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1 O GSA heo

2 Fto Steet London W BQ eephone: + () 7755 Fe: + () Cent Sqe Foth Steet Newte Upon ne NE PL eephone: + () Fe: + () e-: o@p.o Wete: o-otwe.o

3 O GSA O A ght eeved. No pt o th wo e epoded n n o o n en - gph, eeton, o ehn, ndng photoopng, eodng, tpng, o noton toge nd etev te - wthot the wtten peon o the phe. Podt tht e eeed to n th doent e ethe tde nd/o egteed tde o the epetve owne. he phe nd the tho e no to thee tde. Whe eve peton h een ten n the pepton o th doent, the phe nd the tho e no epont o eo o oon, o o dge etng o the e o noton ontned n th doent o o the e o pog nd oe ode tht opn t. n no event h the phe nd the tho e e o n o o pot o n othe oe dge ed o eged to hve een ed det o ndet th doent.

4 O GSA Content Notton 8 Degee o eedo Atve degee o eedo Font odeng Atve degee o eedo Degee o Feedo wth no Lo Stne An Opton Stt & Stt P-det An Stt P-det Mod Mod P-det Rt An 5 Bng Mode Stt An 7 Non-ne Stt An 8 Mt Sove Opton 8 Long e An Dn Reton Sove Apped Dpeent nd Lgnge Mtpe 9 Ae Copote Copote S Eetve Et Popete Condton Ne Contnt & Contnt Eqton 5 Contnt Eqton 5 Jont 5 Rgd Contnt 5 ed ntee Deton Cone 7 Dn Repone An 8 Hon An 8 O Ltd

5 O GSA Peod Lod An Lne e-hto An Foot An Eeent e Seton eeent Non-vet eeent Spng eeent 7 Gonded png nd eeent 7 Ce eeent 8 Ln eeent 8 D eeent e 8 D eeent e 9 Updted eeent e 5 Eeent 5 B nd Rod Eeent 5 Ce, e nd Stt Eeent 5 Be Eeent 5 Spng Eeent 5 Dpe Eeent 59 M Eeent D Eeent Eeent tne Eeent M 7 Eeent Stne 7 Reee 75 Oet 7 Spe Eeent & Sdng Ce 7 Eo No 85 Stt 85 Dn nd ng 85 Ept e ntegton 85 D Eeent Stee nd Foe 8 Ste n D Eeent 8 Ste-tn Retonhp 9 O Ltd

6 O GSA Foe n D Eeent 9 Condtonng 95 ntepoton on ng/qd Fet 9 Lodng 98 Be Lod 98 Be he Lod 99 Be Pe-te Lod nd L-o-t 99 Lod on pn-ended e 99 Pojeted Lod D Bod Lod D Fe Lod D Eeent he Lod D n-pne Lod Gd Lod Lgnge ntepoton 7 M Dtton 8 Mte Mode 9 otop te 9 Othotop te 9 Mng M & Red Rgd Repone Gpt Method Ptpton Fto nd Eetve M Pttened Lod An Rt An 7 teton 7 Pe 8 Convegene 9 Regh Dpng 9 RC S ntodton Dt Reqeent Othe So Ued n heo RC S Sgn Conventon RC S An Poede O Ltd

7 O GSA Reded tne & P-det 9 Se Cton Repone Spet An Eqvent Stt nd Adent oon Lod Rotton t the end o (e) 7 Foe 7 Moent 9 he 5 Pe-te 5 Be dtoton 5 Seond Moent o Ae & Bendng 5 She Ae 5 hn-wed Seton 5 Sod Seton 57 Stoe Dpeent 58 S-ode Etton Stt n t Mod dn nd Rt n e Repone pet n oe Lne oon Contnt Snt Vennt Appoton 5 Retng Seton 5 Othe Seton Ftoed Ve o Conete 8 noton 8 O Ltd

8 O GSA Notton So t M K K g C ~ ~ ~ g,, Repeent e Peod M t Stne t Geoet tne Dpng t Dpeent veto Aeeton veto Mode hpe Egenve o ng od to dgon egenve t Mod Mod tne Mod geoet tne Foe o oe veto Feqen Ang eqen Ptpton to Eetve Dn pton Regh dpng oeent Dpng to n gene qntte e denoted t e.g. o M O Ltd 5 8

9 O GSA veto qntte e denoted owe e pght hte e.g. dpeent t qntte e denoted ppe e, pght hte e.g. tne K O Ltd 5 9

10 O GSA Degee o eedo Atve degee o eedo Beoe the tne t eed t nee to dede whh degee o eedo need to e nded n the oton. he node n e tegoed oow: ntve the node doe not et. Non-tt the node not pt o the tte (e.g. oentton node). Atve the node pt o the tte. Lewe the degee o eedo n e tegoed : Non-etent th degee o eedo doe not et ee the node ndened. ntve th degee o eedo et t not ed (ondeed e etned node). Retned the degee o eedo et nd pt o the tte t t etned nd o t not tve n the tne t. Sve the degee o eedo ontned (thogh eng n gd ontnt, o epet eedo) to ove etve to te degee o eedo nd o t not tve n the tne t. Atve th degee o eedo tve n the tne t. n ettng p t o degee o eedo the oowng opeton e ed ot:. A the node e ed to e ntve.. Loo t eeent tthed to node to ee whh degee o eedo e eqed.. Reove the degee o eedo tht e etned nge pont ontnt o go ontnt.. Reove the degee o eedo tht e ve. 5. Reove degee o eedo tht hve no o tne.. Ne the degee o eedo. Font odeng he w n whh the degee o eedo e odeed potnt n eepng the e o the tne t to n. he ethod oeed n GSA e Geoet the degee o eedo e odeed ong veto. B det th veto ong the onget denon o the ode t n e djted the e. O Ltd 5

11 O GSA Revee Cth-MKee e the ndwdth ne o the e ne,. h oo t the onnetvt o the tte ng gph nd eode the degee o eedo o to ne the ndwdth. Cth-MKee to the Revee Cth-MKee ethod (t gene e opt). Appote n degee th ed o pe ove to vod eeve -n when tong the tne t Atve degee o eedo he degee o eedo e de tve ed on the eeent tthed t the node. he degee o eedo w depend on the eeent tpe: hee e ed n the te eow: Eeent B Atve degee o eedo pe node tnton Ce Rod Be nton png Rotton png M M wth net D pne te D pne tn Aet tnton + otton tnton + otton tnton otton tnton tnton + otton Bne oton: tnton An-Coo oton: tnton + otton D endng Mndn tnton + otton MC tnton + otton D he Mndn tnton + otton MC tnton + otton D w eeent D tnton + otton tnton O Ltd 5

12 O GSA Degee o Feedo wth no Lo Stne t poe to ontt ode nd nd tht thee no tne oted wth pt degee o eedo, ethe o tnton o otton. Fo epe ode de p o he eeent n gene pne degee o eedo w e gned pe node, t thee on tne n 5 o thee. hee e ne o ppohe to vod th poe. Geoet ed tot ontnt At eh node n the tte the tthed eeent e dented. A pedo tne t oted wth otton et p wth ve o one on the dgon the eeent t n tht deton o eo thee no tne. A o-dgon te e et to eo. he pedo tne tnoed nto the nod te (o the o-dgon te e, n gene, no onge eo) nd dded to nod pedo tne t. One th h een done o the tthed eeent n egenve n o the etng pedo tne ed ot to eve the pnp pedo tnee nd the deton. n o the pnp pedo tnee e e tht the pe-et tne toene then thoe degee o eedo e eoved o the oton nd n ppopte otton to pp to the tne t t the node toed. Stne ed tot ontnt h to the geoet ed tot ontnt t nted o ve o one o eo gned to degee o eedo the t tne t ed. he etng tne t the e wod et o etnng the whoe ode eept o the otton t the node o nteet. Agn n egenve n ed ot to eve the pnp tnee nd the deton. n o the pnp tnee e e tht the pe-et tne toene then thoe degee o eedo e eoved o the oton nd n ppopte otton to pp to the tne t t the node toed. At tne n he An tentve nd de ppoh to e e tht thee oe tne n deton ppng n t tne n the deton tht e not t. h done onttng the eeent tne t o he eeent nd then epng the eo on the edng dgon wth ve o /th o the n non-eo tne on the dgon. Sne th ppoh ntode n t tne te tht h not ph t hod e ed wth e. O Ltd 5

13 O GSA An Opton Stt & Stt P-det An he tt n onened wth the oton o the ne te o eqton o the dpeent,, gven the pped od. he pped od gve the od o oe veto,. he eeent ontte tne, K, o the te o eqton K When non-ne eeent h te nd tt e ntoded the n no-onge ne nd eoe tetve. GSA e nt tne ethod to vod eton o go tne t t eh teton. he te o eqton to e oved t eh teton Whee K ed oe o the pevo teton nd nt the hnge n dpeent o ent teton. h ethod oete eqe ge ne o teton to onvege to the oton nd th oet the dvntge o ontnt tne. o pove the onvegene peed eeton hee pped to the oton tteg he eeton hee ette the to o the ogn tngent tne to o ent tne ng the eve hnge n the dpeent. o vod nte ette the to, the eeton hee on pped t eve tentve teton. Stt P-det he tt P-det n to the tt eept tht t p done to te the oe n the eeent. Fo thee oe the deent tne n e ted. he tne o the tte n theeoe e oded to te ont o the odng nd the dpeent e then the oton o K K g he opton ow o A nge od e to e ed the P-det od e Eh od e to e t own P-det od e n the t e the t p o the n ove K PD PD K g O Ltd 5

14 O GSA o the P-det e: then o the od veto K K g oved o dpeent n the eond e thee one o oepondene etween P-det od e nd n e o K K g, then o eh e Mod K K, g he od dn n onened wth the ton o the nt eqene nd the ode hpe o the tte. A n the tt n tne t n e ontted, t n od dn n t o ontted. he ee vton o the ode then gven M K he nt eqene e then gven when K M he egenve poe then K M O o tpe egenve Kφ Mφ whee, e the egenp egenve (the dgon te e the qe o the ee vton eqene) nd the egenveto (the on e the ode hpe) epetve. Mod P-det he od P-det to the no od n t te nto ont tht odng on the tte w et t nt eqene nd ode hpe. n the e w tt P- det n t p ed ot o whh the deent tne n e ted. h ed to od the tne t o the egenpoe oded to K K φ Mφ g O Ltd 5

15 O GSA Rt An Oten the e o od n eqe ge ne o ode to e ted n ode to pte the dn htet o the tte. h pt the e when the hoont nd vet tnee o the tte e gnnt deent (whe the the e). One w to vent th poe to e Rt (o Regh-Rt) n whh ed ppote egenve. Whe thee e ppote the hve oe e htet. he egenve (nt eqene) e ppe ond to the te egenve he ode hpe e ne onton o the et egenveto he ne o Rt veto eqed to pte the dn htet o the tte gnnt e tht tht eqed o pope egenve n. Rt n ethod A et o t veto ed nt on gvt od n eh o the // deton. he eqent t veto e eted o thee wth the ondton tht the e othogon to the pevo veto. he pton tht we n get ppoton to the egenveto tng ne onton o the t veto. So o t veto Let X X nd the ppoton to the egenve, the ed oted wth the ppotng p, gven Kφ Mφ he Regh-Rt ethod eqe the ed veto e othogon to eh o the t veto, o X X K X Stttng o o ove gve o wth X KX X K M M MX O Ltd 5 5

16 O GSA K M X X KX MX h egenpoe then oved o the egenp, nd then the ppote egenveto e evted o X Rt t veto he goth pped n nge deton oow: Cete od veto oepondng to gvt od n the deton o nteet Sove o t veto KX * ove o * X X MX noe M Sove o ddton veto Bng KX * MX ove o j * X MX o j,, j * X * X X jx j othogone M j X MX noe M he poe n th e to detene t ng od (Een ng od) o the tte. he pton tht the deent tne t ne nton o pped od. he o the ng n to te the to tht n e pped to od eoe the tte e. At ng the detennt o the o the et tne nd the t deent (o geoet) tne eo. K K, g t Ung the pton o deent tne ne nton o od gve K g, t K g O Ltd 5

17 O GSA o the eqton K K g nd the egenve poe then Kφ K g φ Mode Stt An When tt ode -ondtoned ( epoted the ondton ne ette) t od e et odeng eo n the ode. hee eo od e o two tpe: Soe eeent not e we onneted o od e d etned, e.g. e eeent pnnng ot the. Soe eeent ve t oped wth othe eeent n the ode, e.g. e eeent o hot ength t ge eton. o detet h eo, ode tt n, whh qttve n ntended to eve the e o o ondtonng n ode, n e e. he n te the et nd get egenve nd oepondng egenveto o the tne t,.e. t ove the poe K o egenp,. Fo eh ode tht eqeted, eeent vt enege e ted o eh eeent n the ode. hee e dened oow. he vt tn eneg e e K e e o ge egenp whee nd vt net eneg ve o egenp, dened ve e e he vt enege n e potted onto eeent onto. p, o n ondtoned ode, hnd o eeent w hve ge etve ve o vt enege. Whee the ondtonng ed o d etned eeent, h eeent w hve ge etve vt net enege. the ondtonng o the peene o eeent wth dpopotonte ge tnee, then thee eeent w hve ge vt tn. he n o epot, n neng ode, the egenve opted. Fo the e o d etned eeent, thee gp n the et egenve. he ne o et egenp to e ened gven the ne o egenve etween eo nd the gp. O Ltd 5 7

18 O GSA Non-ne Stt An he non-ne tt ove wo ng the dn eton ethod. h n tetve ethod whh te poe o dped vton n te neent (e). h peton o the ept te-hto oton ethod. Ftto e nd net e opted o eh ee node. At eh e the oe nd oent whh eeent eet on eh node e ed o the ent dpeent. he ne nd ng eeton o eh node e opted o t tto nd net, dpng pped to the node ent ne nd ng veote nd the node ht nd otton e ted o the e. h poe epeted nt t tented the e o the oton h onveged (the oto-ne oe nd oent (ed) t eve ee node e e thn tget ve). the dpng too hgh o the tto e nd net o the node e too ge, the ht nd otton t eh e w e ve nd n e w e needed to heve et. on the othe hnd the dpng too ow o the e nd net e too, the ted dped vton eoe nte. he two e o n nte tte nd o nte ted dped vton n e dtnghed npetng the et. When the tte nte, the eeent oe hnge tte o e to e nd the ht o the node t eh e e ve ge t do not v gnnt o e to e. the ted dped vton nte, the oe nd nod dpeent ote wd etween e nd nee to enoo ve. he thd e o te ted dped vton onvegng to te oton n e eogned ee the ed nd the ht o the node deee ove o e to e. t hod e noted tht ve ew tte e o nte tht the do not event onvege to oton. Gene eond eet eoe opetve wth ge deeton nd ow the tte to eh oe nd o eq. Mt Sove Opton hee e two n ppohe to the oton o the te o eqton det oton nd tetve oton. he tetve oton n e pt nto one tht nvove the te t nd eeent eeent (EBE) ethod. Fo the det (t) oton thee ne o opton ve. he gene eqton to e ove n GSS K n e the t tht the t K et nd etve pe epoted n the oton. One the t toed the oton o the eqton tghtowd ttton n two pe. O Ltd 5 8

19 O GSA Spe Pe Det Sove he pe pe det ove e toge hee the pe det ove t toe the t n pe, tng tpe oe n CPU. h e e o the 'Pdo' ove o nte Mth Kene L. Pdo e MES ed eodeng o edng -n nd epo Bnh-Kn ed pvotng o pe LDL toton. Spe Det Sove he pe det ove nothe opton wth epot the pt o the tte te. he oton ethod to the tve on ove n tht the oton ethod det thogh the t ethod ed e oewht deent. he pe det ove e e o the ppote n degee (AMD) goth to ode the degee o eedo. h ethod e n nng the ont o when tong the te. he t tong e pe LDL goth. hee goth hve een deveoped t the Unvet o Fod CSE ( Conjgte Gdent Sove he onjgte gdent ove epot the pt o the t to the eepng n nde o the non-eo te n the t. h en tht the tong whh pode -n no onge n e. Conjgte gdent ove wo wth peondtone o e nown peondtoned onjgte gdent (PCG) ove to pove the ondton ne o the t edng to ette onvegene. he gnnt deene wth the PCG tht t tetve. n theo the oton w onvege n no oe teton thn the ne o degee o eedo n the oton, howeve ondng n the ton en tht th nnot e gnteed. Moeove the to get the oton to onvege n h e ne o teton o the peondtone ed to gve te onvegene. he ne Jo peondtone eoended n GSA. he onjgte gdent ethod nd the e o peondtone e deed n n tet oo nd the e deted to the ogph o the noton. Atve Con Sove he tve on ove on e pt e o the pt o the t. he tne t toed ng ne toge on the ove dgon eeent nd tht et eow the ne e toed. Soe o n o the ente wthn the ne e non-eo howeve n the toton thee -n whh ed to thee ente eong non-eo. h tpe o toge wo we wth n tve on ove whee the toed t K LDL whee the (tnpoe o the) owe tnge e ne poe. L nd the dgon D n e toed wthn the O Ltd 5 9

20 O GSA Long e An Long te n not deent tpe o n h. nted t n n whee eep ten nto ont o onete te. A eep oeent peed nd th ed n the n to gve eetve E nd G ve o the onete te. E G e e E G Dn Reton Sove Dn eton n n ethod o non-ne tt oded tte ng det ntegton dn n tehnqe. n dn eton n t ed tht the od e tng on the tte dden, theeoe the tte eted to vte ond the eq poton nd event oe to et on the eq poton. n ode to te the vton, nd net e needed o eh o the ee node. n dn eton n, t nd net e ed whh e ontted odng to the nod tnton tne nd otton tne. thee no dpng pped to the tte, the oton o the tte w go oeve, theeoe, dpng eqed to ow the vton to oe to et t eq poton. hee e two tpe o dpng: vo dpng nd net dpng. Knet dpng n t dpng whh w epoton the node odng to the hnge o te net eneg. Dpng hee e two tpe o vo dpng, one vo dpng nd one t vo dpng. Vo dpng w pp the peed (o tot eeted) peentge o the t dpng to the te. At vo dpng w t ede the veot t eh e the peed (o tot eeted) peentge o veot n pevo e. One t vo dpng ed, net dpng w e ded tot. B ppng one o oth o thee t dpng ethod, the vton w gd oe to et t the eq poton nd th w e the oton gven dn-eton n. he tte eow how the eet o vo dpng on the dn eton n poe. he oton o the tte event oe to et t the tt eq poton vo dpng pped. he poe wth vo dpng tht t not n e t to ette the t dpng o the tte. O Ltd 5

