Molecular recognition of ubiquitin and Lysine 63 linked diubiquitin by STAM2 : the effect of the linkers length and flexibility

HAL Id: tel-03091978

https://tel.archives-ouvertes.fr/tel-03091978

Submitted on 1 Jan 2021

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

diubiquitin by STAM2 : the effect of the linkers length

and flexibility

Minh-Ha Nguyen Thi

To cite this version:

Minh-Ha Nguyen Thi. Molecular recognition of ubiquitin and Lysine 63 linked diubiquitin by STAM2 :

the effect of the linkers length and flexibility. Other. Université de Lyon, 2019. English. �NNT :

2019LYSE1321�. �tel-03091978�

7+(6( GH '2&725$7 '( /·81,9(56,7( '( /<21

RSpUpH DX VHLQ GH

O·8QLYHUVLWp &ODXGH %HUQDUG /\RQ  (FROH 'RFWRUDOH 

(FROH 'RFWRUDOH GH &KLPLH &KLPLH 3URFpGpV (QYLURQQHPHQW 6SpFLDOLWp GH GRFWRUDW  5pVRQDQFH 0DJQpWLTXH 1XFOpDLUH

'LVFLSOLQH  &KLPLH

SUpVHQWpH HW VRXWHQXH SXEOLTXHPHQW OH  SDU 0LQK+D 1*8<(1

0ROHFXODU UHFRJQLWLRQ RI XELTXLWLQ DQG /\VLQH  OLQNHG GLXELTXLWLQ E\ 67$0 7KH HIIHFW RI WKH OLQNHUV OHQJWK DQG IOH[LELOLW\

/D UHFRQQDLVVDQFH GH O·XELTXLWLQH HW GH OD GLXELTXWLQH /\VLQH  SDU OD SURWpLQH 67$0 /· HIIHW GH OD ORQJXHXU HW GH OD IOH[LELOLWp GHV OLQNHUV

'HYDQW OH MXU\ FRPSRVp GH

&KULVWLQD 6,=81 &KDUJpH GH 5HFKHUFKH &156 5DSSRUWHXU

,6&1 *LIVXU<YHWWH

&KULVWLDQ *5,(6,1*(5 3URIHVVHXU 5DSSRUWHXU

8QLYHUVLW\ RI *|WWLQJHQ

$GULDQD 0,(/( 3URIHVVHXUH ([DPLQDWULFH

8QLYHUVLWp GH /\RQ

%HUQKDUG %5876&+(5 'LUHFWHXU GH 5HFKHUFKH &($ ([DPLQDWHXU

,%6 *UHQREOH

)UDQN *$%(/ &KDUJp GH 5HFKHUFKH &($ ([DPLQDWHXU

,%6 *UHQREOH

0DJJ\ +2/2*1( 0DvWUH GH &RQIpUHQFHV &RGLUHFWULFH GH WKqVH

8QLYHUVLWp GH /\RQ

2OLYLHU :$/.(5 0DvWUH GH &RQIpUHQFHV 'LUHFWHXU GH WKqVH

$FNQRZOHGJHPHQWV

7KLV WKHVLV EHFRPHV D UHDOLW\ ZLWK FRQVLGHUDWH KHOS DQG VXSSRUW RI PDQ\ SHRSOH :LWK HQRUPRXV JUDWLWXGH , ZRXOG OLNH WR H[WHQG P\ VLQFHUH WKDQNV WR DOO RI WKHP

)RUHPRVW , ZRXOG OLNH WR WKDQN 'U &KULVWLQD 6L]XQ DQG 3URI &KULVWLDQ *ULHVLQJHU IRU WKHLU WLPH DQG SDWLHQFH WR UHYLHZ DQG HYDOXDWH WKLV ZRUN DV ZHOO DV 3URI $GULDQD 0LHOH 'U %HUQKDUG %UXWVFKHU DQG 'U )UDQN *DEHO IRU DFFHSWLQJ WR EH SDUW RI P\ WKHVLV GHIHQVH FRPPLWWHH

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

0\ VSHFLDO WKDQNV WR 0DULH 0DUWLQ ZKR QRW RQO\ KHOSHG PH WUHPHQGRXVO\ WKURXJKRXW P\ WLPH DW WKH ODERUDWRU\ EXW DOVR EHFDPH D IULHQG WR ZKRP , FRXOG VKDUH P\ HYHU\GD\ SUREOHPV 7KDQNV IRU DOO \RXU HQFRXUDJHPHQW DQG XVHIXO FULWLTXHV RI WKLV UHVHDUFK ZRUN

, ZRXOG OLNH WR WKDQN DOO RWKHU PHPEHUV RI WKH %,26<6 DQG ,17(5$&7 JURXS )ORUHQFH *XLOOLqUH +HQU\ .LP &RULQQH 6DQJOU 0RUHQR 0DUFHOOLQL DQG <RDQ 0RQQHDX IRU \RXU YDOXDEOH VXSSRUWV JUHDW LGHDV DQG DGYLFH

, ZRXOG OLNH WR WKDQN 'U 2OLYLHU &DOD DQG 'U 7KLHUU\ *UDQMRQ IRU WKHLU SDUWLFLSDWLRQ LQ P\ WZR WKHVLV PRQLWRULQJ FRPPLWWHHV DQG IRU WKHLU JUHDW UHFRPPHQGDWLRQV RQ WKH DGYDQFHPHQW RI WKH WKHVLV

, ZLVK WR DFNQRZOHGJH WKH KHOS SURYLGHG E\ 'U )UDQoRLV;DYLHU &DQWUHOOH GXULQJ P\ 7*,5 VHVVLRQ DW WKH 105 SODWIRUP LQ /LOOH DQG WKH DGYLFH JLYHQ E\ 'U 5RODQG 0RQWVHUUHW GXULQJ P\ FLUFXODU GLFKURLVP H[SHULPHQWV DW WKH ,QVWLWXW %LRORJLH HW &KLPLH GHV 3URWpLQHV

, ZRXOG OLNH WR WKDQNV DOO WKH VWDIIV DW WKH ,QVWLWXW GHV VFLHQFHV DQDO\WLTXHV HVSHFLDOO\ 0DL &DQHKDQ (ULF /HJURV 'DYLG 7DWDQJHOR 0DU\OLQH 'HUHJQDXFRXUW ZKR PDGH P\ WLPH KHUH PXFK HDVLHU E\ SURYLGLQJ PH ZLWK WKHLU EHVW VXSSRUW

WKDQNV IRU WDJJLQJ PH DORQJ ZLWK JUHDW UHOD[LQJ WLPH RXWVLGH RI P\ VWUHVVIXO ZRUN

7R P\ IDPLO\ 0RP 'DG DQG P\ GHDU VLVWHU 0LND ZLWKRXW ZKRP , ZRXOG QRW VWDUW WKLV 3K' WKHVLV LQ WKH ILUVW SODFH WKDQN \RX IRU VXSSRUWLQJ PH XQFRQGLWLRQDOO\ WKURXJKRXW P\ OLIH ZLWK ERXQGOHVV ORYH

)LQDOO\ D VSHFLDO WKDQNV WR P\ GHDU IULHQG )] WKDQN \RX IRU DFFRPSDQ\LQJ PH WKURXJK WKRVH WKUHH \HDUV IRU RIIHULQJ PH QRW RQO\ HQRUPRXV KHOSV LQ LQIRUPDWLFV EXW DOVR D ZRQGHUIXO HPSDWK\ IRU P\ HYHU\GD\ VWUXJJOH GXULQJ WKH WKHVLV

$EVWUDFW

3URWHLQSURWHLQ LQWHUDFWLRQ LV FRQVLGHUHG DV DQ LPSRUWDQW ILHOG RI UHVHDUFK DV LW LV WKH NH\ WR FRQWURO YDULDEOH FHOO SURFHVVHV DQG SDWKZD\V ,Q HXFDU\RWLF FHOOV PXOWLGRPDLQ SURWHLQV 0'3V ZKLFK FRQVLVW RI PRUH WKDQ RQH GRPDLQ WDNH XS RYHU   RI WKH SRRO 7KRVH LGHQWLFDO RU GLIIHUHQW GRPDLQV RI D 0'3 DUH FRQQHFWHG WR HDFK RWKHU E\ D OLQNHU RI YDULDEOH OHQJWK DQG IOH[LELOLW\ )RU ORQJ IOH[LEOH OLQNHU LW DOORZV WKH SURWHLQ WR VDPSOH D ZLGH UDQJH RI FRQIRUPDWLRQ DQG WR DGMXVW LQWHUDFWLRQ LQ D VXEWOH ZD\

'HVSLWH QXPHURXV HIIRUWV RI UHVHDUFK RQ WKH ILHOG VRPH LVVXHV UHPDLQ XQDQVZHUHG RU UHTXLUH IXUWKHU LQYHVWLJDWLRQ $V SDUW RI WKLV WKHVLV P\ ZRUN DLPV WR GHILQH WKH UROH WDNHQ E\ WKH LQWULQVLFDOO\ GLVRUGHUHG OLQNHU ZLWKLQ 0'3V )RU WKDW SXUSRVH WKH 67$0 6LJQDO WUDQVGXFLQJ DGDSWHU PROHFXOH  SURWHLQ RI WKH (6&57 (QGRVRPDO 6RUWLQJ &RPSOH[HV 5HTXLUHG IRU 7UDQVSRUW PDFKLQHU\ ZDV FKRVHQ WR H[DPLQH WKH HIIHFW RI WKH IOH[LELOLW\ DQG G\QDPLFV RI WKH OLQNHU UHJLRQV RQ WKH PROHFXODU UHFRJQLWLRQ ZLWK XELTXLWLQ DQG /\VLQHOLQNHG GLXELTXLWLQ .8E 6XFK HIIRUWV ZHUH FDUULHG RXW E\ GHVLJQLQJ

VSHFLILF PXWDQWV DOWHULQJ WKH OLQNHU UHJLRQV LQ GLIIHUHQW ZD\V 7KH YDULRXV WUXQFDWHG YHUVLRQV XQGHUJR KDOI RU FRPSOHWH GHOHWLRQ RI D GRPDLQ RU KDYH WKHLU OLQNHU HLWKHU VKRUWHQHG GHOHWHG RU PRGLILHG LQ WKH DPLQR DFLG FRPSRVLWLRQ :LWK D FRPELQDWLRQ RI WKH VHYHUDO ELRSK\VLFDO PHWKRGV QDPHO\ 105 1XFOHDU 0DJQHWLF 5HVRQDQFH VSLQ UHOD[DWLRQ 6$;6 6PDOO $QJOH ;UD\ 6FDWWHULQJ DQG &' &LUFXODU 'LFKURLVP WKH VWXG\ KDV GHPRQVWUDWHG WKDW WKH DOWHUDWLRQ LQ WKH OLQNHU UHJLRQ PRGLILHV WKH IOH[LELOLW\ DQG WKH G\QDPLFV RI WKH SURWHLQ RQH DPRQJ WKHP SRVVLEO\ LQWURGXFHV VOLJKW FKDQJH LQ FRQIRUPDWLRQ )XUWKHUPRUH WKH PRGLILFDWLRQ RI WKH OLQNHU KDV DQ LPSDFW RQ WKH LQWHUGRPDLQ PRWLRQ DQG DOWHU ELQGLQJ DIILQLWLHV EHWZHHQ 67$0 FRQVWUXFWV DQG GLXELTXLWLQ ZLWKRXW DIIHFWLQJ GRPDLQV LQWHJULW\ RU ELQGLQJ VLWHV

,Q EULHI GLVRUGHUHG OLQNHUV SURYLGH SODVWLFLW\ WR WKH SURWHLQ ZKLFK DOORZ DGDSWDELOLW\ DQG VSHFLILFLW\ WR PROHFXODU UHFRJQLWLRQ SURFHVV $V D IXUWKHU DSSOLFDWLRQ WKH OLQNHUV LQFOXGHG LQ PXOWLGRPDLQ SURWHLQV FRXOG DOVR EH WKH QH[W JHQHUDWLRQ RI GUXJJDEOH WDUJHW DV WKHLU PRGLILFDWLRQ PD\ UHGXFH RU FRPSOHWHO\ DEROLVK LQWHUDFWLRQV

5pVXPp

/HV LQWHUDFWLRQV SURWpLQHSURWHLQH VRQW FRQVLGpUpHV FRPPH XQ GRPDLQH GH UHFKHUFKH LPSRUWDQW SXLVTX·HOOHV FRQWU{OHQW OD SOXSDUW GHV SURFHVVXV FHOOXODLUHV &KH] OHV FHOOXOHV HXFDU\RWHV OHV SURWpLQHV PXOWLGRPDLQHV 0'3 FRQVWLWXpHV G·DX PRLQV GHX[ GRPDLQHV UHSUpVHQWHQW SOXV GH   GHV SURWpLQHV $X VHLQ G·XQH 0'3 FHV GRPDLQHV SHXYHQW rWUH LGHQWLTXHV RX GLIIpUHQWV HW VRQW UHOLpV SDU XQ VHJPHQW LQWULQVqTXHPHQW GpVRUGRQQp GH ORQJXHXU HW GH IOH[LELOLWp YDULDEOH &HV SURWpLQHV SHXYHQW DORUV DGRSWHU GH PXOWLSOHV FRQIRUPDWLRQV GDQV O·HVSDFH HW LQWHUDJLU GH PDQLqUH VSpFLILTXH DYHF OHXUV SDUWHQDLUHV ELRORJLTXHV

