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51 \ �A� ] =plq+4> 4� �HT\ . �HT], � �W +e,

Li �W � 4/ wkhq +d, dqg +e, duh uhvshfwlyho| htxlydohqw wr4� �HT[ . �HT\ � �W +f, dqg4� �HT\ . �HT] � �W +g,1Fdvh 4= �HT[ � �HT\, ��HT[ . �HT\ � 31, +4� �HT\ . �HT], . +��HT[ . �HT\ , � �W +e| +g,,1, +4� �HT[ . �HT], � �W 1 Wkdw lv/ [ �A� ] krogv lq u1Fdvh 5= �HT\ � �HT], ��HT\ . �HT] � 31, +4� �HT[ . �HT\ , . +��HT\ . �HT], � �W +e| +f,,1, +4� �HT[ . �HT], � �W 1 Wkdw lv/ [ �A� ] krogv lq u17, Xqlrq=

41 [ �A� \ = plq+4> 4� �HT[ . �HT\ , � �W / �W � 4 . �HT[ � �HT\ 1

51 [ �A� ]= plq+4> 4� �HT[ . �HT], � �W / �W � 4 . �HT[ � �HT] 1

46

, �W � 4 . �HT[ � plqi�HT\ / �HT]j1, �W � 4 . �HT[ � �HT\ ]1, 4�.�HT[ � �HT\ ] � �W 1 Wkdw lv/ [ �A� \ ] krogv lq u18, Ghfrpsrvlwlrq= li [ �A� \ ] wkhq [ �A� \ dqg [ �A� ][ �A� \ ]= 4� �HT[ . �HT\ ] � �W 1, �W � 4. �HT[ � �HT\ ] 1, �W � 4. �HT[ � plqi�HT\ / �HT]j1, �W � 4. �HT[ � �HT\ dqg �W � 4 . �HT[ � �HT] 1, 4 � .�HT[ � �HT\ � �W dqg 4 � .�HT[ � �HT] � �W 1 Wkdw lv/

[ �A� \ dqg [ �A� ] krog lq u1

Uhpdun ; Iurp wkh gh�qlwlrq ri uh�h{lylw|/ zh fdq frqfoxgh wkdw li \ � [wkhq zh kdyh dozd|v [ �A4 \ 1

Sursrvlwlrq 5 Li [ �A� \ dqg [ �A� \ wkhq [ �A� \ ]zlwk � 9@ � dqg

� @plq+�>�,1

Surri1 Iurp wkh gh�qlwlrq ri xqlrq d{lrp1

Sursrvlwlrq 6 Li [ �A� \ dqg \ �A� ] wkhq [ �A� ]/ zkhuh +� @ 4 ru

� @ 4, dqg � @plq+�> �,1

Surri1 Li [ �A� \ dqg \ �A� ] wkhq [ �A� ]/ zkhuh +� @ 4 ru� @ 4, lv jlyhq iurp wkh gh�qlwlrq ri wudqvlwlylw| d{lrp1 Qrz zh vkrz wkdw� @plq+�>�,1

Fdvh 4= � @ 4 dqg � @ 4, �HT[ � �HT] , [ �A4 ]1Fdvh 5= � @ 4 dqg � ? 4[ �A4 \ , �HT[ � �HT\ , 4�.�HT[ � �HT\ � 41+d,\ �A� ] , �HT\ A �HT] , 4�.�HT\ � �HT] @ �1 +e,+d . e, , 4�.�HT[ � �HT\ . 4�.�HT\ � �HT] � 4. � ,plq+4> 4�.�HT\ � �HT], � �1 Wkdw lv/ [ �A� ] zlwk � @plq+�> �,11Fdvh 6= � ? 4 dqg � @ 4Wkh vdph surri dv fdvh 51

e �L?U*�t�L?

Wklv sdshu lqwurgxfhv d vlpsoh dqg qdwxudo h{whqvlrq ri fodvvlfdo ixqfwlrqdo gh0shqghqf|/ fdoohg g|qdplf ix}}| ixqfwlrqdo ghshqghqf|1 Lw kdv ehhq vkrzq wkdwd GIIG lv d jhqhudol}dwlrq ri ^7/ 54/ 56` sursrvdov1 Wkh dlp ri wklv jhqhudol}d0wlrq lv uhod{lqj wkh elqdu| wuxwk ydolglw| uhvwulfwlrq1 Lw kdv ehhq vkrzq dovr wkdwd GIIG fdq vxffhvvixoo| uhsuhvhqw lqwhjulw| frqvwudlqwv h{suhvvlqj dssur{lpdwhhtxdolw| dqg lqyroylqj dovr ix}}| prgl�huv1 Wkh dvvrfldwhg d{lrpdwlf v|vwhpkdv ehhq suhvhqwhg dqg vkrzq wr eh vrxqg1