21 O GSA Knet dpng neted to onventon onept o dpng ed n tt dn n. t n t onto to ede the gntde o the vton n ode to e t oe to et. t ed on the ehvo o tte wth on one degee o eedo o the vton o tpe degee o eedo tte n nge ode. Fo thee e t nown tht the tte net eneg ehe t the tt eq poton. he tte net eneg ontoed n the n t eh te neent. he Knet eneg nee the node ppoh eq poton nd tt to deee one the O Ltd 5

22 O GSA node e w o eq poton. One the net eneg tt to deee, n ette o the eq poton o the node n e ntepoted o the pevo nod poton nd net enege. At th pont the net dpng poe pped. he vton topped nd the node epotoned to oepond to the net eneg. Ang the etonhp etween tt net eneg nd te po, then the oent t whh the net eneg peed n e ted. Bed on the pevo nod dpeent nd otton, the eq poton o the node n e etted. Ate htng the node to the opt poton, the n w ett gn eettng the te, peed nd eeton to e eo. Sne t ne tht tpe degee o eedo tte w vte n nge ode, t poe to nd the eq poton jt ehng the net eneg o the tte one o twe. Nevethee, pevo epeene h hown tht the e o net dpng ve eent n ehng o the eq poton n dn eton n. Soton Poe he oowng tep e ed n dn eton n.. Copte eqvent nod oe nd oent. n th poe, ee od e onveted nto nod oe o oent. hee e the oe tht ntte vton.. Contt d nd d net o the netned (tve) node odng to the tnton nd otton tne o the ee t the node. Copte the eeton, peed nd dpeent o eh node t eh e.. Copte new nod poton nd otton o eh node t eh e; pdte the nod tne nd ee oe tng on the node. 5. Che the oe nd oent ed t eh node t the ent poton.. no ed eeed the t, the n ondeed to hve onveged nd the n poton ondeed the eq poton o the tte. 7. n ed not ted, the n ontned to the net tep. 8. Copte the tot net eneg o the tte. the net eneg t e ovehoot the, t ondeed tht the eq poton h een ped. heeoe, node w e e-potoned o tht the e oe to the eq poton. Reet the peed nd eeton to e eo nd et the tte tt to vte gn o the new poton. 9. Ate n h een onveged, the eeent oe, oent nd tee e ted odng to the n eq poton o the node. O Ltd 5

23 O GSA Ftto e nd net o peed p nd p dn eton n, tto (d) e nd net the thn e e nd net e ed n dn eton n. he tto e nd net e geneted tot n the ove. Howeve, tto e nd net n e djted pe nd dng n ppng d nd net to nd/o d nd net powe. he tto e nd net ted the pog e degned to e enogh o onvegene to e eon t t ge enogh to pevent node htng too h n one e, whh e the oton ethod to eoe nte. o th end, t og to te the tto e nd net popoton to the nod tnton tne nd otton tne epetve. Fo pevo epeene, t ond tht the et ette o the tto e nd net e two te the nod tnton tne nd otton tne epetve nd the e ted oow Ftto o node = o tnton tne o the eeent onneted to the node Ftto net o node = o otton tne o the eeent onneted to the node Conto pete he tetve dn eton poe ontne nt onvegene te (nned nod oe nd oent) e et. th doe not hppen, the teton w ontne o ne o e, o n te n nte. t ot poe to heve % te et n non-ne n, o n epte ed (toene) oe nd oent hod e peed. he ed e ote o etve. etve ed eeted, the t oe ed nd oent ed t eh node e ted o whee n n, e oe ed nd oent ed epetve, e etve oe ed nd etve oent ed epetve the o the tot poed od ndng oth nod nd ee od n the ne o node n the tte O Ltd 5

24 O GSA thee no poed od, e.g. tte jeted on to ppot etteent, the oe ed nd oent ed e ted o whee.. K, K K n K n e the o nod tnton tne nd otton tne o the node n the tte. n ote ed eeted, the peed oe ed nd oent ed w e ed n the n. Be A oe he oe o e t ted p EA whee p the pe-te oe. th oe gete thn the ed pt n tenon t et to the ed pt n tenon; t e thn the ed pt n opeon t et to the ed pt n opeon. he ed pte e, ten, op A A, ten, op whee, ten the tene ed te nd, op the opeve ed te he tn ted dtne etween node nteedength nteedength he nteed ength the nt dtne etween the end node (o the nt ength peed the e) oded o tepete. Be She oe nd toon he he od o e ed to e E G O Ltd 5

25 O GSA he he tn ed he oe ondeed to e no ove the whoe e o pne no to pnp. he he tn etween pnp nd the o e ten, G G nd the eetve he te ten V A V A Whee e the he to ong the pnp oet to the o e /. he nge whh e twted ot t o p ondeed to e M GJ Be A oe e tne nteton endene eet e to e ondeed the endng tne o e oded odng to the od ng Lvee tt nton. Fo ontno/ontno e wthn the et nge the endng oent t end ten E S SC eqton A M S nd SC e deved o ee S! 5! 7!!! 8! 8 9! 8! SC!! 5! 7! 9! 8 8!!! whee M.R. Hone & W. Mehnt he Stt o Fe Pegon 95 O Ltd 5 5

26 O GSA E nd opeon potve. Fo ontno/pnned e wthn the et nge the endng oent t end ten M E S C M S nd C e deved o ee S!! 5! 7! 8 5! 7! 9!! 5! 7! 9! C 8! 5! 7! 9! eqton B whee M the oent t end nd opeon potve. hee ee e ed to pe-te S, SC, S nd C o ten ve o K. Dng ton e ve o S, SC, S nd C e ntepoted o the ent ve o K. Be Yedng Fo n ept dened eton the endng oent ot the pnp e e ted to the oowng ve, ten op A p.5, Fo eq ed tee th good ppoton to the pt endng oent pt. he oe opted ove. he ton o the oe nd o the endng oent ot the pnp e e peoed ndependent. Be e ed to ehve et p to the tng oe o endng oent. h pt ehvo on odeed wth n degee o e o e whee ethe on oe e gnnt o on endng ot one pnp gnnt, the tene nd opeve ed tee e nd the tnton etween t ed nd ptt n e gnoed. O Ltd 5

27 O GSA the endng oent t one end o e h een ted to the pt oent pt, the endng oent t the othe end otned ng eqton B ove M E S C M p h endng oent n tn ted to the pt oent pt. Fo e wth tndd hpe eton nd peed ed te, the pog te the tene nd opeve ed oe o the eton, whh e ten to e, ten, op A A, ten, op he pog then ontt oo p te o eh hpe eoe the oeneent o ton e. he oo p te ontn ve o endng oent ng t ed (.e. the owet endng oent t whh wth et ehvo ed te ttned n tenon o opeon t one pont n the eton) pt endng oent (.e. the endng oent wth the eton on one de o the net t the tene ed te nd on the othe de o the net t opeve ed te). o nne ve o oe eq ped etween the tene nd opeve ed od o the eton. nge o pped oent t ntev o 5 degee o to 5 degee wth eeene to the pnp tht neet to the e o. Dng ton e the pog opte the endng oent t t ed nd the pt endng oent n e o the ent oe nd nge o pped endng oent ne ntepoton etween the ve n the oo p te (oth endng oent e o oe eo when the oe eq the tene o opeve ed oe, nd the oe o e ted to ve etween the tene nd opeve ed oe) he pog nt te the oe nd endng oent t eh end o e ng et ehvo. the net endng oent t the t end gete thn the oent ng t ed then the endng oent oded odng to the o M M. 5 M M eqton C the endng oent t the t end o e oded, the endng oent t the eond end otned ng eqton B M E S C M,od O Ltd 5 7

28 O GSA the endng oent t the eond end eeed tht t t ed, t oded n the e w w the one t the t end, nd the endng oent t the t end otned ng eqton B M E S C M,od th endng oent gete thn the oent ng t ed, the whoe poe epeted nt the endng oent ee to e oded. Eqton C eqvent to hvng the tne o e t t ed. F- Ste optton he wp nd wet deton e ed to e pepend. he det nd he tn e t opted o the wp nd wet deton ng no tn ove eh tnge nd the tee e ted o the eqton E E A E E B G whee the wp deton nd the wet deton. he pnp tee e then opted. tnge et to te no opeon, opeve pnp tee e et to eo. he oe eeted the tnge e ted o the pnp tee. Eqton A nd B e otned ewtng E nd E Poon to o pe wp te dened n the te te., the Poon to o pe wet te ted o E E no he od peed t ted O Ltd 5 8

29 O GSA G.5 E E.5 Fo otop te whee E E E nd th eqvent to G E h oepond to et ehvo. Apped Dpeent nd Lgnge Mtpe he eqton o ne tt n e K he pped dpeent e pped ng Lgnge tpe. he onept tht the tte t n e oded to pp dpeent ondton K ~ e e λ Whee e the Lgnge tpe ed to enoe ontnt ondton nd ~ e the pped dpeent. Epndng the t eqton gve K e λ ~ e o o K eλ e K eλ ~ e K ~ e K eλ ˆ Kˆ λ Sovng th eqton gve the Lgnge tpe, whh n then e ed n K eλ to ove o the dpeent. O Ltd 5 9

30 O GSA Ae Ae n e ethe Cten, nd o phe. he oodnte n thee e: Cten,, Cnd,, Sphe,, An dened thee veto epetve o tpe. hee dene the oton nd oentton. he veto n veto pontng n the potve deton. he pne veto n veto n the pne o the tht not pe wth the veto. he e e then ontted oow: pne pne he te the Go Cten te, no eeed to the Go te. A othe te e oted etve to the Go te. Go deton e gene denoted X, Y nd Z to dtngh o othe, oe gene deton whh e, nd. A the e te n GSA e ght hnded e te. O Ltd 5

31 O GSA Rotton ot the e oow the ght hnd ew e Copote Copote S Copote e ppoted on tee deng. hee n e odeed od wth djtent to the n-pne (t p) nd endng (t ) thne. Fo nt wdth the e o A onete (A ) nd tee (A ) e nown e the eond oent o e ( nd ) nd the E ve (E nd E ). Reeng to the onete the p te the eetve e A e A E E A And the eetve thne (n-pne) t p A e A A E E A A Gve the entod o the onete ( ) nd tee deng ( ) the entod o the opote eton then e A E A E E E A A O Ltd 5

32 O GSA O Ltd 5 nd the eetve eond oent o e ( e) e e e A E E A And the eetve thne n endng A E E A t e e e

33 O GSA Eetve Et Popete n ode to p ton t poe to detene etve et popete o eton. he pet o thee the e. Conde eton wth oth onete nd tee wth e A nd A epetve. he tnee e A E A E And the tot tne then A E A E o p ton we n hooe eeene te. So o onete eeene te A e E A E A E o A e A A E E Moe gene o oeton o oponent wth eeene eton A e E A E e Fo eton de o tpe oponent the eetve entod dened e A A e e A o popete eetve endng popete n e dened (owng o the deent entod) e A E e e E Condton Ne ondtonng e whe ovng ne eqton o the tpe O Ltd 5

34 O GSA K o gven od nd tne K n () ne tt n, ppoton e ntoded n the oton ee ton e ed ot n nte peon thet. h eoe potnt when K -ondtoned ee thee pot o thee ppoton edng to ge eo n the dpeent. he etent o thee eo n e qnted the 'ondton ne' o the tne t. he ondton ne o t (wth epet to nveon) ee wot-e o hnge n {} oepondng to hnge n K o. t n e ted ng the podt o no o the t te the no o t nvee. K K K whee odnte t no. K et t, the ondton ne κ(k) n e hown to the to o t nd n egenve nd. n K n he n ve o K nd the ve nnt. the ondton ne, the opted oton ee (.e. ee ppoton to the te oton o K. the ondton ne ge, (.e. the t ot ng) the et nnot e tted. GSA opte owe ond ppoton to the -no ondton ne o K nd th epoted pt o the ove otpt. h n e ed to evte the o the oton oth qttve nd qntttve. he (qttve) e o th o n the ne o dgt o n n og n gene n tne t wth ondton ne ove 5 n pode et wth no t. An et poded o te wth ondton ne gete thn t e teted wth ton. Whee ode -ondtoned, Mode Stt n n hep detet the e o ondtonng. Fo gven ondton ne, we n o opte the etve eo n. he. etve eo n dened the to o no o eo n to,.e. e O Ltd 5

35 O GSA Gven t K wth ondton ne, the etve eo n when ovng K whee the ontnt 'nt-ondo' nd eq to.e- o doe peon otng pont ne. he etve eo opted nd epoted pt o ove otpt. de, th hod e, ne etve eo ndte ee oton t, the etve eo gow pd. GSA te the ondton ne ng Hgh nd e' o -No ondton ne etton goth. hee e epoted n the An Det otpt. Contnt & Contnt Eqton Contnt eqton o the o the deent ontnt tpe n GSA: Jont Rgd ontnt Contnt eqton ed ntee Contnt Eqton he o o ontnt eqton, nd ed to te degee o eedo n the ode. Jont Fo jont th eoe et o eqton o the ned degee o eedo o the o Rgd Contnt Fo gd ontnt thee e et o ontnt eqton whh epet the geoet o the ontnt. So o nge ve node the ontnt eqton e O Ltd 5 5

36 O GSA O Ltd 5 w v w v w v w v whee the δ te e o ed nd o pnned gd ontnt. Deent te n the t e dopped o eded ontnt tpe. he two ot oon pe tpe e pne nd pte ontnt wth eqton (o the e) w w v v o n pne ontnt v v w w o pte ontnt. ed ntee ed ntee e opoed o te nd ve e. nten thee e oen down to node on the ve de nd eeent (e) on the te de. he node on the ve de e onneted to the djent te e v et o ontnt eqton. he (,) oodnte o the node etve to the te e e ethed nd then the hpe nton e ed to ontt et o ontnt eqton h,, n the e o qd- e th epnd to,,,,, whh o the ontnt eqton. h epeted o the dpeent deton. he pe e the dng degee o eedo. A the D eeent hve ethe no dng eedo o one whh n wo qte o. Fo th degee o eedo the otton ned to the tnton o the D eeent. the node nten to the eeent e the otton o the eeent whoe. the node on the edge e the otton o jt tht edge.

37 O GSA O Ltd 5 7 Fo eh eeent node dene veto v o the ve node poton to the node n the pne o the eeent. Let v v,, tn v he dpeent t the ente o the D eeent h hen the otton o the node t dtne nd nge o n,,,, So otton t (,) h o n,,,,, O epndng h h o n o n,,,,, j j j j j j h h h h o n o n,,,,, Deton Cone Deton one ontn noton tht ow tnoton etween o nd go et. Gven et o othogon nt veto the deton one dened D An veto o teno n then e tnoed o o to go thogh g g D D t t D v v he nvee tnoton e the tnpoe o the deton one D t D t v D v g g

38 O GSA Dn Repone An Hon An Hon n ed to te the et tte epone to hon (nod vng) od t ted tte. h done ng od pepoton. he dn eqton o oton : M C K pn t Whee p epeent the pt dtton o od nd the te vton. Fo the ode hpe et o od dn n, the nod dpeent, veote nd eeton n e epeed Φ q Φ q Φ q whee q, q, e the dpeent, veot nd eeton n od (geneed) oodnte, o the ode ned. Stttng thee n the ogn eqton gve MΦ q CΦq KΦq pn t Pe-tpng eh te n th eqton the tnpoe o the ode hpe gve Φ MΦq Φ CΦq Φ KΦq Φ pn t Aodng to the othogont etonhp o the ode hpe to the t nd the tne t nd o ng the ode hpe e o othogon to the dpng t (e.g. Regh dpng), th eqton n e eped et o noped dn eqton o oton hown eow. Settng φ Mφ q φ Cφ q φ Kφ q φ pn t O Ltd 5 8

39 O GSA O Ltd 5 9 p φ ˆ Cφ φ ˆ Kφ φ ˆ Mφ φ ˆ p hen the noped eqton n e epeed n gene o oow t p q q q n ˆ ˆ ˆ ˆ whee the te e. Sovng th eqton eqvent to ovng nge degee o eedo poe. Fo the nge degee o eedo poe jeted to hon od, the dn gnton to o the dpeent o ode n ope ne notton,, whee A B A B B A A, nd θ the nt eqen o ode. he dpeent, veot & eeton o ode n the od oodnte e ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ p p q q p p q q p p q Stttng gve the t nod dpeent, veote & eeton t the ted tte o the oed vton q φ φ q φ q Ate otnng the nod dpeent, the eeent oe nd oent et n e ted n tt n.