0DOJUp GH QRPEUHX[ HIIRUWV GH UHFKHUFKH GDQV OH GRPDLQH FHUWDLQHV TXHVWLRQV UHVWHQW HQFRUH QRQ UpVROXHV RX QpFHVVLWHQW XQH pWXGH DSSURIRQGLH 0RQ SURMHW GH UHFKHUFKH HVW G·pWXGLHU HW GH GpILQLU OH U{OH GHV VHJPHQWV LQWULQVqTXHPHQW GpVRUGRQQpV GH OD SURWpLQH 67$0 6LJQDO WUDQVGXFLQJ DGDSWHU PROHFXOH  LPSOLTXpH GDQV OD PDFKLQHULH (6&57 (QGRVRPDO 6RUWLQJ &RPSOH[H 5HTXLUHG IRU 7UDQVSRUW  SUHPLqUH pWDSH GDQV OH SURFHVVXV GH GpJUDGDWLRQ O\VRVRPDOH 3OXV SUpFLVpPHQW O·pWXGH VH IRFDOLVH VXU OHV HIIHWV GH OD IOH[LELOLWp HW OD G\QDPLTXH GH FHV VHJPHQWV GDQV OH FDV GX SURFHVVXV GH UHFRQQDLVVDQFH PROpFXODLUH HQWUH 67$0 HW O·XELTXLWLQH RX GLXELTXLWLQH 'LIIpUHQWV PXWDQWV RQW DORUV pWp FRQoXV  VRLW DYHF XQ GRPDLQH WRWDOHPHQW RX SDUWLHOOHPHQW VXSSULPp VRLW DYHF XQ UDFFRXUFLVVHPHQW RX XQH VXSSUHVVLRQ FRPSOqWH GX VHJPHQW RX VRLW DYHF GH PXOWLSOHV PXWDWLRQV GDQV OD VpTXHQFH SHSWLGLTXH GX VHJPHQW &HV GLIIpUHQWV FRQVWUXLWV RQW pWp DQDO\VpV HQ XWLOLVDQW XQH FRPELQDLVRQ GH WHFKQLTXHV ELRSK\VLTXHV WHOOHV TXH OD UHOD[DWLRQ GH VSLQ SDU UpVRQDQFH PDJQpWLTXH QXFOpDLUH 501 OD GLIIXVLRQ GHV UD\RQV ; DX[ SHWLWV DQJOHV 6$;6 HW OH GLFKURwVPH FLUFXODLUH &' ,O D DORUV pWp GpPRQWUp TX·XQH DOWpUDWLRQ GX VHJPHQW GpVRUGRQQp SHXW HQWUDvQHU XQ FKDQJHPHQW GH OD G\QDPLTXH GH OD SURWpLQH HWRX XQ FKDQJHPHQW FRQIRUPDWLRQQHO /D PRGLILFDWLRQ GH FH VHJPHQW LQIOXH VXU OH PRXYHPHQW LQWHUGRPDLQH HW PRGLILH O·DIILQLWp HQWUH OHV FRQVWUXLWV GH 67$0 HW OD GLXELTXLWLQH VDQV PRGLILHU O·LQWpJULWp GH FKDTXH GRPDLQH HW GH OHXU VLWH GH OLDLVRQ

(Q UpVXPp OHV VHJPHQWV LQWULQVqTXHPHQW GpVRUGRQQpV SURFXUHQW XQH FHUWDLQH SODVWLFLWp j OD SURWpLQH FH TXL OXL SHUPHW GH V·DGDSWHU HW GH UHPSOLU VD IRQFWLRQ ELRORJLTXH ,O HVW DORUV SRVVLEOH G·LPDJLQHU GDQV XQ IXWXU SURFKH TXH FHV VHJPHQWV VRLHQW OD QRXYHOOH JpQpUDWLRQ GH FLEOHV WKpUDSHXWLTXHV SRXYDQW UpGXLUH RX VXSSULPHU FHUWDLQHV LQWHUDFWLRQV QRFLYHV

&RQWHQWV

GL8ELTXLWLQ.8E_FKDLQ   7KH SUREOHPDWLFV RI WKH FXUUHQW VWXG\   ,QWURGXFWLRQ    0HWKRGV    0RGHOLQJ    3URWHLQ SURGXFWLRQ   67$0 FRQVWUXFWV    8ELTXLWLQ DQG /\VLQH OLQNHG GL8ELTXLWLQ FKDLQV .8E_   8ELTXLWLQ 8E    /\VLQH OLQNHG GL8ELTXLWLQ FKDLQV .8E_  

 105 GDWD FROOHFWLRQ DQG SURFHVVLQJ    86ʹ EDFNERQH DVVLJQPHQW    8,0< EDFNERQH DVVLJQPHQW    105 WLWUDWLRQ H[SHULPHQWV    105 UHOD[DWLRQ H[SHULPHQWV    6PDOO $QJOH ;5D\ 6FDWWHULQJ 6$;6 H[SHULPHQWV   &LUFXODU 'LFKURLVP &' H[SHULPHQWV  

 8,06+ DQG WKH OLQNHU OHQJWK  

 6$;6 WR VWXG\ WKH JOREDO FRQIRUPDWLRQ DQG IOH[LELOLW\    ([WUDFWLRQ RI WKH EDVLF SDUDPHWHUV DQG WKH IOH[LELOW\ OHYHO   7KH JOREDO FRQIRUPDWLRQ    105 VSLQ UHOD[DWLRQ DQG WKH G\QDPLFDO FKDUDFWHUL]DWLRQ    &KHPLFDO VKLIW SHUWXUEDWLRQ DQG WKH YLVXDOLVDWLRQ RI PROHFXODU UHFRJQLWLRQ    ,QWHUDFWLRQ ZLWK XELTXLWLQ 8E   ,QWHUDFWLRQ ZLWK /\VLQH OLQNHG GLXELTXLWLQ .8E  

 9+68,0 DQG WKH LPSRUWDQW SUHVHQFH RI LWV IOH[LEOH OLQNHU 

 987 DQG WKH PLVVLQJ OLQNHU    0RGLILFDWLRQ RI WKH SURWHLQ G\QDPLFV    0RGLILFDWLRQ LQ WKH LQWHUDFWLRQ ZLWK .8E 

 &KDQJH LQ DIILQLW\ WRZDUG .8E    'LVFXVVLRQ RQ WKH UROH RI 67$0 OLQNHUV    7KH KHOLFDO VWUXFWXUH RI 8,0   8,0<  8,0< G\QDPLFV   6LGH FKDLQ DVVLJQPHQW 8SFRPLQJ ZRUNV   &RQFOXVLRQ 5HIHUHQFHV 

/LVW RI DEEUHYLDWLRQV

' 7KUHH GLPHQVLRQ

+LV +H[D +LVWLGLQH WDJ

$06+ $VVRFLDWHG 0ROHFXOH ZLWK WKH 6+ GRPDLQ &' &LUFXODU 'LFKURLVP

&6$ &KHPLFDO 6KLIW $QLVRWURS\ &63 &KHPLFDO VKLIW SHUWXUEDWLRQ '77 'LWKLRWUHLWRO

(*)5 (SLGHUPDO JURZWK IDFWRU UHFHSWRU

(6&57 (QGRVRPDO WUDQVGXFLQJ DGDSWRU PROHFXOH )5(7 )|UVWHU UHVRQDQFH HQHUJ\ WUDQVIHU

+56 +HSDWRF\WH JURZWK IDFWRUUHJXODWHG W\URVLQH NLQDVH VXEVWUDWH ,37* ,VRSURS\O β' WKLRJDODFWRS\UDQRVLG ._G 'LVVRFLDWLRQ FRQVWDQW /% /XULD%HUWDQL 0'3 0XOWLGRPDLQ SURWHLQ 09% 0XOWLYHVLFXODU ERG\ 105 1XFOHDU PDJQHWLF UHVRQDQFH 12( 1XFOHDU 2YHUKDXVHU HIIHFW 3% 3KRVSKDWH EXIIHU

SSP SDUW SHU PLOOLRQ

370 3RVWWUDQVODWLRQDO PRGLILFDWLRQ 6$16 6PDOO DQJOH QHXWURQ VFDWWHULQJ 6$;6 6PDOO DQJOH ;UD\ VFDWWHULQJ

7(9 7REDFFR (WFK 9LUXV 7ULV 7ULVK\GUR[\PHWK\O DPLQRPHWKDQH 8E 8ELTXLWLQ 8E_ 'LXELTXLWLQ 8%' 8ELTXLWLQ ELQGLQJ GRPDLQ 8%3< 8ELTXLWLQVSHFLILF SURWHDVH  8,0 8ELTXLWLQ ,QWHUDFWLQJ 0RWLI YY YROXPH SHU YROXPH ZY ZHLJKW SHU YROXPH

/LVW RI )LJXUHV

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

 2YHUOD\ RI 86:7 86ʹ DQG 86ʹ +64& VSHFWUD    &LUFXODU GLFKURLVP VSHFWUD RI 86 FRQVWUXFWV    86ʹ 7$/26 SUHGLFWLRQ    86 FRQVWUXFWV H[SHULPHQWDO VFDWWHULQJ FXUYHV    1RUPDOL]HG GLVWDQFH GLVWULEXWLRQV RI WKH 86 FRQVWUXFWV    1RUPDOL]HG .UDWN\ SORWV    %HVW ILW HQVHPEOH E\ 0XOWL)R;6    5JGLVWULEXWLRQ  

 6SLQ UHOD[DWLRQ SDUDPHWHUV RI 86:7 86ʹ DQG 86ʹ    _{15UDWH DV D IXQFWLRQ RI PROHFXODU PDVV  }

 6SLQ UHOD[DWLRQ SDUDPHWHUV RI 86ʹ DQG 86ʹ    5HGXFHG VSHFWUDO GHQVLWLHV IRU WKH 86 YDULDQWV    2YHUOD\ VSHFWUD RI 86:7 WLWUDWLRQ E\ 8E   &63V PDS RI 86:7 86ʹ DQG 86ʹ E\ 8E    &63V PDS RI 86ʹ DQG 86ʹ E\ 8E    8E WLWUDWLRQ FXUYHV RI WKH 86:7 86ʹ DQG 86ʹ FRQVWUXFWV    8E WLWUDWLRQ FXUYHV RI WKH 86ʹ DQG 86ʹ    2YHUOD\ VSHFWUD RI 86:7 DQG 86ʹ WLWUDWLRQ E\ .8E  

 &63V PDS RI 86:7 86ʹ DQG 86ʹ E\ 8E   .8E_WLWUDWLRQ FXUYHV RI WKH 86:7 86ʹ DQG 86ʹ FRQVWUXFWV   &63V PDS RI 86ʹ DQG 86ʹ E\ 8E  

 6FKHPDWLF UHSUHVHQWDWLRQ RI 98 FRQVWUXFWV    _{+ DQG}_{+ VSHFWUD RI 983  }

 2YHUOD\ RI 98:7 VSHFWUXP ZLWK 9+6 DQG 8,0 VSHFWUD    2YHUOD\ RI 987 VSHFWUXP ZLWK 9+6 DQG 8,0 VSHFWUD    5 5DQG 12( SDUDPHWHUV RI 98:7 DQG 987  

 5HGXFHG VSHFWUDO GHQVLWLHV IRU 98:7 DQG 987 FRQVWUXFWV    &63V PDS RI 98:7 DQG 987 E\ .8E 

 2YHUOD\ VSHFWUD RI 98:7 DQG 987 WLWUDWLRQ E\ .8E_   .8E_WLWUDWLRQ FXUYHV RI WKH 98:7 DQG 987 FRQVWUXFWV    2YHUOD\ RI 983 VSHFWUXP ZLWK 9+6 DQG 8,0 VSHFWUD    5_ 5_DQG 12( SDUDPHWHUV RI 98:7 DQG 983    5HGXFHG VSHFWUDO GHQVLWLHV IRU 98:7 DQG 983 FRQVWUXFWV    &KHPLFDO SHUWXUEDWLRQV PDS RI 98:7 DQG 983 E\ .8E 

 2YHUOD\ VSHFWUD RI 98:7 DQG 983 WLWUDWLRQ E\ .8E_   .8EWLWUDWLRQ FXUYHV RI WKH 98:7 DQG 983 FRQVWUXFWV  

 (IIHFW RI WKH H[FOXGHG YROXPH   2YHUOD\ RI 8,0< DQG 8,0_+_{1+64& VSHFWUD}

 %DFNERQH DVVLJQPHQW RI WKH 8,0<_+_{1+64& VSHFWUD }

/LVW RI 7DEOHV

 /LVW RI EXIIHUV    3HUFHQWDJH RI KHOLFLW\ RI 86 FRQVWUXFWV    5J 'PD[DQG YROXPH H[WUDFWHG IRUP 6$;6 GDWD DQDO\VLV  

 ,QSXW SDUDPHWHUV IRU 0XOWL)R;6    Ο VFRUHV VXPPDU\  

 6XPPDU\ RI DYHUDJHG VSLQ UHOD[DWLRQ SDUDPHWHUV IRU 86 FRQVWUXFWV   6XPPDU\ RI GLIIXVLRQ WHQVRUV IRU 86 FRQVWUXFWV    6XPPDU\ RI ._GEHWZHHQ 86 FRQVWUXFWV DQG 8E RU .8E 

 3HUFHQWDJH RI KHOLFLW\ DQG GLVRUGHUHG UHJLRQ LQ 98:7 DQG 987    $YHUDJH VSLQ UHOD[DWLRQ UDWHV RI 98:7 DQG 987 FRQVWUXFWV    6XPPDU\ RI WKH GLIIXVLRQ WHQVRUV RI 98:7 DQG 987 FRQVWUXFWV    'LVVRFLDWLRQ FRQVWDQW EHWZHHQ 98:7 DQG 987 WRZDUG .8E_   3HUFHQWDJH RI KHOLFLW\ DQG GLVRUGHUHG UHJLRQ LQ 98:7 DQG 983    $YHUDJH VSLQ UHOD[DWLRQ UDWH RI 98:7 DQG 983 FRQVWUXFWV    6XPPDU\ RI WKH GLIIXVLRQ WHQVRUV RI 98:7 DQG 983 FRQVWUXFWV    'LVVRFLDWLRQ FRQVWDQW EHWZHHQ 98:7 DQG 983 WRZDUG .8E 

1

,QWURGXFWLRQ

&HOOV FRPPXQLFDWLRQ LV FUXFLDO IRU WKHLU VXUYLYDO 7KH\ QHHG WR VSHDN ZLWK HDFK RWKHU DQG WKH LQIRUPDWLRQ LV UHFHLYHG H[FKDQJHG DQG SURFHVVHG IURP WKH H[WHUQDO HQYLURQPHQW PRVWO\ E\ SURWHLQSURWHLQ LQWHUDFWLRQ>@_{ $OWHUDWLRQ RI WKLV SURWHLQSURWHLQ QHWZRUN XVXDOO\}

