Evolutionary dynamics in financial markets with many trader types - ltlapril2001

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

Evolutionary dynamics in financial markets with many trader types

Brock, W.A.; Hommes, C.H.; Wagener, F.O.O.

Publication date 2001

Link to publication

Citation for published version (APA):

Brock, W. A., Hommes, C. H., & Wagener, F. O. O. (2001). Evolutionary dynamics in financial markets with many trader types. (CeNDEF working paper; No. 01-01). University of

Amsterdam.

General rights

It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).

Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.

,L*|L?@h) _)?@4Ut ? €?@?U@* 4@h!i|t |

4@?) |h@_ih |)Tit

Ghsduwphqw ri Hfrqrplfv/ FhQGHI/ Xqlyhuvlw| ri Dpvwhugdp

Th* 2ff

Devwudfw

Wklv sdshu ghyhorsv wkh qrwlrq ri d Odujh W|sh Olplw +OWO, ghvfulelqj wkh dyhudjh ehkdylru ri dgdswlyh hyroxwlrqdu| v|vwhpv zlwk pdq| wudghu w|shv1 Lw lv vkrzq wkdw jhqhulf dqg shuvlvwhqw ihdwxuhv ri dgdswlyh hyroxwlrqdu| v|vwhpv zlwk pdq| wudghu w|shv duh zhoo ghvfulehg e| wkh odujh w|sh olplw1 Vwdelolw| dqg elixufdwlrq urxwhv wr lqvwdelolw| dqg vwudqjh dwwudfwruv duh vwxglhg1 Dq lqfuhdvh lq wkh _lqwhqvlw| ri dgdswlrq% ru lq wkh glyhuvlw| ri eholhiv pd| ohdg wr ghyldwlrqv iurp wkh UH ixqgdphqwdo ehqfkpdun dqg h{fhvv yrodwlolw|1 Vlpsoh h{dpsohv ri OWO duh deoh wr jhqhudwh lpsruwdqw vw|ol}hg idfwv/ vxfk dv yrodwlolw| foxvwhulqj dqg orqj phpru|/ revhuyhg lq uhdo qdqfldo gdwd1

MHO fodvvlfdwlrq= H65/ J45/ G;7

Nh|zrugv= pxowl0djhqw v|vwhpv/ erxqghg udwlrqdolw|/ hyroxwlrqdu| ohduqlqj/ elixufdwlrq dqg fkdrv/ foxvwhuhg yrodwlolw|

Dfnqrzohgjphqwv1 Dq hduolhu yhuvlrq ri wklv sdshu zdv suhvhqwhg dw wkh LIDF v|psrvlxp Frpsxwdwlrqdo Hfrqrplfv/ Ilqdqfh dqg Hqjlqhhulqj/ Fdpeulgjh/ Mxqh 5<0Mxo| 4/ 4<<;/ wkh FhQGHI zrunvkrs rq Hfrqrplf G|qdplfv/ Dpvwhugdp/ Mdqxdu| 46048/ 5333 dqg wkh :wk Yl0 hqqhvh Zrunvkrs rq Rswlpdo Frqwuro/ G|qdplf Jdphv dqg Qrqolqhdu G|qdplfv= Wkhru| dqg Dssolfdwlrqv lq Hfrqrplfv dqg RU2PV/ Ylhqqd/ Pd| 57059/ 53331 Vwlpxodwlqj glvfxvvlrqv zlwk sduwlflsdqwv duh judwhixoo| dfnqrzohgjhg1 Wklv uhvhdufk kdv ehhq vxssruwhg e| wkh Qhwkhuodqgv Rujdql}dwlrq iru Vflhqwlf Uhvhdufk +QZR, xqghu d QZR0PdJ Slrqlhu judqw1 Z1D1 Eurfn wkdqnv wkh QVI xqghu Judqw &VHV0<<44584 dqg wkh Ylodv Wuxvw iru hvvhqwldo vxssruw1 Qrqh ri wkh deryh duh uhvsrqvleoh iru huuruv lq wklv sdshu1

Fruuhvsrqglqj dxwkru= Fduv Krpphv/ Fhqwhu iru Qrqolqhdu G|qdplfv lq Hfrqrplfv dqg Ilqdqfh +FhQGHI,/ Xqlyhuvlw| ri Dpvwhugdp/ Urhwhuvvwuddw 44/ QO0434; ZE Dpvwhugdp/ Wkh Qhwkhuodqgv> h0pdlo= krpphvCihh1xyd1qo> kwws=22zzz1ihh1xyd1qo2fhqghi2

L?|i?|t

 W?|hL_U|L? 

2 _@T|i i*iu 5)t|i4t D

2 Ai ,O Mi?U4@h! | h@|L?@* @}i?|t                   S 22 Oi|ihL}i?iLt Mi*iut                               H 2 ,L*|L?@h) _)?@4Ut                              f

 w@h}i A)Ti w4|t 2

 ,L*|L? uLh €?|i*) 4@?) |h@_iht                       2 2 Ai *4| iL*|L?                                e

e L?ih}i?Ui |L *@h}i |)Ti *4|t D

e L|@|L?                                      D e2 Ai UL?ih}i?Ui |iLhi4                             D e TT*U@M*|)                                    S ee hi*4?@hit                                   . eD N?uLh4 *@ Lu *@h}i ?4Miht                          H

D #)?@4U@* UL?ti^i?Uit b

D 5|hU|h@* t|@M*|) @?_ Tihtt|i?Ui                       b D2 TT*U@|L? |L *@h}i |)Ti *4|t                         2

S ,L*|L?@h) _)?@4Ut ? @ t4T*i wAw 2e

.  w Aw | ?Lti 

 W?|hL_U|L?

#L i TiU|@|L?t 4@||ih Lh _L @tti| ThUit u**) hiiU| iUL?L4U u?_@4i?|@*tq #L i| ihL}i?iLt Mi*iut @ih@}i L| _i |L @}}hi}@|L?c Lh U@? LT|4t|U Lh Titt4t|U it U*t|ih |L}i|ih @?_ U@ti ThUit |L _i@|i uhL4 ?_ih*)?} iUL?L4U u?_@4i?|@*tq Aiti ^it|L?t @i Mii? @ 4@||ih Lu i@) _iM@|i @4L?} iUL?L4t|t @t i** @t €?@? U@* Th@U||L?iht uLh 4@?) _iU@_it @*hi@_) ki)?itc uLh i @4T*ic @h}i_ |@| t|LU! ThUit @hi ?L| }Lih?i_ M) @? LMiU|i i Lu u?_@4i?|@*t<c M| M) @| @ih@}i LT?L? i TiU|t @ih@}i LT?L? |L Mi< W? ki)?it Lh_t R W?it|4i?| M@ti_ L? }i??i *L?}|ih4 i TiU|@|L? t tL _U*| @t |L Mi tU@hUi*) Th@U|U@M*i Oi L @||i4T|t | 4t| thi*) *i@_ 4U 4Lhi *@MLhLt _@)t @?_ h? }hi@|ih ht!t |@? i L |hit |L }itt Mi||ih |@? |i UhL_ L |i UhL_ ** Mi@i( @?_c }i? i^@* ?|i**}i?Uic i 4@) 4@!i 4Lhi _t@t|hLt 4t|@!it Eki)?itc bS c TD.

W? UL?|h@t|c ?i U*@ttU@* iUL?L4t|t @i ii_ R4@h!i| Tt)UL*L})c R?it|Lht ti?| 4i?| @?_ R|hi?_ uL**L?} tTiU*@|L? @t Mi?} hh@|L?@* @?_ |ihiuLhi ?UL?tt|i?| | |i h@|L?@* i TiU|@|L?t )TL|itt E+,O @?_ |i iUi?| 4@h!i| )TL|itt E,O 6hi_4@?c uLh i @4T*ic @h}i_ |@| hh@|L?@* tTiU*@|i |h@_iht L*_ Mi _hi? L| Lu |i 4@h!i| M) h@|L?@* |h@_ihtc L L*_ |h@_i @}@?t| |i4 M) |@!?} *L?} LTTL t|i TLt|L?tc |t _h?} ThUit M@U! |L u?_@4i?|@*t W? 6hi_4@?<t Lh_tG RiLT*i L @h}i |@| tTiU*@|L? t }i?ih@**) _it|@M*3?} ti*_L4 hi@*3i |@| |t t *@h}i*) i^@ *i?| |L t@)?} |@| tTiU*@|Lht *Lti 4L?i)c t?Ui tTiU*@|L? U@? Mi _it|@M*3?} ? }i?ih@* L?*) u tTiU*@|Lht L? |i @ih@}i ti** i? |i Uhhi?U) t *L ? ThUi @?_ M) i? | t } di4T@tt @__i_o E6hi_4@?c bDc T.D

W? i4ThU@* Lh! 4U @||i?|L? @t Mii? T@_ |L |i U*Lti*) hi*@|i_ ^it|L? i|ih @tti| ThUit i M| i Uitt L*@|*|)c |@| tc i|ih L*@|*|) Lu @tti| ThUit t *@h}ih |@? L*@|*|) Lu ?_ih*)?} iUL?L4U u?_@4i?|@*t W? T@h|U*@h |i Lh! M) 5**ih EbH.c 2fff @t i4T@t3i_ |i TLttM*|) Lu i Uitt L*@|*|) @?_ Tihtt|i?| _i@|L?t Lu @tti| ThUit uhL4 @ u?_@4i?|@* +, Mi?U4@h! W? Mi@Lh@* €?@?Uic uLh i @4T*ic A@*ih Ebbe @t @h}i_ |@| ^@th@|L?@*|) 4@) Mi @ !i) tLhUi Lu _i@|L?t uhL4 |i +, u?_@4i?|@* Mi?U4@h! @?_ i Uitt L*@|*|) "@t h@|L?@*|) 4i@?t *itt |@? u**) h@|L?@* Mi@Lhc uLh i @4T*ic _i |L ?it|Lht< ti?|4i?|c LihUL?€_i?Ui Lh Lihhi@U|L? OLiih Lh! M) L*_h? @?_ wi?i E2ff @h}it |@| T@||ih?t Lu hi|h?t Mi@Lh |@| *LL! *!i i_i?Ui Lu Rhh@|L?@*|) Lh RML?_i_ h@|L?@*|) 4@) Mi t4T*) h@|L?@* hi@U|L? Lu t|LU! 4@h!i|t |L i@h??}t ThL€*it }i?ih@|i_ M) |iU?L*L}U@* U@?}i h T@Tih t uLUti_ 4Lhi L? }ih uhi^i?U) U|@|L?t |@? L*_h? @?_ wi?i E2ffc M| hi*@|i_ @h}4i?|t 4t| @*@)t 4@!i L?i @h) Lu UL?U*_?} |@| T@||ih?t Lu MLL4t @?_ Uh@tit ? t|LU! 4@h!i| @*it @hi i_i?Ui Lu @?) !?_ Lu hh@|L?@* ThU?} 5ii |i _tUttL? Lu k*i_L?<t Lh! Mi*L