40 O GSA Peod Lod An GSA peod od n to te the et tte epone to gene peod od t ted tte. Mod pepoton ethod ed n GSA peod od n. he dn eqton o oton jeted to peod od M C K p t Whee t hon od nton. Ung Foe See, the peod nton o te n e epeed ne o ne nton t H h h h n t whee h e the Foe oeent (o dn od to) dened the e nd the peod o the peod od eqen nd H the ne o Foe (hon) te to e ondeed. Stttng n the t eqton we n ewte ne o dn eqton o oton jeted to hon od: M C K p h h n t he epone o th n e oved ng hon n o eh o the hon od h,, then the epone o the peod od n e ted ng qe oot o the qe (SRSS) R H R h, h Lne e-hto An Lne te hto n ed to te the tnent ne tte epone to dn od o e eeton ng od pepoton. he dn eqton o oton o tte jeted to dn od M C K p t the etton e eeton p Mv whee v n nene veto tht epeent the dpeent o the e etng o tt ppton o nt e dpeent dened the e etton deton nd the oe de to the e eeton t g t O Ltd 5

41 O GSA o e the et (ode hpe) o od dn n, the nod dpeent, veote nd eeton n e epeed n od oodnte Φ q Φ q Φ q hen ettng gve ˆ ˆ φ ˆ pˆ φ φ φ Mφ Kφ Cφ p ˆ q ˆ q ˆ q pˆ t h gve nge degee o eedo poe tht n e oved ng n o the det ne n ethod h New o ent deene (New ed n GSA). hee e h eqton tht e oepondng to eh o the ode o the od dn n. Spepong the epone o eh o the one degee o eedo poe the tot epone o the tte n e ted o φ q φ q φ q Foot An Foot n (o n, oot nded vton n) ed to te the et vet nod epone (eeton, veot, epone to et.) o tte to hn oot od (etton). he hn oot od Foe See, the peod oot od n e epeed : t G H h h h n t whee G the od weght o the ndvd, nd t e ten peod od. Ung to h e the Foe oeent (o dn od to), the t ve o dn od to n e ond o eeene, 5 nd n the ogph, the peod o the oot (nvee o wng eqen) nd H the ne o Foe (hon) te to e ondeed, ed o wng on oo ng CCP- ethod, ed o wng on oo ng SC ethod nd ed o wng on t. Ate ttng the tt weght o the ndvd (ne t doe not v wth te nd doe not nde n dn epone), the dn pt o the oot od e the o ne o hon od O Ltd 5

42 O GSA t G H h h h n t hee e two dtntve epone o the oot etton, the eonnt (ted tte) nd tnent. the n nt eqen o tte hghe thn te the hghet wng eqen (ee eeene ), the eonnt epone no not eted ne the nt eqene o the tte e o o the wng (etton) eqen, theeoe the tnent epone no n onto, othewe, the eonnt epone po n onto. Both eonnt (ted tte) nd tnent ne e ondeed n GSA oot n, o the epone w w e pted. Reonnt epone n A oot od e opoed o ne o hon od (oponent), hon n ed to get the epone o eh o the hon oponent o oot od nd then to oned the to get the tot epone. Fo one o the hon oponent h o the oot od n eqton ove nd the gven wng eqen, the oowng dn eqton o oton n e otned M h C h K h G h h n t whee nt veto ed to dene the oton o the hon od. A the oponent n th veto e eo eept the te tht oepond to the vet deton o the node jeted oot od. Sne the ne o oot ted nd the eonnt epone o the eqton ove not w e heved, edton to h, o the dn gnton to needed to ont o th non- eonnt epone. he edton to n e ted o h, N e dpng to o ode nd N. 55hW Whee W the ne o oot. wth h the hon od ne nd Appng th edton to to the dn gnton to n Hon An, th eqton n e oved ng the ethod deed n Hon An heo eton. Repetng th n, the epone o the othe hon od o the oot n o e otned. he nteeted et o th n e the tot vet eeton nd the epone to o hon od o the oot. he tot vet eeton ten the qe oot o the o qe o the eeton o eh o the hon ne. he epone to o eh o the hon od the to o the nod eeton to the e ve o the Root Men Sqe eeton gven n eeene 5 hown eow. h tot epone to then ten the qe oot o the o qe o the epone O Ltd 5

43 O GSA to o eh o the hon od. Aodng to th, the tot eeton nd epone to n e ted o H h, h H h, h H h, h w.5 whee the eeton t node the eeton t node the etton o hon od h, h H the ne o hon oponent o the oot od ondeed n the n the epone to t node, the epone to t node the etton o hon od h h w the eqen weghtng to nd t nton o eqen Fo tndd weghtng to ee e o BS8. nent epone n he tnent epone o tte to oot oe hteed n nt pe veot oowed deng vton t the nt eqen o the tte nt the net oot. A the nt eqene o the tte ondeed n th n h hghe the hghet wng eqen, thee no tenden o the epone to d p ove te t doe n eonnt epone n. he epone w e t the egnnng o eh oot. Eh oot ondeed n pe to the tte, odng to eeene 5 & 9, the degn pe n e ted o When wng on oo (Conete Cente/Ap ethod) de, 5.. When wng on oo (SC P5 ethod) de,.. Q 7 When wng on t (Conete Cente/Ap ethod) O Ltd 5

44 O GSA de, 5 5 When wng on t (SC P5 ethod) whee de, de, the degn pe o ode n NS the wng eqen n H the nt eqen o the tte n ode n H Q the weght o the we n N Fo th pe, the pe veot n eh ode gven vˆ e,, de, ˆ nd the pe eeton n eh ode gven ˆ vˆ e,, de, ˆ whee vˆ the pe veot n ode the oot pe â the pe eeton n ode the oot pe e,,, e the vet dpeent t the etton nd epone node epetve n ode ˆ the od n ode he vton o the veot wth te o eh ode gven v t t vˆ e n t nd the vton o the eeton wth te o eh ode gven: t t ˆ e n t whee the dpng to oted wth ode O Ltd 5

45 O GSA he n veot nd eeton t the epone node e the o the veote nd eeton o the ode M tht e ondeed v t t M M v t t h gve the pe veot nd pe eeton. he oot en qe veot nd oot en qe eeton n e ted o the peod o the oot v RMS RMS v t t dt dt he epone to t te t (t o to nd the peod o the oot od) n e ted o whee R t.5 M t w w the eqen weghtng to oepondng to the eqen o ode he n tnent epone to, ed on the oot en qe pnpe, gven R R t dt O Ltd 5 5

46 O GSA Eeent e he oentton o eeent depend on the eeent tpe. hee e epeented the deton one ed on the eeent, nd deton. Seton eeent Seton eeent nde e,, od, te nd tt e dened two node otng the end o the eeent. he o the eeent ong the o the eeent (tng ont o n oet) o the t topoog te to the eond. he denton o the eeent nd e then depend on the eeent oentton, vett, oentton node nd oentton nge. he eeent ondeed vet n GSA the eeent wthn the vet eeent toene. Non-vet eeent n oentton node not peed, the eeent o non-vet eeent det to ng n the vet pne thogh the eeent nd deted n the potve ene o the go Z deton. he eeent othogon to the eeent nd e. he eeent nd e e otted ot o th det poton the oentton nge. Vet eeent n oentton node not peed, the eeent o vet eeent det to eng pe to nd deted n the potve ene o the go Y. he eeent othogon to the eeent nd e. he eeent nd e e otted ot o th det poton the oentton nge. O Ltd 5

47 O GSA Oentton node n oentton node peed, the eeent - pne dened the eeent nd veto o the t topoog poton to the oentton node, h tht the node h potve oodnte. he eeent othogon to the eeent nd e. Speng n oentton node ovede the vet eeent nd non-vet eeent denton deed ove. he eeent nd e e otted ot o th det poton the oentton nge. Oentton nge he eeent nd e e otted o the det poton ot the eeent the oentton nge n the deton oowng the ght hnd ew e. h o egde o whethe o not the eeent vet nd o whethe o not n oentton node peed. Spng eeent he denton o the eeent e o png depend on the png eeent. Fo two-noded eeent wth non-eo ength the denton o the o the e o e eeent. the eeent gond png o h eo ength the te et n the png popet. the te o then the e o oenttng eton eeent pp. the te go o e dened, thee e ed nd the topoog, oentton node nd oentton nge e gnoed. Ue dened e n e Cten, nd o phe. Gonded png nd eeent he denton o the eeent e o gonded png o depend on the te et n the png o popet. the te go o e dened, thee e ed. O Ltd 5 7

48 O GSA the te o the eeent ten go. Ue dened e n e Cten, nd o phe. Ce eeent Ce eeent t on n the deton, o on the dened oowng the e denton the o e eeent. Ln eeent he o e o n eeent e the e thoe o the te node. D eeent e D eeent o e e dened ethe eeene to n et o topoog. h detened the te dened n the D eeent popet. the te go o e dened then the peed et ed. the te o then the topoog denton pped. Ue dened e n e Cten, nd o phe. p denng D eeent o e eeene to n et et n oe ontent o e n the eh. he o e o t D eeent e hoen o tht the pne o the eeent the o - pne. he no to the eeent dened n Whee n oet, the oodnte on pont on the eeent,.e. the oodnte o the node,, p o, t tht topoog poton., o D eeent e dened et the D eeent popet et to othe thn 'o' then the peed te pojeted on to the eeent. Fo Cten e the o the et pojeted onto the eeent n n n n he eepton to th e when the o the et wthn o the eeent no n whh e veto o n nte dened O Ltd 5 8

49 O GSA O Ltd 5 9 n n n n h et then otted ot the eeent no eqvent to n oentton nge o 9. Fo Cnd nd Sphe e the o the et pojeted on to the eeent to eoe the o. n n n n opoog denton o D eeent e the D eeent popet et to 'o' the o nd e e ed on the topoog o the eeent. v n v n n n oentton nge dened thee e e otted the oentton nge n potve deton ot the eeent. D eeent e D eeent o e e dened ethe eeene to n et o topoog.

50 O GSA Updted eeent e n geoet non-ne n the e o the eeent t deo wth the eeent. h h to eove the deene etween the ogn (ndeoed) ongton nd the ent (deoed) ongton. Fo D eeent the deoed deton one n e epeented new veto ed on the deoed poton o the end o the eeent nd the vege otton o the eeent ot t -. Fo D eeent the ndeoed ongton n e epeented deton one ed on the,, t e. D t O Ltd 5 5

51 O GSA O Ltd 5 5 he deoed ongton t n e epeented deton one ed on the deoed t,, e. t D he e deton one e D n then e pdted ng e e D D D D Eeent B nd Rod Eeent he eeent tne K AE he t M A And the geoet tne K F g he od eeent tne

52 O GSA O Ltd 5 5 K GJ AE GJ GJ AE AE Ce, e nd Stt Eeent hee eeent e vnt on the eeent. Ce nd te eeent n on tene oe, whe tt eeent n on opeve oe. he tne t o te nd tt dent to tht o eeent. he non-ne pet eng pt o the ove, oton poe. he tne o e eeent to eeent t the AE eped tne te whee the e tne e AE

53 O GSA O Ltd 5 5 Be Eeent he e eeent tne E GJ A E GJ E GJ A A E K hee e oded o he e oow j A A GA E,,, E E E E E E E E he t

54 O GSA O Ltd M A J A J A J A And the geoet tne K F F V V A F F M F F M F F V F F F V F F V V A F M M V V A F F M F F M F F M F F M F g whee

55 O GSA Non-et Be Seton n e wth et eton the endng popete depend on on the nd te. h e oded n the o the deeton n the deton o the odng. When the eton not et nd oded n the o deton thee oponent o deeton othogon to the odng. h ee the endng popete depend on nd., B ottng the eton to pnp e th o te n e otted nd the e oded n the o v (pnp) the deeton n the deton o the odng. n th e the tne t o the eeent ted ng the pnp eond oent o e nd then otted nto the eeent o te. Fo e wth non-et eton the e t onde the e etned (o tht deeton e ontned to e n the deton o the odng) o t w t n oton (etng n deeton othogon to the odng). the e to t ontned the e hod e the gnoe opton. n th e the nd ve e ed nd the ve dded. the e to t n oton the e hod not e the gnoe opton. n th e the tne t o the eeent ted ng the pnp eond oent o e nd then otted nto the eeent o te. n th e GSA e tht the ve the e the ve. o whheve o o oet to the, nd ewe o the Whee the e h peed eton ode on the o the ve thee no w to tne thee ode to the nd v deton. n thee tton gnoe t e ed. A toge nd tndd eton eept nge e et. Ept eton e ed to e dened h tht the pnp nd o e onde o thee no. Geoet (peete nd ne egent) eton e ed to e non-et. v O Ltd 5 55

56 O GSA O Ltd 5 5 Spng Eeent Spng eeent n one o eve tpe. he gene png h degee o eedo. Fo ne png the gene o o the tne t K non-ne png e eqed thee n e geneted gnng te ve (oe/dpeent o oent otton) to eh o the degee o eedo. A / toon png Fo n o toon png on the o te e peed, the et e ed to e eo. Spng t Fo gond png et o tne te n e dened o the ppe tnge. h ow nteton etween nd endng te. he tne t then o the o,,,,,,,,,,,,,,,,,,,,, K

57 O GSA Copeon-on png Copeon on png eeent e n nonne png eeent. hee eeent hve no tne when jeted tene odng/dpeent. Unde tene odng thee eeent w ete gp. enon-on png enon on png eeent e o n nonne png eeent. hee eeent hve no tne nde opeve odng. Lo-p Lo-p eeent e o n png eeent wth peed nt gp. Lo-p eeent n e ved the onton o opeon on nd tenon on png wth nt gp. hee png eeent do not oe n tne whe the dpeent e wthn the peed gp. Potve Gp w oe no etne n the tenon de nd ve ve. Both potve nd negtve gp hve to e peed potve ve n GSA. O Ltd 5 57

58 O GSA Gp Copeon on -ve Gp Conneto Conneto eeent e ne et png eeent. hee eeent onnet p o node n tnton we otton. he e o the tne t nd the e w e tot ted ed on the tne o the ondng eeent. he etng tne ge enogh to pode negge dpeent nd t the e te t w vod the ne ntte. Gp eeent Gp eeent e the opeon on png eeent wth nt gp. hee eeent w hve eo tne n the n whe the dpeent e wthn the peed gp. he tne n othe deton (o nd deton) e gnoed. hee eeent e e n ontt poe ton dng not onen. O Ltd 5 58

59 O GSA O Ltd 5 59 Fton eeent Fton eeent e thee deton tnton png eeent ontng o one nd two tnton deton. n deton, thee eeent wo Gp eeent. n tnton deton thee eeent ehve et pt eeent. Pt t ted ng oo ton w,, Whee the oe n deton ted o the gp eeent. Spng e ed to e e. Dpe Eeent Dpe eeent e eeent wth no tne t wth vot, o thee do not o tne te t nted dpng t. he gene o o the dpng t C

60 O GSA Fo n o toon dpe on the e eo. Dpe e ed to e e. M Eeent o te e peed, the et e ed to M eeent n hve on nd net. n the no e the t M t ode e nded the t eoe M net teno qntt wth the oowng te whee the te n the net teno e dened whee V V V, dv V dv V dv dv, e the oodnte o the ente o. non-eo ve e peed o the o-dgon te, t potnt tht thee e ontent wth the dgon te. th not done the pnp net ve n eoe negtve. he net t neve oded o deton. D Eeent An eg hped ontn dened ond nd e o odng h to e dvded nto eh o nte eeent. he e nd hpe o the eeent hoen o tht the ppote tne ped the nte eeent oe enogh to the t tne o the ontn n tht egon. h the nte eeent e nd hpe w e detened the V dv dv O Ltd 5

61 O GSA tpe o eeent eng ed, the hpe o the ond n egon oe to the ond, the odng pped nd the epeene o the e. Eeent tne o genete tne t o vne qdte o tng eeent new ppoh t e ed. Mot nte eeent ode ed n ppoh ed on opet o eeent. n n opet eeent the eeent dpeent e ntepoted n the e w the geoet, eg pne te eeent. n pepet o degenete opet eeent the ntepoton on the geoet o hghe ode thn the ntepoton o the dpeent, eg pte eeent. n pet eeent the ntepoton o the geoet o owe ode thn the ntepoton o the dpeent, e.g. n eght noded tght ded qdte eeent, whee deent geoet ntepoton nton ed o the geoet o tht o the dpeent. he te opet oten ed gene te to ove thee eeent tpe. Fo pne te poe, we n eth te t C tht ete te nd tn. he dpeent n o oodnte te e,v O Ltd 5

62 O GSA the tn e ε,,, nd the tee e σ,,, Fo n et-otop te the te t E C p whee E, e the Yong od nd Poon to epetve. Note tht thee n ot o pne tn, whh we n gnoe t p no pt n the eeent oton. he tn e dened n te o the dpeent v v he pet eeent to onde e the noded nd 8 noded qdte eeent, o whh the noded eeent n e ondeed pton o the 8 noded eeent. A tp 8 noded eeent hown eow. he eeent h n t o oodnte te ed on the oton o the node nd the eeent popet (, ), nd nt (vne) oodnte te (, ) ed on the topoog o the node. O Ltd 5

63 O GSA We n et p ntepoton nton to ntepote the geoet oow, h, whee the h e the ntepoton nton dened eow. hee ntepoton nton e hoen o tht h when node A the eeent e opet we e the e ntepoton nton o the dpeent o the dpeent n the eeent eted to the nod dpeent, h, O Ltd 5

64 O GSA O Ltd 5 o evte the tne t we need the tn-dpeent tnoton t. he eeent dpeent e otned n te o devtve o the eeent dpeent wth epet to the o oodnte te,. Bee the eeent dpeent e n the nt oodnte te, we need to ete the devtve n the o oodnte te to thoe n the nt oodnte te. We n wte n eqton o the devtve wth epet to n te o devtve wth epet to, to eth thee devtve we e the hn e to et p the oowng etonhp o n t notton J whee J the Jon opeto etng nt oodnte devtve to o oodnte devtve. Gven tht we now nd n te o the ntepoton nton the Jon opeto e ond J h eqe tht the nvee o the Jon et, whh eqe tht thee one to one oepondene etween nt nd o oodnte. h w e the e povded the eeent not go dtoted o qe nd tht t doe not od on te. We n then evte v v,,, nd th we n ontt the tn-dpeent tnoton t, B B ε whee the veto o nod dpeent. he eeent tne oepondng to the o eeent degee o eedo then V C BdV B K