OHDGV WR GLVHDVHV>@ >@ >@_{ ZKLFK PDNHV LW LPSRUWDQW WR XQGHUVWDQG WKH PHFKDQLVP RI WKHLU}

LQWHUDFWLRQ ,Q  WKH KXPDQ JHQRPH ZDV IXOO\ VHTXHQFHG IRU WKH FRGLQJ SDUW>@_{ :KLOH}

WKH JHQRPH VWD\V UDWKHU VWDWLF H[FHSW PXWDWLRQV WKDW RFFXU WKURXJKRXW LWV HYROXWLRQ WKH SURWHRPH ZKLFK LV WKH IXOO VHW RI SURWHLQV SURGXFHG E\ WKDW SDUWLFXODU JHQRPH EOXHSULQW LV PXFK PRUH FRPSOH[>@_{ ,QGHHG GHSHQGLQJ RQ WKH FHOO W\SH DQG GLIIHUHQW OLIH VWDJH SURWHLQV}

DUH SURGXFHG FRQWLQXDOO\ LQ UHVSRQVH WR WKH H[WHUQDO DV ZHOO DV LQWHUQDO HYHQWV ,Q WKHRU\ RQH JHQH VKRXOG EH FRGLQJ IRU RQH SURWHLQ ZKLFK LV QRW WKH UHDO FDVH GXH WR YDULRXV IDFWRUV VXFK DV DOWHUQDWLYH VSOLFLQJ>@_{DQG SRVWWUDQVODWLRQDO PRGLILFDWLRQV 370V}>@ >@_{ 7KH SURWHRPH}

WKHUHIRUH LV KLJKO\ G\QDPLF DQG UHTXLUHV GLIIHUHQW DSSURDFKHV>@ >@ _{WR IXOO\ GHFLSKHU LW} 

RWKHU WKDQ VHTXHQFLQJ DV IRU WKH JHQRPH

0RUHRYHU SURWHLQV FRXOG EH UHSUHVHQWHG DV D PRGXODU VWUXFWXUH ZKHUH WKH EORFNV DUH QDPHG GRPDLQV ,Q IDFW PRUH WKDQ   RI WKH HXNDU\RWLF SURWHLQV FRQVLVW RI PRUH WKDQ RQH GRPDLQ DQG WKH\ DUH FDOOHG PXOWLGRPDLQ SURWHLQV 0'3V ZKLFK DOVR HYROYHV FRQWLQXDOO\>@ >@_{ 9LD PXWDWLRQ GXSOLFDWLRQ DQG UHFRPELQDWLRQ RI YDULRXV GRPDLQV RXW}

RI DQ LQLWLDO UHSHUWRLUH>@ >@_{ WKH GLYHUVLW\ RI WKH SURWHRPH EHFRPHV KLJKO\ ODUJHU ,Q}

DGGLWLRQ LGHQWLFDO RU GLIIHUHQW GRPDLQV LQ 0'3 DUH XVXDOO\ FRQQHFWHG WR HDFK RWKHU E\ GLVRUGHUHG VHJPHQWV FKDUDFWHUL]HG E\ YDULDEOH OHQJWKV DQG VHTXHQFHV>@ _{WKDW DUH FDOOHG}

OLQNHUV ([DPSOH LQ )LJXUH  7KH EHQHILWV RI KDYLQJ PXOWLSOH GRPDLQV RYHU D VLQJOH GRPDLQ FRPH IURP WKHLU IOH[LEOH FRQIRUPDWLRQ EXW DOVR IURP WKH VWDELOLW\ DQG IROGLQJ DGYDQWDJHV>@_{)XUWKHUPRUH WKH FRPELQDWLRQ RI GLIIHUHQW GRPDLQV PDNHV WKH 0'3V DEOH}

WR H[HFXWH VHTXHQWLDO VWHSV RI LQWHUDFWLRQ DQG IXQFWLRQ

)LJXUH  ²([DPSOHV RI PXOWLGRPDLQ SURWHLQV ZLWK WZR W\SHV RI OLQNHU DUH VKRZQ LQ WKLV ILJXUH D WKH LPPXQRJOREXOLQ * DQG LWV KHDY\ FKDLQ FRORUHG LQ JUHHQ ZKLFK LV D 0'3 ZLWK GLIIHUHQW GRPDLQV WKDW DUH OLQNHG E\ ORQJ IOH[LEOH OLQNHUV DQG E WKH S\UXYDWH NLQDVH HQ]\PH DOVR D 0'3 EXW ZLWK YHU\ VKRUW OLQNHUV LQ D PRUH FRPSDFW FRQIRUPDWLRQ

,Q WKH FDVH RI PXOWLGRPDLQ SURWHLQV ZLWK ORQJ IOH[LEOH OLQNHUV WKH\ SRVVHVV WKH FKDUDFWHULVWLFV RI ERWK LQWULQVLFDOO\ GLVRUGHUHG DQG ZHOOIROGHG SURWHLQV WKDW PDNHV WKHLU VWXG\ PRUH FRPSOLFDWHG>@_{ 7R HQKDQFH WKH XQGHUVWDQGLQJ RI 0'3V D ODUJH QXPEHU RI WHFKQLTXHV}

KDYH EHHQ SUDFWLFHG QDPHO\ )5(7>@_{ 6$;6}>@_{ 6$16}>@_{ 105}>@ _{RU D FRPELQDWLRQ RI}

WKH PHQWLRQHG WHFKQLTXHV>@ >@_{ 5HJDUGOHVV RI WKH H[WHQVLYH UHVHDUFK LQ WKH ILHOG VRPH}

LVVXHV UHPDLQ XQDQVZHUHG RU UHTXLUH IXUWKHU LQYHVWLJDWLRQ RQH RI ZKLFK LV WKH TXHVWLRQ RQ WKH IXQFWLRQ RI WKH OLQNHU IOH[LELOLW\ DQG G\QDPLFV ZLWK UHVSHFW WR PROHFXODU UHFRJQLWLRQ SURFHVVHV OLNH DOORVWHU\ FRRSHUDWLYLW\ RU DYLGLW\ 7R DQVZHU WKDW TXHVWLRQ LQ WKH SUHVHQW VWXG\ D ELRORJLFDO V\VWHP ZDV FKRVHQ WKDW LQYROYHV WKH 67$0 6LJQDO WUDQVGXFLQJ DGDSWHU PROHFXOH  SURWHLQ DQG LWV GLIIHUHQW ELQGLQJ SDUWQHUV ZLWKLQ WKH (6&57  (QGRVRPDO 6RUWLQJ &RPSOH[HV 5HTXLUHG IRU 7UDQVSRUW PDFKLQHU\



7KH (6&57 PDFKLQHU\

7KH (6&57 PDFKLQHU\ LV D FRPSOH[ V\VWHP RI VLJQDOLQJ ZKLFK LQYROYHV YDULDEOH PHFKDQLVPV>@ >@ >@_{ ,Q IDFW WKH PDFKLQHU\ FRQVLVWV RI GLIIHUHQW FHOOXODU SURFHVVHV}

VXFK DV HQGRF\WRVLV RI WUDQVPHPEUDQH SURWHLQ DQG JURZWK IDFWRU XSRQ OLJDQGVWLPXOL ELQGLQJ>@_{ IRUPDWLRQ RI H[RVRPH IRU VHFUHWLRQ}>@ _{RU HYHQ DXWRSKDJ\}>@ _{IRU UHJXODWLRQ}

RI FHOO KRPHRVWDVLV )LJXUH  $V SDUW RI WKLV VWXG\ WKH HQGRF\WRVLV SDWKZD\ ZLOO EH VROHO\ IRFXVHG ,Q JHQHUDO XSRQ OLJDQG ELQGLQJ WKH WUDQVPHPEUDQH UHFHSWRUVSURWHLQV JR WKURXJK HLWKHU FRQIRUPDWLRQDO FKDQJH RU SRVWWUDQVODWLRQDO PRGLILFDWLRQV VXFK DV XELTXLWLQDWLRQ RU SKRVSKRU\ODWLRQ ZKLFK LQLWLDWHV WKH VLJQDOLQJ FKDLQ UHDFWLRQ VWDUWLQJ E\ WKHLU LQWHUQDOL]DWLRQ 7KH SURFHVV RI HQGRF\WRVLV FRXOG EH GRQH LQ GLIIHUHQW PHFKDQLVPV FODWKULQPHGLDWHG>@ >@_

FDYHROLQPHGLDWHG>@ >@ _{RU FODWKULQ DQG FDYHOROLQLQGHSHQGDQW}>@_{ 5HJDUGOHVV RI WKH}

PHFKDQLVP WKH LQWHUQDOL]HG PHPEUDQH SURWHLQV DUH GHVWLQHG WR WKH HDUO\ HQGRVRPH WKHQ WUDQVIHUUHG WR WKH ODWH HQGRVRPH WKURXJK PDWXUDWLRQ>@_{ 'XULQJ WKLV VWDJH WKH IDWH RI}

WKH LQWHUQDOL]HG SURWHLQV ZLOO EH HLWKHU UHF\FOLQJ>@ _{EDFN WR WKH SODVPD PHPEUDQH DQG WKH}

WUDQVJROJL QHWZRUN E\ IROORZLQJ WKH WXEXODU V\VWHP RU EHLQJ WUDQVSRUWHG WR WKH O\VRVRPDO FRPSDUWPHQW IRU GHJUDGDWLRQ 7KLV IDWH LV LQGHHG GHWHUPLQHG E\ WKH W\SH RI VXVWDLQHG SRVWWUDQVODWLRQDO PRGLILFDWLRQV )RU LQVWDQFH /'/5V /RZ'HQVLW\ /LSRSURWHLQ 5HFHSWRUV

)LJXUH  ²6FKHPDWLF SUHVHQWDWLRQ RI WKH (6&57 SDWKZD\>@_

DUH UHF\FOHG EDFN WR WKH PHPEUDQH ZLWKRXW DQ\ VLJQDO>@ _{ZKLOH VHYHUDO SURWHLQV DUH}

UHFRJQL]HG E\ WKHLU F\WRSODVPLF SHSWLGH VHTXHQFH>@_{ ,Q WKLV FXUUHQW VWXG\ WKH IRFXV ZLOO EH}

SODFHG RQ WKH /\VLQH OLQNHG XELTXLWLQ FKDLQV .8E FKDLQV>@ >@_{WKDW WDJ DQG JXLGH D}

SURWHLQ WRZDUG WKH O\VRVRPDO GHJUDGDWLRQ SDWKZD\ ,Q IDFW XSRQ XELTXLWLQDWLRQ WKH SURWHLQV ZLOO WUDYHO WKURXJK GLIIHUHQW FRPSOH[HV RI WKH (6&57 PDFKLQHU\ QDPHO\ (6&57 (6&57, (6&57,, (6&57,, DQG 9VS9WD>@ >@_{ ,W KDV EHHQ SURYHG WKDW WKH (6&57 FRPSOH[}

ZKLFK ORFDWHV XSVWUHDP RI WKH SDWKZD\ LV DEOH WR FOXVWHU XELTXLWLQDWHG FDUJR>@ >@ _DQG

VHTXHQWLDOO\ UHFUXLWV WKH IROORZLQJ FRPSOH[HV 7RJHWKHU ZLWK +UV WKH SURWHLQ RI LQWHUHVW 67$0 EHORQJV WR WKLV (6&57 FRPSOH[>@ _{DQG H[HFXWHV LWV UHFUXLWPHQW IXQFWLRQ E\ LWV}

DELOLW\ WR UHFRJQL]H .8E FKDLQV 6HH )LJXUH 

)LJXUH  ²6LPSOLILHG VFKHPDWLF SUHVHQWDWLRQ RI WKH O\VRVRPDO GHJUDGDWLRQ SDWKZD\ WKDW LQYROYH 67$0+UV RI (6&57 DQG .OLQNHG XELTXLWLQ FKDLQ DV VLJQDO



67$0 DQG WKH ELQGLQJ SDUWQHUV 8ELTXLWLQ DQG WKH /\VLQH

OLQNHG GL8ELTXLWLQ.8E

FKDLQ

67$0 DV PHQWLRQHG DERYH LV SDUW RI WKH (6&57 FRPSOH[ WKDW LV ORFDWHG LQ WKH ILUVW VWHS RI WKH HQGRF\WLF SDWKZD\ LQ HDUO\ HQGRVRPH 67$0 FRQWDLQV RI  DPLQR DFLGV DQG KDUERUV PXOWLSOH GRPDLQV VXFK DV 9+6 936 +UV DQG 67$0 6+ 65& +RPRORJ\  8,0 8ELTXLWLQ %LQGLQJ 0RWLI DQG ,7$0 ,PPXQRUHFHSWRU W\URVLQHEDVHG DFWLYDWLRQ PRWLI 7KH ILUVW WKUHH GRPDLQV 9+6 8,0 DQG 6+ WRJHWKHU FRQVLVW RI WKH PLQLPXP UHTXLUHPHQW IRU WKH SURWHLQ 67$0 )LJXUH  WR HQVXUH WKH UHFRJQLWLRQ RI WKH SURWHLQ ELQGLQJ SDUWQHU DQG LWV SURSHU IXQFWLRQ 9+6 LV D ZLGHO\ NQRZQ GRPDLQ WKDW FRQWDLQV D VHULHV RI αKHOLFHV ZKLFK IROG WRJHWKHU WR D VXSHU KHOL[ 3'% VWUXFWXUH ;% ZKLOH WKH VWUXFWXUH RI 6+ LV FRQVWLWXWHG RI DQWLSDUDOOHO βVKHHWV VHYHUDO WXUQV DQ 57 ORRS DQG VKRUW KHOLFHV 3'% VWUXFWXUH ;4

$V IRU WKH 8,0 GRPDLQ LW LV FRPPRQO\ NQRZQ DV DQ αKHOL[ ZLWK D FRQVHUYHG VHTXHQFH SDWWHUQ WKURXJKRXW LWV GLIIHUHQW YHUVLRQV LQ YDULDEOH SURWHLQ>@_

