Team#13059
P
(0≤
P
≤1)
.
Page70f14
•
If
P
≥0.8
,wethinkheors heisoneoftheconspirators.
•
If
0.6≤
P< br>≤0.7
,wehighlydoubtheisoneoftheconspirators.
•
If
0.4≤
P
≤0.5
,wemoderatelys uspectedthatheisoneoftheconspirators.
•
If0.2≤
P
≤0.3
,wemildlysuspectedheisoneof theconspirators.
•
If
P
≤0.1
,webel ieveheisinnocent.
Accordingtothesemetrics,wecar rythejudgingmetricsonthiscompany's
seniormanage rJerome,Dolores,thattheprobabilityofJerome,
Dol ores,andGretchenrespectivelyare0.6,0.8,orewehaveth efull
reasontothinkthatDoloresisaplotter,andwea lsocannotgetridofthesuspicion
thatJeromeandGret chenarecriminals.
2
Problemanalysis,modelbui ldingandsolvingofRequirement
2
5.5.2Requirem ent2
5.2.1AnalysisofRequirement2
Comparingwi thRequirement1,
thesetwocluesare:Topic1isasuspi ciousmessagetopicandChrisisoneofthe
lusethesame modelinRequirement1tosolvethisquestion.
5.2.2Mo delbuildingandsolvingofRequirement2
Wecalculate theprobabilityofthe68suspectsaccordingtothemodelan d
solvingprocessinRequirement1,thenweprioritize the83workers
bylikelihoodof
beingpartoftheco nspiracy(
8knowncriminals'probabilityare1,7inno cents'
probabilityare0).completesortingresultis in
.
Table3:sortingbyeachworker's
likelih oodofbeingpartoftheconspiracy
Theprobability
NamethatheisaNotes
conspirator
thisformatre presentknown
Chris1
criminal
Elsie1
Je an
Alex
Paul
1
1
1thisformatreprese ntknown
thisformatrepresentsenior
manager
SortingNode#
1
2
3
4
5
0
718
21
43

Team#13059Page80f14
innocentman
6
7
8
9
10
11
12< br>13
14
15
...
49
54
67
3
10
81
20
16
17
34
...
Harvey
Ulf
Yao
Sherri
Dolores
Seeni
Cr ystal
Jerome
Neal
Jerome
...
1
1
1
1
0.9
0.9
0.8
0.7
0.7
0 .7
...
thisformatrepresentsuspect
5.2.3An alysisofthesortingresult
,wefindthat
number3 suspectSherri'sprobabilitychangefrom0.6to1,sowehav ethefullreason
probabilityofnumber10seniormanag er
ingtothejudgingmetricsgiveninRequirement1,we
ghtheprobabilityofnumber16
seniormanagerJen omeincreaseto0.7,wedonothavethefullreasontoconfirm that
ber25Claireandnumber82Renichangefromtheori ginal
non-suspicioustomildlysuspicious.
5.3P roblemanalysis,modelbuildingandsolvingofRequiremen t3
5.3.1AnalysisofRequirement3
Afterlearning andunderstandingsemanticnetworkanalysis,weuseitto< br>optimizeourmodelonthebasisofconditionsgivenbyRe quirement1and
y,,
then,wehavethemdividedinto fourcategoriesandsettheweightsaccordingtotheir
degreeofcorrelationwithsuspicioustopics.
Requir ement2givesustwoclues,andinRequirement3'ssolvingpr ocess,westill
,webelievethatthereareeightknown< br>criminals(thepossibilityofbeingoneoftheconspira torsis1)andsevenknown
innocents(thepossibilityo fbeingoneoftheconspiratorsis0),andtopic1isa
ini shingthesesettings,thecomputedresultshows
thatm anysuspects'totalweightarebiggerthan1,inordertofac ilitatethejudgment,
here,wehaveallsuspects'tota lweightdividedbyN(Nrepresentsthebiggestnumber
o f68totalweight)tomakeallofthembetween0and1,andthis totalweightis