65 O GSA he eeent o B e nton o the nt oodnte te,,. heeoe the voe ntegton etend ove the nt oodnte voe o the voe deent need to e wtten n te o the nt oodnte dv det J d d he voe nteg not no ene to n ept ntegton o no ne ntegton tehnqe ed. he nteg n e wtten K, Fd d whee F B CBdet J nd the nteg peoed n the nt oodnte te o the eeent. h onvenent the t o the ntegton e then ±. he tne n then e ted K jfj whee the t F evted t the Gn ntegton pont, nd j weght. n w the t nd the od veto e ethed. M H H dv V H dv H ds B dv V S V whee H t o ntepoton nton nd,,, oe veto nd nt te veto epetve. Geoet tne t o he eeent he geoet tne t ted o: e Gn e the od oe veto, e K g A, G NG da G NGdet J dd whee O Ltd 5 5

66 O GSA O Ltd 5 N N N N N Wth N N N,, e the n-pne oe o the he eeent n, nd he deton epetve. G n G G G nd n the ne o node o the eeent G h h D Pte Eeent he oton o D pte nd he eeent onde oth n-pne nd tnvee (ot-opne) dpeent. Foowng Mndn-Rene pte theo, n ddton to the endng tn we onde the eet o tnvee he tn n o opete epeon o the eeent tn w w whee w the ot-o-pne dpeent nd ntoded n ndependent ve to epe the eton otton (.e. otton o the tnvee no ot the o nd e). We n dene epte te te C nd C tht ete te nd tn o the pe endng nd he tn epetve nd o the pe endng oent nd he oe n e wtten C nd

67 O GSA epetve. C w w n th w we n then epe the o eeent tne t ton o the npne nd ot-o-pne tne whee K B C B B V B nd oponent epetve. C B dv B epeent the tn-dpeent tno o the endng nd he Whe e, th otne the ppoh to the Mndn-Rene D eeent tne oton. n GSA we e th one the Mndn oton. MC Eeent Foton We nd tht the Mndn oton n eetve ppoh o D po eeent whee the 8-noded eeent oodte ent te n the tne t to ent dene the ehvo o the eeent ne. Howeve the e oton dened ove ne eeent eoe note oe poet whee the ene o ve te n o - noded tne t ed to ne dte n epeng the e eeent ehvo. Spe we nd dt n tteptng to epeent the tnvee he tn te. Ant eoe we n epe the tnvee he tn w w thogh ne, the deene n the ode o te o the he tn ed to t tenng o the eeent whee the he te e ne ontned o ppohng eo. See eeene n the ogph o the noton. h etton wod e pt notee whee the thne o the pte. A wde pted eed to nde-ntegte the he te nd whe eetve, t e t the ot o eded nd tt o the eeent. he poe o tt one oten o getet onen whee the phenoenon o hogng n eoe ppent n eeent whee the thne to ength to ge. An tentve oton w pt owd Bthe nd Dvon nd h een ond to e epe eetve t eovng thee dte. he oton etende to hghe ode eeent thogh we nd the ppoh ot eetve when eovng the dte ot ppent n ne eeent. he oton ed pon the theo o Med ntepoted O Ltd 5 7

68 O GSA eno Coponent (MC). Fo the pe dpeent-ed Mndn oton we e the ndependent ve w n n h h w whee Bthe now ntode epte ndependent ve to epeent the tnvee he te We e n h * P * h to epeent n ddton et o ntepoton nton o o new ve whh we nd det evton o the he tn t pont P, tht P w P Fo ne D eeent we otn det ve o the he tn t o pont A, B, C, D on the eeent nd o we evte the dpeent nd eton otton t thee pont thogh det ntepoton. We n then ontt the ntepoton O Ltd 5 8

69 O GSA O Ltd 5 9 B D C A ng det ve o the he tn otned t the o pont. h epe o ogn epeon o the he te nd we ontne to ontt the o tne t no n ppoh eoe n D opet eeent. t t wothwhe to note tht the ntepoton ove e o eeent n the opet oodnte te. Fthe tnoton e nee to ntepote the he tn det thogh n t eeent n o pe. ndeed, when th done the eeent how onde poved pedtve pte o dtoted eeent. Eeent hpe nton he eeent hpe nton o D eeent e h,, Fo t- eeent thee e h h h Fo qd- eeent thee e h h h h Fo t- eeent thee e h h h h h h h h h h h h 5 5 Fo qd-8 eeent thee e

70 O GSA O Ltd h h h h h h h h h h h h h h h h Fo -8 eeent thee e t h t h t h t h t h t h t h t h W Eeent W eeent pe eeent, nten t ehed qd8 he eeent, nd theeoe the e o w eeent n e etve ge wthot ong the o n et. p w o one oo to the net n e odeed nge w eeent the thn he eeent eh. he nten node o w eeent e ondened ot nd do not ontte to the ne o degee o eedo n go n, t the dde node ong the edge e ondeed n go n, t the e hdden o e, the dde node ong edge do ontte to the tot ne o degee o eedo o the ode. A w eeent e ge, the ontnt t the hdden node ong the edge w et w eeent tne nd n et. he ontnt o the dde node ong the edge e ondeed n the oowng w, the two one node o n edge hve the e nod ontnt, e.g. oth node hve nd ontnt, then the dde node ong th edge w e ontned n nd. Howeve on one o the two node o the edge h ontnt n etn deton, the dde node ong th edge w e ee, e.g. one one node h ontnt nd the othe one node h ontnt, then the dde node ong th edge w e ee. he ove ontnt pnpe o ppe to gd ontnt, n eeent nd jont,.e. oth one node o n edge e n the e gd ontnt, the e n o the e jont, the hdden node ong the edge w e o n the e gd ontnt, the e n o the

71 O GSA e jont epetve. h w gntee thee no noptt etween the dpeent ong the edge nd the two edge node. D Eeent Shpe Che A ne o eeent he e ed ot GSA po to GSS n. Othe n pog hve deent t t the e pnpe pp. Fo GSS the oowng wnng, evee wnng nd eo e poded. whee nge Wnng Sevee wnng Eo n 5 n Qd Wnng Sevee wnng Eo n n h. h. onget de / hotet de n nge n nge Note: h dtne ot o the pne o the eeent o edge / onget de he dtne ot o pne o edge ted h n Whee n the eeent no,, e the oodnte o the t nd eond one node nd the ength o the onget de o the eeent. O Ltd 5 7

72 O GSA Md-de node oton not heed t hod e ppote hw ong edge. No he on to thne/hotet de. Hogng When Qd eeent wth the Mndn oton e ed n endng t poe to enonte hogng poe. h poe tht e wth nde-ntegted eeent whee thee e nent tne te to epeent the tne o the eeent. he poe notee n the et n hog ptten n the eh hown eow. h poe voded ng the MC oton o Qd eeent. h oton e epte ntepoton ethod o the tnvee he tn nd povde onde gete tt thn the ogn Mndn ethod. he ogn Mndn ethod ept n GSA o optt wth pevo ode thogh o new ode the MC oton eoended. Atentve when po eqed Qd 8 eeent e eoended. hee o ote eeent tht e t t n ode o deoton, even when ndentegted. Ln Eeent Ln eeent e deent to the othe eeent tpe n tht the pp ontnt etween p o node. he te node the t node peed n the eeent topoog nd th the node tht etned n the oton. he othe node (the ve node) eted to the te node. he degee o eedo t the ve tht e ned w depend on the tpe o n. he n ow the ve node to e ed (whee the otton t the ve node depend on the otton o the te) o pnned (whee the otton t the ve node e ndependent o the otton o the te). he te node w h the otton ned to the et o the tte. he n n t n deton o e etted to t n pne (, o ) whee the node e gd onneted o oton n the pne t e ndependent o ot o pne oton. O Ltd 5 7

73 O GSA O Ltd 5 7 he ontnt ondton e ed eow: A deton whee / ed / pnned Pne ( pne epe) whee / ed / pnned Lod pped to n eeent w e oet tneed to the te degee o eedo oe + oent o no po oent et. he net popete o n eeent n e ted o the e t the node tthed to the gd eeent oow. he nd the oodnte o the ente o e he net ot the go ogn then nd etve to the ente o,, th

74 O GSA he ontnt eqton o n eeent e dpeent. When ge dpeent e pped to n eeent the ontnt eqton no onge pp nd the n etween ve nd te get tethed. h eet n e notee n dn n whee the et e ed to n t ge ve. When thee e ed to et ve th eo hod e ngnnt. Eeent M he t o n eeent n e deved deed ove. h nown ontent t. n n tton t onvenent to p the t. One w o dong th to dgone the t. n th e the te etng to otton e eoed nd then ow ton ed ot on the enng ente. j j h h the eet o png the t the node. he othe pton tht ed to gnoe the o eeent eept ped e. Wth oth thee pton t e poe to dgone the tte t, howeve th not poe the net o ped eeent e non-eo o thee e gd eeent n the tte. (Rgd eeent genete o dgon te when the e e eped net t the te.) Eeent Stne he eeent tne eted nt n the o e o the eeent. h gve qe et t. K e e e h need to e tnoed eoe t dded to the tte tne t, howeve oe degee o eedo e eeed nd thee e etned on the eeent. h epeented the t eqton e K K e K K e ee e he tte degee o eedo need to e tnoed to go deton, ng the deton one D. O Ltd 5 7

75 O GSA O Ltd 5 75 e g ee e e e g K D K K D D K D Oet n go deton then ete the go tt degee o eedo to the nod degee o eedo thogh gd tnoton e n ee e e e n K D K K D D K D Reee Reee e pped t the node (o pedo node n the e o oet eeent) o tht the eeent do not hve n oent onneton. h n e pped to the eeent eognng tht n oent pped to node not eted the eeent. h ondton ed to ptton the eeent tne t. e ee e e e Whee the pt ee to the tte nd e ee to the eeent. One pttoned the degee o eedo eted to the tte e oned nto the tte tne t whe the eeent degee o eedo e nded n the tte tne t (t do not ntet wth the tne t o n othe eeent). n the e o tnee t the eee we dd the tne te o the eee nto the pttoned tne t. So n the e o e wth eee t end nd tne oted wth the eeed degee o eedo the t pttoned eow. e e e ~ ~ ~ ~ ~ ~ he tne te t node whee eee e pped e pt, o ej j j ~ ~ he eee tne te e to png tne t:

76 O GSA Oet Eeent oet e dened go veto etve to the node. hee ote pedo node tht dene the ee pt o the eeent. Eeent tnee e ted o the ee pt nd oded to gve the eqed nod tnee. Reee ondton e pped eoe the oet (.e. the e pped to the pedo node). he eeent o e e dened wth epet to the ee pt o the eeent. he oet n then e ondeed gd n nd ontnt eqton et ethed nng pedo node to t node φ pedo φ node whee the tnoton ed on the oton o the pedo node,, etve to the t node he dpeent t the pedo node n then e eted to the dpeent t the t node. pedo node he oe t the node n e eted to the oe t the pedo node. node pedo he eeent tne n then e oded on node node ng, pedo, node K j K j j, pedo j j, node Spe Eeent & Sdng Ce Spe eeent nd e eeent e ntended to e ed pt o t-noded peeeent o hn n the dn eton ove. o dene the hn, o pe-eeent, the pog oo o pe o e eeent wth the e popet ne, nd jon thee t oon node. So the eeent n ontno ength o pe o e t hve oon popet ne, nqe to tht hn. n othe wod eh pe-eeent dented nqe popet ne. A Spe eeent nnot e dontno o ted. O Ltd 5 7

77 O GSA Wth pe eeent, the ode o the npt o eeent potnt the to ete djt the etve dtne etween node nd e the t eeent the onto:.e. the to gete thn one, the t eeent w e the et. t e thn one, the t eeent w e the get. he node o pe eeent hod e dened o tht the n e joned togethe to o pe n hed-to-t eqene. Gene pe hod not o eh othe. pe e eqed n two deton, the pe n the n deton hod e ed thogh o one edge o e to the othe nd the pe n the d deton hod jon node n djent n pe. Ce nd Sdng Ce e hd o o e eeent, ntended o e n dn eton n o e (not o-ndng ) tt ode. n th n the e ee to de t nten node whee e eeent e onneted. he e, opoed o ne o e eeent, ondeed nge eeent n dn-eton. he e n ee de ond the nten node o the eeent the e ove ond pe. A et, the tene oe o the e eeent n e e the e. p needed ong the ength o Sdng Ce, two Sdng Ce eeent hod e dened, jonng t the ped node. he e popet dened tne pe nt ength whh eq to EA whee E et od A e o eton e he tene oe n the e ted o EA n whh the tot nteed ength o the e the tot deoed ength o the e he nod no deton n e dened the ne tht wthn the pne dened the two eg nd t even dvde the nge opoed the two eg. On the no oponent o oe tneed etween the node ong e nd the e. O Ltd 5 77

78 O GSA Fo the poton o e hown ove e the e eeent e n the - pne. F A,, he e oe ontnt ong t ength. heeoe the oponent o the e eeent ong X t node A e eq nd oppote. And the etnt oe n th deton. he oponent ong Y pped to node A. he oponent ong Z the e n the - pne. F A,, Fee pe nd e n e thoght o oppote n the w n whh oe e tneed to the nteedte node. Fee pe on pp tngent oe n the pne o the pe, whee e on pp no oe. Spe Eeent Spe e degned o op- o-ndng on nd t w e gnoed n othe ne even thogh t h een dened n the ode. n op-, o-ndng n, pe eeent e ed to e p tpe node pe eeent ed pe. A pe ed to ntn o djt the nod dtne ong the pe eeent hn deed n the oond tte. Spe hod e ove D eeent e o ong o te eeent wth op- o-ndng popete (.e. eeent wth eo tne) A pe n e ondeed hn o wth nt ength eng et to ot h o the t ength (to ene tht the Spe en n tenon nde eone ondton), the tne AE o pe eeent e dened n pe popetee. o ede the nene o the pe eeent on the o-ond hpe o the tte, the tne o pe eeent hod e poe ong t n ntn the eqed nod png. Dependng on the pe tpe, one o two oponent o the pe oe e ppeed, o pe eeent w on onto the nod png nd not et the o-ond hpe. A oe oponent o pe oe e ppeed, the node tthed to geode nd ee pe eeent e not e n eq t the end o o-ndng n. n th epet pe de o othe eeent. hee e thee tpe o pe eeent Geode O Ltd 5 78

79 O GSA Fee B he tpe o pe eeent dened n the pe popete. he de n the w tht the oe eeted the pe on the nten node teted. Fo eh nten node, veto dene whh oponent o the etnt pe oe on the node e ten nto ont. h oe p the node ong the pe veto. he enng oponent e gnoed. he pe tpe o de n the w n whh the png e (dened pe eg ength tpe) e pped wthn the pog. Gene geode pe hod e ed ong D eeent e. Fee pe hod e ed to onto the nod png ong n o te eeent. S to ee pe, pe n e ed to onto nod png ong o te eeent, the deene etween ee nd eeent tht no oponent o B pe eeent oe w e ppeed. B nd ee pe p djt the png o the node ong the ondent o te eeent. Geode pe ht the nten node ove the e o to ne the ove ength etween the end node ( geode the hotet ote ove e etween two pont) nd o ntn the png o the node. o ndetnd the deent pe tpe, t e to onde hot ength o pe hn opoed o two pe eeent jonted t the oon node. Geode Spe Fo geode pe the oponent o eh pe node eton whh no to the e o the djent op- tnge nd qd eeent ppeed nd o the pe do not et the o-ond e; the on onto the poton o node on the e whh oed. he tenon o the geode pe ene tht the pe node ht to o geode pon the op- e tht tneo oed the tnge nd qd eeent. he geode pe no ted oow. he pog ehe o tnge nd qd eeent tht e onneted to the nten node o eh geode pe nd ttept to o oette o eeent ond eh node. Fe e pog eo. he node o the eeent n the oette e ed onto node to te the no o the e on whh the pe e. nt, the no deton dened o the eeent geoet o the ondng D eeent. h then djted dng n ed on the dpeent o the ondng node. O Ltd 5 79

80 O GSA he nt no o geode pe t node 5 n the ove epe eq to n whee the 8 e the oodnte o the node. Lte n the o-ndng n, the no w e otted ed on the dpeent o the node. he degee o the otton ted ng the ondng node (,,,, 7 nd 8) e onneted to the pe node (5) e. he e e pn-onneted t the ote de nd ed t node 5. he E o the e popoton to the o the nge eh de o the e. he ed end oent o eh e t the end o node 5 ted. he etnt o the oent t node 5 w otte node 5, nd th otton w e the one tht otte the pe no t node 5. he no o the end node o Geode Spe e ond ( eqed) t optng the no o n nten node eept tht he oette o tnge nd qd e nopete. he ent no on otted ot n ng n the pne o the no nd the end pe eg. he no o the net nten node then pojeted onto the pne o the otted end no nd the end pe eg, nd eeted ot the pne no to the end pe eg. No e ted eve e. O Ltd 5 8

81 O GSA Fo the ove poton o geode pe, e the no o the pne o op tnge nd qd joned to node A n the deton. he pe oe pped t node A F, F,. So the pe w ove node A n the X & Y deton. he geode pe ppe the pe eg ength e t the tt o n. he node poton e djted t the tt o the n to eet the e tong the nteed eeent ength. On onvegene, the node poton not eet the eg ength e et. th pove poe, the e o ge poe etnt o pe od e ondeed o n tge o-ndng n ttng o the onveged o-ond hpe. Wth oth opton, ot-o-ne oe w et when onvetng o the op to the e ode, nd e needed n the ntepetton. Fee Spe Fo ee pe on the oponent o nod eton tht t ong pe tngent peeved. So ee pe on nene the png o node, ong the ength o D ondng eeent. he nt tngent o ee pe t node n the oowng epe eq to Note: v tngent the tngent veto t node (= X)., e oodnte o the node nd. Lte n the o-ndng n, the no w e otted odng to the dpeent o the node. he degee o the otton ted ng node nd e onneted to the pe node () e. he e e pn-onneted t the node nd nd ed t node. he E o the two e e eq. he ed end oent o the two e t the end o node ted. he etnt o the oent t node w otte node, nd th O Ltd 5 8