7KH WKUHH GRPDLQV DUH DOO XELTXLWLQ ELQGLQJ GRPDLQ 8%' WKDW FDQ UHFRJQL]H DQG LQWHUDFW ZLWK 8E PRLHWLHV ,Q D SUHYLRXV ZRUN LW KDV EHHQ GHPRQVWUDWHG KRZ GLIIHUHQW IUDJPHQWV RI 67$0 LQWHUDFW ZLWK 8E DQG /\VLQH OLQNHG GLXELTXLWLQ FKDLQV .8E_ 9+68,0 98:7 DQG 8,06+ 86:7 KDYH VKRZQ DQ H[TXLVLWH FDSDELOLW\ WR ELQG 8E DQG /\V8E>@ 86:7 LV DGGLWLRQDOO\ DEOH WR ELQG WR WKH GHXELTXLW\ODVH HQ]\PHV 8%3<

DQG $06+ WKURXJK LWV 6+ GRPDLQ>@ >@_{ 7KH GLIIHUHQW VWUXFWXUHV WKDW KDYH EHHQ VROYHG}

LQ SUHYLRXV VWXGLHV DUH UHSUHVHQWHG LQ )LJXUH 

)LJXUH  ²7KH WKUHH GRPDLQV RI 67$0 9+6 8,0 DQG 6+ LQ VFKHPDWLF DQG FDUWRRQ UHSUHVHQWDWLRQ

)LJXUH  ²7KH VROYHG VWUXFWXUHV RI WKH LQWHUDFWLRQ EHWZHHQ GLIIHUHQW SDUWQHUV D 105 VWUXFWXUH RI 9+68,0.8EFRPSOH[>@ E WKH 105 VWUXFWXUH RI 6+ GRPDLQ VXUIDFH

DQG WKH 6%0 SHSWLGH LVVXHG IURP $06+ GHXELTXLW\ODVH VWLFN>@_{DQG F WKH 105 VWUXFWXUH}

RI 9+68E FRPSOH[>@_

8ELTXLWLQ LV D VPDOO SURWHLQ RI  DPLQR DFLGV WKDW FRXOG EH IRXQG LQ PRVW HXNDU\RWLF FHOO W\SHV 8ELTXLWLQ RU D FKDLQ RI XELTXLWLQV FDQ EH DWWDFKHG WR RWKHU SURWHLQ E\ FRYDOHQW OLQNDJH WKH SURFHVV RI ZKLFK LV FDOOHG XELTXLWLQDWLRQ DQG DFWV DV D VLJQDO IRU YDULRXV FHOO SDWKZD\>@_

:KLOH PRQRPHU XELTXLWLQDWLRQ LV ZLGHO\ NQRZQ WR EH WKH VLJQDO IRU FODWKULQPHGLDWHG HQGRF\WRVLV RU FKURPDWLQ UHPRGHOLQJ>@_{ /\VLQHOLQNHG XELTXLWLQ FKDLQ .8E FKDLQ}

LV WKH FDQRQLFDO PDUNHU IRU WKH GHJUDGDWLRQ SDWKZD\ E\ WKH 6 SURWHDVRPH>@ >@_{ $V IRU}

.8E FKDLQ LW KDV DOVR EHHQ VKRZQ WR EH LQYROYHG LQ YDULRXV FHOOXODU SURFHVVHV VXFK DV '1$ UHSDLU>@ >@_{DQG HQGRVRPDO VRUWLQJ}>@ >@_



7KH SUREOHPDWLFV RI WKH FXUUHQW VWXG\

$V PHQWLRQHG EHIRUH WKLV VWXG\ DLPV WR HOXFLGDWH WKH UROH RI WKH GLVRUGHUHG OLQNHU LQ SURWHLQSURWHLQ LQWHUDFWLRQ 67$0 ZDV FKRVHQ WR EH WKH V\VWHP RI LQWHUHVW DV LWV WZR IUDJPHQWV 9+68,0 DQG 8,06+ DUH LQYHVWLJDWHG ZLWK DQ HPSKDVLV RQ WKH OLQNHU UHJLRQ E\ XVLQJ D FRPELQDWLRQ RI GLIIHUHQW DSSURDFKHV 7KH OLQNHUV DUH ILUVW PRGLILHG LQ GLIIHUHQW ZD\V WR EH VKRUWHQHG PXWDWHG E\ VXEVWLWXWLRQ RU HYHQ UHPRYHG FRPSOHWHO\ 7KH PXWDQWV ZLWK WKH PRGLILHG OLQNHU DUH IXUWKHU H[DPLQHG E\ PHDQV RI D FRPELQDWLRQ RI GLIIHUHQW ELRSK\VLFDO WRROV VXFK DV L FLUFXODU GLFKURLVP ZKHUH DQ DYHUDJH FRQWULEXWLRQ RI GLIIHUHQW VHFRQGDU\ VWUXFWXUH FRXOG EH H[WUDFWHG LL 6$;6 ZKHUH WKH LQIRUPDWLRQ RQ WKH FRQIRUPDWLRQ VSDFH VDPSOHG E\ WKH FRQVWUXFWV FRXOG EH REWDLQHG ZLWK D UHVROXWLRQ RI≈ c DQG LLL 105 ZKHUH WKH G\QDPLFDO SURSHUWLHV DW WKH SVQV WLPH VFDOH FRXOG EH GHVFULEHG WKURXJK VSLQ UHOD[DWLRQ H[SHULPHQWV )LQDOO\ 105 WLWUDWLRQ H[SHULPHQWV FRPSOHWH WKH VWXG\ ZKHUH WKH LQWHUDFWLRQ RI 8E DQG .8E_ZLWK DOO WKH QHZO\ GHVLJQHG FRQVWUXFWV LV YLVXDOL]HG DQG WKH DIILQLW\ LV TXDQWLILHG 7KLV VWXG\ LQWHQGV WR GUDZ D FOHDU SLFWXUH RI WKH FRQQHFWLRQ EHWZHHQ WKH PROHFXODU UHFRJQLWLRQ DELOLW\ RI PXOWLGRPDLQ DQG LWV SODVWLFLW\ E\ KDYLQJ ORQJ IOH[LEOH OLQNHU

2

0HWKRGV



0RGHOLQJ

7KH ' VWUXFWXUH RI WKH YDULRXV FRQVWUXFWV ZDV REWDLQHG E\ KRPRORJ\ PRGHOLQJ IROORZLQJ D PHWKRGRORJ\ VLPLODU WR WKH PRGHOLQJ RI WKH 9+68,0 FRQVWUXFW GHVFULEHG LQ WKH SUHYLRXV ZRUN RI /DQJH HW DO>@_{ 7KH 8,0 GRPDLQ}>@_{RI 9SV 3'% FRGH 49 ZDV XVHG WR PRGHO}

WKH VWUXFWXUH RI WKH 8,0 SDUW RI DOO FRQVWUXFWV 9+68,0 8,06+ DQG PXWDQWV ZKLOH WKH 67$0·V 6+ GRPDLQ 3'% FRGH ;4 ZDV XVHG WR PRGHO WKH 6+ SDUW DQG WKH 67$0·V 9+6 GRPDLQ 3'% FRGH ;% ZDV XVHG WR PRGHO WKH 9+6 SDUW 0RGHOV ZHUH JHQHUDWHG E\ XVLQJ WKH 0RGHOOHU SURJUDP>@ _{DQG E\ FRQVLGHULQJ WKH OLQNHU UHJLRQ DV IOH[LEOH $IWHU DQ}

DOLJQPHQW RI WKH TXHU\ DQG WHPSODWH VHTXHQFHV ZLWK $OLJQ' WKH WHPSODWH VHTXHQFHV 3%' VWUXFWXUHV 49 ;4 ;% ZHUH XVHG DV LQSXW LQ 0RGHOOHU $ WRWDO RI WHQ VWUXFWXUHV ZHUH JHQHUDWHG IRU WKH GLIIHUHQW FRQVWUXFWV

)L JXUH  ² 6HTXHQFHV DQG QDPHV RI WKH GLIIHUHQW FRQVWUXFWV XVHG LQ WKH SUHVHQW VWXG\ DORQJ ZLWK WKHLU UHVSHFWLYH VHTXHQFH DQG QXPEHULQJ 7KH VFKHPDWLF UHSUHVHQWDWLRQ RI WKH VHFRQGDU\ VWUXFWXUH RI 8,06+ FRQVW UXFWV D DQG 9 +68,0 E KDV EHHQ REWDLQHG E\ PHDQV RI GVVS >@ >@ HPEHGGHG LQWR FDUWRRQ UHSUHVHQWDWLRQ SURJUDP 666GUDZHU  



3URWHLQ SURGXFWLRQ



67$0 FRQVWUXFWV

7KH  KXPDQ 67$0 FRQVWUXFWV 67$0  86:7 DQG 67$0  98:7 LQ S(70 YHFWRU ZHUH SURYLGHG E\ 'U 'DQLHOD +|HOOHU 7KH PXWDQW FRQVWUXFWV ZHUH HQJLQHHUHG ZKHUH WKH OLQNHU WKDW EULGJHV 8,0 DQG 6+ RU 9+6 DQG 8,0 KDV EHHQ PRGLILHG LQ GLIIHUHQW ZD\V )RU 86:7 GHULYHG FRQVWUXFWV 86ʹ DQG 86ʹ KDYH WKHLU OLQNHU VKRUWHQHG IRU  DQG  DPLQR DFLGV UHVSHFWLYHO\ :KLOH 8,0 ZDV FRPSOHWHO\ UHPRYHG LQ 86ʹ WKDW OHDYHV RQO\ 6+ GRPDLQ ZLWK WKH IXOO OHQJWK OLQNHU KDOI RI 8,0 UHPDLQV LQ 86ʹ VHH )LJ D $V IRU 98:7 GHULYHG FRQVWUXFWV WKH OLQNHU EHWZHHQ 9+6 DQG 8,0 ZDV FRPSOHWHO\ GHOHWHG LQ 987 ZKLOH  DPLQR DFLGV RI WKDW OLQNHU ZHUH VXEVWLWXWHG E\ SUROLQHV LQ 983 VHH )LJXUH E )LQDOO\ RQ DQ DWWHPSW WR VROYH WKH VWUXFWXUH RI WKH 8,0 GRPDLQ D PXWDQW FDOOHG 8,0< ZDV DOVR GHVLJQHG ZLWK D VLQJOH PXWDWLRQ DW WKH SRVLWLRQ RI 7KUHRQLQH  ZKHUH LW LV VXEVWLWXWHG E\ D 7\URVLQH WR PDNH WKH FRQVWUXFW YLVLEOH XQGHU 89  QP VSHFWURVFRS\ DQG WR IDFLOLWDWH LWV SXULILFDWLRQ

$OO FRQVWUXFWV ZHUH H[SUHVVHG ZLWK WKHLU 1WHUPLQXV IXVHG WR 1XV$ DQG D KH[DKLVWLGLQH WDJ +LVWDJ XQGHU WKH UHJXODWLRQ RI D ODF RSHURQ DQG KDYH EHHQ SXUFKDVHG IURP WKH *HQHFXVW FRPSDQ\ 7KH SODVPLGV FRQWDLQLQJ WKH UHFRPELQDQW SURWHLQV ZHUH WKHQ WUDQVIRUPHG LQWR ( FROL %/ *2/' 0LOLSRUH &HOOV ZHUH JURZQ LQ /% PHGLXP ZLWK  ΔJPO NDQDP\FLQ RU 0 PHGLXP VXSSOHPHQWHG ZLWK  P0 0J62_  P0 &D&O_  PJO WKLDPLQH   YY WUDFH HOHPHQWV VROXWLRQ > JO ('7$  JO )H&O_+_2  PJO =Q2  PJO &X&O_+_2  PJO &R12_+_2 DQG  PJO 1+_0R_2_+_2@  ΔJPO NDQDP\FLQ DQG  JO

₁₊

&O DV VROH QLWURJHQ VRXUFH IRU DQ XQLIRUP1 ODEHOOLQJ )RU&ODEHOOLQJ  JO RI _&

'*OXFRVH ZHUH XVHG LQVWHDG RI&'*OXFRVH 7KH FHOOV FXOWXUH ZDV JURZQ DW  ƒ&

WR DQ 2' QPRI  DQG WKH RYHUH[SUHVVLRQ LV LQGXFHG E\ DGGLQJ  P0 ,37* DQG WKH

LQGXFWLRQ LV SHUIRUPHG DW  ƒ& IRU  KRXUV

)RU 98:7 DQG LWV GHULYHG PXWDQWV SDUWLDO GHXWHUDWLRQ ≈  LV QHHGHG WR UHGXFH VSLQ GLIIXVLRQ 7KH GHXWHUDWLRQ SURWRFRO LV DGDSWHG IURP 'U &KULVWLQD 6L]XQ SURWRFRO 7KH

FHOOV ZHUH ILUVW JURZQ LQ ULFK /% PHGLXP WR FUHDWH WKH ELRPDVV WKHQ WUDQVIHUUHG WR  VXFFHVVLYH 0 PHGLD   +_2 WKHQ   '_2 7KH ODVW FXOWXUH LQ '_20 PHGLXP ZDV JURZQ DW  ƒ& XQWLO 2'_{ QP}UHDFKHG  7KH RYHUH[SUHVVLRQ LV LQGXFHG E\ DGGLWLRQ RI  P0 ,37* DQG E\ DQ RYHUQLJKW LQFXEDWLRQ DW  ƒ&

)LJXUH  ²$ VLPSOLILHG VFKHPDWLF UHSUHVHQWDWLRQ RI WKH RYHUH[SUHVVLRQ DQG SXULILFDWLRQ RI 67$0 DQG PXWDQWV ZLWK RU ZLWKRXW LVRWRSH ODEHOOLQJ