47

Lw vkrxog eh srlqwhg rxw wkdw wklv zrun lv qhlwkhu d frpsohwh qru d frqfoxvlyhh{srvlwlrq ri wkh srlqwv wkdw vkrxog eh vwxglhg1 Zlwklq wkh sursrvhg dssurdfkdqg dv dq h{whqvlrq ri wklv zrun/ zh fdq phqwlrq wkh vwxg| ri frpsohwhqhvv ri wkhdvvrfldwhg d{lrpdwlf v|vwhp/ wkh lqwurgxfwlrq ri wkh frqfhsw ri qxoo ydoxhv dqgwkh vwxg| ri rwkhu w|shv ri gdwd ghshqghqflhv/ vxfk dv pxowl0ydoxhg ghshqghqf|/glixqfwlrqdo ghshqghqf| ^6/ 48`/ hwf1

Dfnqrzohgjphqw Zh wkdqn Nlqj Idkg Xqlyhuvlw| ri Shwurohxp dqg Plq0hudov dqg wkh Jhqhudo Gluhfwlrq ri Vflhqwl�f Uhvhdufk ri Wxqlvld +GJUVW, irusduwldoo| �qdqflqj wklv zrun1

+iuihi?Uit

^4` Z1Z1 Dupvwurqj1 Ghshqghqf| vwuxfwxuhv ri gdwdedvh uhodwlrqvklsv1 LqLILS Frqjuhvv/ sdjhv 8;3~8;6/ Vhswhpehu 4<:71

^5` S1 Dw}hql dqg Q1P1 Pruixql1 Ixqfwlrqdo ghshqghqflhv dqg frqvwudlqwv rqqxoo ydoxhv lq gdwdedvh uhodwlrqv1 Lqirupdwlrq dqg Frqwuro/ +:3,=4~64/ 4<;91

^6` V1 Ehq\dkld dqg D1 Mdrxd1 Hwxgh ghv g�hshqgdqfhv �rxhv +Vwxg| ri ix}}|ghshqghqflhv, 1 Pdvwhu uhsruw/ HUSDK Odrudwru|/ Vflhqfhv Idfxow| riWxqlv/ Mxo| 4<<91

^7` E1 Ekxql|d dqg S1 Ql|rjl1 Orvvhohvv mrlq surshuw| lq ix}}| uhodwlrqdo gdwd0edvhv1 Gdwd dqg Nqrzohgjh Hqjlqhhulqj/ sdjhv 43<~457/ 4<<61

^8` E1 Erxfkrq0Phxqlhu1 Od orjltxh �rxh +Wkh ix}}| orjlf,1 Suhvvhv Xqlyhuvl0wdluhv gh Iudqfh/ lq v�hulh %TXH VDLV0MHB%/ 4<<61

^9` E1S1 Exfnohv dqg I1H1 Shwu|1 D ix}}| uhsuhvhqwdwlrq ri gdwd iru uhodwlrqdogdwdedvhv1 Ix}}| Vhwv dqg V|vwhpv/ +:,=546~559/ 4<;51

^:` E1S1 Exfnohv/ I1H1 Shwu|/ dqg K1V1 Vdfkdu1 D grpdlq fdofxoxv iru ix}}|uhodwlrqdo gdwdedvhv1 Ix}}| Vhwv dqg V|vwhpv/ +5<,=65:~673/ 4<;<1

^;` J1T1 Fkhq/ H1H1 Nhuuh/ dqg M1 Ydqghqexofnh1 D frpsxwdwlrqdo dojrulwkpiru wkh IIG wudqvlwlyh forvxuh dqg d frpsohwh d{lrpdwl}dwlrq ri ix}}| ixqf0wlrqdo ghshqghqflhv1 Mrxuqdo ri Lqwhooljhqw V|vwhpv/ 8+<,=754~773/ 4<<71

^<` J1T1 Fkhq/ H1H1 Nhuuh/ dqg M1 Ydqghqexofnh1 Wkh ghshqghqf|0suhvhuylqjghfrpsrvlwlrq dqg d whvwlqj dojrulwkp lq d ix}}| uhodwlrqdo gdwd prgho1Ix}}| Vhwv dqg V|vwhpv/ +:5,=5:~6:/ 4<<81

^43` H1I1 Frgg1 D uhodwlrqdo prgho ri gdwd iru odujh vkduhg gdwd edqnv1 Frp0pxqlfdwlrqv ri wkh DFP/ 46+9,=6::~6;:/ Mxqh 4<:31

48

^44` G1 Gxerlv dqg K1 Sudgh1 Wk�hrulh ghv srvvlelolw�hv= Dssolfdwlrq �d od

uhsu�hvhqwdwlrq ghv frqqdlvvdqfhv hq lqirupdwltxh1 Hglwlrq PDVVRQ/Sdulv/ 4<;;1

^45` O1W1 IDQ1 Ixqfwlrqdo ghshqghqflhv dqg qrupdo irupv lq wkh ri ix}}| uhod0wlrqdo gdwdedvh prgho1 Lqirupdwlrq Vflhqfhv/ 93+405,=4~5;/ Mxqh 4<<51