82 O GSA otton the one tht otte the pe tngent veto t node. he otton w e ot the no o the pne o the djent pe eg. he tngent o the end node o ee pe e ond ( eqed) eetng the tngent o the net nten node ot the pne no to the end pe eg. ngent e ted eve e. Fo the ove poton o ee pe, e the no o the pne o the thee pe node n the deton. he pe oe pped t node A F node A n the X deton on.,,. So the pe w ove he ee pe ppe the pe eg ength e t the tt o n. he node poton e djted t the tt o the n to eet the e tong the nteed eeent ength. On onvegene, the node poton not eet the eg ength e et. th pove to e poe, onde epng the ee pe wth pe o n tge o ndng n ttng o the onveged o-ond hpe. B Spe B pe hod n pe to D te eeent wth op- popete, nd the two eeent hod hve oon node. No oponent o pe oe ppeed o pe nene the png o node, ong the ength o the op- te, nd the poton o the op- te. he op- te h eo tne, t the pe h tne. heeoe oe v ong the pe. o ntn eq pot o-ndng, pe oe hod e dded to the te pe-te n the n ode pe eeent e on ondeed dng o-ndng n. he eet o the pe on the n oond hpe nee wth the pe tne. he pe, n eet, t-noded pe-eeent, o hn, wth ow tne tht ope wth png e o the node ong t ength (dened the pe eg ength tpe) O Ltd 5 8

83 O GSA Fo the ove poton o B SPACER, e the no o the pne o the thee pe node n the deton. he pe oe pped t node A F, F, ove node A n the X nd Y deton.. So the pe w he pe ppe the pe eg ength e epeted n. he node poton e djted t the tt o the n to eet the e. On onvegene, the node poton e djted ong the ength o the pe, nd the n epeted. h ontne nt the png e e et. he poton o the node djted tong the nteed eeent ength. Spe eg ength tpe hee e thee e, o opton, to onto nod png ong pe, whh n e eeted when denng the pe popete. hee png e e popoton, to, nd pojeted to. Fee nd Geode pe pp thee e to the nt eg ength t the tt o n t do not ehe on onvegene. Fo pe nded n op tte, the to o the n eg ength to the nt eg ength w e ppote ontnt nd the png e w e et ppote. Howeve vng pont od o othe ontnt e pped ong the ength o the pe the n png e too ppote to e tto. n th e the e o B Spe e ondeed. Fo B Spe, the png e e heed on onvegene, nd the n epeted nt the eg ength e e et et. he thee opton oeed eg ength tpe e: Popoton the n ength o the pe eg w e popoton to the ogn ength. o heve th, the nt ength o eh pe eg et to h the nt dtne etween end node. Rto the pe eg ength to w e eq to tht peed, e.g. the to peed, the n eg ength o the nd eeent w e twe ong the eg ength o the t nd o on. to o peed, the nt ength o the pe eg w e de eq. Pojeted-to Spe n et n the pe popet te. e dened et not peed, the go et w e ed. he pe eg e pojeted onto the - pne o the peed et. he pog djt the nt ength o the pe h O Ltd 5 8

84 O GSA tht the pojeted ength o eh pe eg on the - pne oow the peed to e. to o peed, the pojeted ength o eg w e eq. to o peed, the pojeted eg ength o the nd eeent w e twe ong the pojeted eg ength o the t nd o on. O Ltd 5 8

85 O GSA Eo No When ng GSA t potnt tht the e n e ondent n the o the et. hee e ne o he tht the e n ot to he, howeve GSA povde oe ee o the o the dpeent oton. h epoted n the An Det otpt. he denton o the eo no deent o tt nd od dn o ng et. Stt n tt n the eo no not ted ne the ode how gn o eng ondtoned. he ton oow. Cte the ed.. Sove o the dpeent etng o the ed nd ope thee wth the t dpeent.. Cte the eo no. h whee R R e K K R R Dn nd ng n dn n the eo no w ted oow e K M K nd n the e o ng e K K K g Ept e ntegton he ept te ntegton hee n e wtten O Ltd 5 85

86 O GSA O Ltd 5 8 t v t v v t t t t t t t t t t t t,,,,,,,, he oe veto t te t the o the oe tng on the node (degee o eedo). nt pp,, Fo n eeent the nten oe veto o ne nd geoet non-ne poe ted o nt t K nd Regh dpng nded t t t nt v M v K D Eeent Stee nd Foe Ste n D Eeent Stn Denton he no denton o tn ed e oow w w v v w v An tentve denton whh t oe net n teno o w w v v w v wth the tn teno dened ε

87 O GSA he ton o pnp tn,, oow o E E E he he tn ted o the pnp tn o he he n w to the denton o vege nd von Me te voet nd eetve tn n e ted vm v O Ltd 5 87

88 O GSA Ste Denton Ste n e ondeed teno qntt whoe oponent n e epeented n t o σ whee eh te oepond to oe pe nt e. he oowng notton o the te oponent oon he pnp tee,, e ted the oot S o the S S S whee the te,, e te nvnt dened Atentve the pnp te eqton n e wtten S S S he he te ted o the pnp te wo othe te ee tht e ed e the vege o hdott te nd the von Me te; thee e dened O Ltd 5 88

89 O GSA v vm Ste n D eeent he te n D eeent ted v the tn. he tn e ted o the dpeent ng the tn dpeent etonhp B (ee D eeent). Ung the ntepoton nton thee n e ted t n pont n the eeent. One the tn e ted the te n e ted ng the te et t C o epe o nd et otop te the te t E C h the tn e ε B nd the tee e σ Cε CB h n e ed to evte the te t n pont n the eeent. Howeve the te ed on the tn whh n tn ed on the dpeent gdent n the eeent. h oe o the tn te n n eeent tht h po dpeent ed e ne. t h een ond tht the et te et e otned evtng the te t pt pont (the pont ed o the eeent ntegton) nd etpotng the et to the node. n ode to hve good te et the eh w hve to e ne tht the eh eqed o the dpeent oton nd the te et e e to e nened hgh dpeent gdent n the eeent. Det etpoton o et n the e o det etpoton nton hoen to epeent the vton o te ove the eeent ed on the ne o G pont. n pte th ed when thee e, o G pont. he oepondng pono nton e d Fo G pont the ve e ed to e ontnt ove the whoe eeent o the G pont ve e p oped to the node. O Ltd 5 89

90 O GSA O Ltd 5 9 Fo G pont the ve e the G pont e nown o the oowng et o eqton n e et p h n then e ed to te the oeent,, Fo G pont ppoh n e ed, t n th e the oton o the G pont e t, o the eqton n e wtten n the o d d d d h n then e oved o the oeent d,,, One thee e ethed the pono nton n e ed to eth the ve t n poton on the eeent. Let qe etpoton o et n th e nton hoen to t thogh the pont wod p hghe ode pono thn the one ed to ntepote the geoet, o et qe ppoh ed to nd the

91 O GSA pono to p the tee o the G pont to the node. he ntepoton nton ed o node nd 8 node eeent e epetve he qe o the eo o n pont then e p, h ed ove the G pont nd then the devtve wth epet to the oeent e et to eo (eetng the oeent tht ne the eo). h ed to the t eqton o 8 node eeent n 5 7 he node veon the e eept tht the nd 7 te e gnoed. h n then e oved o the oeent. Ste-tn Retonhp he etonhp etween te nd tn depend on the tpe o poe Poe Dpeent Stn Ste Pne te, v,,,, Pne tn Aet, v, v,,,,,,,, Pte Bendng w,, M, M, M Gene, v, w,,,,,,,,,, Whee o e nd pte endng poe the etonhp etween oent nd vte w w w O Ltd 5 9

92 O GSA O Ltd 5 9 he te-tn te o otop te e Poe Ste-tn t Pne te E Pne tn E Aet E Pte endng Et Gene E he te-tn te o othotop te: Poe Ste-tn t Pne te G et E E E

93 O GSA O Ltd 5 9 Pne tn G et D E D E D E Whee D Aet G et E E E E E E Pte endng G et E E E t Gene G et G G E E E E E E Foe n D Eeent he oheno onventon ed o oe n D eeent. h en tht oent M ed on the te n the deton. Wth the oheno onventon n opeon on the top e n oth the nd deton the oent e oth negtve.

94 O GSA Coneqent ttng o the pton tht tene te potve, we hve the oowng etonhp o the oe N t d t N t t d N t d t Q t t d Q t t d nd oent M t t d M t t d M t t d Foowng o th pte tht h potve n-pne te n / w hve potve oe etnt nd potve endng te n / (.e. potve te t the top e etve to the otto e) w hve potve oent. When the tte ne thee p to: N p, t N p, t N p, t Q t Q t nd M, t M, t M, t whee the pept p nd ee to n-pne nd endng te te. When n-pne nd endng thne ode e e the n-pne oe e ed on the npne thne nd the oent nd he oe e ed on the endng thne. Stee e w ed on the t thne o the eeent. O Ltd 5 9

95 O GSA Condtonng n the vt jot o e the ove w gve oet oton to the poe. Howeve, oe poe e nte -ondtoned n whh e hnge n the npt dt n ed to oe gnnt hnge n the et. ng pe epe to oo t -ondtonng; onde pe two png te, whee the png e onneted n ee. he tne o the t png nd tht o the eond nd we e tht h gete thn. n th e the eqton deng the te A n ove ed on Gn enton tehnqe, we e thee eqton to ve t etonhp etween nd whh when ttted n the othe eqton gve: o Wth et thet the te wod e eo, howeve, ge oped wth nd de to ted peon, oe eo w e ntoded n the ton. th eo denoted e, then the eqton we hve e We hve then te hown eow whee the eo e ddng thd png, whh t n pe wth. O Ltd 5 95

96 O GSA O Ltd 5 9 he epeted eton, t the eton tht ted e h the eton n eo to e ntepoton on ng/qd Fet he, oodnte o tng et n e detened o the e o ntepoton (hpe) nton. Let v v v v hee n e ewtten v v v v v v nd then v v v v v v v v hen On qdte et ng the ntepoton nton gve v v v v v thee n e ewtten

97 O GSA O Ltd 5 97 v v v v v d d Ung the t o thee gve d whh n e ttted nto the eond to gve v v v v v d d h n then e oved o & nd then the ntepoton nton ed o the tng et.

98 O GSA Lodng Be Lod he eeene ehn od the pont od; the othe ehn od tpe n e ethed ntegtng the et o pont od ove the oded pt o the e. he ppoh to tng the od on the e o oe t poton to onde the e pt t nto two epte e. Fet te n e ethed o, toon nd e odng EA to GJ E, e E GA hee t e ontnt o dpeent nd otton etween the two e nd the oe nd oent t ne the pped od. h ow et o eqton to e et p o the -e nd whh n e oved o the he oe nd endng oent t the oded pont. w w Whee the veto w epetve o nt oe nd nt oent w w One the oe nd oent t the oded pont hve een ethed the end oe nd oent (nd hene the eqvent nod oe) et o eq o the two -e. he gene dtted odng n the pth od, vng n ne n ntent o poton to poton. he nod oe nd oent e then gven ntegtng the et o pont od whee p w w d p the oe de to pont od t nd w w w w w w he t-ne od opton p epeted et o pth od. O Ltd 5 98

99 O GSA Be he Lod he the od ow o the ntodton o od de to tepete vton n the e eeent. Fo n the odng the epnon o the eeent ed to oe, o the gdent thogh the thne o the eeent oth oe nd end oent e nded. EA NA d E d d E d whee the tepete oeent o epnon, tepete nd the pt NA ee to the net. Be Pe-te Lod nd L-o-t Pe-te nd o t od e, t the denton de. A pe-te ondeed oe pped to the eeent t oe poton n the eton etve to the net. A o t ed to et on the te etng to the eeent. Fo pe-te o oe nd oet o nd the etng nod oe nd oent e p p p Fo the o t nd the nt tn the nod oe e epetve EA EA Lod on pn-ended e When the end o e e not ed, oe djtent h to e de to the oe nd oent tht e pped t the node nd the pnned end nnot tn n oent. he pet e when oth end e pnned o he oe nd oent e then oded to ntn eq oow,, O Ltd 5 99

100 O GSA o /. When the eeent pnned t one end on the oeton depend on the te popete n the gene e whee pn t end pn t end E GA A A Fo pe e th ede to pn t end pn t end Pojeted Lod When the od on e dtted the tot od n e ed on the t ength o the eeent o on the pojeted ength o the eeent. h od no to the o the eeent wod hve pojeted ength eq to the e ength whe od pe to the o the e wod hve pojeted ength o eo. n the gene e o od n the deton dened nt veto w nd whee the e od denoted the to tht h to e pped to the od ntent, dened n te o the nge etween the two veto, n w D Bod Lod he ot oon o o od od e gvt od. he gene epeon o od od gven O Ltd 5

101 O GSA h dv whee ntegton ove the voe o the eeent. Ung Gn ntegton th n e epeed h, det J Whee e the Gn weght nd det J the detennt o the Jon. D Fe Lod Fe od n e ontnt o vng o the e o n eeent. Fo pont od on the e the od veto h h n e geneed o the dtted e gvng the od veto h ds whee ntegton ove the e o the eeent. Ung Gn ntegton th n e epeed h, det J, Whee e the Gn weght nd det J the detennt o the Jon. D Eeent he Lod he od n e ethe ontnt tepete e n the whoe eeent o tepete gdent, vng ove the e eeent. o evte the eqvent nod oe the tepete hve to e onveted to tn, ng the tepete oeent o epnon. he tn e then eted to the te thogh the te t nd then the nten tee e ntegted ove the eeent. he the eet e the e n deton o thee e no he tn ntoded. Fo n-pne eet (ontnt tepete) the tn ε p Fo endng eet (tepete gdent) the tn nd te e κ t hee e onveted to tee thogh the te t O Ltd 5

102 O GSA σ p C p ε p σ C κ D n-pne Lod n-pne od e down nto two tegoe, pe-te od nd nt tn. Pe-te od e dened oe pe nt wdth n ethe, o oth nd deton, ong wth n oet o the net. nt tn e dened n ethe, o oth nd deton, t no oet e petted. he pe-te od n e onveted det to et o eeent tee, whh e ntegted ove the eeent to get the nod oe. he oet oe gve e to oent on the eeent o p F t M t F t he nt tn n e onveted to tee n nne nogo to tht ed o the od. Gd Lod Gd odng odng pped n pe en o gd pne. hee e thee tpe o gd odng: pont od, ne od nd e od. he e od n e dvded nto od on the whoe gd pne nd thoe on dened e onded pone denng oed pogon. he pne to whh the od e pped n e one-w pnnng o two-w pnnng o t-w pnnng. Gd Ce A odng gd ed to ntegte e od nd o dtton o gd pont od on to e eeent ond the pne. he gd ed need to e ne enogh to gve n deqte epeentton o the od, o t need to e ed on the e o the pne tht e oded. he e nd hpe o the pne n v gnnt, o ot w o detenng the gd e eqed. Fo qe pne the od n po e epeented deqte gd, t o ong thn pne the e gd wod e nte. he gd e ethed oow: Cte the e o the pne nd et epeenttve pne denon to e the qe oot o th. hen the gd e th ve dvded the gd eneent to. h det to gve tp e ong the edge o qe pne. he e n djt the gd eneent to to owe o hghe ve eqed. Fo ee o pet to wth eneent to o the eh dente e oow. Apet to Ce dent : : : 8 O Ltd 5

103 O GSA :.5.5 : he ton o the odng gd e n then e ted on pne pne nd the n e eeted to gve deqte epeentton on the e pne, wth not eng ewed nd ew ve pne. o ene tht th the e the vege,, nd tndd devton,, o the ndvd pne odng gd e n e ted nd the odng gd e et to. Gd Pont Lod he w n whh the od e pped depend on the tpe o tte epeented the pn tpe. One w pnnng od e ted ng the od pped to pn pnnng o one de o the pne to the othe n the pn deton. n the e o odng ove the whoe pne th en tht the od pe pn the podt o the od ntent nd the pn ength, pt even etween eh end. he goth epe the pne ne wth od ntent pped to eh end o the ne. he ttng pont o the two w dtton o od to onde e o nt d ented on the od pont. he t ntent t the edge ted etpotng o th pont ng pne. nton whee the dtne o the od pont to the edge o the We n t thee eqeent wth dtton o the o Ao We eqe tht thee oe nd oent eq. he o o thee nton te the oent eq eqeent nd we n oo o oton o n t od. he te o te ont o the pet to o the pne n detenng the pt etween the ong nd hot deton. the pne qe we epet the A oeent to e nd o n nnte ong pne. o dene the oeent nd phe nge we dene ength deton o the pne nd wdth deton. he ength hoen to e n the deton o the o deene o the onget dgon, whheve h the gete gntde. he wdth deton no to the ength deton. Fo etng pne th od wth the no denton o ength nd wdth. We then dene ve oow: deton, nd n denon o pont to pne edge n ength n deton w, w nd n denon o pont to pne edge n wdth n O Ltd 5

104 O GSA the nge o the wdth deton o the gd then we n te the oeent o A w w n n n n w w n n n n w w n n n n he od ntent t the edge o the pne then ted o the dtne o the pont on the edge o the od pont. p we onde e t nt d o the gd pont od we hve od ntent nton o the o Ao h t e pped on to the ondng eeent. We n e the gd e e,, when ethng the e o the oded pthe on eeent ond the pne ond. he dtton o pont od n then e detened t ee o pont tht e dtne pt ong the eeent on the ond wth n o tt nd end pont on eh ond eeent. he ne o egent o the od dtton n then e detened o the gd e e nd eeent ength, n e Fo the det ve o gd od eneent nd no ed qe pne th w gve o od pthe ong eh de o the pne. he ength o the pthe then n Conde two ne o the od pont to the tt nd nh o the eeent egent. hee w e t nge nd. he od ed th egent t then e F W d whee W the od ntent. he nge t whh th ppe detened o M W d O Ltd 5