&HOOV ZHUH KDUYHVWHG E\ FHQWULIXJDWLRQ DW  USP %HFNPDQ -$ DQG WKH SHOOHWV ZHUH UHVXVSHQGHG LQ O\VLV EXIIHU  P0 7ULV EXIIHU  P0 1D&O  P0 LPLGD]ROH  YY βPHUFDSWRHWKDQRO  YY JO\FHURO DQG  WDEOHW RI WKH &PSOHWHŠ SURWHDVH LQKLELWRUV IURP 52&+( DQG O\]HG E\ PLOG VRQLFDWLRQ 7KH O\VDWH ZDV FODULILHG E\ FHQWULIXJDWLRQ DW  USP %HFNPDQ -$ IRU  PLQXWHV 7KH FODULILHG FHOOV O\VDWH ZDV ORDGHG RQ D +LVWUDS 6HSKDURVHŒ )DVW )ORZ FROXPQ *( +HDOWKFDUH HTXLOLEUDWHG ZLWK ORDG EXIIHU  P0 7ULV+&O S+   P0 1D&O  P0 LPLGD]ROH  YY JO\FHURO DQG  YY βPHUFDSWRHWKDQRO 7KH ERXQG SURWHLQ ZDV HOXWHG ZLWK D LPLGD]ROH JUDGLHQW DQG FRPHV RXW RI WKH FROXPQ DW DURXQG  P0 LPLGD]ROH  +LV1XV$ ZHUH FOHDYHG E\

7REDFFR (WFK 9LUXV 7(9 SURWHDVH DW ƒ& RYHU QLJKW ZKLOH GLDO\]LQJ DJDLQVW ORDG EXIIHU 7KH 7(9 VLWH FOHDYDJH OHDYHV  DPLQR DFLGV *$0*0 DW WKH 1WHUPLQXV ZKLFK GR QRW EHORQJ WR WKH SURWHLQ VHTXHQFH 7KH GLDO\VDWH ZDV WKHQ DSSOLHG WR WKH +LVWUDS FROXPQ IRU D VHFRQG WLPH WR KDYH +LV1XV$ DQG 7(9 ELQGLQJ WR WKH FROXPQ 7KH IORZWKURXJK ZKLFK FRQWDLQV WKH FOHDYHG SURWHLQV ZDV FRQFHQWUDWHG WR OHVV WKHQ  PO VXSSOHPHQWHG ZLWK   JO\FHURO DQG IXUWKHU SXULILHG E\ D +LORDG 6XSHUGH[Œ   FROXPQ *( +HDWKFDUH HTXLOLEUDWHG LQ  P0 VRGLXP SKRVSKDWH EXIIHU S+  DQG  P0 1D&O 7KH HOXWLRQ SHDN ZDV GHVDOWHG DQG FRQFHQWUDWHG LQ D $PLFRQŠ 8OWUD FHQWULIXJDO ILOWHUV ZLWK  N' FXWRII 7KH SXULW\ RI WKH SURWHLQ ZDV YHULILHG E\ 6'6JHO HOHFWURSKRUHVLV DQG WKH SURWHLQ FRQFHQWUDWLRQ ZDV GHWHUPLQHG E\ PHDVXULQJ WKH DEVRUEDQFH DW  QP RQ WKH 1DQRGURSŒ XVLQJ WKH 3URWHLQ $QP SURJUDP )RU HDFK SURWHLQ WKH FRQFHQWUDWLRQ ZDV FDOFXODWHG XVLQJ WKH H[WLQFWLRQ FRHIILFLHQW HVWLPDWHG E\ 3URW3DUDP>@_{RQ WKH ([3$6\ VHUYHU EDVHG RQ WKHLU RZQ VHTXHQFH}



8ELTXLWLQ DQG /\VLQH OLQNHG GL8ELTXLWLQ FKDLQV .

8E

 8ELTXLWLQ 8E

3ODVPLGV IRU WKH ZLOGW\SH XELTXLWLQ ZHUH D JLIW IURP 3URI 'DYLG )XVKPDQ DQG WKH WZR PXWDQWV 8E.5 DQG 8E' ZHUH SURYLGHG E\ 3URI &HFLOH 3LFNDUW $GGJHQH SODVPLG  DQG  ([SUHVVLRQ DQG SXULILFDWLRQ RI XELTXLWLQ DQG PXWDQWV IROORZ WKH VDPH SURWRFRO 7KH XELTXLWLQ SODVPLGV ZHUH H[SUHVVHG LQ WKH 5RVHWWDŒ'(S/\V6 VWUDLQV FDUU\LQJ WKH FKORUDPSKHQLFROPDUNHG KHOSHU SODVPLG S-< $ VWDUWHU FXOWXUH RI  YROXPH LQ ULFK PHGLD VXSSOHPHQWHG ZLWK  ΔJPO DPSLFLOOLQ DQG  ΔJPO FKORUDPSKHQLFRO ZDV JURZQ IRU  KRXUV DW  ƒ& WKHQ GLOXWHG LQ WKH DXWRLQGXFWLRQ PHGLXP  J 1+_62_  J .+_32_  J 1D_+32_  J WU\SWRQH  J \HDVW H[WUDFW  P0 0J&O_  J JOXFRVH  J ODFWRVH DQG  J JO\FHURO SHU  OLWHU PHGLXP ZLWK WKH VDPH FRQFHQWUDWLRQ RI DQWLELRWLFV LQ WKH SUHYLRXV VWHS 7KH DXWRLQGXFHG FXOWXUH ZDV JURZQ RYHUQLJKW DW  ƒ& &HOOV ZHUH WKHQ KDUYHVWHG DQG IUR]HQ DW  ƒ& IRU DW OHDVW  KRXUV EHIRUH WKH QH[W VWHS 7KH IUR]HQ FHOO SHOOHW ZDV WKHQ UHVXVSHQGHG LQ  P0 7ULV+&O S+   P0 306)  PJPO O\VR]\PH DQG 

WDEOHW RI &PSOHWHŠ SURWHDVH LQKLELWRUV 5RFKH  P0 0J&O_DQG  ΔJPO '1DVH, ZHUH DGGHG WR WKH O\VDWH DQG LQFXEDWHG RQ D VKDNHU IRU  PLQXWHV DW URRP WHPSHUDWXUH 7KH O\VDWH ZDV FODULILHG E\ FHQWULIXJDWLRQ DW  USP %HFNPDQ -$ IRU  PLQXWHV DQG SUHFLSLWDWHG E\ DFLGLILFDWLRQ ZLWK  YY SHUFKORULF DFLG XQGHU KLJK VSHHG VWLUULQJ 7KH SUHFLSLWDWH ZDV UHPRYHG E\ FHQWULIXJDWLRQ ZKLOH WKH VXSHUQDWDQW ZDV GLDO\]HG DJDLQVW  P0 DPPRQLXP DFHWDWH EXIIHU S+  EHIRUH EHLQJ ORDGHG RQWR D  PO 63 6HSKDURVHŒ )DVW )ORZ FROXPQ *( +HDOWKFDUH 8ELTXLWLQ ZDV FKDUJHG QHJDWLYHO\ DW WKH DFLGLF S+  DQG ERXQG WR WKH FDWLRQ H[FKDQJH FROXPQ DV DOO RWKHU FRQWDPLQDQWV SDVVHG WKURXJK WKH FROXPQ )RU WKH HOXWLRQ VWHS D JUDGLHQW RI 1D&O IURP  0 ZDV DSSOLHG RQWR WKH FROXPQ DQG XELTXLWLQ FRPHV RXW DW ≈ 0 RI 1D&O 7KH IUDFWLRQV ZHUH SRROHG DQG H[FKDQJHG LQWR WKH ZRUNLQJ EXIIHU DFFRUGLQJ WR WKH W\SH RI H[SHULPHQWV 6HH 7DEOH  SDJH 

)LJXUH  ² 6FKHPDWLF UHSUHVHQWDWLRQ RI WKH DXWRLQGXFHG FXOWXUH RI XELTXLWLQ DQG WKH SXULILFDWLRQ XVLQJ SHUFKORULF DFLG SUHFLSLWDWLRQ SULQFLSOH

 /\VLQH OLQNHG GL8ELTXLWLQ FKDLQV .8E

7KH SUHSDUDWLRQ RI .8E_ZDV DGDSWHG IURP D SUHYLRXVO\ GHVFULEHG PHWKRG E\ 3LFNDUW 5DDVL>@_{ 7KUHH HQ]\PHV ZHUH UHTXLUHG IRU WKH XELTXLWLQDWLRQ UHDFWLRQ WKH KXPDQ (}

HQ]\PHV 8%( DQG WKH WZR VSHFLILF ( HQ]\PHV 8%& DQG 8(9$ IRU .OLQNHG FKDLQV ,QVWHDG RI XVLQJ ZLOGW\SH XELTXLWLQV WZR PXWDQWV .5 DQG ' ZHUH XVHG WR UHVWUDLQ WKH UHDFWLRQ WR VWRS DW WKH IRUPDWLRQ RI D GLPHU DQG QRW WR IRUP ORQJHU FKDLQV

)LJXUH  ²7KH 8E( HQ]\PH ELQGV WR 8E ' RU .5 PXWDQW E\ XVLQJ  $73 LQ RUGHU WR EULQJ WKHP WR WKH FRQMXJDWLRQ HQ]\PH 7KH ODWWHU LV D FRPSOH[ RI 8%& DQG 8(9$ WKDW DOORZ WZR XELTXLWLQV WR IRUP DQ LVRSHSWLGLF OLQNDJH EHWZHHQ WKH UHVLGXH * RI 8E.5 DQG . RI 8E'

8%(

8%( SODVPLG ZDV SURYLGHG E\ 'U &\QWKLD :ROEHUJHU $GGJHQH SODVPLG  7KH H[SUHVVLRQ RI KXPDQ 8%( LV GRQH LQ WKH 5RVHWWDŒ'(S/\V6 FHOOV &HOOV ZHUH JURZQ LQ ULFK PHGLD XQWLO 2'_{ QP}UHDFKHG  WKHQ WKH LQGXFWLRQ LV SHUIRUPHG ZLWK  P0 ,37* DW  ƒ& IRU  KRXUV 7KH SXULILFDWLRQV ZHUH SHUIRUPHG RQ LFH WKURXJKRXW HYHU\ VWHS

&ROG O\VLV EXIIHU  P0 7ULV+&O S+   P0 1D&O  P0 306)   7ULWRQ ;  PJPO O\VR]\PH DQG  WDEOHW RI &PSOHWHŠ SURWHDVH LQKLELWRUV ZDV DGGHG WR WKH IUR]HQ SHOOHW )RU WKH O\VLV WKH FHOO SHOOHW ZDV UHVXVSHQGHG WKHQ  ΔJPO '1DVH, DQG  P0 0J&O_

)LJXUH  ² 6FKHPDWLF UHSUHVHQWDWLRQ RI WKH +LV WDJJHG ( XELTXLWLQ HQ]\PH DQG LWV SXULILFDWLRQ E\ DIILQLW\ FROXPQ

ZHUH DGGHG DQG WKH O\VDWH ZDV LQFXEDWHG IRU  PLQXWHV RQ WKH VKDNHU DW  ƒ& 7KH O\VDWH ZDV FODULILHG E\ FHQWULIXJDWLRQ DW  USP IRU  PLQXWHV WKHQ  P0 LPLGD]ROH ZDV DGGHG WR WKH FODULILHG O\VDWH EHIRUH ORDGLQJ LW RQWR D +LVWUDS 6HSKDURVHŒ )DVW )ORZ FROXPQ *( +HDOWKFDUH 7KH FROXPQ ZDV HTXLOLEUDWHG ZLWK ORDG EXIIHU  P0 7ULV+&O S+   P0 1D&O  P0 LPLGD]ROH  YY JO\FHURO DQG  YY βPHUFDSWRHWKDQRO 7KH ERXQG SURWHLQ ZDV HOXWHG ZLWK D  P0 LPLGD]ROH JUDGLHQW 8%( FRPHV RXW RI WKH FROXPQ DW≈ P0 RI LPLGD]ROH 7KH IUDFWLRQV ZHUH SRROHG WRJHWKHU DQG FRQFHQWUDWHG LQ D 0LFURFRQŠ 9LYDVSLQ 5 FHQWULIXJDO ILOWHUV ZLWK  N' FXWRII ZKLOH H[FKDQJLQJ WR  P0 7ULV S+  IRU WKH HQ]\PDWLF UHDFWLRQ

(V 8%& DQG 8(9$

*678%& DQG *678(9$ SODVPLGV ZHUH NLQGO\ SURYLGHG E\ 'U 0LFKDHO *OLFNPDQ )RU H[SUHVVLRQV RI WKH SURWHLQV WKH SODVPLGV ZHUH LQVHUWHG LQ ( FROL %/ *2/' 7KH FHOOV ZHUH JURZQ LQ /% PHGLD XQWLO 2'_{ QP}  DQG ZHUH LQGXFHG E\  P0 ,37* IRU  KRXUV DW  ƒ& &HOOV ZHUH KDUYHVWHG E\ FHQWULIXJDWLRQ WKHQ O\VHG E\ VRQLFDWLRQ LQ O\VLV EXIIHU  P0 7ULV+&/ S+   JO\FHURO  P0 '77  PJPO O\VR]\PH DQG  WDEOHW RI &PSOHWHŠ SURWHDVH LQKLELWRUV 7KH O\VDWHV ZHUH FODULILHG E\ FHQWULIXJDWLRQ DW  USP IRU  PLQXWHV WKHQ PL[HG WRJHWKHU WR IRUP WKH FRPSOH[ *678%&*678(9$ EHIRUH EHLQJ ORDGHG RQWR D *67 )DVW )ORZ FROXPQ 7KH ERXQG FRPSOH[HV RI *678%& DQG *678(9$ ZHUH HOXWHG E\  P0 UHGXFHGJOXWDWKLRQH DQG H[FKDQJHG LQWR  P0 7ULV S+  DQG FRQFHQWUDWHG LQ D 0LFURFRQŠ 9LYDVSLQ 5 FHQWULIXJDO ILOWHUV ZLWK  N' FXWRII