, Tih4i?|@* Lh! @t @*tL @__hitti_ |i ^it|L? Lu TLttM*i _i@|L?t uhL4 |i Mi?U 4@h! +, u?_@4i?|@* ? tTiU*@|i @tti| 4@h!i|t 6Lh i @4T*ic 54|c 5U@?i! @?_ `**@4t EbHH tLi_ |@| tTiU*@|i MMM*it @?_ _i@|L?t uhL4 @ Mi?U4@h! +,,

u?_@4i?|@* @hi uhi^i?|*) LMtihi_ ? i Tih4i?|@* @tti| 4@h!i|t Aiti |i4TLh@h) MMM*it |i?_ |L _t@TTi@h Liih |L@h_t |i i?_ Lu |i i Tih4i?|@* @tti| 4@h!i| @?_ @*tL |i?_ |L MiUL4i t4@**ih @t |h@_iht MiUL4i 4Lhi i Tihi?Ui_ k*i_L? Ebbe @t h||i? @ hiUi?| hii T@Tih @ML| 4@h!i| RT@|L*L}it tU @t Uh@titc M*L Lgtc i Uitt L*@|*|)c @?L4@*itc i|U( tii @*tL *L|| @?_ 5?_ih EbHH @?_ @4ihih EbHb W? T@h|U*@h i TL?|t L| L |i i Tih4i?|@* *|ih@|hi ? @? @t)44i|hU ?uLh4@ |L? ti||?} @t tL? |@| +,, t ?L| @Uii_ 44i_@|i*) M| |i?_t |L Mi @Uii_ M) i Tihi?Ui_ |h@_iht k*i_L? t|@|itc RAi *@MLh@|Lh) hit*|t ThLi_ ?t}| ?|L i? 4TihuiU| @}}hi}@|L? t 4Lhi *!i*) |L LUUhc ?@4i*) @? @Mti?Ui Lu UL44L? ?uLh4@|L? @ML| Thiuihi?Uit Lh Mi*iut Lu L|ih |h@_iht @?_ @ *@U! Lu |h@_iht< i Tihi?Ui ? |i 4@h !i| ti||?} k*i_L? Ebbec T ec D t|hittit |i U@hiu* _gihi?|@|L? Mi|ii? 4L_i*?} R?i i |ih?@*< ?uLh4@|L? @ML| u?_@4i?|@*tc |@| tc ?uLh4@|L? @ML| i TiU|i_ u |hi U@t Lt Lh _tUL?| h@|it |@| hi@Uit @?) |h@_ih Lh ?it|Lh uLh |i €ht| |4i @?_ 4L_i*?} Rh@|L?@* U@?}it ? ?|ih?@* ?uLh4@|L? @ML| u?_@4i?|@*t

Ai _iM@|i i|ih i TiU|@|L?t @giU| @tti| ThUit @?_ 4@) *i@_ |L i Uitt L*@|*|) tL*_ Mi ii_ ? |i *}| Lu |L 4TLh|@?| _ii*LT4i?|t ? |i hiUi?| *|ih@|hiG ML?_i_ h@|L?@*|) @?_ i|ihL}i?iLt @}i?|t t)t|i4t L?_i_ h@|L?@*|) @?_ i|ihL}i ?iLt @}i?|t 4@) Mi ii_ @t M*_?} M*LU!t ? Mi@Lh@* €?@?Uic ihi |h@_iht @hi ii_ @t ML?_i_*) h@|L?@* @}i?|t t?} t4T*ic @M|@* h*i Lu |4M h*itc tii i} 5iuh? E2fff *|L} h@|L?@* i TiU|@|L?t hi4@?t @? 4TLh|@?| Mi?U4@h!c Lh! L? ML?_i_ h@|L?@*|) ? |i T@t| _iU@_i 4@) Mi ii_ @t @? @||i4T| |L i T*Lhi _i@|L?t uhL4 |t Mi?U4@h! Bi?ih@* thi)t L? ML?_i_ h@|L?@*|) ? i TiU|@|L?t @?_ *i@h??} @hi i} 5@h}i?| Ebbc Bh@?_4L?| EbbH @?_ ,@?t @?_ OL?!@TL@ E2ff W? T@h |U*@hc 5@h}i?| Ebbb @h}it |@| 4@?) Lu |i ML?_i_ h@|L?@* i TiU|@|L?t i^*Mh@ 4@) Mi ii_ @t @TThL 4@|i< h@|L?@* i TiU|@|L?t i^*Mh@

W? |i *@t| _iU@_ic @ h@T_*) ?Uhi@t?} ?|ihit| ? 4*|@}i?| t)t|i4t U@? Mi LMtihi_ @h!i|t ii_ @t iL*|L?@h) @_@T|i t)t|i4t | ML?_i_*) h@|L?@* ?|ih@U|?} @}i?|t @i i} Mii? t|_i_ ? h|h i| @* Ebb.c hLU! @?_ OL44it Ebb.cbbHc @hi**@ @?_ Oi Ebbbc 2fff 6@h4ih EbbHc B@?iht_Lhuih @?_ OL44it E2fffc kh4@? Ebbc wi@hL? i| @* Ebbbc w EbbD @?_ w @?_ @hUit Ebbb@M Aiti _ii* LT4i?|t ? 4*|@}i?| t)t|i4t @hi U*Lti*) hi*@|i_ |L hiUi?| Lh! ? €?@?Ui L? t4@h| 4L?i)< @?_ ?Lti |h@_iht i} M) 6h@?!i* @?_ 6hLL| EbHHc #i wL?}c 5*iuihc 544iht @?_ `@*_4@?? EbHbc bbfc @?_ `@?} Ebbe  UL44L? ui@|hi Lu |iti UL?|hM|L?t t |@| |ihi @hi |L _gihi?| U*@ttit Lu ?it|Lht |@| U@? @*tL Mi LMtihi_ ? €?@? U@* Th@U|UiG u?_@4i?|@*t| @?_ |iU?U@* @?@*)t|t 6?_@4i?|@*t|t M@ti |ih uLhiU@t|t Lu u|hi ThUit @?_ hi|h?t TL? iUL?L4U u?_@4i?|@*tc tU @t __i?_tc ?|ihit| h@|itc ThUii@h??} h@|L<tc i|U W? UL?|h@t|c |iU?U@* @?@*)t|t @hi *LL!?} uLh T@||ih?t ? T@t| ThUit @?_ M@ti |ih uLhiU@t|t TL? i |h@TL*@|L? Lu |iti T@||ih?t ? ?|ihit|?} L|UL4i Lu |iti iL*|L?@h) i|ihL}i?iLt @}i?| t)t|i4t t |@| |i 4L_i*t 44U @ ?4Mih Lu t|)*3i_ u@U|t uhi^i?|*) LMtihi_ ? €?@?U@* tihitc tU @t ?Thi_U|@M*|) Lu hi|h?tc u@| |@*tc L*@|*|) U*t|ih?} @?_ *L?} 4i4Lh) hUi _i@|L?t uhL4 |i +, u? _@4i?|@* @?_ i Uitt L*@|*|) @hi |h}}ihi_ M) ?Uih|@?|) @ML| iUL?L4U u?_@4i?|@*t

M| 4@) Mi @4T*€i_ M) iL*|L?@h) ?|ih@U|L? Lu UL4Ti|?}c ML?_i_*) h@|L?@* |h@_ ?} t|h@|i}it Lt| Lu |t Lh! t UL4T|@|L?@**) Lhi?|i_ @?_ M@ti_ TL? UL4T|ih t4*@|L?t Lu UL4T*i @_@T|i t)t|i4t

Ai Thiti?| T@Tih ThL_it @ |iLhi|U@* uh@4iLh! uLh iL*|L?@h) 4@h!i|t | 4@?) _gihi?| |h@_ih |)Tit `i ?|hL_Ui |i ?L|L? Lu @ tLU@**i_ w@h}i A)Ti w4| EwAwc U t @ t4T*ic *L _4i?tL?@* t)t|i4 _itUhM?} |i iL*|L?@h) _)?@4Ut ? @ 4@h !i| | 4@?) |h@_ih |)Tit Ai UL?UiT| Lu wAw @t t!i|Ui_ ? hLU! Ebb.c hLU! @?_ OL44it Ebbb @?_ hLU! @?_ _i 6L?|?Li**i E2fff M| t @U|@**) h}LhLt*) _ii* LTi_ ? |t T@Tih_{ Ai wAw t @ |)Ti Lu i?ti4M*i *4| h@|ih *!i |ih4L_)?@4U *4|t}