105 O GSA O Ltd 5 5 F M the veto v nd v e veto o the od pont to the end o the e egent then the gd od F n e thoght o pont od ong the veto F v, t n nge F o v. he odng nton ontn te o the o d n o whh ntegte to gve n n n o n he od F n n o A d A d W F nd od oent M o n o n o A d A d W M h pont od t then e djted to ow o the dtne o the e o the od pont. h n e to to peeve oent eq. h pont od n then e epeented ne vng pth od ong the egent ength. the pojeton o the Lod pont on to the eeent t poton ong the egent nd the end e nd j then the eq ondton eqe tht

106 O GSA F F j j Knowng thee eqton n e oved o j F F nd j. Gd Ae Lod When gd e od pped n t-pnnng pne the ppoh to onde the odng to e epeented gd o pont od dtted ove the oded e. he dtted od then onted o ng the pont od. Hvng ethed the odng gd e then we n then wo thogh the gd nd detene e oded o not. Whee e eted the od ond then the od ntent eded n popoton to the oded e nd djtent de o the poton o the od. Whee e eted the tte ond the pont o ppton o the od t e oved o tht the od pped to the tte nd not n pe. n thee e the entod o the ted odng gd e ted nd the (eded) od on the whoe e pped t the eted entod. Whee e eted pne edge the od pped to the pne t the entod o the gd e. Fo the e whee th too oe the gd eneent to n e need. O Ltd 5

107 O GSA Gd e od n e pojeted. When th the e the od ntent eded dependng on the pojeted e o the pne to the odng. the no deton o the od nd the no deton to the pne n p. hen the od ntent djted n n p When the od not pojeted then the ntent depend on the pne e etve to the pne n e pojeted on to the gd pne (no n g ) o the ntent h to e oded n g n p When the pne e n the gd pne th to nt. Note: pogon whh et n oded e eng pt nto two egon, the whoe e ed to e oded. h et n (ght) ove nee n the pped od. h etton n ode to eep the od dtton t poe. Gd Lne Lod Gd ne od e teted n nne to gd e od n tht the e oen down nto ee o gd pont od ong the ength o the ne. he e gd e e ed to detene the ne o egent ong the ne nd theete the poede the e o e od. Lgnge ntepoton Lgnge ntepoton gve w o ttng pono thogh t et o pont. he pono whee P( ) n j P j ( ) P ( ) j n j, j j n ode to genete ve n pe t onvenent to onde th o denon poe wth pete t the ndependent ve. h ene tht t onoton vod ngte. he etng oded eqton e Ahe, Bnden nd Weten, E W. "Lgnge ntepotng Pono." Fo MthWod-- A Wo We Reoe. O Ltd 5 7

108 O GSA O Ltd 5 8 n j j t t ) ( ) P( P whee n j j j j t t t t t, ) ( P Fo onvenene the t ve e ed to e n the nge [:] M Dtton he ton o the nd net o the tte e oow whee the ton e ove the node nd,, e the oodnte o the node etve to the ente o. the opton et to gnoe the eeent, th ton on ed ot ove the eeent. n ddton de to od et the od veto etng o the od depton ted nd the eqed oponent etted ed nd onveted to g j, whee the e to, j the peed oponent nd g the gvt ve.

109 O GSA O Ltd 5 9 Mte Mode otop te he te popete e E Yong od G he od Poon to he gene ett t G G G E E E E E E E E E C he he od eted to the Yong od nd Poon to thogh E G Othotop te he te popete e E Yong od n the deton E Yong od n the deton E Yong od n the deton G he od n the pne G he od n the pne

110 O GSA G he od n the pne Poon to, deton tn geneted nt tn n the deton Poon to, deton tn geneted nt tn n the deton Poon to, deton tn geneted nt tn n the deton he othe thee Poon' to,, n e otned o the oowng etonhp. E E E E E E he gene ett t C E E E E E E E E E G G G he von Me te VM Yed o when VM ed he ed nd tte te nd the hdenng pete e not ed n ne n. Fo non-ne n n GSA, on the ed te ed nd tte te nd hdenng pete e gnoed. n gene, te edng oow the ne dened the hdenng od. Ethe otop hdenng o net hdenng n e dened. O Ltd 5

111 O GSA the hdenng pete, (otop hdenng hown ove) the ed te etn t ve on eve o te. A ve o oepond to net hdenng, whee the dete o the ed e en ontnt o on eve o te the te ed when the te eve twe the ogn ed te. Mng M & Red Rgd Repone A od n te ont o how the oed n dn n. Howeve on etve ne o ode e ted, o not o the oed. Povded the ode p to hgh enogh eqen e ted the enng epone n e ondeed n eent tt epone. hee e poede o eth the ng nd tng th nto ont thogh tt n. On gven the U.S Ne Regto Coon. Fo gven etton deton j the oted wth the ode n e ted o eh degee o eedo o ˆ N n nj n U.S Ne Regto Coon, Regto Gde.9 Conng Mod epone nd Spt Coponent n Se Repone An, Revon, J O Ltd 5

112 O GSA he ng then ˆ Gven the gond eo peod eeton (ZPA) he ng epone n e teted tt od e ˆ ZPA A et o tt od oepondng to the deent deton n then e ethed/ Gpt Method he Gpt ethod w o ndng the ed gd epone ong wth the epone pet n. h dene gd epone oeent, α o tht the peod epone p he oeent α dened Gpt n n whee pet,, vpet, gd O Ltd 5

113 O GSA O Ltd 5 Ptpton Fto nd Eetve M he od o ode dened Mφ ˆ φ he deton noton n e etted ng the ptpton to. he ptpton to o ode n the j deton gven j j ˆ M φ whee the j veto gd od veto n the j deton. he eetve t dened ˆ ˆ M φ ~ j j j he gd od veto e dened...,, So gd od veto o otton o ot go n e dened n o n o

114 O GSA he eetve n otted te n e ted o the ptpton to nd eetve e. φ M ˆ φ M ˆ φ o M ˆ n o n So o ~ ˆ ˆ n he o the eetve n n gven deton ove the ode the tot. Stng wth the denton o eetve ~ j φ M ˆ he gd od veto n e wtten Φ j j j So the te n the neto o the eetve eoe φ MΦ j o ~ j Ao the tot φ ˆ MΦ j j ˆ ˆ ˆ j Mj j Φ MΦ j nd MΦ j Φ dg ~ o j Φ MΦ j ~ j So the o the eetve e ove the ode the tot. Pttened Lod An B the pnpe o pepoton o ne et tt te, the nten oe n eton n e ted A A wd d whee, A the oo e don o the - pne, the nene e nton o the - pne, nd w n n-toed dtted od nton vng o the - pne. O Ltd 5

115 O GSA Fo the nten oe n eton w nd w n e ted n A A p w p w n dd whee, p n nton eted to the nene e eted nde nge o dtted od A p And th the eqton n the e ewtten A n n d d A w w A w w d d he oo e don A n w e epted nto ee o e nd non-oveppng e, whh eve ove the ente e. Ae the gn o n eh ndvd epted e doe not hnge,.e. w potve o negtve o the - pne wthn n e, then the eqton n e epnded A n n dd w w A w w whh n e the ped n ote nton dd A en whee denton en A w w dd d d A w w n n dd d d And, the n nten oe n eton A, n An n e deved A n en n ot tton, o w nd w de on to, whh eted to the od to n et n tte t tte degn. Pttng O Ltd 5 5

116 O GSA w w n n w w the eqton n e ped en n n A A wd d wd d B opng thee eqton to t eqton, t n e een tht det o the n wth e oded, nd n wth od eng on pped to the e ped en n n A A A en n e evted n e evted det o the, whh en the eqton n e the h te w wtten. D. Don Y.B. Ho o Ove Ap & Ptne, Hong Kong Ltd nd epoded hee wth peon O Ltd 5

117 O GSA Rt An Rt n o-tte nteton n, tetng etween oton o the tt n ng G nd the o n ng Pdp nt onvegene o nod dpeent heved. teton Fo the o nteton node on t, the n tete thogh the oowng tep nt onvegene ehed:. Fo eh o nteton node, png ppot w e geneted wth det ppot tne t doe not et. the ppot png et, t w e ed nd t tne w e oded dng the n. Ate n, t tne w e etoed.. Rn G ne tt n to otn the dpeent t nd png-ppot oe o eh o the nteton node. Cte o pee p nde eh o the o nteton node ng p p p A ( p, p n( p, p n ) ) Whee A the e oted wth nteton node nd the ontt pee n : p jet to owe nd ppe t p.. Rn Pdp n to otn the etteent o o, o nde the pped pee od 5. Che the deene etween t dpeent nd o etteent, the e e thn the ed t, ve the et nd top the n, othewe go to tep. Re-te the ppot png tnee odng to the ppot png oe nd the o etteent ng the oowng eqton nd go to tep. o A dpng oeent tht n e ed to od the tne pdte,.e. eeve oe peentge o the pevo tne. he ve o dpng oeent etween nd. dpng oeent peed, the new tne w e ted o: O Ltd 5 7

118 O GSA, pev o Pe Fo the o nteton node on the pe, the n tete thogh the oowng tep nt onvegene ehed:. Fo eh o nteton node, genete png ppot n X, Y & Z deton wth ppot tne ted o o etteent nde nt pont od.. Rn G ne tt n to otn the dpeent t nd png-ppot oe o eh o the nteton node. Cte the o eton oe to the nteton node o A A A whee the nteton e o the nteton node e A B H A B H A PH Pe nteton node nd eevnt denon wth P the peete o the pe nd whee C C C,,, nd C,, C C e the pe o nteton oeent nd deved o the Pe So nteton Coeent (PSC) ve dened the e hown eow. O Ltd 5 8

119 O GSA Pe So nteton Coeent Cve whee the deene o the pe dpeent nd the o etteent t the oepondng pont nd the pe denon dete. B, B n nd deton o D. Cte the pee od on o de to the o eton oe, nteton e A, A, A, nd the 5. Rn o etteent n ng the eedded Pdp pog. Cte the openton oe to onte ne the ppot png oe de to the e o ontnt ppot png tne. 7. Che onvegene, ted, top, othewe, goto Step. Convegene he oton onveged the deene o t/pe dpeent nd o etteent e e thn the pedened epte ed. he ed n e dened n two w. Aote ed - the ed dened det h.,. o 5.. Retve ed - peentge dened tht ed to te the t ed ed on the get o etteent. he t ed eq to the dened peentge o the get o etteent. Regh Dpng Regh dpng onde dpng to e eted to oth the nd tne C M K Fo t dpng to O Ltd 5 9

120 O GSA Fo two dtnt dpng to j j j h n e oved to detene the oeent,. n the e o the e dpng t oth eqene th pe to RC S ntodton j j RCS degn potpoeo wthn GSA o enoed onete two-denon eeent o no thne jet to n onton o n-pne o he oe nd ot-o-pne endng oent nd toon. he ton n e de oowng the pnpe o ot o the ode ed wthn Ap. RCS ne to ow o ot-o-pne he nd thoghthne oe. he npt to the potpoeo ope pped oe nd oent, eton depth, enoeent poton, nd te popete. he enoeent oentton n e n et ope ethe e o enoeent o eh e o the eton n the two peed deton, o ee n ndto to the eet tht RCS ne to nd oton o the ent dt. E veon o the pog wee nown RCD. Dt Reqeent Eh n o RCS otn the oowng dt n n ontent et o nt o the GSA n o RCS degn dt ppopte: N N tte pped oe pe nt wdth n the -deton tte pped oe pe nt wdth n the -deton h te ed on Note n Stte wtten n Feth [n Ap nten pton] (7) nd epoded hee wth peon O Ltd 5

121 O GSA M M N M e dd e n tte pped endng oent pe nt wdth ot the - tte pped endng oent pe nt wdth ot the - tte pped n-pne he oe pe nt wdth tte pped toon oent pe nt wdth ddton eentt (e dd > ) ondeed tng n oth ene n eentt (e n > ) ondeed tng n oth ene h eton thne (h > ) t t poton o top enoeent entod n deton ( < t < h/) poton o top enoeent entod n deton ( < t < h/) poton o otto enoeent entod n deton (-h/ < < ) poton o otto enoeent entod n deton (-h/ < < ) nge o enoeent n deton, ntowe wth epet to - nge o enoeent n deton, ntowe wth epet to - A t,n n top enoeent to e povded n deton ( < A t,n) A t,n n top enoeent to e povded n deton ( < A t,n) A,n n otto enoeent to e povded n deton ( < A,n) A,n n otto enoeent to e povded n deton ( < A,n) d opeve degn tength o onete ( d > ) d,t opeve degn tength o top e o onete ( d > ) d, opeve degn tength o otto e o onete ( d > ) d ed opeve degn tength o onete ( d > ) d ned opeve degn tength o onete ( d > ) dt tene degn tength o onete ( dt > ) tn opeve pte onete tn ( tn ) opeve onete tn ( tn) e opeve onete tn ( ) popoton o depth to net ove whh etng te o t ( ) (/d) ve o /d, the to o net to eetve depth, o ee: (/d) n < (/d) t, t, -, - }/h)] E et od o enoeent O Ltd 5

122 O GSA d degn tength o enoeent n tenon ( d > ) d degn tength o enoeent n opeon, ( d > ) ne tee te o enoeent ( > ) ε p p > ) ε p p > ) ε ϕ Δ degn ve o tn n enoeent petted nge etween pped nd etng pnp te n ddton, the pog need to now whethe to e, whee ppopte, the te ppoh nd, o, wht the e o enoeent o ted hod e eoe the goo ppoh ed. Wthn RCS the enoeent poton e eed wth epet to the d-heght o the eton, the poton eng eed potve pwd. he enoeent nge e peed wth epet to the - nd eed potve n n ntowe deton oong o ove. t hod e noted tht the onete ed to hve eo tene tength n the n; the tene tength, dt, on ed to te the opeve tength when tene tn e peent. he et o eh n ont o the eqed e o enoeent, negtve tene, n eh deton n the top nd otto e o n eo g ndtng tht oton od not e ond. Othe So Ued n heo te α ε φ popoton o tot thne opng eh ote e tn nge o pnp opeve te nd tn, eed ntowe wth epet to Se A B C etng to p A etng to p B etng to p C o opeon-on enoeent etng to tenon-on enoeent pped otto e o e onete O Ltd 5

123 O GSA e eetve dde e n gene deton = o t tee top e o e t eve o enoeent deton deton > pnp deton wth gete opeon o ee tenon < pnp deton wth gete tenon o ee opeon RC S Sgn Conventon Wthn RCS the gn onventon hown eow; note tht thogh t deent o tht ed GSA, the ntee onvet nee: M M N M M Z Y M M X N M N N M Copeon nd ggng oent e potve. O Ltd 5

124 O GSA RC S An Poede he oowng e the poede oowed RCS:. Adjt, whee nee, the pped oent o n eentte.. Spt the eton nto thee e wth the ent e nteed nd the ote e tng n-pne tee, the thnee oepondng to n epte net depth; te the tee pped to eh e.. Cte the te to e ten the onete n eh e nd the te o eh e to e ten enoeent.. Cte the oe to e ten eh o the o et o enoeent (two e, two deton) tng nto ont the poton etve to the e. 5. Detene eton tn opte wth the net depth ped the e thnee n 5.. nd the onete tn n the ote e o 5.. o top nd otto e.. Detene enoeent tn opte wth the eton tn. 7. Fo the tn, te the te n eh o the o et o enoeent. 8. Knowng the oe to e ten eh o the o et o enoeent nd the te n eh et o enoeent, te the enoeent e eqed; thee hod not e e thn the peed n ve. 9. Repet nee o 5.., djtng the e thnee to heve the n tot e o enoeent.. Whee n-pne eet donte, epet o 5.. doptng ode wth the ent e teed.. he degn enoeent e oepond to the e ngeent gvng the n tot e o enoeent.. o peed p the ton, n opton ve to dopt non-tetve tehnqe whee the odng p ethe n-pne o ot-o-pne. non o oent etng o ddton nd n eentte he pped oent e djted to te nto ont the ddton nd n eentte o pped oe. he ddton eentt, whh n e ed to ode toene nd eond-ode eet, detened the e; pped endng oent e need opeve pnp oe t e not djted o tene pnp oe. he oponent o n-pne oe n the othogon deton o e wth the ddton eentt, N,dd, N,dd nd N,dd, e ted ng the nge etween the pnp deton nd the - nhnged. O Ltd 5

125 O GSA θ θ (N, N ) (N,dd, N,dd ) (N, -N ) (N,dd, -N,dd ) he det ve o the n eentt, whh n e ovewtten, ten o the hoen degn ode; th ve, nd othe ode-dependent ve, e gven n Append. the ote ve o the pped oent eeed the o the ddton nd n eentt oent o M, M nd M, then the pped oent e need n gntde the epetve ddton oent. Othewe two et o pped oent e ted, oepondng to eentte pped n the two ene. M d M Mdd n Mn M j (Mdd M M Mdd n Mn n ) whee j te the ve o - o the t et nd + o the eond et. Fo epe, the pped, ddton nd n eentt oent wee 75N, 5N nd N epetve, the degn oent o the two et wod e = -5N nd 75+5 = 5N epetve. t hod e noted tht no pe owne de o endene. Dvon o eton nto e he eton dvded nto thee e, eh wth ontnt n-pne te. he ote e oth hve thne o αh, whee α the popoton o the tot eton thne, h; the nne e theeoe o thne (-α)h. n-pne oe e eted ethe the ote e one o, thee ent n-pne opeon, thee e. he ote e o et the oent etng o ot-o-pne oe. O Ltd 5 5