)LJXUH  ² 6FKHPDWLF UHSUHVHQWDWLRQ RI WKH SXULILFDWLRQ RI WKH (V FRPSOH[ RI *6789($*678%&

&KDLQ V\QWKHVLV

7KH UHDFWLRQ FRQVLVWV RI RQHILIWK YROXPH RI 3%'0  P0 7ULV+&O S+   P0 0J&O_  P0 FUHDWLQH SKRVSKDWH 6LJPD  8PO LQRUJDQLF S\URSKRVSKDWH 6LJPD  8PO FUHDWLQH SKRVSKRNLQDVH 6LJPD DQG  P0 $73  PJPO RI HDFK PXWDQW RI XELTXLWLQ .5 DQG '  P0 '77 DQG  Δ0 RI WKH (V FRPSOH[ *678%&*678(9$ 7KH UHDFWLRQ LV DFWLYDWHG E\ DGGLQJ  Δ0 8%( DQG LQFXEDWHG RYHUQLJKW DW  ƒ& 7KH UHDFWLRQ VWRSSHG E\ DGGLQJ  P0 '77 DQG  P0 ('7$ WR UHGXFH WKH GLVXOILGH OLQNV DQG VR WKH GLPHUV ERXQG WR ( HQ]\PHV DUH GHWDFKHG $IWHU  PRUH PLQXWHV RI LQFXEDWLRQ DW URRP WHPSHUDWXUH RQHILIWK YROXPH RI  1 DFHWLF DFLG ZDV DGGHG WR EULQJ WKH S+ GRZQ WR≈ 7KH UHDFWLRQ ZDV WKHQ ORDGHG RQWR D 63 6HSKDURVHŒ )DVW )ORZ FROXPQ *( +HDOWKFDUH HTXLOLEUDWHG ZLWK  P0 DPPRQLXP DFHWDWH S+  $ JUDGLHQW RI 1D&O ZDV DSSOLHG WR WKH FROXPQ DQG WKH GLPHU ZDV HOXWHG DW≈ 0 1D&O 7R IXUWKHU SXULI\ WKH GLPHU D VL]H H[FOXVLRQ FROXPQ +LORDG 6XSHUGH[Œ   FROXPQ ZDV SHUIRUPHG 7KH ILQDO IUDFWLRQ ZDV SRROHG DQG H[FKDQJHG WR WKH ZRUNLQJ EXIIHU DFFRUGLQJ WR WKH W\SH RI H[SHULPHQWV 6HH 7DEOH 



:RUNLQJ EXIIHUV

7KH EXIIHUV ZHUH RSWLPL]HG IRU HDFK VHW RI SURWHLQV DQG IRU GLIIHUHQW W\SH RI H[SHULPHQWV ZKLFK DUH GHWDLOHG LQ WKH IROORZLQJ WDEOHV 6RGLXP SKRVSKDWH EXIIHUV ZHUH D PL[ RI   EDVH 1D_+32_ DQG   DFLG 1D+_32_ $V IRU 7ULV+&O EXIIHU D PL[ RI  EDVH DQG  DFLG ZDV XVHG )RU GL8ELTXLWLQ 98:7 DQG FRQVWUXFWV GXH WR D KLJK PROHFXODU ZHLJKW DQG D KLJK VWUXFWXUH OHYHO '77 ZDV DGGHG WR DYRLG GLVXOILGH ERQGV WKXV WR SUHYHQW DJJUHJDWLRQ 1D&O ZDV UHPRYHG WR DYRLG LQWHUIHULQJ ZLWK WKH UHFRUGHG VLJQDO LQ FLUFXODU GLFKURLVP &' DQG 105 H[SHULPHQWV

D &RPSRVLWLRQ

%XIIHUV 5HDJHQWV S+

3%  P0 VRGLXP SKRVSKDWH 

3% '77  P0 VRGLXP SKRVSKDWH  P0 '77 

7ULV  P0 7ULV+&O 

7ULV '77  P0 7ULV+&O  P0 1D&O  P0 '77 

E 8VDJH

3URWHLQV VHWV ([SHULPHQWV

105 6$;6 &' 8E_UHDFWLRQ

86:7 PXWDQWV 3% 7ULV '77 3% 

98:7 PXWDQWV 3% '77 7ULV '77 3%  8E GHULYHG PXWDQWV 3% 7ULV '77  7ULV

.8E_FKDLQV 3% '77 7ULV '77  

8ELTXWLQDWLRQ HQ]\PHV    7ULV '77

7DEOH  ² 7KH VRGLXP SKRVSKDWH EXIIHU ZDV XVHG LQ 105 DQG &' H[SHULPHQWV DQG 7ULV+&O ZDV WKH RSWLPDO EXIIHU IRU 6$;6 H[SHULPHQWV  P0 '77 ZDV DGGHG IRU .OLQNHG GLXELTXLWLQ 98:7 DQG WKH GHULYHG PXWDQWV



105 GDWD FROOHFWLRQ DQG SURFHVVLQJ

$OO H[SHULPHQWV ZHUH SHUIRUPHG DW  . DQG WKH 105 VDPSOHV ZHUH H[FKDQJHG LQWR  P0 SKRVSKDWH S+  VHH 7DEOH  VXSSOHPHQWHG ZLWK  YY '_2 DQG   ZY 1D1_ )RU 86:7 DQG PXWDQWV 105 H[SHULPHQWV ZHUH DOO UHFRUGHG RQ D %UXNHU $YDQFH ,,,  0+] VSHFWURPHWHU HTXLSSHG ZLWK D WULSOH 7&, FU\RSUREH DW WKH 105 IDFLOLW\ RI WKH &501 /\RQ $V IRU UHOD[DWLRQ PHDVXUHPHQWV DQ DGGLWLRQDO VHW RI H[SHULPHQWV ZDV SHUIRUPHG RQ WKH %UXNHU $YDQFH 1(2  0+] VSHFWURPHWHU HTXLSSHG ZLWK D WULSOH 7&, FU\RSUREH DW WKH 8&&6  8*6) /LOOH 7KH ODWWHU ZDV DOVR WKH VSHFWURPHWHU RQ ZKLFK DOO 105 H[SHULPHQWV RI 98:7 DQG PXWDQWV ZHUH UHFRUGHG 'DWD ZDV SURFHVVHG ZLWK 1053LSH>@ _{DQG DQDO\]HG}

ZLWK &&3105>@_



86ʹ EDFNERQH DVVLJQPHQW

7KH EDFNERQH DVVLJQPHQW RI 86ʹ ZDV FDUULHG RXW E\ XVLQJ D FRPELQDWLRQ RI WKH IROORZLQJ H[SHULPHQWV +1&2 +1&$&2 +1&$&% DQG +1&2&$&% )LJXUH  ZKLFK ZHUH DFTXLUHG RQ D GRXEOH ODEHOHG_&_{186ʹ VDPSOH 7KH H[LVWLQJ DVVLJQPHQW RI 86:7}

ZDV XVHG DV D VWDUWLQJ SRLQW PRVWO\ IRU WKH 6+ SDUW

7R DVVLJQ WKH FDUERQ\O_{& ZH PDNH XVH RI WKH FRPELQDWLRQ RI WZR H[SHULPHQWV +1&2}

DQG +1&$&2 ,Q WKH +1&2 H[SHULPHQW PDJQHWL]DWLRQ LV WUDQVIHUUHG IURP_{+ WR}_{1 RI WKH}

UHVLGXH L WKHQ WR WKH FDUERQ\O_{& RI WKH SUHFHGHG UHVLGXH L E\ WKH}_1+²_{&2 -FRXSOLQJ}

DQG WKHQ ILQDOO\ UHWXUQV EDFN WR +L IRU GHWHFWLRQ )LJXUH D 7KLV H[SHULPHQW LV XVHG LQ

FRQMXQFWLRQ RI WKH +1&$&2 ZKHUH PDJQHWL]DWLRQ LV SDVVHG IURP₊

LWR1LDQG WKHQ YLD

WKH 1&α -FRXSOLQJ WR WKH_{&α RI ERWK UHVLGXH L DQG L )LJXUH E )URP WKHUH LW LV}

WUDQVIHUUHG WR WKH WZR_{&2 WKURXJK WKH}_{&α }_{&2 -FRXSOLQJ 7KH ILQDO VLJQDO LV GHWHFWHG}

IRU_{&2 RI ERWK UHVLGXHV L DQG L}₁

LDQG ILQDOO\+L

)LJXUH  ²6FKHPDWLF UHSUHVHQWDWLRQ RI ' 105 H[SHULPHQWV +1&2 D +1&$&2 E +1&$&% F DQG +1&2&$&% G 7KH UHG DUURZ UHSUHVHQWV WKH SDWK RI WKH PDJQHWL]DWLRQ WUDQVIHU 7KH DWRPV WKDW DUH FLUFOHG LQ JUHHQ UHSUHVHQWV WKH GHWHFWHG DWRP ZLWK HYROYHG FKHPLFDO VKLIW ZKLOH WKH SXUSOH FLUFOHG DWRPV VWD\ XQGHWHFWHG

)RU WKH &α DQG &β DVVLJQPHQW WZR H[SHULPHQWV +1&$&% DQG +1&2&$&% ZHUH SHUIRUPHG ,Q WKH +1&$&% H[SHULPHQW )LJXUH F WKH PDJQHWL]DWLRQ LV WUDQVIHUUHG IURP

_{+α DQG} _{+β WR}_{&α DQG}_{&β RI ERWK UHVLGXH L DQG L 7KH PDJQHWL]DWLRQ LV WKHQ}

SDVVHG IURP_{&β WR}_{&α WR UHDFK}_{1 DQG ILQDOO\ WKH DPLG}_{+ IRU GHWHFWLRQ 7KH FKHPLFDO}

VKLIW LV WKHUHIRUH HYROYHG RQ_{&α DQG}_{&β RI ERWK L DQG L UHVLGXHV}₁

LDQG+L EXW

QRW RQ_{&2 7KH FRPSOHPHQW RI WKLV +1&$&% H[SHULPHQW LV WKH +1&2&$&% )LJXUH G}

ZKHUH WKH PDJQHWL]DWLRQ LV GHVLJQHG WR EH WUDQVIHUUHG IURP_{+α DQG}_{+β RI WKH UHVLGXHV L}

WKURXJK_&2

L− EHIRUH UHDFKLQJ1LDQG+L 7KH FKHPLFDO VKLIW LV WKHUHIRUH HYROYHG RQO\

IRU_{&α DQG}_{&β RI WKH UHVLGXH L SOXV}_1LDQG_+L



8,0< EDFNERQH DVVLJQPHQW

7KH EDFNERQH DVVLJQPHQW RI WKH 8,0< FRQVWUXFW ZDV FRQGXFWHG ZLWK WKH XVH D VHW RI WKUHH H[SHULPHQWV_+_{1+64& +1&2&$1+ )LJXUH  DQG +1&$&% )LJXUH F}

,Q WKH +1&2&$1+ H[SHULPHQWV WKH WKUHH DWRP_+L₊

(L−) DQG +1L− LV GHWHFWHG

WKURXJK WKH PDJQHWL]DWLRQ WUDQVIHU SDWK DV VKRZQ LQ )LJXUH 

)LJXUH  ²6FKHPDWLF UHSUHVHQWDWLRQ RI ' 105 H[SHULPHQWV +1&2&$1+ 7KH UHG DUURZ UHSUHVHQWV WKH SDWK RI WKH PDJQHWL]DWLRQ WUDQVIHU 7KH DWRPV WKDW DUH FLUFOHG LQ JUHHQ UHSUHVHQWV WKH GHWHFWHG DWRP ZLWK HYROYHG FKHPLFDO VKLIW ZKLOH WKH SXUSOH FLUFOHG DWRPV VWD\ XQGHWHFWHG



105 WLWUDWLRQ H[SHULPHQWV

_+_{1 +64& VSHFWUD ZHUH UHFRUGHG RQ WKH} _{1ODEHOHG 67$0 FRQVWUXFWV XSRQ}

DGGLWLRQ RI_{1PRQR8ELTXLWLQ RU}_{1.OLQNHG GL8ELTXLWLQ DV OLJDQGV XQWLO VDWXUDWLRQ} 

7KH ZHLJKWHG DPLGH FKHPLFDO VKLIW SHUWXUEDWLRQV &63V LV FDOFXODWHG DV IROORZHG ʹΌ=



(ʹΌ₊)_{+ (Ή.ʹΌ1)}

 

ZKHUH ʹΌ₊ DQG ʹΌ₁DUH WKH &63V LQ WKH_{+ DQG}_{1 GLPHQVLRQV LQ D VXFFHVVLYH DGGLWLRQ RI}

WKH OLJDQGV DQG Ή LV WKH VFDOLQJ IDFWRU ZKLFK UDQJH IURP  WR >@_{ ,Q WKLV VWXG\ Ή LQ WKH}

HTXDWLRQ  ZDV HVWLPDWHG DV  EDVHG RQ WKH VFDOLQJ RI_{+ VSHFWUDO ZLGWK RYHU}_{1 VSHFWUDO}

ZLGWK ,Q RUGHU WR H[WUDFW WKH GLVVRFLDWLRQ FRQVWDQW ._G GLIIHUHQW VWRHFKLRPHWU\ PRGHOV ZHUH XVHG DFFRUGLQJ WR WKH SUHYLRXV ZRUN RI 9DUDGDQ HW DO>@_{ZKHUH LW LV DVVXPHG WKDW LQ IDVW}

H[FKDQJH WKH &63V DW D JLYHQ LQWHUPHGLDWH VWDWH ʹΌ FDQ EH OLQNHG WR WKH ERXQG VWDWH &63V ʹΌ_ERXQG E\ D OLQHDU IXQFWLRQ ZKLFK YDULHV DFFRUGLQJ WR GLIIHUHQW VWRHFKLRPHWU\ PRGHOV

,W ZDV IRXQG LQ D SUHYLRXV ZRUN WKDW XELTXLWLQ KDV QR SUHIHUHQWLDO ELQGLQJ WR 6+ RU 8,0 GRPDLQ>@_{ &RQVLGHULQJ WKDW RQH 8E FDQ ELQG WR RQH RI WKH WZR GRPDLQV 8,0 DQG}

6+ LQGHSHQGHQWO\ D  VWRHFKLRPHWU\ ZDV DSSOLHG IRU DOO 86 FRQVWUXFWV XSRQ 8E DGGLWLRQ )LJXUH D ,Q WKH FDVH RI .8E_WLWUDWLRQ IRU 86ʹ DQG 86ʹ ZKHUH WKH 6+ GRPDLQ VROHO\ UHPDLQV LQWDFW WKH VDPH VWRHFKLRPHWU\ PRGHO ZDV DOVR DSSOLHG GHVSLWH WKH SUHVHQFH RI  ELQGLQJ VLWHV RQ WKH OLJDQG