? t|@|t|U@* 4iU@?Ut W| t 4L|@|i_ M) LMtih?} |@| 4@h!i| i^*Mh4 i^@|L?t |i?_ |L @i @ uLh4 U t @ u?U|L? Lu i ThittL?t |@| *LL! *!i t@4T*i 4L4i?|t Ai wAw t |i? t4T*) LM|@?i_ M) hiT*@U?} t@4T*i 4L4i?|t M) TLT*@|L? 4L4i?|t 6Lh T@h|U*@h _t|hM|L?t Lu U@h@U|iht|Utc L?i 4@) LM|@? U*Lti_ uLh4 tL*|L?t uLh |iti TLT*@|L? 4L4i?|t @?_ |t LM|@? U*Lti_ uLh4 i ThittL?t uLh LMiU|t |@| @T Ti@hi_ ?|h@U|@M*i Ai wAw U@? @*tL Mi ii_ @t @ _iUi |@| igiU|i*) hi_Uit @ *@h}i ?4Mih Lu T@h@4i|iht ?ihi?| ? 4L_i*t | @ *@h}i ?4Mih Lu _gihi?| Mi*iu |)Tit M) ?|hL_U?} @? ?_ih*)?} U@h@U|iht|Ut _t|hM|L? U |ti*u U@? Mi U@h@U|ih3i_ M) @ t4@** ?4Mih Lu T@h@4i|iht At i4ThU@* Lh! U@? Mi @ttt|i_ M) |t |)Ti Lu T@h@4i|ih hi_U|L? |iU?^i `i |?! |t t @ ?i 4i|L_ Lu @?@*)tt U t Lu ? _iTi?_i?| ?|ihit| Ai wAw |iLh) _ii*LTi_ ihi U@? Mi ti_ |L uLh4 @ Mh_}i Mi|ii? @?@*)|U@* hit*|t @?_ |i *|ih@|hi L? iL*|L?@h) t4*@|L? Lu @tti| |h@_?}c U @t MiUL4i ih) TLT*@h ? |i *@t| ui )i@ht Etii i} h|h i| @* Ebb.c wi@hL? E2fff @?_ OL44it E2ff uLh hiit W? u@U|c |i 4@? hit*| Lu |i Thiti?| T@Tih t |@| |i wAw i** @TThL 4@|it |i iL*|L?@h) _)?@4Ut ? @ 4@h!i| | 4@?) |h@_ih |)Tit ? |i ti?ti |@| @** }i?ihU @?_ Tihtt|i?| ui@|hit Lu @? iL*|L?@h) @_@T|i t)t|i4 | 4@?) |h@_ih |)Tit @hi Thitihi_ ? |i wAw Oi?Uic |i wAw U@? Mi ti_ |L t|_) *L U@* t|@M*|) Lu |i Mi?U4@h! +, u?_@4i?|@* t|i@_) t|@|i @t i** @t TLttM*i _i@|L?t uhL4 |i +, Mi?U4@h! @?_ MuhU@|L?t hL|it |L ?t|@M*|) @?_ UL4T*U@|i_ TihL_U Lh ii? U@L|U _)?@4Ut ? @_@T|i iL*|L?@h) t)t|i4t | 4@?) |h@_ih |)Tit 6h|ih 4Lhic i ** Thiti?| @ t4T*i i @4T*i Lu @? wAw Mgi|i_ | _)?@4U ?Ltic }i?ih@|?} tL4i 4TLh|@?| t|)*3i_ u@U|t LMtihi_ ? hi@* €?@?U@* _@|@ W? T@h|U*@h i Thiti?| @ t4T*i i @4T*ic ihi |i @|LULhhi*@|L? T@||ih?t Lu ?Lt) wAw }i?ih@|i_ |4i tihit Lu hi|h?tc @MtL*|i hi|h?t @?_ t^@hi_ hi|h?t 4@|U |i ULhhitTL?_?} @|LULhhi*@|L? T@||ih?t Lu 2f )i@ht Lu 5: Dff _@|@

wi| t ?L _tUtt tL4i U*Lti*) hi*@|i_ hiUi?| Lh! hLU! @?_ OL44it Ebb. ?|hL_Ui_ @ |h@U|@M*i uLh4 Lu iL*|L?@h) _)?@4Ut ? |i ULMiM _i4@?_tTT*) 4L_i* | @ ULt|*)c tLTt|U@|i_ uLhiU@t|?} h*i tU @t h@|L?@* i TiU|@|L?t UL4Ti|?} @}@?t| @

4_{Wkh qrwlrq ri OWO lv uhodwhg wr wkh zhoo nqrzq phdvxuh vsdfh dssurdfk lq jhqhudo htxloleulxp}

wkhru| +Vhh Nlupdq +4<;4, dqg Kloghqeudqg +4<;5, iru uhylhzv,1 Wkh pdlq glhuhqfh olhv lq orfdwlqj lqwhuwhpsrudo g|qdplfdo htxloleulxp uhodwlrqvklsv wkdw uhvhpeoh vdpsoh prphqw frqglwlrqv wr vxjjhvw wkh irup ri wkh dssursuldwh olplw dqg hvwdeolvklqj zklfk g|qdplfdo skhqrphqd duh _shuvlvwhqwc* xqghu _qlwh% hfrqrp| olplwv/ vr wkdw wkh olplw lwvhoi fdq eh gluhfwo| xvhg wr frqvwuxfw elixufdwlrq gldjudpv dqg suhglfw wkh g|qdplfdo elixufdwlrq ehkdylru iru odujh hqrxjk _vdpsohv1% Ghwdlov zloo iroorz1

Ui@T @M|@* h*i Lu |4M uLhiU@t|?} h*i tU @t @_@T|i i TiU|@|L?t hLU! @?_ OL44it EbbHc i?UiuLh| Oc U@**i_ |t iL*|L?@h) _)?@4Ut @? _@T|i i*iu 5)t |i4 E5 @?_ @TT*i_ |i uh@4iLh! |L @tti| ThU?} |iLh) ? @ 4L_i* | L?i ht!) @tti| @?_ L?i ht! uhii @tti| Ah@U|@M*|) t @Uii_ M) |i ti Lu h@?_L4 |*|) 4L_i*t |L 4L_i* €|?itt< @?_ ?@|h@* ti*iU|L?< hi_U|Lh ULUi @UhLtt |i ti| Lu Thi_U|Lht t iL*|L?@h*) h@|L?@* ? |i ti?ti |@| @}i?|t ULLti |i Thi_U|Lht @UULh_?} |L }it| €|?ittc tU @t T@t| ThL€|t W? |i 5 t|_i_ M) O |ihi ihi L?*) ui |h@_ih |)Titc |)TU@**) L?*) |Lc |hii Lh uLh Ai Thiti?| T@Tih }i?ih@*3it |i 5 |L @? iL*|L?@h) t)t|i4 | 4@?) _gihi?| |h@_ih |)Tit @?_ ThLTLtit |L @TThL 4@|i |i iL*|L?@h) _)?@4Ut | 4@?) |h@_ih |)Tit M) @ wAw B@?iht_Lhuih @?_ OL44it E2fff ?it| }@|i |4i tihit ThLTih|it Lu @ t4T*i 5 | |L |h@_ih |)Titc u?_@4i?|@*t|t ihtt |hi?_ uL**Lihtc Mgi|i_ | _)?@4U ?Lti @?_ 4@|U |i @|LULhhi*@|L? T@||ih?t Lu hi|h?tc @MtL*|i hi|h?t @?_ t^@hi_ hi|h?t |L ef )i@ht Lu 5: Dff _@|@ 54T*i ih tL?t Lu |i 5 |t 4@) i T*@? LMtihi_ t|)*3i_ u@U|t tU @t ?Thi_U|@M*|) Lu @tti| hi|h?tc u@| |@*tc U*t|ihi_ L*@|*|) @?_ *L?} 4i4Lh) B@?iht_Lhuihc OL44it @?_ `@}i?ih E2fff ?it|}@|i MuhU@|L? hL|it |L UL4T*U@|i_ _)?@4Ut Lu |t t)t|i4c @?_ tL ? T@h|U*@h |@| ULi t|i?Ui Lu @ t|@M*i t|i@_) t|@|i @?_ @ t|@M*i U)U*ic 4@) i T*@? |i LMtihi_ t|)*3i_ u@U|t Lu |i 4L_i* Mgi|i_ | ?Lti

? 4TLh|@?| ui@|hi Lu |i O uh@4iLh! t |@| |i +, Mi?U4@h! t ?it|i_ |? |i iL*|L?@h) 4L_i* @t @ tTiU@* U@ti Ai Mi?U4@h! u?_@4i?|@* hiThiti?|t |i |h@_iht< hitTL?ti |L UL44L? !?L*i_}i i L}i?Lt ?itc tU @t ?|ihit| h@|i 4Li4i?|tc }hL| Lu |i €h4t ThL€|tc i@h??}t Lh __i?_tc @ hiTi@* Lu |i U@T|@* }@?t |@ c i|U Ah@_iht< Mi*iut @ML| u|hi ThUit @hi uLh4*@|i_ ? |ih4t Lu _i@|L?t uhL4 @ Mi?U4@h! +, u?_@4i?|@* Aiti _i@|L?t U@? Mi ii_ @t i@U +, |h@_ih<t Mi*iu @ML| L |i _i@|L?t uhL4 +, M) |i hit| Lu |i |h@_?} UL44?|) 4}| tL T ? i^*Mh4 ThUit W? |t ti?ti Lh |iLh) t u**) h@|L?@* ? |i ti?ti |@| |h*) h@|L?@* |h@_iht 4t| |@!i ?|L @UUL?| |i Mi@Lh Lu L|ih |h@_iht ? |i |h@_?} UL44?|) Ai O uh@4iLh! t 4L|@|i_ M) |i !?_t Lu i_i?Ui hiii_ @MLi @?_ t|@h|t |i |@t! Lu M*_?} @ |iLh) |@| RM@U!t Lg uhL4 +, ? |i 4@??ih Lu 5@h}i?| Ebbc M| ?it|t +, ? tU @ @) |@| +,iUL?L4i|hU |iU?L*L}) tU @t 4i|L_t M@ti_ TL? Lh|L}L?@*|) UL?_|L?t U@? Mi hi@_*) @_@T|i_ |L |it| |i Rt}?€U@?Ui Lu |i i |h@ Ruhii T@h@4i|iht |@| Lh |iLh) @__t |L +, |iLh) hL+, iUL?L4t|t *LLti*) @h}i |@| |i t|@|L?t ? U |iti i |h@ uhii T@h@4i|iht @hi t}?€U@?| 4@) ?L| Mi uhi^i?| ?|+, |)Tit @h}i |@| tU _iT@h|hit 4@) Mi uhi^i?| uLh @?|+, |)Tit `i |?! @ |iLh) t ?ii_i_ |@| ?it|t ML| it ? @ @) tU |@| iUL?L4i|hU 4i|L_t @hi t}}it|i_ |L |it| |i ?** Lu +, @}@?t| |i @*|ih?@|i `i t |L UL?|hM|i |L |i |@t! Lu M*_?} @ |iLh) ? U |i _@|@ U@? tTi@! |L |i UL?|hLiht) L? +, @?_ i Uitt L*@|*|) W| t Lh|*i ?L|?} |@| @@! Ebbb @?_ @@t E2fff @i h? i4ThU@* |it|t uLh i|ihL}i?i|) ? i TiU|@|L?t ? @}hU*|h@* _@|@ @?_ ?_ii_ €?_ i_i?Ui uLh |i Thiti?Ui Lu ML?_i_*) h@|L?@* |h@_iht ? |i L} @?_ U@||*i 4@h!i|t Ai |iLh) _ii*LTi_ ? |t T@Tih @*tL )i*_t @ _iUL4TLt|L? Lu hi|h?t ?|L @ @h|?}@*i #gihi?Ui 5i^i?Uic ihi@u|ih R#5c @?_ @? Ri |h@ i?_L}i?Lt _)?@4Ut T@h| Ai #5 UL4TL?i?| Lu hi|h?t ULhhitTL?_t