Team#13059
exactlythepr obabilityofthesuspectofbeingaconspirator.
5.3.2 ModelbuildingandsolvingofRequirement3
Page90f14
Weknowthattheconspiracyistakingplacetoembezzle fundsfromthe
companyanduseinternetfraudtostealf undsfromcreditcardsofpeoplewhodo
arryontheclass ificationtotheremaining11
messagetopicsandexcep t4knownsuspiciousones:Topic1,7,11,and13,andset
theirweights.
Throughanalysistotheconspiracyand 15messagetopics,wefindoutthat
2andTopic12are
conspiracyisrelatedtocomputernetworksecurity,
thus,topicsaboutcomputersecurityshouldalsobetakens eriously,andwecansee
4stressesthatwereallyneedt o
noticetheintenseargumentamongAlex,eabove,weli st
Topic2,4,5,12,and15asthesecondkindoftopic,ic
opic3,14,8,
and10,wethinkthattheyhavenothin gtodowiththeconspiracy,soitsweightis0.
•
Sol vingprocessofthemodel
Accordingtoanalysisoftheq uestion,weestablisha
83×83
matrixA(the
). Here
a
(
i
,
j
),
i
<
j
standforthesumofweightsof
alltopicsinvolved inthewordsnumber
i
suspectsaidtonumber
j< br>suspect,incontrast
and
a
(
j
,i
),
i
<
j
standforthesumofweight sofalltopicsinvolvedinthewords
number
j
s uspectsaidtonumber
i
suspect.
•
Algori thm:
thesumofallthedatainthe
thesumofallthed atainthe
III
.
C
i
n
(1≤
n
≤83)
rowas
a
.
n
(1≤
n
≤83)< br>columnas
b
.
=
a
+
b
,(1≤< br>i
≤83)
,itistheweightofwhichnumber
isuspectisa
conspirator.
IV
.
P
i< br>=
C
i
,(1≤
i
≤83)
,itisthepro babilityofwhichnumber
i
max
{
C
i}
isaconspirator.
WeusetheMATLABsoftwareto realizethisalgorithm(programmingisin
AccessaryR equirement3.m),andsorttheobtainedresultsinEXCEL(we stillassume

Team#13059Page100f14
that theprobabilityofthe8knowncriminalsis1,andtheprobab ilityofthe7known
innocentsis0).Partofthesorting isinTable4,andthecompletesortingresultisin
.
Table4:sortingbyeachworker's
likelihoodofbeing partoftheconspiracy
SortingNode#Name
Theprob abilitythat
heisaconspirator
1
1
1
1
1
1
1
1
1
0.97058823529
0.8 8235294118
0.86764705882
0.79411764706
0. 79411764706
0.77941176471
...
thisformatr epresent
suspect
thisformatrepresent
know ninnocentman
thisformatrepresent
seniormanag er
Notes
thisformatrepresent
knowncrimina l
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
...
0
7< br>18
21
43
49
54
67
3
32
15
10
17
34
22
...
Chris
Elsi e
Jean
Alex
Paul
Harvey
Ulf
Yao< br>Sherri
Gretchen
Julia
Dolores
Neal< br>Jerome
Eric
...
5.3.3Analysisoftheresu lt
ThroughanalysisofthesortingresultsinTable2，
Table3andTable4,wecan
confirmthatnumber3 suspectisaconspirator,besides,wefindoutthat,aftera nalysis
ofspeech,theprobabilityofnumber24suspec tFranklinofbeingaconspiratorraised
ingtojudging metricsofmodelinRequirement1,wehighly
'smore,th eprobabilityofnumber26
suspectMarianraisedfrom0 .1to0.441,andtheprobabilityofnumber42dsuspect
t hattheimprovedmodelmakepeoplelike
Franklin,Mari anandKatherinedifficulttobeatlarge.

Team #13059Page110f14
5.4Problemanalysis,modelbuildi ngandsolvingofRequirement4
5.4.1AnalysisofRequi rement4
WethinkRequirement4givesus3questions:1
:Ithopesourmethodologywillcontributetosolvi ngimportantcasesQuestion1
•
Question
arou ndtheworld,especiallythosewithverylargedatabasesof messagetraffic.
:
Discusshowmorethoroughnetw ork,semantic,andtextanalysesofQuestion2:
•
Q uestion2
themessagecontentscouldhelpwithourmode landrecommendations，andexplain
thenetworkmodeli ngtechniquesyouhaveusedandwhy.
:
on3:
•Question3
Wetaketurnstosolvethe3questionsandt akethevirusinfectionprocessasan
,weassumethere< br>isasmallviruspropagationenvironment,and
draw outtheircontactnetworkdiagramwith
,wefigureoutt ouch
numberoftimesofa
unknowncellandthevirus intermsofthenetworkdiagram,and
figureouttotalprobabilityofeachunknowncellinaccordancewiththep robabilityofbeinginfectedineach
y,wesortalltheu nknowncellsbylikelihoodofbeinginfectedordiseasedce llsto
findouttheunknowncellsthataremostlikelyto beinfectedordiseasedcells.
5.4.2Modelbuildingan dsolvingofRequirement4
•
Question1：
Forth osewithverylargedatabasesofmessagetraffic,wefirstu tilizethe
semanticnetworkanalysisandthetextanal ysisinRequirement3toidentify
suspiciousdegreeof eachtopic,anddividethesuspectedextentintoseveralle vels,
ly,usingEXCELsoftwaretocountthe
amount andthekindoftopicsinvolvedineverytwonodes,andmakea large-scale
matrixsimilartothe83×y,figureout
a
(
i
,
j
)
in
thematrixinac cordancewiththealgorithminRequirement3,andconverti ttoa
n
×
n
large-scalematrix
A
n
×
n
.Thenwecangetthesuspecteddegreeofeac hnode
hosenodeswhosetypeshave
beenknown,,wes orttheremainingnodesinaccordance
withsuspectedd egree,inthisway,wecandeterminewhoisthemostlikelyconspiratorintermsofthejudgingmetrics.
•
Q uestion2：
InRequirement3，weutilizesemanticnetwo rkanalysisandtextanalysis
technologytoanalysist hecasetoenableustofigureoutwhichwordsaremostlikely