126 O GSA Ste wth ent e nteed h N/[h] + M/[(-)h ] h h N/[h] - M/[(-)h ] N M Ste wth ent e teed h (-)h N/h+M/[(-)h ] h N/h-M/[h ] N M (n th ge, N epeent N, N o N nd M epeent M, M o M epetve.) he pog detene tetve the ve o α tht gve the owet tot e o enoeent, α opt. Cton e t peoed o the ondton wth the ent e nteed, nd then epeted o the ondton wth t teed, thogh the tte et e on vd thee no tenon enoeent, o tenon enoeent eqed n oth e, n pt deton. he n vd ve o α eo; n ode-peed eve onveted nto n eqvent tn n the enoeent, whh ept heed. Whee the ent e nteed, nd the opeon n the enoeent deton wth the ge oe eentt e thn. d.h, the vd ve α gven α = β(/d).(.5 + n{ t, t, -, - }/h); whee the opeon n th deton eeed.5β d.h, αβ =.5; o nteedte ve o opeon, the ve o α ne ntepoted etween thee two etee. Whee thee e e teed, the vd ve o α gven α =.5. he nt ve o α ten α /. th ve doe not gve vd et, ton e peoed o α = α / nd α = α /. nethe o thee ve et n vd et, the ddton o ve t the eghth pont o the nge e ted. h poe epeted, ng teenth pont et, nt thee t et one vd et o the ntev etween djent ve o α eow tng ve o.. One vd ve o α h een detened, on the ve ng etween th ve nd the pevo ted ve o α on ethe de e ondeed, hvng the ntev. h epeted, hvng the ntev o eh tn, nt t eow tng ve o.5. n the oowng epe, t h een ed tht α n =, α =.5, vd et e otned o. α.5, α opt =., nd, o pt, the e o enoeent nee ne wth the deene etween α nd α opt. he optton poe top when the ntev e thn.5. he pog wod te e o enoeent o the oowng ve o α. O Ltd 5

127 O GSA Ve o α n t ndte no vd oton; ve n od ndte th eved opt ve. Ve o α o whh enoeent e ted Cent ve o α opt Cent ve o ntev he oowng poede t e opeted o eh t ve Cton o te to e ten enoeent n e he degn tength o the onete, d, depend on the etent o ng nd need not e the e n deent e. Fo eh e, the pnp pped tee, < nd > wth < eng oe tene, e ted o the othogon tee. < opeve, the ned onete tength, d, ed. Othewe the degn tength depend on the to o < to the tene tength o the onete, dt; the tength ted d [ - ( </ dt)²], t not e thn the ed onete tength, d. he onete tength e ode dependent. < not tene nd > not gete thn d, then enoeent not eqed to te n te o th e. Othewe, the enoeent t te ent te to heve eq wthot ethe oveteng the onete o eqng t to te tenon. he gene epeon e gven n Append. he oowng dg tte the tton wthn e whee the enoeent gned wth the nd deton. Conde D eeent o no thne wth pped n-pne no tee nd nd he te. Ae tht the eton n pne t nge to the pne, eed ntowe. he pped oe e eted the onete, tng n opeon, nd enoeent n the othogon deton tng tenon o opeon nee. O Ltd 5 7

128 O GSA he nge t whh the o nde the degn od,, not gene eq to the nge o the nt, whh depend on the deton o pnp tene te. A enoeent ed, the nge o ng otte, nd th nge e ted degn ode o the e. RCS eet the nge, opng wth n tton, whh et n the owet tot e o enoeent. h oten oepond to the nge tht o gve e to the n te n the onete. p /tn p v Conde eq o the tnge eow the ; nd e the tee ten enoeent: p Reovng hoont p v /tn.( + ) =. /tn =.tn - Reovng vet.( + ) = /tn. = /tn - Conde eq o the tnge wth e no to the ; > the te n the onete: > > p v p v /n Reovng hoont p.( + ) + /tn. = (/n. > ).n > = + + /tn =.tn + /tn > = /n p oth nd e potve, tene te t e ten enoeent n oth nd, o whh nge = -, = - nd > =. O Ltd 5 8

129 O GSA Moh e povde e too o detenng the te to e ten the enoeent nd the te n the onete. he e epeentng the opeve tength o onete h pnp ve o the ogn nd the onete degn tength. th e doe not enop the e epeentng the pped te, enoeent eqed. pnp tene te ( < ) he te X (, ) opeve tength o onete ( d ) opeve te Y (,- ) pnp opeve te ( > ) pped te Renoeent eqed ee the pped te e doe not e wthn the e epeentng the tength o ed onete he te ten the enoeent tted o the pped te to gve ed te n the onete, whh t w wthn the e epeentng t opeve tength. th not heve, then t not poe to enoe o the pped te wth enoeent n the deton hoen; the enoeent t e oentted oe to the pnp deton, o ee tonge onete hod e ed. the enoeent gned wth the nd e, then the oet epeentng the te ten the enoeent e hoont; othewe the oet e t n nge wth the vet oet eq n gntde t o oppote gn. < he te te ten -deton enoeent X (, ) X (, ) opeve tength o onete ( d ) opeve te > (t e e thn d ) Y (,- ) Y (,- ) te n onete te ten -deton enoeent pped te Note tht o =5, the te ten -deton enoeent eq to ( - ) nd tht ten the -deton enoeent eq to ( - ) O Ltd 5 9

130 O GSA Cton o oe to e ten enoeent Hvng detened the tee to e ten enoeent n thee e, the oe n the o et o enoeent t e detened ondeng eq. he deene etween the entod o the teed e nd the poton o the enoeent t e ten nto ont. th ton ndeten n one tge, noe od o h tenon enoeent eng eqed whee the ondng onete n opeon. o vod th, the ton de n thee tge. he poede wo ette the ge oent et n tenon on the otto. the ge oent et n tenon t the top, the eton nd pped oe e nveted eoe the ton ndeten, nd the et nveted t the end. n tge A, the oe eqed n the top tee, N ta, e ted ng tht the tee to e ten the otto enoeent e dtted no o the otto e, A. h hown dgt eow; thee wod o oe e n eqvent dg o the eond tee deton. he ove dtton o onete nd tee tee n the otto e then eheed to ee whethe n o A n n t e eted the onete; th ton et n tee o B to e ten the otto enoeent. Stge A h (-)h h t edtted to N ta A t h(-)/ n tge B, the oe eqed n the otto tee, N B, e ted etnng the top enoeent oe to tee dtted no o the top e, tb. he ove dtton o onete nd tee tee n the top e then eheed to ee whethe n o tb n e eted the onete; th ton et n tee o tc to e ten the top enoeent. Stge B t N ta edtted tb h(-)/ h(-)/ B to N B O Ltd 5

131 O GSA n the n tge, C, n enoeent, top nd otto, eqed to te the oded tee n the top e ted. B ondeng the top e t, thee w e pe whee no top tee eqed. Athogh tge C od et n otto tee n oton whee t wod e nnee wth the tonton, the enoeent e wod e nd e thn non otto tee. Stge C h(-)/ tc edtted N tc t N B to N C Athogh th thee tge ppoh te enoeent oe eon eono, t et n deene n the e o top nd otto enoeent o pe od. Detenton o eton tn opte wth onete tn n ote e o detene the o et o enoeent e eqed to te thee et o oe, degn tn, opte wth the onete te o, needed o eh et. he t tge o tng thee tn to detene the opeve tn t the ote o nne onde o the onete te o. he ton o the pnp opeve tn t the top deed eow; oepondng poede ed to ette the pnp opeve tn t the otto. <.n ( t - ) + >.o ( t - ) < ( t - ) >t > Athogh t th pont n the poede, pnp opeve tee n the onete hve een detened o the top, >t, nd otto, >, e, the Cton o te >t n otto e t the nge o pnp tn t, w not n the top e gene e gned. n ode to ette the tn poe o the top e, >t, the te n the otto e n the e deton >t, ted. Knowng >t ene the opeve pnp tn n the top e to e ted. >t/ d,t eq >t/ d,, then the oe >t, t the top o the eton nd ten the tng tn,. h h te >t >t tn O Ltd 5

132 O GSA >t/ d,t e thn >t/ d, >t t the ente o the top o nd ted the opeve pte tn o onete, tn, toed >t/ >t. h h >t >t h/ t t tn te tn >t/ d,t oe thn >t/ d, >t t the top o the eton nd ted o tht t doe not eeed the tng tn,, nd tht the tng tn,, not eeeded t poton (- / )h o the e, ng tn t the ente o the otto o o tn toed >t/ >t. h h te >t >t h/ tn >t ( / )h Aed te-tn eton o onete te >t >t he opeve tn on the oe opeed e n eeed tn even the opeve te e thn the onete tength d ne the tte tn od e otned wth e te o, h, t oe voe eve >t tn tn <t >t. the e opeve pnp te, <t <t, ten tn toed <t/ >t, whee <t the e opeve pnp te n the top o. he e onete tn e ode-dependent. Detenton o opte enoeent tn Hvng etted the onete tn, the net tge to detene opte enoeent tn. hee e thee deent poede o tng the enoeent tn, the hoe o whh depend on the eton etween the enoeent oe, ed n the oowng te. Deent poede e ppopte o eh e nd deton. the to o the depth o the etng te o to the depth o the net, whh ode-dependent. O Ltd 5

133 O GSA C = opeon Renoeent N = none eqeent: = tenon Pnpe n Fe ondeed U = none; onete nteed Oppote e Poede detenng enoeent tn Deton Othe Deton Othe ondeed deton ondeed deton Pnp tene tn hoen to gve C C An /U /U An A n e o enoeent; ton de t eve o opeon enoeent. O the ende: Stn optt not /U C/N /U /U /U C/N B eqed ne oth e n tenon nd no net n othe deton. onete ed, ond tn ted to e opte wth pnp opeve A othe C tn on oppote e nd net depth ontent wth depth o te o. Stn t enoeent eve ntepoted o ond tn. he poede e deed eow n det. O Ltd 5

134 O GSA Poede A he pnp tene tn ted o tht the tot e o enoeent n th e t n. Note tht the tene tn not ge enogh, the tene enoeent w e wong t ow te, o even e n opeon, t the tene tn too ge, the opeve enoeent w e wong t ow te, o even e n tenon. he oe to te the opt ve o the tene tn e gven n Append. he ton de t the eve o the opeon enoeent. Athogh the tenon enoeent w e t ght deent eve, t ed tht the tn n t ppote eq to the tn n t deton t th eve; ne the enoeent n the oppote e n the e deton w w e n tenon, th hod e eone pton. he te Reton etween tee nd tn t the eve o the top enoeent, deton, wth poede A tene tn n enoeent deton he tn / opeve tn n enoeent deton Y Y <t X >t opeve te <t X opeve tn >t opeve tn n onete te n onete tn n enoeent & onete Note tht pnp tee nd tn e gned he notton e tht th the top e wth opeon enoeent n deton o ette the pnp opeve tn t the eve o the opeon enoeent, the vton n gntde nd deton o the pnp opeon etween the top nd otto e t e ondeed. Fo thee pen ton, the gntde o the pnp tene tn ten eq to tht o the pnp opeve tn. he tn n the enoeent deton e ted ng the poede n the ge eow o oth top nd otto e t the ppopte o ond; o thee tn, the ve t the eve o the opeon enoeent ne ntepoted. Fo the no nd the he tn t the eve o the opeon enoeent, the gntde nd oentton o the pnp tn t th eve n e etted. O Ltd 5

135 O GSA Ettng gntde nd oentton o pnp tn n onete t eve o opeon enoeent wth poede A <t >t. o( n - t ) N ( n - t ) tn >t >t. n( n - t ) h/ whee >t > tn tn tn tn n Mn tn, <t, ed to e - >t o th ton h/ tn tn tn Fo ε tn nd the oepondng he tn, the gntde nd oentton o the pnp tn t the eve o the opeon enoeent, ε> t, n e etted whee >t < tn n he n tge o tng enoeent tee e owne o the e o onete dped opeon ttng the onete te t the eve o the enoeent o the tee te. o opente o th when detenng the opt tene tn wth poede A, oe, etted to eq the oe n dped onete, dded to opeon. h heved tong the opeon : t o n,e tn n o n >t o (θ n -ϕ) >tn o(θ n -ϕ) n pnp te w eo ne tene enoeent eqed N (θ n -ϕ) >t n tn ed to e - >tn o th ton N (θ n -ϕ) >tn te n onete tn n enoeent & onete Poede B h poede dopted when tn optt not eqed o tenon enoeent; the degn tength o the enoeent ed. Poede C he t tge o th poede to te the tene tn n the opeon o t ethe t e o nne ond, ppopte, n the deton o the enoeent. the O Ltd 5 5

136 O GSA te o n opeon, the tn detened o the onete te, t t ed, the tn opte wth the pnp opeve tn on the oppote e nd the depth o the net detened. >t Ctng tn n enoeent deton, tn, o ed top te o wth poede C tn N >t h/ whee >t > tn > θ n ( - t ) <t t >t >t h/ X h/ whee >t < tn > Stn t ond o top te o <t = [ >t - >t o ( - t )] / n ( - t ) tn = <t n (θ n - t )+ >t o (θ n - t ) Hvng otned the tn n the enoeent deton t the onde o the te o, the tn t the eve o the enoeent n e ted. Ctng enoeent tn, tn nd n, wth poede C tn tn tn n n h/ whee >t = tn n h/ tn tn tn n n whee >t < tn n Detenton o te n enoeent he te n the enoeent ted o the tn; t-ne te-tn eton ed o the enong tee n oth tenon nd opeon, o whh the ent pont e O Ltd 5

137 O GSA ode-dependent. the to te opeon, the ted te n the enoeent eded the e onete te n the enoeent deton to ow o the dped onete. Cton o e o enoeent the oe nd te e o oppote gn then the ton o th pt ve o α ne. the oe eqed to e ten the enoeent o the e gn the te ted n tht tee, the e ted dvdng the oe the te; the e ted to h the eton thne. he peed n e ed ppopte. Fn, the o enoeent e e ed to gve tot tht oped wth the tot etng o othe teton: the enoeent e wth the et tot e otpt the pog, wth opeve enoeent dented negtng t e, oowng GSA gn onventon. Non-tetve tehnqe o peed p the ton, n opton ve, whee the odng p ethe n-pne o ot-o-pne, to dopt non-tetve tehnqe. h ppoh e to ed to ght oe onevtve et. he e n hooe to e th ppoh n ppopte tton nd n pe tot e o enoeent, peentge o the o-eton e, ove whh goo, tetve oton ed. P n-pne he pped od e ten p n-pne the eentte o the oent eq the n eentt o eh oponent o whh thee oepondng oe. Whee od e p n-pne, α ten.5. the opeve te n the e eeed t tength, the eton nenoee; othewe, enoeent e e ted. P ot-o-pne he pped od e ten p ot-o-pne the oe opeve pnp e thn. d. ene no tee do not pevent e o th tehnqe. Whee od e p ot-o-pne, the ent e nteed nd the ve o α nt et to α. the opeve te n the opeve ote e eeed the tength, the eton nenoee. opeon enoeent eqed, the tetve oton ed. Othewe, eded ve o α ted o tht the etve oe hgh teed o the top nd otto e jt eow t opeve tength, whe enng n eq wth the pped oent; t on the hnge n α e poed. he tee e eted o th ve o α, nd the eved ve o α ted. the hnge n α eeed., the tee e eted gn. Renoeent e e ted o the n ve o α. Dtton o enoeent RCS te the e o enoeent eqed t eh node. Sne the enoeent dtton oepond to the oe nd oent dtton wth the onentton nd pe, thee e oton whee no tto enoeent ngeent n e O Ltd 5 7

138 O GSA detened ee the onete oveteed n he. thee pont, whh e et when ontong, e oted, the n po e gnoed t ge e w eqe hnge to the geoet o te popete. t o ppopte to vege ve o enoeent n e o get hnge. Fo epe, enoeent eqeent n t n e veged ove the ent h o the on tp, the ote poton o the on tp nd the dde tp, when oowng ode ethod. t hoped tht te deveopent wthn GSA w hep tote th vegng poe. O Ltd 5 8

139 O GSA Reded tne & P-det he eeent tne n e pttoned nto tte () nd etned () degee o eedo K K K K So K K K Gvng the eded eqton K K K K K K o ~ K ~ K ~ When etng the tte tne t the eeent t n e eed nd then eded ove eoe eng nded n the tte eqton. K S SS S One the tte dpeent e ted the eeent dpeent n e ethed o K e K And the eeent oe K e ee e K Fo P-det n the go oton oded to S K SS K gss S Kˆ SS S t the eeent oe ton nhnged. h en tht one the tte dpeent e ted the eeent dpeent nd oe e ted o Kˆ Kˆ e K e ee e Kˆ O Ltd 5 9

140 O GSA Se Cton Repone Spet An Repone Spet he epone o nge degee o eedo te ode (eqen, pet eeton pet) q ( ) pet Mod n ede ope tte to n eqvent te o nge degee o eedo oto o th n e pped to the tte whoe o n eeted ode. he epone n gven ode n deton j j j ( pet ) Whee j he ptpton to to ont o the deton o etton. he te j pet ( ) the od tpe. Fo go & we e &. So o etton t n nge α we wnt to e to the denton o the ptpton to n nd deton: α. Gong M ˆ M ˆ Whee & oepond to gd od dpeent n the & deton. So the gd od veto t α o n And the othogon deton α wod hve gd od veto ' n o h en tht o otted etton deton we jt need to otte the ptpton to nd we don t need to tno the dpeent, et. O Ltd 5

141 O GSA ' M M o n ˆ ˆ M M n o ˆ ˆ o ' o n n o ht eve the on tnoton we need eng the tnoton o go dpeent to o o node n ontnt e. Fo thee we wnt to tno od et o go to o, do the onton nd tno oned ve o o to go. he od epone e then oned ng one o eve onton ethod. Conton he n onton ethod e: ABSSUM SRSS CQC 5 j j j whee j 8 j j j j j j j j j j whee ζ nd ζ the dpng oted wth eqene nd j. j j j 5 Won, de Keghn & Bo, 'Ethqe Engneeng nd Stt Dn', Vo 9, pp 87-9 (98), O Ltd 5

142 O GSA the dpng ontnt th pe to j Roenth 8 j j j j j whee CQC j j j j j j j j j n SRSS ethod, the pet, e pped to % on the pnpe deton. he epone otned o SRSS onton h eq ontton o the deton. Howeve, n pte the e gond oton w not o n oth the deton. heeoe, SRSS ed onevtve et. Menn nd De Keghn 7 (998) peented the CQC onton ethod o onton o the othogon pet. Let e, e the jo nd no pet pped t n t nge o the tt. o p the n the e the pet oe ton o pet. ASCE -9 Se n o et eted ne tte nd oent', Chpte. An o Stte (9) 7 Menn, C., nd A. De Keghn A Repeent o the % Re o Mtoponent Etton, Ethqe Spet. Vo., Ne. Fe. O Ltd 5