|L UL?i?|L?@* h@|L?@* i TiU|@|L?t |iLh) E+, @?_ ,Ui?| @h!i|t AiLh) E,O Ai Ri?_L}i?Lt _)?@4Ut T@h| t h@|ih *!i Ri?_L}i?Lt ?Uih|@?|) ? |i ti?ti Lu kh3<t MLL! Ebb. U _ii*LTt |i |iLh) Lu h@|L?@* Mi*iut E+, +iUi?| i4ThU@* Lh! M) 5@h4@ E2ff L? €?@?U@* 4@h!i|t U t T@||ih?i_ @u|ih |@| Lu @@t E2fff @__Uit tL4i Thi*4?@h) i_i?Ui uLh |i Thiti?Ui Lu tL4i ML?_i_*) h@|L?@* |h@_iht ? @? iUL?L4i|hU ti||?} ihi +,,%,O t R?it|i_ |? @ }i?ih@* iL*|L?@h) 4L_i* h@|ih *!i |i L?i i @hi M*_?} ihi

Ai T*@? Lu |i T@Tih t @t uL**Lt W? tiU|L? |Lc i hiU@** |i ?L|L? Lu _@T|i i*iu 5)t|i4 E5 ? @? @tti| ThU?} uh@4iLh! 5iU|L?  _i€?it |i ?L|L? Lu w@h}i A)Ti w4| EwAw 5iU|L? e ThLit @ |iLhi4 @ML| UL?ih}i?Ui Lu @? 5 |L @ wAwc i? |i ?4Mih Lu |h@_ih |)Tit }Lit |L ?€?|) 5iU|L? D _tUttit |i UL?ti^i?Uit Lu |i UL?ih}i?Ui |iLhi4c @?_ tLt ? T@h|U*@h |@| @** }i?ihU @?_ Tihtt|i?| ui@|hit Lu @? 5 | 4@?) |h@_ih |)Tit LUUh | } ThLM@M*|) ? |i wAw 5iU|L? SThiti?|t @ t4T*i i @4T*i Lu @? wAw LM|@?i_ i? Mi*iut @hi h@?_L4*) _h@? uhL4 *?i@h uLhi U@t|?} h*it wLU@* t|@M*|) @t i** @t }*LM@* MuhU@|L? hL|it |L ?t|@M*|) @?_ t|h@?}i @||h@U|Lht @hi ?it|}@|i_ uLh |t U@ti 5iU|L? . ?it|}@|it |4i tihit ThLTih|it Lu @ wAw Mgi|i_ | ?Ltic @?_ tLt |@| @? wAw U@? 4@|U |i @|LULhhi*@|L? T@||ih?t Lu hi|h?tc t^@hi_ hi|h?t @?_ @MtL*|i hi|h?t Lu 2f )i@ht Lu 5: Dff _@|@ 6?@**)c tiU|L? H UL?U*_it

2 _@T|i i*iu 5)t|i4t

W? Lh_ih |L Mi ti*u UL?|@?i_c |t tiU|L? hiU@**t |i ?L|L? Lu @? _@T|i i*iu 5)t|i4 E5c @t ?|hL_Ui_ ? hLU! @?_ OL44it EbbHc @TT*)?} |i iL*|L?@h) uh@4iLh! _ii*LTi_ ? hLU! @?_ OL44it Ebb.( tii @*tL hLU! Ebb. @?_ OL44it E2ff uLh i |i?ti _tUttL?t ? 5 t ? u@U| @ t|@?_@h_ _tUL?|i_ @*i @tti| ThU?} 4L_i* _ihi_ uhL4 4i@?@h@?Ui 4@ 43@|L?c i |i?_i_ |L |i U@ti Lu i|ihL}i?iLt Mi*iut }i?|t U@? i|ih ?it| ? @ ht! uhii @tti| Lh ? @ ht!) @tti| Ai ht! uhii @tti| t TihuiU|*) i*@t|U@**) tTT*i_ @?_ T@)t @ € i_ h@|i Lu hi|h? o( |i ht!) @tti|c uLh i @4T*i @ *@h}i t|LU! Lh @ 4@h!i| ?_i c T@)t @? ?Uih|@? __i?_ wi| R|Mi |i ThUi Tih t@hi

Ei __i?_ Lu |i ht!) @tti| @| |4i |c @?_ *i| +| Mi |i t|LU@t|U __i?_ ThLUitt Lu

|i ht!) @tti| `i@*| _)?@4Ut t }i? M) 

`|n ' -`|n ER|nn +|n -R|5|c E

ihi - '  n o t |i }hLtt h@|i Lu ht! uhii hi|h?c @h@M*it | @ |*_i tU @t +|n _i?L|i h@?_L4 @h@M*it @| _@|i | n  @?_ 5| _i?L|it |i ?4Mih Lu t@hit Lu |i

ht!) @tti| ThU@ti_ @| _@|i | wi| .| @?_ T| _i?L|i |i UL?_|L?@* i TiU|@|L? @?_

UL?_|L?@* @h@?Ui M@ti_ L? @ TM*U@**) @@*@M*i ?uLh4@|L? ti| tU @t T@t| ThUit @?_ T@t| __i?_t wi| .|@?_ T| _i?L|i |i Mi*iut< Lh uLhiU@t|t Lu |h@_ih |)Ti  @ML|

UL?_|L?@* i TiU|@|L? @?_ UL?_|L?@* @h@?Ui }i?|t @hi @tt4i_ |L Mi 4)LTU 4i@? @h@?Ui 4@ 43iht tL |@| |i _i4@?_ 5| Lu |)Ti  uLh |i ht!) @tti| tL*it

@ 5|i.|d `|no 

@

2T|d `|nojc E2

ihi @ t |i ht! @ihtL? T@h@4i|ih Ai _i4@?_ 5| uLh ht!) @tti|t M) |h@_ih |)Ti 

t |i?

5|' _@T.|dR|nn +|n -R|o |dR|nn +|n -R|o '

.|dR|nn +|n -R|o

@j2 c E

ihi |i UL?_|L?@* @h@?Ui T| ' j2 t @tt4i_ |L Mi i^@* uLh @** |)Tit @?_ UL?t|@?|2

wi| 5r _{_i?L|i |i tTT*) Lu L|t_i ht!) t@hit Tih ?it|Lhc @tt4i_ |L Mi UL?t|@?|c @?_}

*i| ?| _i?L|i |i uh@U|L? Lu |)Ti  @| _@|i | ,^*Mh4 Lu _i4@?_ @?_ tTT*) )i*_t M

[

'

?|.|dR|nn +_@j2|n -R|o ' 5rc Ee

ihi M t |i ?4Mih Lu _gihi?| |h@_ih |)Tit Ai uLhiU@t|t .|dR|nn+|no Lu |L4LhhLt

ThUit @?_ __i?_t @hi 4@_i MiuLhi |i i^*Mh4 ThUi R| @t Mii? hii@*i_ M) |i

4@h!i| @?_ |ihiuLhi ** _iTi?_ TL? @ TM*U@**) @@*@M*i ?uLh4@|L? ti| U|3 '

iR|3c R|32c ( +|3c +|32j Lu T@t| ThUit @?_ __i?_t @h!i| i^*Mh4 Ee |i? 4T*it

|@| |i hi@*3i_ 4@h!i| ThUi R|** Mi |i ?^i ThUi uLh U _i4@?_ i^@*t tTT*)

Ai 4@h!i| i^*Mh4 i^@|L? U@? Mi hih||i? @t -R| '

M

[

'

?|.|dR|nn +|no  @j25r ED

Ai ^@?||) @j2₅r _{4@) Mi ?|ihThi|i_ @t @ ht! Thi44 uLh |h@_iht |L L*_ @** ht!)}

@tti|t

2 Ai ,O Mi?U4@h! | h@|L?@* @}i?|t

wi| t €ht| _tUtt |i ,OMi?U4@h! | h@|L?@* i TiU|@|L?t W? @ Lh*_ ihi @** |h@_iht @hi _i?|U@* @?_ i TiU|@|L?t @hi L4L}i?iLt |i @hM|h@}i 4@h!i| i^*Mh4 i^@|L? ED hi_Uit |L

-R|' .|dR|nn +|no  @j25rc ES

5_{Jdxqhuvgruihu +5333, lqyhvwljdwhv wkh fdvh zlwk wlph ydu|lqj eholhiv derxw yduldqfhv dqg vkrzv wkdw}

wkh uhvxowv duh txlwh vlplodu wr wkrvh iru frqvwdqw yduldqfh1 Xqghu dvvxpswlrqv E5 dqg E6 ehorz/ lw fdq eh vkrzq wkdw frqvwdqw frqglwlrqdo yduldqfh eholhiv lv qrw frqwudglfwru| zlwk khwhurjhqhrxv frqglwlrqdo phdq eholhiv ri wkh irup lq dvvxpswlrq E41 Iru h{dpsoh li wkh i|wj surfhvv lv LLG/ wkh ixqgdphqwdo sulfh

lv d frqvwdqw/ dqg wkh frqglwlrqdo yduldqfh ri hdfk eholhi ri wkh irup srvlwhg lq dvvxpswlrq E4 lv mxvw wkh yduldqfh ri |w1 Wklv dujxphqw fdq eh jhqhudol}hg wr wkh fdvh zkhuh i|wj lv dq dxwruhjuhvvlrq ri qlwh

rughu gulyhq e| LLG vkrfnv1 Vhh Eurfn +4<<:, iru glvfxvvlrq1

ihi .| _i?L|it |i UL44L? UL?_|L?@* i TiU|@|L? Lu @** |h@_iht @| |i Mi}???}

Lu TihL_ |c M@ti_ L? @ TM*U@**) @@*@M*i ?uLh4@|L? ti| U| At @hM|h@}i 4@h!i|

i^*Mh4 i^@|L? ES t|@|it |@| |L_@)<t ThUi Lu |i ht!) @tti| 4t| Mi i^@* |L |i t4 Lu |L4LhhL<t i TiU|i_ ThUi @?_ i TiU|i_ __i?_c _tUL?|i_ M) |i ht! uhii ?|ihit| h@|i W| t i** !?L? |@|c t?} |i @hM|h@}i i^@|L? ES hiTi@|i_*) @?_ @tt4?} |@| |i |h@?tiht@*|) UL?_|L?