ʹΌ=ʹΌ_ERXQG.([/] + [3] +.G−



([/] + [3] +.G)−[/][3]

[3_] ) 

)RU 86:7 86ʹ 86ʹ 98:7 983 DQG 987 XSRQ .8E_ WLWUDWLRQ D  VWRHFKLRPHWU\ ZDV DSSOLHG ZKHUH HDFK GRPDLQ LQWHUDFWV ZLWK RQH XQLW RI .8E_)LJXUH E ʹΌ=ʹΌ_ERXQG.([/_] + [3_] +._G−  ([/_] + [3_] + .G)−[/][3] [3] ) 

7KH GLVVRFLDWLRQ FRQVWDQW ._GDQG ʹΌ_ERXQGZHUH WKHQ ILWWHG ZLWK QRQOLQHDU UHJUHVVLRQ E\ XVLQJ DQ LQKRXVH 0DWODE 0DWK:RUNV EDVHG SURJUDP (UURUV ZHUH HVWLPDWHG E\ VDPSOLQJ  LQLWLDO JXHVVHV DVVXPLQJ  HUURU RQ WKH SURWHLQ DQG OLJDQG FRQFHQWUDWLRQV

D PRGHO

E PRGHO

)LJXUH  ²6WRHFKLRPHWU\ PRGHOV XVHG IRU WKH LQWHUDFWLRQ EHWZHHQ 8E RU .8E_DQG 67$0 FRQVWUXFWV 7KH JUHHQ URXQG VKDSHV UHSUHVHQW XELTXLWLQ OLQNHG WRJHWKHU RU QRW ZKLOH WKH SXUSOH DQG RUDQJH VKDSHV UHSUHVHQW GLIIHUHQW GRPDLQV RI WKH 67$0 FRQVWUXFWV 7KH LQWHUDFWLRQV LQ WKH  PRGHO D ZHUH FRQVLGHUHG DV VLPXOWDQHRXV ZKLOH WKH GRWWHG VKDSHV PHDQ D QRQVLPXOWDQHRXV LQWHUDFWLRQ RI WKH WZR .8E_PROHFXOHV LQ WKH  PRGHO E



105 UHOD[DWLRQ H[SHULPHQWV

6SLQ UHOD[DWLRQ LV D SRZHUIXO PHWKRG ZKLFK PDNHV D PDMRU FRQWULEXWLRQ WR UHVHDUFK RQ WKH G\QDPLFDO SURSHUWLHV RI SURWHLQV>@ >@_{ ,Q WKH OLPLWDWLRQ RI WKH SUHVHQW VWXG\ RQO\ EDVLF}

GHILQLWLRQV DQG DSSOLFDWLRQV RI WKH PHWKRG ZLOO EH EURXJKW XS>@_

,Q EULHI DW WKH HQG RI WKH H[FLWDWLRQ E\ WKH PDJQHWLF ILHOG %_ WKH WRWDO VSLQ RI WKH QXFOHL LQ WKH VDPSOH EHJLQV WR UHWXUQ WR WKH LQLWLDO HTXLOLEULXP VWDWH ZKLFK LV DOLJQHG ZLWK WKH %

ILHOG 7KLV SURFHVV FRUUHVSRQGV WR WKH GLVDSSHDUDQFH RI WKH WUDQVYHUVH FRPSRQHQW 0[\DQG

WKH UHVWRUDWLRQ RI WKH ORQJLWXGLQDO FRPSRQHQW 0] 7KH UHWXUQ WR HTXLOLEULXP LV WKHUHIRUH

FKDUDFWHUL]HG E\ WZR SDUDPHWHUV WKH ORQJLWXGLQDO UHOD[DWLRQ WLPH 7_ ZKLFK LV OLQNHG WR WKH HYROXWLRQ RI WKH 0]FRPSRQHQW DQG WKH WUDQVYHUVH UHOD[DWLRQ WLPH ZKLFK GHVFULEHV WKH

HYROXWLRQ RI WKH 0[DQG 0\FRPSRQHQWV ,Q SULQFLSOH 7LV WKH WLPH LW WDNHV IRU WKH VLJQDO WR

GHFD\ GXH WR WKH GHSKDVLQJ EHWZHHQ PXOWLSOH QXFOHL SUHVHQWHG LQ WKH PROHFXOH ,Q VKRUW

7_ DQG 7_ UHOD[DWLRQ WLPHV KDYH D WLJKW FRQQHFWLRQ WR WKH FRUUHODWLRQ WLPH Μ_& RI WKH PROHFXOH 7KH ODWWHU LV WKH WLPH LW WDNHV WR URWDWH E\  UDGLDQ DQG KDV D WLJKW FRQQHFWLRQ WR WKH PDFURPROHFXOH VL]H 7KH UHOD[DWLRQ UDWHV 5DQG 5 ZKLFK DUH VLPSO\ WKH UHYHUVH RI

7_DQG 7_UHVSHFWLYHO\ FDQ EH REWDLQHG E\ SHUIRUPLQJ DQ LQWHUOHDYHG SVHXGR' H[SHULPHQWV SUHYLRXVO\ GHVFULEHG E\ )XVKPDQ HW DO>@_{ )RU WKH 5 UHOD[DWLRQ GHOD\V UDQJLQJ IURP  WR}

 PV ZHUH XVHG ZLWK D UHF\FOLQJ GHOD\ RI  V ,Q WKH FDVH RI 5_H[SHULPHQWV WKH GHOD\V DUH UDQJLQJ IURP  WR  PV ZLWK D UHF\FOLQJ GHOD\ RI  V 'DWD ZHUH SURFHVVHG ZLWK 1053LSH>@

DQG 5 5YDOXHV DUH H[WUDFWHG LQ &&3105 XVLQJ WKH µ)ROORZ ,QWHQVLW\ FKDQJHVµ WRROV>@

$QRWKHU SDUDPHWHU XVHG LQ WKH SUHVHQW VWXG\ LV WKH_1_{+ FURVVUHOD[DWLRQ UDWHV YLD}

VWHDG\VWDWH _1_{+ 12( 1XFOHDU 2YHUKDXVHU (IIHFW ,Q VKRUW WKH KHWHURQXFOHDU 12(}

KHWHUR12( FRUUHVSRQGV WR WKH FURVV UHOD[DWLRQ HIIHFW ZKLFK UHVXOWV LQ D PDJQHWL]DWLRQ H[FKDQJH EHWZHHQ WZR VSLQV LQ GLSRODU LQWHUDFWLRQ _{1 DQG} _{+ VSLQV LQ WKLV FDVH 7KH}

PHDVXUHPHQW RI WKH KHWHUR12(V LV GRQH E\ WZR +64&_1_{+ H[SHULPHQWV ZLWKRXW RU ZLWK}

SUHVDWXUDWLRQ ZKHUH DQ LUUDGLDWLRQ LV H[HUWHG RQ WKH_{+ QXFOHL WR FUHDWH D VWHDG\ VWDWH DQG}

WKH SHUWXUEDWLRQ RQ WKH ORQJLWXGLQDO PDJQHWL]DWLRQ RI_{1 LV REVHUYHG}>@ >@_{ 7KH UHOD[DWLRQ}

GHOD\ ZDV VHW WR  V LQ RUGHU WR DOORZ WKH EXON ZDWHU PDJQHWL]DWLRQ WR UHWXUQ DV FORVH DV SRVVLEOH WR WKH HTXLOLEULXP VWDWH 7KH KHWHUR12( LV ILQDOO\ REWDLQHG E\ FDOFXODWLQJ WKH UDWLR RI WKH LQWHQVLWLHV RI WKH_1_{+ FRUUHODWLRQ SHDNV EHWZHHQ WKH WZR ' H[SHULPHQWV ,Q WKH}

SUHVHQW VWXG\ ZKLOH WKH GLVWDQFH RI WKH 1+ ERQGV LV FRQVLGHUHG WR EH NQRZQ DQG FRQVWDQW WKURXJKRXW WKH SURWHLQ KHWHUR12(V LQGLFDWH WKH IOH[LELOLW\ RI WKH 1+ ERQGV 7KH PRUH ULJLG WKLV OLQNDJH LV WKH OHVV WKH SURWRQ SHUWXUEDWLRQ DIIHFWV WKH_{1 VSLQ UHOD[DWLRQ DQG WKH FORVHU}

WKH KHWHUR12( LV WR  2Q WKH FRQWUDU\ DV WKH OLQNDJH EHFRPHV PRUH IOH[LEOH WKH_{1 VSLQ}

UHOD[DWLRQ LV PRUH DIIHFWHG E\ WKH SURWRQ SHUWXUEDWLRQ DQG KHWHUR12( YDOXH GHYLDWHV IDUWKHU DZD\ IURP  5 5DQG KHWHUR12(V DUH GLUHFWO\ UHODWHG WR WKH PRWLRQ RI D 1+ YHFWRU DQG

DUH H[SUHVVHG DV D OLQHDU FRPELQDWLRQ RI VSHFWUDO GHQVLWLHV -ω WKDW GHVFULEH WKH HIILFLHQF\ RI D JLYHQ UHOD[DWLRQ PHFKDQLVP DW D JLYHQ IUHTXHQF\ 7KHVH SDUDPHWHUV DUH GHILQHG DV

5_=G[-(Ρ+−Ρ1) +-(Ρ++Ρ1)] +(F+G)-(Ρ1) 

5_= G_[-(Ρ₊−Ρ₁) +-(Ρ₊) +-(Ρ₊+Ρ₁)] + (F_+G_{)[-() +} -(Ρ1)] +5H[  12(=+G₍΋+ ΋₁) [ -(Ρ₊+Ρ₁) −-(Ρ₊−Ρ₁)] 5  ZKHUH G= −(Δ Θ)( ΋₊΋₁K ΘU +1)  DQG F= ΋1%_ʹΛ 

U+1LV WKH LQWHUPROHFXODU1−+ GLVWDQFH ʹΛ LV WKH DQLVRWURS\ RI WKH1 FKHPLFDO

VKLIW WHQVRU ΋₊ ΋₁ Ρ+ Ρ1 DUH WKH J\URPDJQHWLF UDWLRV DQG UHVRQDQFH IUHTXHQFLHV RI WKH

QXFOHL K LV 3ODQFN FRQVWDQW DQG 5H[ LV WKH FRQIRUPDWLRQDO H[FKDQJH FRQWULEXWLRQ LI DQ\ WR

WKH PHDVXUH RI 5

$ FRPSOHWH GHVFULSWLRQ RI WKH GLIIHUHQW PRWLRQV RFFXUULQJ DW WKH ILYH UHVRQDQFH IUHTXHQFLHV ZRXOG UHTXLUH WKH PHDVXUHPHQW RI ILYH LQGHSHQGHQW UHOD[DWLRQ SDUDPHWHUV $ UHFHQW GHYHORSPHQW RI )DUURZ HW DO>@_{JDYH ULVH WR UHGXFHG VSHFWUDO GHQVLWLHV DQG DOORZV WKH}

PHDVXUHPHQW RI WKUHH UHOD[DWLRQ SDUDPHWHUV RQO\ 7KH SUHYLRXV UHOD[DWLRQ SDUDPHWHUV FDQ EH UHFDVW DV 5=.G-(.Ρ+) +(F+G)-(Ρ1)  5=.G-(.Ρ+) + (F+G)[-() +_-(Ρ1)] +5H[  (−12()5_|΋_΋1 +| =G _{-(.Ρ+) }

$ FRPSOHWH DQDO\VLV RI WKH JLYHQ UHOD[DWLRQ SDUDPHWHUV ZRXOG UHTXLUH WKH XVH RI JLYHQ G\QDPLFDO PRGHO $QRWKHU LVVXH LV WR UHVRUW WR D GLUHFW DQDO\VLV RI WKH GLIIHUHQW VSHFWUDO

GHQVLWLHV 1+ YHFWRUV ZKLFK UHRULHQW IDVWHU ZLOO KDYH D EURDGHU GLVWULEXWLRQ IRU -Ρ (TXLYDOHQWO\ VPDOOHU - YDOXHV LPSO\ VKRUWHU ΜFYDOXHV DQG WKHUHIRUH PRUH UDSLG URWDWLRQDO

IOXFWXDWLRQV RI WKH 1+ YHFWRU 7KXV WKH UHVSHFWLYH UHGXFHG VSHFWUDO GHQVLWLHV FDQ EH H[SUHVVHG DV -(.Ρ+) = (−_G12(_ )5|_΋΋1 +|  -(Ρ1) = 5_(−.(−12()|΋1 ΋+|) (F_+G₎  -() = 5−5(| ΋1 ΋+|(.−.12() +. (F_+G₎ 

6WDUWLQJ IURP WKH VSLQ UHOD[DWLRQ SDUPHWHUV ZH FDQ GLUHFWO\ GHULYH WKH FRUUHVSRQGLQJ UHGXFHG VSHFWUDO GHQVLWLHV

:LWK WKH 5_ 5_DQG KHWHUR12(V LQ KDQG FRUUHODWLRQ WLPHV ZHUH DQDO\]HG DQG GHULYHG XVLQJ WKH 527',) VRIWZDUH>@ >@_{E\ RQO\ FRQVLGHULQJ YDOXHV RI WKH UHVLGXHV WKDW EHORQJ WR}

WKH VHFRQGDU\ VWUXFWXUH RI WKH SURWHLQ



6PDOO $QJOH ;5D\ 6FDWWHULQJ 6$;6 H[SHULPHQWV

6$;6 LV D WRRO WKDW VWXGLHV WKH RYHUDOO VKDSH RI ELRORJLFDO PDFURPROHFXOHV LQ VROXWLRQ DW ORZ UHVROXWLRQ ≈ c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