Team#13059Page120f14
tobecodewordsus edbycriminalsintheircommunicationorwhichtopicsarec losest
sprobabilityisexactlytheweightmentionedi n
Requirement1,2,llhaveinfluenceonourmodelandgr eatlypromoteitto
avoidsuchsituationsthatpeoplel ikeCarolarefalselyaccusedandpeoplelikeInez
goun punished.
•
Question3：
TosolveQuestion3，w eassumethereisasmallviruspropagationenvironment,and
drawouttheircontactnetworkdiagram(inFigur e1).
1
3
2
Unknown cell
Virus
1< br>5
7
4
6
10
9
8
Figure1：Con tactnetworkdiagramofvirusandunknowncells
Accord ingtotheknownconditions,weassumetheprobabilitythat anormalcell
isinfectedwhenithasdirectcontactwit hvirusis
t
(0<
t
<1)
.Unknowncellnumbersare:1,2,3,4,6,andinfectednodesarenumber5, 7,8,9,hese
conditionsandthenetworkdiagram,wecar ryoutcalculationsonalltheunknown
cellstogetthei rinfectionprobability.
Here,wedefine
p
j< br>(0<
p
j
<1)
astheprobabilitythatnum ber
j
unknowncell
isinfected
(
j
=1,2,3,4,6)
.
Algorithmanalysis:Forthenumbe r1unknowncell,itrespectivelyhascontactwith

< br>Team#13059Page130f14
unknowncellsnumber2,3,a nd5,becausethosewhohavecontactwithnumber2are
al lunknowncells,5
isainfectednode,sotheprobabilit ythatnumber5makesnumber1intoadiseased
cellis
t
.Asnumber3contactdirectlywiththeviralcells,t hus,wecannotneglect
theeffectofnumber3onnumber1 ,sotheprobabilitythatnumber5makesnumber1
intoad iseasedcellis
t
×
p
3
.Inconclusion ,wegettheprobabilitythatnumber1is
infectedis
p
1
=
t
+
t
×
p
3
.The probabilityoftheremainingfourunknowncellscan
be figuredoutinaccordancewiththismethod.
Algorithm :
⎧
p
1
=2
t
2
+
t
⎧
p
1
=
t
+
t
×
p
3
⎪
⎪
p
=
t
×
p
+
t
×
p
32
p
=2
t
+3
t
2132
⎪⎪
⎪⎪
⇒
⎨
p
3
=2
t
⎨
p
3
=
t
+
t
⎪
p
=
t
⎪
p
=
t
4
⎪⎪
4
⎪
⎪
⎩
p
6
=
t
+
t
⎩
p
6
=2
t
(1)
Note:robabilityvaluecomputedusingthismethodisb iggerthan1,we
recordthisprobabilityvalueas1.
l3contactmuchwithinfectedcells,sotheeffectofunkno wncell1
onitcannotbeneglected.
Finally,wesor tthevaluesof
infectedordiseasedcells.
p
j
(
j
=1,2,3,4,6)
informula(1)tofindout the
luationofthemodel
Strengths
Simplicit y:Thismodelissimpleenoughthatitentailsasmallamount of
tion,itiseasytobeconvertedintoanelectronicform,forexample,Matlab,tobevisuallydisplayedsoth atnearlynomathematical
knowledgeisnecessarytoun derstandthemodel.
:
Themodelusedinthisproble mcouldbeeasilyExtensibility:
•
FlexibleandEx tensibility
appliedtostudyotherissues.
•
Theuseoftheweight:Bysettingtheweight,wemakethecalc ulationofcomplex
messagenetworkbecomesimple.
Weaknesses
•

Team#13059Page140f14
•
Assumptions:Simplifyingassumptionshadtobemad einordertocreatea
solvablemodel.
•
Estima ted
：
Becauseoftheuncertainties,somevaluesli ketheweightusedinthe
calculationshadtobeestimat ed.
Reference
[1]ArizonaStateUniversity(2010 ,April2).OutofThisWorld:NewStudy
eDaily,.
12 Feb.2012.
[2]unityGenesSurvive:StudyImplicatesA rms
eDaily,.12Feb.
2012.
[3]:.
[4]Gil, EnricoMotta,dBenjamins,,editors,ISWC
2005,volum e3729
[5]NetworkAnalysis:Methodsand
Applicat ions,dge
UniversityPress,Cambridge,1edition,199 9.
[6]giesAreUs:AUnifiedModelofSocialNetworksan d
ndaGil,EnricoMotta,dBenjamins,andMarkA.
Mu sen,editors,ISWC2005,volume3729ofLNCS,pages522–536 ,Berlin
Heidelberg,er-Verlag.
[7]tedatDagstu hl
seminar03361:AlgorithmicAspectsofLargeandCom plexNetworks,
AugustSeptember2003.
[8]udinal non- euclideannetworks:
Networks,7:287–322,1985.