*4

|<"

.|dR|n&o

-& ' f E.

L*_tc |i ThUi Lu |i ht!) @tti| t ?^i*) _i|ih4?i_ M) RW | ' " [ &' .|d+|n&o  @j25r -&  EH Ai ThUi RW

| ? EH t U@**i_ |i ,O u?_@4i?|@* h@|L?@* i TiU|@|L?t E+, ThUic

Lh |i u?_@4i?|@* ThUi uLh tLh| Ai u?_@4i?|@* ThUi t UL4T*i|i*) _i|ih4?i_ M) iUL?L4U u?_@4i?|@*t @?_ }i? M) |i _tUL?|i_ t4 Lu i TiU|i_ u|hi __i?_t 4?t |i ht! Thi44 W? }i?ih@*c |i ThLTih|it Lu |i u?_@4i?|@* ThUi RW

| _iTi?_

TL? |i t|LU@t|U __i?_ ThLUitt +| `i ** 4@?*) uLUt L? |i U@ti Lu @? WW#

__i?_ ThLUitt +|c | UL?t|@?| 4i@? .d+|o ' 7+ `i ?L|i Liih |@| @?) L|ih

h@?_L4 __i?_ ThLUitt +| 4@) Mi tMt|||i_ ? @| uL**Lt 6Lh @? WW# __i?_

ThLUitt +| | UL?t|@?| 4i@?c |i u?_@4i?|@* ThUi t UL?t|@?| @?_ }i? M)

RW _'[" &' 7+ -& ' 7+  @j2₅r o  Eb

Aihi @hi |L UhU@* @tt4T|L?t ?_ih*)?} |i _ih@|L? Lu |i +, u?_@4i?|@* ThUi Ai €ht| t |@| i TiU|@|L?t @hi L4L}i?iLtc @** |h@_iht @hi h@|L?@* @?_ | t UL44L? !?L*i_}i |@| @** |h@_iht @hi h@|L?@* ?*) ? tU @? _i@*c TihuiU|*) h@|L?@* Lh*_ |i u?_@4i?|@* ThUi U@? Mi _ihi_ uhL4 iUL?L4U u?_@4i?|@*t W? UL?|h@t|c ? @ Lh*_ | i|ihL}i?iLt |h@_iht @?} _gihi?| Mi*iut Lh i TiU|@|L?t @ML| u|hi ThUit @?_ __i?_tc _ih@|L? Lu @ +, u?_@4i?|@* ThUi hi^hit TihuiU| !?L*i_}i @ML| |i Mi*iut Lu @** L|ih |h@_iht W? @ hi@* 4@h!i| ?_iht|@?_?} |i Mi*iut @?_ t|h@|i}it Lu @** L|ihc UL4Ti|?} |h@_iht t h|@**) 4TLttM*ic @?_ |ihiuLhi ? @ i|ihL}i?iLt Lh*_ _ih@|L? Lu |i +,u?_@4i?|@* ThUi MiUL4it 4TLttM*i Ai tiUL?_ UhU@* @tt4T|L? ?_ih*)?} |i _ih@|L? Lu |i u?_@4i?|@* ThUi t |i |h@?tiht@*|) UL? _|L? E.c hi^h?} |@| |i *L?} h? }hL| h@|i Lu ThUit E@?_ ht! @_t|i_ __i?_t t t4@**ih |@? |i ht! uhii }hL| h@|i o W? u@U|c ? @__|L? |L |i u?_@4i?|@* tL*|L? EH tLU@**i_ tTiU*@|i MMM*i tL*|L?t Lu |i uLh4

R|' RW| n -|ERf RWf Ef

6_{Eurfn dqg Krpphv +4<<:e, iru h{dpsoh glvfxvv d qrq0vwdwlrqdu| h{dpsoh/ zkhuh wkh glylghqg surfhvv}

lv d jhrphwulf udqgrp zdon 1

@*tL t@|tu) |i @hM|h@}i i^@|L? ES W| t 4TLh|@?| |L ?L|i |@| @*L?} |i tTiU*@|i MMM*i tL*|L? Efc |h@_iht @i h@|L?@* i TiU|@|L?t 5L*|L?t Lu |i uLh4 Ef @hi |ihiuLhi U@**i_ h@|L?@* MMM*it Aiti h@|L?@* MMM*i tL*|L?t @hi ?ML?_i_ @?_ _L ?L| t@|tu) |i |h@?tiht@*|) UL?_|L? W? @ TihuiU|*) h@|L?@* Lh*_c |h@_iht hi@*3i |@| tTiU*@|i MMM*it U@? ?L| *@t| uLhiih @?_ |ihiuLhi |i) ** ?iih }i| t|@h|i_ @?_ |i €?|i u?_@4i?|@* ThUi RW

| t ?^i*) _i|ih4?i_ W? @ TihuiU|*) h@|L?@* Lh*_c @**

|h@_iht |t Mi*ii |@| |i @*i Lu @ ht!) @tti| i^@*t |t u?_@4i?|@* ThUi uLhiih @?}it ? @tti| ThUit @hi tL*i*) _hi? M) ?i TiU|i_ U@?}it ? __i?_t @?_ h@?_L4 ?it< @ML| iUL?L4U u?_@4i?|@*t W? @ i|ihL}i?iLt iL*|L?@h) Lh*_ Liihc |i t|@|L? ** Mi ^|i _gihi?|

22 Oi|ihL}i?iLt Mi*iut

W? |i @tti| ThU?} 4L_i* | i|ihL}i?iLt Mi*iutc 4@h!i| i^*Mh4 ? ED t|@|it |@| |i ThUi R| Lu |i ht!) @tti| i^@*t |i _tUL?|i_ @*i Lu |L4LhhL<t i TiU|i_

ThUi T*t |L4LhhL<t i TiU|i_ __i?_c @ih@}i_ Lih @** _gihi?| |h@_ih |)Tit W? tU @ i|ihL}i?iLt Lh*_ |i4TLh@h) T@h_ Lh _L?@h_ MMM*it | ThUit _i@|?} uhL4 |i u?_@4i?|@* 4@) @htic i? |i uh@U|L?t Lu |h@_iht Mi*i?} ? |Lti MMM*it t *@h}i i?L} ?Ui @ E|i4TLh@h) MMM*i @t t|@h|i_c iL*|L?@h) uLhUit 4@) hi?uLhUi _i@|L?t uhL4 |i Mi?U4@h! u?_@4i?|@* `i t@** ?L Mi 4Lhi ThiUti @ML| |h@_iht< i TiU|@|L?t EuLhiU@t|t @ML| u|hi ThUit @?_ __i?_t W| ** Mi UL?i?i?| |L Lh! |

%|' R| RW|c E

|i _i@|L? uhL4 |i u?_@4i?|@* ThUi `i 4@!i |i uL**L?} @tt4T|L?t @ML| |i Mi*iut Lu |h@_ih |)Ti G

 T|dR|nn +|n -R|o ' T|dR|nn +|n -R|o ' j2c uLh @** c |

2 .|d+|no ' .|d+|noc uLh @** c |

 ** Mi*iut .|dR|no @hi Lu |i uLh4

.|dR|no ' .|dRW|non.|d%|no ' .|dRW|nonsE%|3c c %|3uc uLh @** c | E2

UULh_?} |L @tt4T|L?  Mi*iut @ML| UL?_|L?@* @h@?Ui @hi i^@* @?_ UL?t|@?| uLh @** |)Titc @t _tUtti_ @MLi @*hi@_) tt4T|L? 2 t|@|it |@| i TiU|@|L?t @ML| u|hi __i?_t +|n @hi |i t@4i uLh @** |h@_ih |)Tit @?_ i^@* |L |i UL?_|L?@* i TiU|@|L?

UULh_?} |L @tt4T|L? c Mi*iut @ML| u|hi ThUit UL?tt| Lu |L T@h|tG @ UL44L? Mi*iu @ML| |i u?_@4i?|@* T*t @ i|ihL}i?iLt T@h| uLh i@U |)Ti  Ai Mi?U4@h! u?_@4i?|@* hiThiti?|t |i |h@_iht< hitTL?ti |L UL44L? !?L*i_}i i L}i?Lt ?itc tU @t ?|ihit| h@|i 4Li4i?|tc }hL| Lu |i €h4t ThL€|tc i@h??}t Lh __i?_tc i|U ** |h@_iht @hi @M*i |L ti |t ?uLh4@|L? |L _ihi |i u?_@4i?|@* ThUi RW

| ? EH |@| L*_

Thi@* ? @ TihuiU|*) h@|L?@* Lh*_ UULh_?} |L @tt4T|L? c |h@_iht ?iih|i*itt Mi*ii |@| ? @ i|ihL}i?iLt Lh*_ ThUit 4@) _i@|i uhL4 |ih u?_@4i?|@* @*i RW

| M) tL4i u?U|L? s _iTi?_?} TL? T@t| _i@|L?t uhL4 |i u?_@4i?|@* ,@U

uLhiU@t|?} h*i s hiThiti?|t |i 4L_i* Lu |i 4@h!i| @UULh_?} |L U |)Ti  Mi*iit

|@| ThUit ** _i@|i uhL4 |i UL44L?*) t@hi_ u?_@4i?|@* ThUi 6Lh i @4T*ic @ uLhiU@t|?} t|h@|i}) s 4@) ULhhitTL?_ |L @ |iU?U@* |h@_?} h*ic M@ti_ TL? tLh| h?

