MCM 美国数学建模 3Word格式文档下载.docx

MCM 美国数学建模 3Word格式文档下载.docx

《MCM 美国数学建模 3Word格式文档下载.docx》由会员分享，可在线阅读，更多相关《MCM 美国数学建模 3Word格式文档下载.docx（13页珍藏版）》请在冰豆网上搜索。

T4

TeamControlNumber

7210

ProblemChosen

B

F1

F2

F3

F4

2010MathematicalContestinModeling（MCM）SummarySheet

Abstract

Ourworkisfindthatthenextplacewherethekillerkillpeople,tostoptheperpetratorscontinuetocommitcrimes.

Therearetwomainmethodstocalculatetheplaceofcommission.

Circlemethod:

Thenextplaceofcommissioncontainedinthecirclewhosediameteristhetwocrimesthatarefarthestapart.Itisalittlesimplebutalsoitwasusedintoday'

sfinding.

Probabilitymethod:

Inaparticularareatofindthebiggestpointoftheprobabilityofoccurrenceofcrime,andthispointmaybepredictedpoint.

Atfirst,weusecirclemethodbegantodrawaprojectionsofcriminalarea,andmarkcenterofthecircleasacrime-point.However,aftercheckingwefoundthatthemodel’sanswerisnotreliable.SowequotedDr.MikeO'

Learycriminalprobabilityformula,calculatedintheregionofallpointsoftheprobabilityofcrime，firstofall,therearestillmanythingswehaven'

tconsideredyet.Likeconsidertheoffender'

shobbyandwhattherealenvironmentwillbeintheplace.Theshopthere,theplacewhichhasmorepeopleandmaybethetimeisaveryimportantquestion.Theoffendermayliketocrimeinthenight.Therestillneedfartherresearch.Thenwereachedthegreatestpointoftheprobability,thispointiswearelookingforcrime-point.

Themodelcancalculatemajorityofexampleaccuratelypredict,anditneedn’tconsidertheotherfactors（suchastime,environment,etc.）,simplifyoperationandpractical.

Contents

1.Introduction..............................................................................................................3

2.TheDescriptionofProblem....................................................................................3

2.1Howdoweapproximatethewholecourseofsearchingkiller?

.........................3

2.2Howdowedefinetheserialcriminal?

................................................................3

2.3Thedifferencesindifferentenvironment.............................................................3

2.4Whatifthereisnodataavailable.........................................................................4

3.Models.......................................................................................................................4

3.1BasicModel.........................................................................................................4

3.1.1Terms,DefinitionsandSymbols.................................................................4

3.1.2Assumptions................................................................................................4

3.1.3TheFoundationofModel...........................................................................4

3.1.4SolutionandResult.....................................................................................6

3.1.5AnalysisoftheResult..................................................................................6

3.1.6StrengthandWeakness...............................................................................7

3.2ImprovedModel..................................................................................................7

3.2.1ExtraSymbols.............................................................................................7

3.2.2AdditionalAssumptions..............................................................................7

3.2.3TheFoundationofModel...........................................................................7

3.2.4SolutionandResult.....................................................................................8

3.2.5AnalysisoftheResult................................................................................10

3.2.6StrengthandWeakness.............................................................................10

4.Conclusions.............................................................................................................11

5.FutureWork...........................................................................................................11

5.1Anothermodel....................................................................................................11

5.1.1Thelimitationsofprobabilitytheory........................................................11

5.1.2ImproveModel..........................................................................................11

6.References...............................................................................................................12

7.Executivesummary................................