QRLVH

)LJXUH  ²7KH SULQFLSOH RI D 6$;6 PHDVXUHPHQW

7KH PHDVXUHPHQWV ZHUH SHUIRUPHG DW WKH (65) %LR6$;6 EHDPOLQH %0 *UHQREOH )UDQFH XVLQJ D ' 3LODWXV GHWHFWRU DW DQ ;UD\ ZDYHOHQJWK Γ  c ZLWK D VWDQGDUG VLQJOH LQVWUXPHQWDO FRQILJXUDWLRQ VDPSOHV EHLQJ DXWRPDWLFDOO\ PRXQWHG WR D FDSLOODU\ DQG  IUDPHV ZLWK  V H[SRVXUH XVLQJ WKH IORZWKURXJK PRGH DW  ƒ& 'DWD SURFHVVLQJ DQG UHGXFWLRQ ZHUH SHUIRUPHG XVLQJ DQ DXWRPDWHG VWDQGDUG (65) EHDPOLQH VRIWZDUH %6[&X%(>@_{DQG 35,086}>@_{ZKLOH WKH RYHUDOO SDUDPHWHUV GHULYHG IURP 6$;6 GDWD ZHUH}

SURFHVVHG ZLWK 6&c77(5>@_{ 86:7 DQG WKH WUXQFDWHG IRUPV 86ʹ 86ʹ DQG 86ʹ}

ZHUH H[FKDQJHG LQWR D  P0 7ULV+&O EXIIHU S+  ZLWK  P0 1D&O DQG  P0 '77 'DWD ZHUH PHDVXUHG DW  GLIIHUHQW FRQFHQWUDWLRQV UDQJLQJ IURP  WR  PJPO WR HOLPLQDWH DQ\ LQWHUSDUWLFOH HIIHFWV DQG WR REWDLQ KLJK TXDOLW\ GDWD IURP ERWK WKH ORZ DQJOH UDQJH ORZ SURWHLQ FRQFHQWUDWLRQ WR DFFXUDWHO\ H[WUDFW WKH UDGLL RI J\UDWLRQ DQG IURP WKH KLJK DQJOH UDQJH KLJK SURWHLQ FRQFHQWUDWLRQ IRU DQ DFFXUDWH VROYHQW VXEWUDFWLRQ DQG PHUJHG ZKHUH QHHGHG ,Q RUGHU WR ILQG WKH HQVHPEOH RI VWUXFWXUH DQG WKHLU UHVSHFWLYH ZHLJKW WKDW EHVW ILW WKH H[SHULPHQWDO 6$;6 GDWD EDFN FDOFXODWLRQV ZHUH GRQH RQ WKH 0XOWLIR[V VHUYHU>@_{ $PRQJ WKH}

LQLWLDO PRGHO JHQHUDWHG E\ 0RGHOOHU VHFWLRQ  RQH SGE ZLWK WKH EHVW Ο VFRUHV ZDV VHOHFWHG DV LQSXW )OH[LEOH UHVLGXHV KDYH EHHQ GHILQHG EDVHG RQ SUHYLRXV NQRZOHGJHV RI WKH SURWHLQ VHFRQGDU\ VWUXFWXUH DQG  FRQIRUPHUV KDYH EHHQ VDPSOHG $W ILUVW 0XOWL)R;6 VDPSOHV WKH LQSXW VWUXFWXUHV ZLWK D 557 DOJRULWKP>@ _{WKDW VLJQLILFDQWO\ LPSURYHV WKH VDPSOLQJ}

HIILFLHQF\ FRPSDUHG WR UDQGRP VDPSOLQJ $IWHUZDUG D 6$;6 SURILOH LV FDOFXODWHG IRU HDFK VDPSOHG FRQIRUPDWLRQ )LQDOO\ WKH  WRS PXOWLVWDWH PRGHOV DUH VRUWHG DFFRUGLQJ WR WKHLU

Ο YDOXHV



&LUFXODU 'LFKURLVP &' H[SHULPHQWV

7KH IDU89 &' H[SHULPHQWV ZHUH SHUIRUPHG RQ D &KLUDVFDQ &LUFXODU 'LFKURLVP &' VSHFWURPHWHU $SSOLHG 3KRWRSK\VLFV /WG XVLQJ FXYHWWHV RI  PP SDWK OHQJWK DW URRP WHPSHUDWXUH 7KH LQVWUXPHQW SDUDPHWHUV ZHUH VHW WR D VWHS VL]H RI  QP D VSHFWUDO EDQGZLGWK RI QP DQG  SRLQW ZDV PHDVXUHG SHU VHFRQG 7KH GLIIHUHQW VDPSOHV ZHUH H[FKDQJHG LQWR P0 VRGLXP SKRVSKDWH EXIIHU S+ DQG ZHUH PHDVXUHG DW D FRQFHQWUDWLRQ UDQJLQJ IURP  WR  Δ0 7KH &' VSHFWUXP RI HDFK VDPSOH ZDV WKHQ VXEWUDFWHG WR WKH EXIIHU QRUPDOL]HG WR WKHLU UHVSHFWLYH FRQFHQWUDWLRQ DQG WKHQ FRQYHUWHG WR WKH PHDQ UHVLGXH PRODU HOOLSWLFLW\ 050( XQLW 7KH ILQDO VSHFWUD ZHUH GHFRQYROXWHG XVLQJ WKH &'6675 DOJRULWKP>@ _{ZLWK WKH UHIHUHQFH VHW 603}>@ _{DYDLODEOH RQ WKH ',&+52:(%}

VHUYHU KWWSGLFKURZHEFU\VWEENDFXNKWPOKRPHVKWPO

3

8,06+ DQG WKH OLQNHU OHQJWK

,Q RUGHU WR VWXG\ WKH LPSDFW RI WKH OLQNHU OHQJWK RQ WKH ELRORJLFDO DQG G\QDPLFDO FKDUDFWHULVWLFV RI D PXOWLGRPDLQ SURWHLQ 86:7 GHULYHG YDULDQWV ZHUH HQJLQHHUHG ZKHUH WKH OLQNHU EHWZHHQ 8,0 DQG 6+ GRPDLQV KDV EHHQ VKRUWHQHG E\  DQG  DPLQR DFLGV 86ʹ DQG 86ʹ UHVSHFWLYHO\ DQG HLWKHU 8,0 86ʹ RU KDOI RI 8,0 86ʹ KDV EHHQ GHOHWHG VHH )LJXUH 

$ SUHYLRXV VWXG\ KDV GHPRQVWUDWHG WKDW 8,0 DQG 6+ GRPDLQV GR QRW LQWHUDFW ZLWK HDFK RWKHU ZLWKLQ WKH 86:7 FRQVWUXFW>@_{ :LWK WKLV LQ PLQG DOO 86:7 GHULYHG PXWDQWV}

KDYH EHHQ FKHFNHG WR FRQILUP ZKHWKHU WKH\ LQKHULW WKLV FKDUDFWHULVWLF )RU HDFK FRQVWUXFW D

_+_{1+64& VSHFWUXP ZDV UHFRUGHG DQG FRPSDUHG ZLWK WKH 86:7 VSHFWUXP}

)LJXUH  ² 6FKHPDWLF UHSUHVHQWDWLRQ RI 86:7 86ʹ 86ʹ 86ʹ DQG 86ʹ FRQVWUXFWV

)RU 86ʹ DQG 86ʹ D JRRG RYHUODSSLQJ ZLWK 86:7 VSHFWUXP ZDV REVHUYHG LQ WKH DOLJQHG UHJLRQV ZKLOH WKH SHDNV WKDW EHORQJ WR WKH WUXQFDWHG UHJLRQV GLVDSSHDUHG )LJXUH  7KLV UHVXOW FRQILUPV WKDW WKH OLQNHU VKRUWHQLQJ KDV EHHQ VXFFHVVIXOO\ GRQH ZLWKRXW DIIHFWLQJ WKH VWUXFWXUH RI WKH UHPDLQLQJ GRPDLQV 8,0 DQG 6+ DQG WKH RYHUODSSLQJ PHDQV WKDW WKHUH LV QR LQWHUDFWLRQ EHWZHHQ WKH GRPDLQV D FKDUDFWHULVWLF WKDW ZDV SDVVHG RQ IURP 86:7

)LJXUH  ²2YHUOD\ RI_+_{1+64& VSHFWUD RI 86:7 UHG DQG 86ʹ EOXH D DQG}

86:7 DQG 86ʹ JUHHQ E )RU UHVLGXHV SUHVHQW LQ ERWK 86:7 DQG 86ʹ RU 86ʹ FRUUHODWLRQ SHDNV QLFHO\ RYHUODS 7KH VSHFWUD ZHUH UHFRUGHG DW D_{+ IUHTXHQF\ RI 0+]}

DQG DOO SURWHLQV DUH_{1 ODEHOHG}

$V IRU 86ʹ DQG 86ʹ WKH SHDNV WKDW EHORQJ WR 6+ LQ_+_{1+64& VSHFWUXP DOVR}

VKRZV D QLFH RYHUODSSLQJ ZLWK 86:7 ZKLFK VKRZV WKH LQWHJULW\ RI WKH UHPDLQLQJ GRPDLQ 6+ LQ VSLWH RI WKH UHPRYDO RI KDOI RU WKH IXOO 8,0 GRPDLQ $GGLWLRQDOO\ WKH 86ʹ VSHFWUXP VKRZV D VLJQLILFDQW VKLIW LQ VHYHUDO SHDNV VXFK DV ( / 4 ( 4 / EOXH ODEHO LQ ILJXUH  7KRVH SHDNV EHORQJ WR WKH UHPDLQLQJ RI 8,0 GRPDLQ LQ WKH &WHUPLQXV WKDW LQGLFDWHV D SRVVLEOH FKDQJH LQ FRQIRUPDWLRQ RI WKLV KHOLFDO PRWLI )RU WKLV UHDVRQ D EDFNERQH DVVLJQPHQW RI 86ʹ KDV EHHQ FDUULHG RXW ZLWK D IRFXV RQ WKH 1WHUPLQXV UHJLRQ :LWK WKDW DVVLJQPHQW WKRVH VKLIWHG SHDNV ZHUH LGHQWLILHG WR IDFLOLWDWH IXUWKHU 105 H[SHULPHQWV

)LJXUH  ² 2YHUOD\ RI_+_{1+64& VSHFWUD RI 86:7 UHG DQG 86ʹ SXUSOH D}

DQG 86ZW DQG 86ʹ GDUN EOXH E )RU UHVLGXHV WKDW EHORQJ WR 6+ GRPDLQ DQG OLQNHU FRUUHODWLRQ SHDNV QLFHO\ RYHUODS LQ ERWK PXWDQWV 7KH FURVV SHDNV RI WKH UHPDLQLQJ 8,0 DUH VKLIWHG IURP 86:7 EODFN ODEHO WR D QHZ SRVLWLRQ LQ WKH VSHFWUXP EOXH ODEHO ZKLFK LQGLFDWHV D FKDQJH LQ FRQIRUPDWLRQ RI WKH KHOL[ 7KH VSHFWUD ZHUH UHFRUGHG DW D_{+ IUHTXHQF\}

RI 0+] DQG DOO SURWHLQV DUH_{1 ODEHOHG} 

0RUHRYHU WKH XQZLQGLQJ RI WKH UHPDLQLQJ 8,0 KHOL[ LV OLNHO\ UHVSRQVLEOH IRU WKH FRQIRUPDWLRQDO FKDQJH RI 86ʹ 7KHUHIRUH D VHULHV RI FLUFXODU GLFKURLVP H[SHULPHQWV ZHUH SHUIRUPHG RQ WKH 86:7 DQG GHULYHG PXWDQWV WR JHW LQIRUPDWLRQ RQ WKH KHOLFLW\ )LJXUH 

)LJXUH  ² &LUFXODU GLFKURLVP VSHFWUD REWDLQHG IRU 86:7 EODFN 86ʹ OLJKW EOXH 86ʹ JUHHQ 86ʹ GDUN EOXH DQG 86ʹ UHG ([SHULPHQWDO SRLQWV DUH UHSUHVHQWHG E\ RSHQ V\PEROV ZKLOH WKH ILWWHG SRLQWV DUH UHSUHVHQWHG E\ JUD\ OLQHV

7DNLQJ LQWR DFFRXQW DQ HUURU RI   E\ XVLQJ WKH &'6675 DOJRULWKP>@_{ WKH KHOLFLW\}

SHUFHQWDJH RI 86ʹ GRHV QRW FKDQJH FRPSDULQJ WR 86:7 ZKLOH LW VKRZV D VOLJKW LQFUHDVH LQ 86ʹ 7DEOH  0RUHRYHU DFFRUGLQJ WR WKH KRPRORJ\ DQDO\VLV GHVFULEHG LQ VHFWLRQ  RI FKDSWHU  WKH αKHOL[ RI 8,0 KDV D OHQJWK RI  DPLQR DFLGV ZKLFK IDOOV QLFHO\ LQ WKH UDQJH RI 86:7  86ʹ  DQG 86ʹ  DYHUDJH KHOL[ OHQJWK 7KHVH UHVXOWV FRQILUP WKH IDFW WKDW 8,0 DQG 6+ GRPDLQV NHHS WKHLU LQLWLDO IROG DQG VWUXFWXUH GHVSLWH D VKRUWHQLQJ RI WKH OLQNHU )RU WKH WZR PXWDQWV ZLWK DOWHUDWLRQ LQ WKH 8,0 PRWLI 86ʹ VKRZV DERXW WKH VDPH KHOLFLW\ SHUFHQWDJH WKDQ 86ʹ ZKLOH KDYLQJ D ORQJHU VHTXHQFH ZKLFK FRUUHVSRQGV WR D JUHDWHU DYHUDJH QXPEHU RI KHOL[ UHVLGXHV ≈ IRU 86ʹ RYHU≈ IRU 86ʹ

86ʹ ZDV DOVR SXULILHG ZLWK D & DQG 1 GRXEOH ODEHOLQJ IRU D 105 EDFNERQH DVVLJQPHQW H[SHULPHQW ZKLFK DOORZHG XV WR KDYH LQIRUPDWLRQ RQ WKH FKHPLFDO VKLIWV RI WKH EDFNERQH FDUERQ QLWURJHQ DQG K\GURJHQ 7KH EDFNERQH WRUVLRQ DQJOHV KDV EHHQ DQDO\]HG DQG WKH SUHGLFWLRQ RI WKH VHFRQGDU\ VWUXFWXUH RI WKH SURWHLQ KDV EHHQ GRQH XVLQJ WKH 7$/26 WRROV>@_{ 7KH UHVXOWV KDYH EHHQ WDNHQ LQWR DFFRXQW WR UHFRQVWUXFW D VFKHPD RI 86ʹ}