143 O GSA Y Spet (S) Y X Spet (S) θ X Epente he pe epone ve n e etted ng the ndent CQC eqton Q Q Q Q Q n Q n o Q whee Q Q Q Q j j j j q q j j q q j j j q q j j q q j nd q, q e the od qntte poded pet pped t nd deton, q the od ve poded the vet pet nd the t nge t whh the te pet pped. No, the ve o not nown. he t nge tht pode epone n e ted ng tn Q Q Q And the t epone eoe Q Q Q Q Q n Q n o Q the ve o, CQC onton ede to SRSS onton. he pe epone ve not dependent on the nd the pe epone n e etted ng. O Ltd 5

144 O GSA Q Q Q Q hee no pe gdene ve to hooe the ve o. Menn nd De Keghn peented n epe o CQC onton wth ve ngng o.5 to.85. Stoe net Foe he toe net oe n e ted o the toe, nd net,, epone pet nd the od et. he toe od tnton (, )nd otton (θ) e ted (ee eow) he oe nd oent o etton n the th deton e then detened o M.. ode CQC ode CQC. pe ode CQC pe pe Whee ode the ode ng to, pe the pet eeton nd the ptpton to. Eqvent Stt nd Adent oon Lod Mn e ode hve poede o ton o eqvent tt o dent toon od. GSA povde ethod o tng thee od. he t tge n the ton to eth the nod e. h nde the o eeent p the ddton deved o n od. od n h pevo een ed ot th noton ped p o tht n t. Fo eh toe we n te the toe M ng the o node n tht toe. epone pet e h een eeted the e he, V, etted o tht ton, othewe the e he ted ng the ode eqton (e.g. UBC, BC o FEMA). At th pont deent ode hve deent eqeent. n UBC 997, dependng on the peod, n ddton oe, F t, dded to the top toe. F F F t t t.5v.7 V Fo BC nd FEMA n eponent K on the dtton nton eqed O Ltd 5

145 O GSA K.5 K K.5.5 Fo othe ode K et to. Eqvent Stt We then te the oe to e pped to eh toe,, t heght, h F M M K H K H V F t And o the top toe F M M K H K H V Ft Ft h toe oe then dtted to the node, n, n popoton to the M Fn M n F Adent oon Fo the dent toon we te the toe e o the eqvent tt nd we te the ente o o eh toe. Stoe ton e etve to the ente o. We o need the wdth o the toe whh ted the deene n the etee oodnte n the deton o nteet. We hve n oet, o, whh ed on the wdth o the toe. he dent toon oent o the toe M, M, then F o h then pped oe to the node n the toe Fˆ n M M n F o A we etng toon on the toe th ed to oe Fˆ ˆ F n node So we oet o th djtng thee oe O Ltd 5 5

146 O GSA O Ltd 5 n n n F M M F F ˆ ˆ ~ And the oent on the toe node n n o F M, ~ Fn we djt thee oe ve o tht we hve the oet oent on the toe n n M M F F,, ~ ~

147 O GSA Rotton t the end o (e) Foe Pont od W t poton Fo Ro 8, the end otton o pont od e W E W E Lettng the dtne o end e thee eqton n e ewtten W E W E Vng od o : wth ntent w nd w. Ung the eqton ove o Ro the end otton o pont od t e W E W E Ung thee nd ntegtng ove the eeent gve E w d () E w he od ntent ne nton n the nge : d () 8 Ro Fo o Ste nd Stn, e (.e) O Ltd 5 7

148 O GSA O Ltd 5 8 w w w w w w w w w w w w w w w w w w w O w w w q p () whee w w w w w w q p Stttng eqton n o end q p q p q p q p d E w d E w d E w d E w d E w d E w d w w E o E w E w E w E w q p q p Stttng eqton n o end

149 O GSA O Ltd 5 9 q p q p q p d E w d E w d E w d E w d w w E o E w E w E w E w q p q p Moent Pont oent M t poton Fo Ro 9, the end otton o pont od t e E M E M Lettng the dtne o end e thee eqton n e ewtten E M E M Vng od o : wth ntent nd. Ung the eqton ove o Ro the end otton o pont oent t e E M 9 Ro Fo o Ste nd Stn, e (.e)

150 O GSA O Ltd 5 5 E M Ung thee nd ntegtng ove the eeent gve d E () d E (5) A wth the oe the oent ntent n e wtten q p () whee q p Stttng eqton n o end q p q p d E d E d E o E E E E q p q p Stttng eqton n 5 o end q p q p d E d E d E

151 O GSA O Ltd 5 5 o E E E E q p q p he Fo the gdent pped to e the vte So the d o vte Ang the otton t the end pepend to the d en o the. h en tht the nge o the d ne to the e ogn ongton o o And o o Pe-te On the tendon pe-te P wth n oet o w gve e to otton. he eet o th no oent ove the ength o the eeent o Po h e n then e teted ove o pth oent.

152 O GSA Be dtoton A e dtoton n e dpeent dontnt o otton dontnt. Fo dpeent dontnt o v t the otton then v Fo otton dontnt o t the otton ted denng dpeent o h t then the nge nd end nd t end gve the et o eqton n tn o n tn o h h Stttng o n the t eqton gve o n h n o o n ho o n n n n n o ho n o o Stttng o te n n ho h o hn nh o h n hen the otton nge t end nd e tn tn h h Seond Moent o Ae & Bendng he eond oent o e e dened O Ltd 5 5

153 O GSA A A A da da da Fo et eton eo. Fo n endng o endng ot pnp e M M E E When thee endng thee hve to e oded to M M E A the eond oent o e o teno thee n e otted to deent e ng otton t ~ ~ ~ ~ o n n o o n n o O ~ ~ ~ o n n o n o n o n o n o o n O n te o doe nge ~ ~ ~ n o o o n n O Ltd 5 5

154 O GSA She Ae hn-wed Seton he eet o he deoton on the et o tt n negge. Whee t oe gnnt, t w e to e pe ppoton to the he deoton e o ee wth o-eton h thoe hown n Fg. he ppoton, nog wth pe etng e, to te 5 o o the tot we e (ove depth we thne). Fo thoe e tte whee the he deoton ve potnt t e nee to e oe et ve o the e. h Note gve oe o F o the o-eton o Fg. whee dt A F O Ltd 5 5

155 O GSA hee wee deved o the vt wo o, he deeton pe nt ength = q d. Hee q the he ow t n pont t the dde o the w thne, the he te Gt q t ed ontnt o the w thne t, nd the ntegton etend ove the whoe oeton. o ee wht the oe en n pte, the wee pped to tee eton ten o the hndoo wth the et hown n the te eow. n we o nge wth vng thne, t w ed ontnt t t vege ve. he e ve o F n nge oepond to o-eton wth qe pet to. Spe on o UB, UC nd hnne wee ten. t n e een tht, o eton wth top nd otto nge endng, nte ntended, n the tong deton, the ppoton tto (thogh t hod e noted tht d the dtne etween nge ente, not ove depth). Fo the oe e eton ed n endng, ve o F e een to e owe thn epeted, epe when the e pevee ent n the weet deton. Seton F Bendng n tong deton UB 5.7 to 5.8 Jot 5.7 to 5.78 UBP 5.5 to 5.8 UC 5.8 to 5.5 SHS 5. RHS 5. to 5.9 d : Chnne 5. to 5. Ange.8 to. d : ee o UB.78 to.97 ee o UC. to.5 Co 5 Bendng n we deton Chnne. to.78 RHS. to 5. : d ) Ange.55 to.8 (o d =.5 to ),, & o 5. O Ltd 5 55

156 O GSA Wth egd to tng he tee, the et dtton not no eqed, o even e, ee Code o Pte e the he tength on n owe vege he te ted on the tot net e Dt. Howeve, the he dtton oete eqed to degn wed o onete tthe, nd, ne t w ond n the poe o devng the oe o F, oe o the te to nd e gven. Hee, q V d the he ow n the we t the jnton wth the nge, nd q V d the he ow n the we, n whh V the he oe t the eton. Fo nn, ng tht the te ontnt o the w thne t, oth the deeton nd te n e otned ng he e o h the t e, tht t whee the en d. Foe dt She deoton e pe A dt A F t d d F. pe A & A F. Spe e o A wth ontnt w thne o tht t,, F 5 5 pe B F... O Ltd 5 5

157 O GSA Spe e o B wth ontnt t,, F 5 pe B & B F.5... Spe e o B wth ontnt thne t,, F 5 pe C F 5 Ste Fto pe A, A & A j pe B, B & B j Sod Seton Fo etng e t ent te to te the he e o deeton 5 d whee the edth nd d the depth o the eton. he oepondng he te V d. t hod e noted howeve tht o wde e the he te ndeetted th o: o e wth n pet to o the te.% hghe. (Fo e wth n pet to o 5 (o epe ) the te ot % hghe t, th Poon to eet, t dt to eeve tht th h n pt gnne! ) oheno, S.P. nd Goode, J.N. heo o ett. d edton. MGw-H, 97. O Ltd 5 57

158 O GSA Fo eton the he e o deeton 7 whee Poon to nd the d. he epeon ve nentve to the ve o. he he te gven.5 V whh ve o V.5 o to V. o. 5 wth V.8 o. h te w wtten John Bnhd nd n Feth o Feed Note [n Ove Ap & Ptne nten pton] (99 NS/) ogn phed n Otoe 99. nopote 99NS/ nd epoded hee wth peon. Stoe Dpeent Stoe dpeent e ted o n Whee e the node n the toe nd n the ne o node n the toe. he otton e the ted etve to the ente o,. he poton o node etve to the ente o the dtne o the ente o O Ltd 5 58

159 O GSA O Ltd 5 59 nd the oponent o dpeent gvng e to otton he otton o the toe then dened n

160 O GSA S-ode Etton h ete ow -ode to e etted o GSA, o tht the -ode n e nvetgted n oe det. hee e two pet to the -ode: the eeent tht o the -ode nd the t tht e to e oted wth the -ode. he node tht o the -ode nd the node tht o the ond etween the ode nd the ende o the ode e dented. A new ode then eted o the ode. Node on the ond e etned. Popete e oped det. Contnt nd odng e pdted to nde on thoe oted wth the -ode. e pdted ed on the t eeted o the -ode. Stt n t Fo tt n t the dpeent t the ond node e etted o eh n e. hee e then pped n new od e etteent, nd the n e pdted to nde thee etteent. Mod dn nd Rt n e Fo dn t thee the opton o Lo o Go epone. Lo the ode pedonnt o t e oe ppopte to onde the ond o the ode ed nd to ot od n o the -ode. n th e the ode etton tghtowd. n th e the n t oped det Go t not poe to ot -ode ode n when the ode go. n th e the od et e ed to ete et o tt od he od n o the ode gve egenve nd egenveto whh t K M h n e enged n the o K M Whh we n onde tt (pedo od) n o whee K p p M O Ltd 5

161 O GSA When ettng the -ode the eqen (egenve) nd ode hpe (egenveto) n e ed to ete et o node od: n n p p n M n n n. M he od t n the ode pped to tt t n the -ode. A o the tt n the dpeent t the ond node e ed to detene etteent t the ond node nd the net od e ved node od. he tt n o thee od w then eove the ode hpe o the ogn ode. Repone pet n Repone pet n onton o od et ed to th gven epone pet. Ettng the od et e tt od e en tht the dn det e ot to the -ode. o oveoe th poe the epone pet t e pped to pedo epone pet t. A pedo epone pet t e tht tt n e epeent ode hpe. he dn det e pped det to the t n the o o eqen, od nd eetve e. When epone pet t etted o the ode thee det e eoveed o the od n nd nded n the pedo epone pet n t. Gven hpe o pedo od n the ng o eh ode, o etton n the j deton :, j pet Whee j j ~,, the pedo od n ed ot ng the tt poede ove, nd the eqen nd ptpton to e nown o the te ode, then the od ontton to the epone pet n n e etted. heete the onton jt o n no od n. O Ltd 5

162 O GSA oe Lne GSA gve the opton o pottng oe ne, whh e to tht ne t nde the eet o toon. he e eq o pne e. Good tt degn eqe e thnng hed, we-peented noton nd oe etve. At the deted eve degn poge tetve evoton nd the qt o the degn depend on the eetvene o the nteton etween the degne nd the noton whh dee the ehvo o the tte n the ent e. n tod wod th noton ot w peented opte. Gph pot o the pete ed n the ne ne e oten egono neent, enng tht thogh the ontn the noton the to tnt nght o ndetndng nto the hed o the degne. Bette epeentton e needed. Fo n ppton tht ne eet th need. he e e whee ee e jeted to oned od nd endng, pt o opeon ee de o te tht te no tenon. n thee e the deq o the ee n oten e eon deed t on the eentt o the tht ne. ht ne e eqent ed the degne o on he. A tht ne the o ong ee o pont dwn t n eentt o M F o the entod o the ee, whee M the oent nd F the oe. t oow the ne o ton o the oe ed the ee nd two eted pont oow o th: No e needed when dwng tht ne. t not dg pepoed on vew o tte. t ope the poton whee t hown. t not jet to n gn onventon. Howeve the e ete o the tht ne whh e t o e tht t opete depton o the oe ed the ee. Bee o th opetene popet degne n, wth no o o, ttte tht ne, whh he o he n ve, o the onton o the thee ne epeentng the oe, oent nd he, whh en ton tt. n opte ode o tte the tht ne deved o the oe n ee t ee t ope the t poton o the oe tntted thogh the tte eng odeed t oow tht t poton en ed n pe even the ee whh ppot t oved, povdng the oveent o the ee doe not hnge the oe eng tntted. h n e eeed to the nvne popet o tht ne. he ove tteent ee to tht ne n two denon, n pne e ode. ht ne n o e dwn n thee denon t notnte n htng p denon the oe oth the opetene nd nvne popete nd o the oe the ene to the degne. O Ltd 5

163 O GSA he gene tte o oe n eton o ee n thee denon nnot e eded to nge oe, t t n e eded to onton o oe nd toqe o, oe opete, to n one o n nnte ne o oe/toqe p. hee jt one oe/toqe p, heete eeed to the toe, o whh the oe nd the toqe e pe. n thee denon t toe ne tht hve the opetene nd nvne popete nd o t toe ne whh n e ed degne to ve tt ton. he poton o toe ne deved o the oe n eton o ee oow he etnt he oe, Q, nd t nge to the,, e gven Q F tn F F F he nge etween the ee nd the tht ne gven tn Q F he toqe,, o the toe eoved nto oent ot the thee ee e. he oponent ot the the toqe M n the ee. he othe two oponent od the endng oponent M nd M. Bee the oe oponent o the toe ( oppoed to the oent oponent) e the e thoe on the ee, the tht ne nd the toe e pe. Hene heeoe o M M e Eentte o the toe, t ndt, e gven t t M M n n F n n F hene O Ltd 5

164 O GSA t t M M M F F M F F F F How do toe ehve? A toe nqe epeentton o the oe tte n eton o tte. oe n e dded o tted. hee w nqe et. Note tht two toe e n the e pne the ddton o tton not nee n tht pne. n thee denon o oe on od n eq e nee ondent. he e not te o toe. Conde o ondent toe n eq. one o the toe tnted wthot hngng t deton then the od jeted to oent. Eq n e etoed djtng the toqe n the othe thee toe. Hene eq heved wth o non-ondent toe. Oten t w e nown tht one o oe o the toe hve eo toqe. Fo epe gvt poe eo toqe on od. How n toqee toe e needed to etoe the ondene e? he nwe o. h the e the o oe on od e. jt one o the o e toqe t n e eted onton o te ht o the othe thee oe nd ondene ot. he ene o the onept o ondene ted to tteent h : he o two ondent toe, one o whh toqee, ondent wth t oponent. Fo the degne the eon o th tht, ne tte oneved eng t thee denon, t oten ette to ne t two denon pne e dng the degn evoton phe o the ondene e n e ed to ndetnd wht dvng the gntde o the oe. h te w wtten Ang Low o Feed Note [n Ap nten pton] (999 NS/7) nd epoded hee wth peon oon Contnt n tt eeent pe o tnng toon oent t nee to dene ontnt to pe the twtng tne. h te eeed to the oon Contnt. he oowng note oe gdne on how to te the oon Contnt. Moe deted noton e ond n the tndd tet. n the tete thee oe onon ove the o ed to epeent the oon Contnt. n n tet t eeed to J. Eewhee the o C ed n n eot to dtngh the oon Contnt o the po oent o net. n GSA nd n thee note the o J dopted. o ontnt o eton nd o ength jeted to ontnt toqe, the nge o twt etween the end O Ltd 5

165 O GSA G whee G the he od nd the po oent o net. When the o eton o the non-, pne o eton do not en pne te deoton nd wpng w o. Nevethee the ove eqton n t e ed wth good, t hod e ten the ppopte oon Contnt J dened eow. Snt Vennt Appoton Snt Vennt epeented the toon ontnt (J) o od eton nton etng the ed nown htet ve o o eton th J A, A K Fo now etnge (.e. thn pte): J A whh ede to J Fo eton J whh the po oent o net. t n e hown tht o ee opoed o thn etnge, the toon ontnt eq to the o the J-ve o oponent etnge, eept when the eton oed o hoow. Retng Seton he toon ontnt J gven J K whee K ontnt dependng on the to o, whh n e ed ethe o the te eow. Lne ntepoton e ed o nteedte ve. O Ltd 5 5

166 O GSA o o the gph K K K K Note tht K onvege to o now etnge. Atentve K. gene, o nd o then K. Othe Seton he oowng te o Gh nd Neve (978) gve ve o the toon ontnt (J) o vo o-eton hpe. O Ltd 5

167 O GSA J J. J J. J 8 J d t whee the e enoed ne thogh the ente o the thne nd the nteg ed ot ove the eene J t t t t t t t t O Ltd 5 7