Lh *L?} h? 4L?} @ih@}itc Lu |i |)Ti ti_ ? hi@* 4@h!i|t `i ** ti |i tLh| @?_ ?L|@|L?

s| ' sE%|3c c %|3u E

uLh |i uLhiU@t|?} t|h@|i}) i4T*L)i_ M) |h@_ih |)Ti  hLU! @?_ OL44it EbbH @i ?it|}@|i_ iL*|L?@h) UL4Ti||L? Mi|ii? |i t4T*it| *?i@h |h@_?} h*it | L?*) L?i *@}c i

s| ' }%|3n K Ee

54T*i uLhiU@t|?} h*it 4@) Mi hi*i@?| ? hi@* 4@h!i|tc MiU@ti uLh @ UL4T*U@|i_ uLhi U@t|?} h*i | tii4t ?*!i*) |@| i?L} |h@_iht ** ULLh_?@|i L? |@| T@h|U*@h h*i tL |@| | @giU|t 4@h!i| i^*Mh4 ThUit *|L} |i *?i@h uLhiU@t|?} h*i Ee t i |hi4i*) t4T*ic | _Lit ? u@U| hiThiti?| @ ?4Mih Lu 4TLh|@?| U@tit 6Lh i @4T*ic i? ML| |i |hi?_ T@h@4i|ih @?_ |i M@t T@h@4i|ih } ' K ' f |i h*i hi_Uit |L

|i uLhiU@t| Lu u?_@4i?|@*t|tc i

s|  fc ED

Mi*i?} |@| |i 4@h!i| ThUi ** Mi i^@* |L |i u?_@4i?|@* ThUi RW_{c Lh i^@*i?|*)}

|@| |i _i@|L? % uhL4 |i u?_@4i?|@* ** Mi f |ih 4TLh|@?| U@tit ULihi_ M) |i *?i@h uLhiU@t|?} h*i Ee @hi |i Thi |hi?_ uL**Liht

s|' }%|3c ES

@?_ |i Thi M@ti_ Mi*iu

s| ' K E.

L|Ui |@| |i t4T*i Thi M@t E. h*i hiThiti?|t @?) TLt|i*) Lh ?i}@|i*) M@ti_ ThUi uLhiU@t| |@| |h@_iht 4}| @i W?t|i@_ Lu |iti i |hi4i*) t4T*i @M|@* h*i Lu |4M uLhiU@t|?} h*itc tL4i iUL?L4t|t 4}| Thiuih |i h@|L?@*c TihuiU| uLhit}| uLhiU@t|?} h*i

s| ' %|n EH

`i i4T@t3i Liihc |@| |i TihuiU| uLhit}| uLhiU@t|?} h*i EH @tt4it TihuiU| !?L*i_}i Lu |i i|ihL}i?iLt 4@h!i| i^*Mh4 i^@|L? EDc @?_ ? T@h|U*@h TihuiU| !?L*i_}i @ML| |i Mi*iut Lu @** L|ih |h@_iht *|L} |i U@ti | TihuiU| uLhit}| Uih|@?*) @t |iLhi|U@* @TTi@*c |t Th@U|U@* hi*i@?Ui ? @ UL4T*i i|ihL}i?iLt Lh*_ tL*_ ?L| Mi Liht|@|i_ t?Ui |t ?_ih*)?} @tt4T|L? tii4t }*) ?hi@*t|U OL iihc ? |i 4@??ih Lu hLU! @?_ OL44it Ebb. @?_ _i 6L?|?Li**i E2fffc L?i UL*_ 4@!i Thi_U|Lh EH ELh @ t}?@* Lu } ThiUtL? L? %|n @@*@M*i @| @ ULt|c @?_ @__ |

|L |i ti| Lu Thi_U|Lht i UL?t_ih `i *i@i |t |L u|hi hiti@hU M| hi4@h! |@| | 4@) }i?ih@|i ?|ihit|?} _)?@4Ut

? 4TLh|@?| @?_ UL?i?i?| UL?ti^i?Ui Lu |i @tt4T|L?t  UL?Uih??} |h@_iht< Mi*iut t |@| |i i|ihL}i?iLt @}i?| 4@h!i| i^*Mh4 i^@|L? ED U@? Mi hiuLh4 *@|i_ ? _i@|L?t uhL4 |i Mi?U4@h! u?_@4i?|@* W? T@h|U*@h tMt|||?} |i ThUi uLhiU@t| E2 ? |i 4@h!i| i^*Mh4 i^@|L? ED @?_ t?} |i u@U|t |@| |i u?_@ 4i?|@* ThUi RW

| t@|t€it -RW| ' .|dRW|nn +|no  @j25r @?_ |i ThUi R| ' %|n RW| )i*_t

|i i^*Mh4 i^@|L? ? _i@|L?t uhL4 |i u?_@4i?|@*G -%|' M [ ' ?|.|d%|no  M [ ' ?|s|c Eb

| s| ' sE%|3c c %|3u ? 4TLh|@?| hi@tL? uLh Lh 4L_i* uLh4*@|L? ? |ih4t Lu

_i@|L?t uhL4 @ Mi?U4@h! u?_@4i?|@* t |@| ? |t }i?ih@* ti|Tc |i Mi?U4@h! h@|L?@* i TiU|@|L?t @tti| ThU?} 4L_i* t ?it|i_ @t @ tTiU@* U@tic | @** uLhiU@t|?} t|h@|i}it s  f W? |t @)c |i @_@T|i Mi*iu t)t|i4t U@? Mi ti_ ? i4ThU@*

@?_ i Tih4i?|@* |it|?} i|ih @tti| ThUit _i@|i t}?€U@?|*) uhL4 @?)L?i<t u@Lh|i Mi?U4@h! u?_@4i?|@*

2 ,L*|L?@h) _)?@4Ut

Ai iL*|L?@h) T@h| Lu |i 4L_i* _itUhMit L Mi*iut @hi T_@|i_ Lih |4ic |@| tc L |i uh@U|L?t ?| Lu |h@_ih |)Tit ? |i 4@h!i| i^*Mh4 i^@|L? Eb iL*i Lih

|4i 6h@U|L?t @hi T_@|i_ @UULh_?} |L @? iL*|L?@h) €|?itt Lh TihuLh4@?Ui 4i@thi Ai €|?itt 4i@thit Lu @** |h@_?} t|h@|i}it @hi TM*U@**) @@*@M*ic M| tMiU| |L ?Lti 6|?itt t _ihi_ uhL4 @ h@?_L4 |*|) 4L_i* @?_ }i? M)



L| ' L|n "|c E2f

ihi L|t |i _i|ih4?t|U T@h| Lu |i €|?itt 4i@thi @?_ "|hiThiti?|t WW# ?Lti @UhLtt

 ' c M W? Lh_ih |L LM|@? @?@*)|U@* i ThittL?t uLh |i ThLM@M*|it Lh uh@U|L?tc | ** Mi @tt4i_ |@| |i ?Lti "| t _h@? uhL4 @ _LM*i i TL?i?|@* _t|hM|L? W?

|@| U@tic ? |i *4| @t |i ?4Mih Lu @}i?|t }Lit |L ?€?|)c |i ThLM@M*|) |@| @? @}i?| ULLtit t|h@|i})  t }i? M) |i i** !?L? _tUhi|i ULUi 4L_i* Lh BMMt< ThLM@M*|ite ?|' e qLc|3 S_M 'eqLc|3  E2

L|i |@| |i uh@U|L?t ?| @__ T |L  Ai UhU@* ui@|hi Lu E2 t |@| |i }ih |i

€|?itt Lu |h@_?} t|h@|i}) c |i 4Lhi |h@_iht ** ti*iU| t|h@|i})  Ai T@h@4i|ih q ? E2 t U@**i_ |i ?|i?t|) Lu ULUic 4i@th?} L ti?t|i |i 4@tt Lu |h@_iht t |L ti*iU|?} |i LT|4@* Thi_U|L? t|h@|i}) Ai ?|i?t|) Lu ULUi q t ?ihti*) hi*@|i_ |L

7_{Vhh Pdqvnl dqg PfIdgghq +4<;4, dqg Dqghuvrq/ gh Sdopd dqg Wklvvh +4<<6, iru h{whqvlyh glvfxvvlrq}

ri glvfuhwh fkrlfh prghov dqg wkhlu dssolfdwlrqv lq hfrqrplfv1

|i @h@?Ui Lu |i ?Lti |ih4t "| Ai i |hi4i U@ti q ' f ULhhitTL?_t |L |i U@ti Lu ?€

?|i @h@?Ui ?Ltic tL |@| _gihi?Uit ? €|?itt U@? ?L| Mi LMtihi_ @?_ @** uh@U|L?t E2 ** Mi € i_ Lih |4i @?_ i^@* |L *M Ai L|ih i |hi4i U@ti q ' n4 ULhhitTL?_t |L |i U@ti |L| ?Ltic tL |@| |i _i|ih4?t|U T@h| Lu |i €|?itt U@? Mi LMtihi_ TihuiU|*) @?_ ? i@U TihL_c @** |h@_iht ULLti |i LT|4@* uLhiU@t| ? ?Uhi@ti ? |i ?|i?t|) Lu ULUi q hiThiti?|t @? ?Uhi@ti ? |i _i}hii Lu h@|L?@*|) h| iL*|L?@h) ti*iU|L? Lu |h@_?} t|h@|i}it Ai |4?} Lu |i ULT*?} Mi|ii? |i 4@h!i| i^*Mh4 i^@|L? ED Lh Eb @?_ |i iL*|L?@h) ti*iU|L? Lu t|h@|i}it E2 t UhU@* Ai 4@h!i| i^*Mh4 ThUi R| ? ED _iTi?_t TL? |i uh@U|L?t ?| Ai ?L|@|L? ? E2 t|hittit

|i u@U| |@| |iti uh@U|L?t ?| _iTi?_ TL? T@t| @?_ 4Lt| hiUi?|*) LMtihi_ €|?ittit

Lc|3c U ? |h? _iTi?_ TL? T@t| ThUit R|3 @?_ __i?_t +|3 ? TihL_t | @?_

uh|ih ? |i T@t| @t ** Mi tii? Mi*L u|ih |i i^*Mh4 ThUi R| @t Mii? hii@*i_

M) |i 4@h!i|c | ** Mi ti_ ? iL*|L?@h) T_@|?} Lu Mi*iut @?_ _i|ih4??} |i ?i uh@U|L?t ?c|n Aiti ?i uh@U|L?t ?c|n ** |i? _i|ih4?i @ ?i i^*Mh4

ThUi R|nc i|U W? |i 5c 4@h!i| i^*Mh4 ThUit @?_ uh@U|L?t Lu _gihi?| |h@_?}

t|h@|i}it |t ULiL*i Lih |4i

 ?@|h@* U@?__@|i uLh iL*|L?@h) €|?itt t @UU4*@|i_ hi@*3i_ ThL€|tc @t }i? M)D

L| ' ER|n +| -R|3.c|3dR|n +_@j2| -R|3o n Lc|3c E22

ihi - ' no t |i }hLtt ht! uhii h@|i Lu hi|h?c @?_ f     t @ 4i4Lh) T@h@4i|ih 4i@th?} L u@t| T@t| hi@*3i_ €|?itt t _tUL?|i_ uLh t|h@|i}) ti*iU|L? Ai €ht| |ih4 ? E22 hiThiti?|t *@t| TihL_<t hi@*3i_ ThL€| Lu |)Ti  }i? M) |i hi@*3i_ i Uitt hi|h? Lu |i ht!) @tti| Lih |i ht! uhii @tti| |4it |i _i4@?_ uLh |i ht!) @tti| M) |h@_iht Lu |)Ti  W? |i i |hi4i U@ti | ?L 4i4Lh)c i  ' fc €|?itt L| i^@*t ?i| hi@*3i_

ThL€| ? |i ThiLt TihL_c ihi@t ? |i L|ih i |hi4i U@ti | ?€?|i 4i4Lh)c i  ' c €|?itt L| i^@*t |L|@* i@*| @t }i? M) @UU4*@|i_ hi@*3i_ ThL€|t Lih |i

i?|hi T@t| W? |i ?|ih4i_@|i U@tic |i i}| }i? |L T@t| hi@*3i_ ThL€|t _iUhi@tit i TL?i?|@**) | |4i W| ** Mi tiu* |L UL4T|i |i hi@*3i_ i Uitt hi|h? -| ?

8_{Jlyhq wkdw lqyhvwruv duh ulvn dyhuvh phdq0yduldqfh pd{lpl}huv/ pd{lpl}lqj wkhlu h{shfwhg xwlolw| iurp}

zhdowk dqrwkhu qdwxudo fdqglgdwh iru wqhvv duh wkh ulvn dgmxvwhg surwv1 Lq idfw/ wkh wqhvv phdvxuh +55, edvhg xsrq uhdol}hg surwv grhv qrw wdnh lqwr dffrxqw wkh yduldqfh whup lq +5, fdswxulqj wkh lqyhvwruv* ulvn wdnhq ehiruh rewdlqlqj wkdw surw1 Rq wkh rwkhu kdqg/ lq uhdo pdunhwv uhdol}hg qhw surwv ru dffxpxodwhg zhdowk pd| eh zkdw lqyhvwruv fduh derxw prvw/ dqg wkh qrq0ulvn dgmxvwhg wqhvv phdvxuh +55, pd| wkxv eh sudfwlfdoo| lpsruwdqw1 Vhh EK 4<<; dqg Krpphv +5334, iru d glvfxvvlrq ri wklv srlqw1 Jdxqhuvgruihu dqg Krpphv +5333, lqyhvwljdwh dq hyroxwlrqdu| prgho zlwk wqhvv jlyhq e| ulvn dgmxvwhg surwv1 Lq dq| hyhqw wkh phwkrgrorj| ri OWO ghyhorshg lq wklv sdshu fdq eh ghyhorshg iru dowhuqdwlyh wqhvv ixqfwlrqv wr +55,1 Wkh jhqhudo srlqw wkdw wdnlqj wkh OWO gudvwlfdoo| uhgxfhv wkh qxpehu ri _sdudphwhuv% lq khwhurjhqhrxv eholhi prghov zlwk odujh qxpehuv ri vxfk eholhiv wr wkh vpdoo vhw ri sdudphwhuv wkdw ghwhuplqh _xqghuo|lqj fkdudfwhulvwlfv% ri xqghuo|lqj _eholhi glvwulexwlrqv% uhpdlqv lqghshqghqwo| ri zkdw fkrlfh wkh prghohu pdnhv iru wkh wqhvv ixqfwlrq1

_i@|L?t uhL4 |i u?_@4i?|@* |L LM|@?

-| ' R|n +| -R|3 ' %|n RW| n +| -%|3 -RW|3

' %| -%|3n RW| n +| .|3dR|Wn +|o n .|3dRW| n +|o  -RW|3

 %| -%|3n @j25rn B|c

E2

ihi i ti_ |@| .|3dRW| n +|o  -R|3W ' @j25r t?Ui |i u?_@4i?|@* RW| t@|t€it |i

4@h!i| i^*Mh4 i^@|L? ESc @?_ B| RW|n +| .|3dRW|n +|o t @ 4@h|?}@*i _gihi?Ui

ti^i?Ui Ai h@?_L4 |ih4 B| i?|iht MiU@ti |i __i?_ ThLUitt t t|LU@t|Uc @?_

|t hiThiti?|t ?|h?tU ?Uih|@?|) @ML| iUL?L4U u?_@4i?|@*tS_{ UULh_?} |L |i}

_iUL4TLt|L? E2 i Uitt hi|h? UL?tt|t Lu @ UL?i?|L?@* ,O |ih4 B| T*t @ ht!

Thi44 @j2₅r _{@?_ @? @__|L?@* tTiU*@|i |ih4 %}

| -%|3 Lu |i 5 |iLh) h

5 |iLh) |t @**Lt uLh |i TLttM*|) Lu i Uitt L*@|*|) Ai i |h@ |ih4 t 3ihL u i|ih %| fc |@| t ThUit i^@* |ih u?_@4i?|@* @*ic Lh u %|' -%|3c |@| t i?

ThUit uL**L @ +, MMM*i tL*|L? Ai 5 |iLh) Thi_U|t i Uitt L*@|*|) ? TihL_t i? @tti| ThUit }hL u@t|ih Lh t*Lih |@? |i ht! uhii h@|i Lu hi|h?c Lh i? ThUit t|U Mi|ii? @ |i4TLh@h) MMM*i tL*|L? @?_ |i u?_@4i?|@*

6|?itt U@? ?L Mi hih||i? ? _i@|L?t uhL4 |i u?_@4i?|@* @t L|' E%| -%|3n @j25rn B|Esc|3 -%|3n @j

2₅r

@j2  n Lc|3 E2e

 w @h}i A)Ti w 4|t

At tiU|L? ?|hL_Uit |i ?L|L? Lu @ w@h}i A)Ti w4| EwAwc U t LM|@?i_ @t @ *4| @TThL 4@|L?< Lu @? 5 | Mi*iu |)Tit _h@? h@?_L4*) uhL4 @ € i_ _t|hM |L?c @t |i ?4Mih Lu |)Tit |i?_t |L ?€?|)

 ,L*|L? uLh €?|i*) 4@?) |h@_iht

Ai t|@h|?} TL?| t |i i^*Mh4 i^@|L? uLh @ 4@h!i| | i|ihL}i?iLt Mi*iutG -%|'

M

[

'

?|s|c E2D

ihi %|t |i _i@|L? uhL4 |i u?_@4i?|@* ThUi @?_ ?||i uh@U|L? Lu |)Ti  |h@_ihtc

@t MiuLhi Ai u?U|L? s|c i Thitt?} |i Mi*iu Lu |)Ti  L? |i ThUi Lu |i ht!) @tti|

@| |4i | n c t @tt4i_ |L @i |i uL**L?} }i?ih@* uLh4G s|' sE%|3c c %|3_c bc i 

9_{Lq wkh vshfldo fdvh ri dq LLG glylghqg surfhvv |}

w @ | . w zh vlpso| kdyh w@ w1

Ai %|3c  ' c c _c @hi |i T@t| ThUi _i@|L?t T |L |i 4@ 4@* |4i _i*@) _c b t

@ 4*|_4i?tL?@* t|hU|h@* T@h@4i|ih EUL?|@??} @** iUL?L4U T@h@4i|ihtc tU @t |i ?|ihit| h@|i o Lh |i 4i@? __i?_ 7+c |@| 4@) Mi ti_ ? |i uLhiU@t|?} u?U|L?tc @?_ |i Mi*iu @h@M*i i t @ 4*|_4i?tL?@* t|LU@t|U @h@M*i U U@h@U|ih3it

|i Mi*iu  At Mi*iu t t@4T*i_ uhL4 @ }i?ih@* _t|hM|L? Lu Mi*iut AL € _i@tc UL?t_ih @t @? i @4T*i |i U@ti ihi Mi*iut @hi *?i@h | |i t|LU@t|U @h@M*i i

_h@? uhL4 @ 4*|@h@|i ?Lh4@* _t|hM|L?G

s| ' s|Ei ' ifn i%|3n  n i_%|3_

+iU@** |@| |i uh@U|L?t ?| @hi }i? M) |i _tUhi|i ULUi 4L_i* ThLM@M*|it

?|' e qLc|3

S_M

'eqLc|3

 E2S

5?Ui |i €|?itt u?U|L? Lc|3Lu |)Ti  _iTi?_t TL? %|3c %|32@?_ TL? |i uLhiU@t|?}

u?U|L? sc|32 |ih }i?ih@* uLh4 tG

Lc|3' LE%|3c %|32c c %|3_32c bc i c

ihi |i T@h@4i|ih b t |i t|hU|h@* T@h@4i|ih @t MiuLhic ?U*_?} uLh i @4T*i |i ht! @ihtL? ULiUi?| @ @TTi@h?} ? |i |h@_iht< _i4@?_ u?U|L? uLh |i ht!) @tti| Ai i^*Mh4 i^@|L? E2D U@? Mi hih||i? |LG

%| ' _- S_M 'eqLc|3s| S_M 'eqLc|3  E2.