^46` M1 Kdoh dqg V1 Vkhqrl1 Lpsuhflvh gdwdedvh lqihuhqfh xvlqj ixqfwlrqdo gh0

shqghqflhv/ Dgydqfhv lq ix}}| wkhru| dqg whfkqrorj|/ sdjhv 63:~6591 GxnhXqlyhuvlw|/ 4<<81

^47` W1 Lfklndzd dqg P1 Kludndzd1 DUHV= D uhodwlrqdo gdwdedvh zlwk Wkhfdsdelolw| ri shuiruplqj �h{leoh lqwhusuhwdwlrq ri txhulhv1 LHHH wudqvdfwlrq

rq vriwzduh Hqjlqhhulqj/ 45+8,=957~967/ Pd| 4<;91

^48` D1 Mdrxd/ Q1 Ehonklwhu/ dqg W1 Prxndp1 Sursul�hw�hv ghv g�hshqgdqfhv gl0irqfwlrqqhoohv gdqv ohv edvhv gh grqq�hhv uhodwlrqqhoohv1 LQIRU/ 63+4,/ 4<<51

^49` D1 Nlvv1 � 0ghfrpsrvlwlrq ri ix}}| uhodwlrqdo gdwdedvhv1 Dqqdohv Xqly1 Vfl1Exgdshvw/ Vhfw1 Frps1/ 4<+45,=466~475/ 4<<41

^4:` D1 Prwur1 Dffrpprgdwlqj lpsuhflvlrq lq gdwdedvh v|vwhpv= Lvvxhv dqgvroxwlrqv1 VLJPRG uhfrug/ 4<+7,=9<~:7/ Ghfhpehu 4<<31

^4;` P1 Qdndwd1 Ghshqghqflhv lq ix}}| gdwdedvhv= Ixqfwlrqdo ghshqghqflhv1 Lqwkh Lqwhuqdwlrqdo mrlqw frqihuhqfh ri wkh 7wk LHHH Lqwhuqdwlrqdo frqihuhqfh

rq Ix}}| V|vwhpv/\rndkdpd +Mdsdq,/Yro1 LL/ sdjhv 4~;/ Pdufk 4<<81

^4<` Y1 Qrydn1 Ix}}| vhwv dqg wkhlu dssolfdwlrqv1 Dgdp Kljohu/ 4<;<1

^53` K1 Sudgh1 dqg F1 Whvwhpdoh1 Jhqhudol}lqj gdwdedvh uhodwlrqdo dojheud iruwkh wuhdwphqw ri lqfrpsohwh ru xqfhuwdlq lqirupdwlrq dqg ydjxh txhulhv1Lqirupdwlrq Vflhqfhv/ +67,=448~467/ 4<;71

^54` N1Y1V1Y1Q1 Udmx dqg D1N1 Pdmxpgdu1 Ix}}| Ixqfwlrqdo ghshqghqflhv dqgOrvvhohvv mrlq ghfrpsrvlwlrq ri ix}}| uhodwlrqdo gdwdedvhv v|vwhpv1 DFP

Wudqvdfwlrqv rq Gdwdedvh V|vwhpv/ 46+5,=45<~499/ Mxqh 4<;;1

^55` H1D1 Uxqghqvwhlqhu dqg O1 Elf1 Hydoxdwlqj djjuhjdwhv lq srvvlelolvwlf uhod0wlrqdo gdwdedvhv1 Gdwd dqg Nqrzohgjh Hqjlqhhulqj/ +:,=56<~59:/ 4<<51

^56` S1F1 Vd{hqd dqg E1N1 W|djl1 Ix}}| Ixqfwlrqdo ghshqghqflhv dqg lqghshq0ghqflhv lq h{whqghg ix}}| uhodwlrqdo gdwdedvhv prghov 1 Ix}}| Vhwv dqg

V|vwhpv/ +9<,=98~;</ 4<<81

^57` V1 Vkhqrl/ D1 Pdowrq/ dqg O1W1 Idq1 Dq htxlydohqfh fodvvhv prgho ri ix}}|uhodwlrqdo gdwdedvhv 1 Ix}}| Vhwv dqg V|vwhpv/ 6;+5,=486~4:3/ 4<<31

49

^58` U1F1 Wulsdwk| dqg S1F1 Vd{hqd1 Pxowlydoxhg ghshqghqflhv lq ix}}| uhod0wlrqdo gdwdedvh 1 Ix}}| Vhwv dqg V|vwhpv/ 6;+6,=59:~5:</ 4<<31

^59` O1D1 ]dghk1 Ix}}| vhwv1 Lqirupdwlrq dqg Frqwuro/ +9<,=66;~686/ Mxqh 4<981

4: