionsandfuturework……………………………………………………25

8.References………………………………………………………………………..27

9.Appendix…………………………………………………………………………..28

ExecutiveSummary

Theanalysisoftheserialcrimes’GeographicProfilingisarelativelymaturestudydirectioninthefieldofcrimestudy.Becausewecanpredictthetime、locationandthebasepoint（generallyconsideredtobethelivingorworkingplaceofcriminals）thatoffenderscommitthecrimenexttimeaccordingtothepsychologicalcharacteristicsofoffendersandlocalfactorssuchasgeographicinformation.Inthisway,itwillhelpthepolicetocrackthecriminalcases.Sincetheearly1990sKinRossomofficerbegantoinvestigatetheGeographicProfiling,GeographicProfilinghasbecomeapracticallyusefulmethodincriminalinvestigatingandjudicialpracticing.Butinactualoperation,theseresultsaretoocomplicatedanddifficulttooperate.Thepurposeofthispaperistoproposeasimple,practical,easytooperate,andhighreliabilityofthepredictionprograms.

Inourmodels,wehaveusedthephysicalprinciples,mathematicalcalculations,computersimulationandotheradvancedtechnologytosolvethisproblem.Insomeway,weshouldtrytolearntothinklikeoffenders.weassumethatthecrimestatesisaplacewherehasthemaximizechancestocommitcrimessuccessfully,atthesametimeithastheminimizedangerous.Ononehand,thisincreasesthereliabilityofourprojections.Ontheotherhand,duetothedensityofpopulationdistributionandtopographicfactors,Theanalysisoftheserialcrimes’GeographicProfilingisarelativelymaturestudydirectioninthefieldofcrimestudy.Becausewecanpredictthetime、locationandthebasepoint（generallyconsideredtobethelivingorworkingplaceofcriminals）thatoffenderscommitthecrimenexttimeaccordingtothepsychologicalcharacteristicsofoffendersandlocalfactorssuchasgeographicinformation.Inthisway,itwillhelpthepolicetocrackthecriminalcases.Sincetheearly1990sKinRossomofficerbegantoinvestigatetheGeographicProfiling,GeographicProfilinghasbecomeapracticallyusefulmethodincriminalinvestigatingandjudicialpracticing.Butinactualoperation,theseresultsaretoocomplicatedanddifficulttooperate.Thepurposeofthispaperistoproposeasimple,practical,easytooperate,andhighreliabilityofthepredictionprograms.

Inourmodels,wehaveusedthephysicalprinciples,mathematicalcalculations,computersimulationandotheradvancedtechnologytosolvethisproblem.Insomeway,weshouldtrytolearntothinklikeoffenders.weassumethatthecrimestatesisaplacewherehasthemaximizechancestocommitcrimessuccessfully,atthesametimeithastheminimizedangerous.Ononehand,thisincreasesthereliabilityofourprojections.Ontheotherhand,duetothedensityofpopulationdistributionandtopographicfactors,theserialcrimesshouldbedividedintofourkindsofcircumstances.Astheflowingwords:

●Iftheoffender'smodussitedistributesinapopulousandlittleaffectedbytopographicfactors,wehaveprovedthatthebaseofoffendersislargelythegeometriccenterofgravityformedbyallhissites.Thisresultisagoodguidanceforthepopulouslargecitiessearchingforserialcriminals.

●Fortheevenlydensityofpopulationdistributionandmoreinfluencedbythetopographyareas,becausecriminalsneedtoconsidertravelproblems,thenwehavereasontobelievethatthebaselocationofoffenderisthepointthattheminimumsummaryofEuclideandistancebetweenthebasepointandthecrimestates.Forthisproblem,wehavetwoprograms,thesecondoneisanumericalcalculationmethod,thefirstoneistheanalogsimulationofaphysicalprocesstoseekthispoint.Weproposetoadoptthefirstoption.

●Forthenotevenlydensityofpopulationdistributionandnotinfluencedbythetopographyareas,werecommendtousethecriminalbehaviorModel,developedbyTowsonUniversityMikeO'Leary,ProfessorofMathematical.

●Forthenotevenlydensityofpopulationdistributionandmoreinfluencedbythetopographyareas,wecanusethepriordatatotrainaBPneuralnetworktopredictthenextlocationofoneoffendercommittingthecrime.

Sothatweusingdifferentstrategytomakepredictionforeachcase,ratherthanageneralsingleapproach.Soitishighlyadaptableandpromotional.Althoughthisissuehasbeensolvedrelativesuccessful,anewproblemcomesoutagain,thatisiftheoffenderunderstandtheabovetheory,thenhewillnolongerorlesscommitthecrimeinsuchgeographicalcontoursandtheychooseotherpointsastheirtargets,thistimewecannotusetheseprogramsindirect.

I.Introduction

InU.S.andEurope,PeterSutcliffe'sserialmurdercasescausethestudysuchcrimes.Inrecentyears,ithasbecomearelativelynewfieldofstudythatusestheGeographicProfilingtoframetheinvestigatingscopeoftheserialcrime.Itisconsideredasamoreeffectivemethodinthedetectionofmajor,difficultseries.Sincetheearly1990sKinRossomofficerbegantoinvestigatetheGeographicProfiling,GeographicProfilinghasbecomeapracticallyusefulmethodincriminalinvestigatingandjudicialpracticing.ThereisextensiveliteratureondefiningtheGeographicProfiling,andrecentdebateshaveemergedonhowbesttocombineatleasttwomethodssothatamoreaccuratescopecanbefound.CombinationofmethodsrequiresatleasttwodifferentkindofGeographicProfilingmodelandasuitablemethodtomakeanaccuratescope.

Soourgoaliscleargreatly:

●CreatingatleasttwokindsofGeographicProfilingmodels

●Accordingtothegivendata,operatetheGeographicProfilingmodel.

●DeviseamethodtocombinetheGeographicProfiling.

●writeareporttothepersoninchargeoflawenforcementagencies

Ourapproachis:

●Searchtheliteratureonexistingevaluationmethods

●Developacomprehensivemethodthatasksonlyforexisting

evidencesorevidenceseasytomeasureandcollect.

●Collectexperimentaldatathatcanbeusedinourmethod.

●Comparecurrentmethodsanddeterminetheircharacteristics

●Doasensitivityanalysisofvariationsofourmodels.

●Searchtheliteratureonexistingevaluationmethodsandfindtheirshortcomings.

●Dofurtherdiscussionbasedonourwork.

II.Thefactorsthataffecttheserialcrimes

ThedefinitionofSerialkilleriscommittingthecrimemorethanthreetimeswithinamonthandthemodusoperandiisgenerallythesameorsimilar.Soitisverynecessarytoposittheirlivingsets.Researchinthisareahastakenabroadapproachbyincludinginitsanalysesoperational,perceptual,behavioral,physical,social,psychological,legal,cultural,andgeographicsettings.（【5】D.KimRossmoPLACE,SPACE,ANDPOLICE）.Andthesecharacteristicsaremorelikelytobecomeparametersinamathematicalmodel