W| }it hti |L @ _)?@4U@* t)t|i4 ? |i uL**L?} @) Ai t|@|i @h@M*it | '

E%|c c %_n2c| @hi ?|hL_Ui_ M) %| ' %|3c     _ n 2 Ai t|@|i tT@Ui f t |@!i? |L

Mi @? LTi? tMti| Lu +_n2_

Ai i^*Mh4 i^@|L? E2. _i|ih4?it |i iL*|L? Lu |i t)t|i4 | M |h@_ih |)Tit  |t ?uLh4@|L? t UL_i_ ? |i iL*|L? 4@T )ME c bc iG

)ME c bc i ' _- S_M 'e qLE c bci sE c bc i S_M 'e qLE c bci  E2H

Ai t|hU|h@* T@h@4i|ih b ' Eqc -c bc c b^ |@!it @*it ? @ ML?_i_ LTi? tMti| \

Lu +^_{c @?_ UL?|@?t @** t|hU|h@* T@h@4i|iht Lu |i iL*|L?@h)c i|ihL}i?iLt @}i?|t}

iUL?L4)c tU @t |i ?|i?t|) Lu ULUi qc |i ?|ihit| h@|i o ELh }hLtt h@|i Lu hi|h? - ' noc |i ht! @ihtL? ULiUi?| @c i|U `i? |i ?4Mih Lu |h@_ih |)Tit M t *@h}ic |i iL*|L? 4@T )M UL?|@?t @ *@h}i ?4Mih Lu t|LU@t|U @h@M*it i ' Eic c iMc

| |i i ?_iTi?_i?|*) _i?|U@**) _t|hM|i_ Ei?UiuLh|G WW#c | _t|hM|L? u?U

|L? 8> Ai _t|hM|L? u?U|L? Lu |i t|LU@t|U Mi*iu @h@M*i i _iTi?_t L? @ 4*|

_4i?tL?@* T@h@4i|ih >c U@**i_ |i Mi*iu T@h@4i|ihc U |@!it @*it ? @ ML?_i_ LTi? tMti|  Lu +o_{ At ti|T @**Lt |L @h) |i TLT*@|L? L| Lu U |i ?_}

_@* Mi*iut @hi t@4T*i_ Ai i T*U| _iTi?_i?Ui Lu @ ThLM@M*|) L? > t _i?L|i_ M)  ' >

Wu |i t|@|i |@| |4i | t !?L?c |i t|@|i |n@| |4i |n t }i? M) |n ' xME |c bc ic

ihiG

xME c bc i ' E)ME c bc ic %c    c %_n  E2b

Ai 4@T xM _i€?it |i _)?@4U@* t)t|i4 @ttLU@|i_ |L |i iL*|L? 4@T )M ULhhi

tTL?_?} |L @ 4@h!i| | M _gihi?| Mi*iu |)Tit

2 Ai *4| iL*|L?

Ai 4@? UL?|hM|L? Lu |t T@Tih t |L tL |@| |i |4i iL*|L? Lu @ 4@h!i| | @ *@h}ic M| €?|ic ?4Mih Lu Mi*iut Mc h@?_L4*) _h@? uhL4 @ € i_ _t|hM|L?c t i** _itUhMi_c ? |i ti?ti |L Mi 4@_i ThiUti Mi*Lc M) @ 4U t4T*ih t)t|i4 U@**i_ |i *@h}i |)Ti *4| EwAw Ai wAw hiThiti?|t ? @ @) |i @ih@}i< _)?@4U@* Mi@Lh Lu @** ?|ih@U|?} |h@_iht Mtihi |@| ML| |i _i?L4?@|Lh @?_ |i ?L4?@|Lh Lu |i iL*|L? 4@T )M ? E2H 4@) Mi __i_ M) |i ?4Mih Lu |h@_ih |)Tit M @?_ |t 4@)

Mi tii? @t t@4T*i 4i@?t Ai iL*|L? 4@T  Lu |i *@h}i |)Ti *4| t |i? t4T*) LM|@?i_ M) hiT*@U?} |i t@4T*i 4i@?t ? |i iL*|L? 4@T )M M) TLT*@|L? 4i@?tc |L

LM|@?G E c bc > ' _- ,> k eqLE cbcifsE c bc i_f l ,> k eqLE cbcif l  Ef

Oihi if t @ t|LU@t|U @h@M*i U t _t|hM|i_ ? |i t@4i @) @t |i ic |

_t|hM|L? u?U|L? 8> Ai t|hU|h@* T@h@4i|ih iU|Lh b Lu |i iL*|L? 4@T )M @?_

|i wAw iL*|L? 4@T  UL?U_i OLiihc ihi@t |i iL*|L? 4@T )M ? E2H Lu

|i i|ihL}i?iLt @}i?| t)t|i4 UL?|@?t M h@?_L4*) _h@? 4*|_4i?tL?@* t|LU@t|U @h@M*it ic |i wAw iL*|L? 4@T  ? Ef L?*) UL?|@?t |i Mi*iu T@h@4i|ih iU|Lh

> _itUhM?} |i L?| ThLM@M*|) _t|hM|L? A@!?} @ *@h}i |)Ti *4| |t *i@_t |L @ }i hi_U|L? ? t|LU@t|U Mi*iu @h@M*it W? tiU|L? Si ** UL?t_ih @? i @4T*i ihi |i h@?_L4*) _h@? Mi*iut @hi *?i@hc | 4*|@h@|i ?Lh4@**) _t|hM|i_ Mi*iu @h@M*itc @?_ |i wAw UL?|@?t @t Mi*iu T@h@4i|iht |i 4i@?t @?_ |i @h@?Uit Lu |i ULhhitTL?_?} 4*|@h@|i _t|hM|L?

Ai _)?@4U@* t)t|i4 ULhhitTL?_?} |L |i wAw iL*|L? 4@T  t _i?L|i_ M) [E c bc > @?_ }i? M)G

[E c bc > ' EE c bc >c %c    c %_n  E

5iU|L? e ** t|@|i @?_ ThLi @ |iLhi4 t@)?} |@| |i wAw t @ }LL_ @TThL 4@|L? Lu @? 5 | 4@?) Mi*iu |)Titc @?_ tiU|L? D ** tL |@| @** }i?ihU< @?_ Tihtt|i?|< _)?@4U ThLTih|it ** Mi Thitihi_ | } ThLM@M*|)

e L?ih}i?Ui |L *@h}i |)Ti *4|t

At tiU|L? t|@|it @?_ ThLit |i |iLhi4 @ML| UL?ih}i?Ui |L |i *@h}i |)Ti *4| Lhi ThiUti*)c | ** Mi tL? |@| |i 4@T xMc _itUhM?} |i iL*|L?@h) _)?@4Ut

? @ 4@h!i| | M h@?_L4*) _h@? Mi*iutc UL?ih}it @*4Lt| thi*) |L |i wAw 4@T [ @t |i ?4Mih Lu |h@_ih |)Tit M |i?_t |L ?€?|)

e L|@|L?

W? Lh_ih |L uLh4*@|i |i |iLhi4 Mi*L tUU?U|*)c |i uL**L?} ?L|@|L? t ?|hL_Ui_ Wu |i ?@|h@* ?4Miht @hi _i?L|i_ M)  ' ifc c 2c jc |i? *i| k 5 _n^ _{Mi @ 4*|?_i G}

k ' Ekc c k_n^ 

wi| mkm 'Smkmc @?_ *i| (k _i?L|i _gihi?|@|L? | hitTiU| |L @?_ b @t uL**LtG

(k ' Y k Y%k   Yk_ Y%k_ _ Yk_n Ybk_n   Yk_n^ Ybk_n^ ^ 

W| t @tt4i_ |@| @?_ b |@!i @*it ? ML?_i_ LTi? ti|t T  +_ _{@?_ \ 5 +}^

hitTiU|i*) 6Lh u?U|L?t |@| @hi & |4it _gihi?|@M*i L? T \c @?_ |@| @i |L}i|ih | |ih _ih@|itc UL?|?Lt i |i?t|L?t |L |i U*Lthi T  \c |i uL**L?} &_?Lh4

t ?|hL_Ui_G

nsn&' 4@

ƒkƒ$&T f\tTm(ksE c bm

Ai ?Lh4 Lu iU|Lh @*i_ u?U|L?t t _i€?i_ @?@*L}Lt*)c M) |@!?} @TThLTh@|i iU|Lh ?Lh4t L? |i h}| @?_ t_i

e2 Ai UL?ih}i?Ui |iLhi4

L|i |@| |i t|LU@t|U @h@M*it Lu |i ThiLt tiU|L? @hi @** Lu |i }i?ih@* uLh4G f ' }EXc r c

ihi X t @?L|ih E4*|_4i?tL?@* t|LU@t|U @h@M*ic @?_ ihi r t @? Lh_?@h) @h@M*i( uLh ?t|@?Uic r ' E c b UL?tt|t Lu @ iU|Lh Lu t|@|i @h@M*it @?_ @ iU|Lh b Lu t|hU|h@* T@h@4i|iht `i U@** f @ T@h@4i|ih _iTi?_i?| t|LU@t|U @h@M*i wi| 8>

Mi |i _t|hM|L? u?U|L? Lu Xc _iTi?_?} L? @ iU|Lh > Lu Mi*iu T@h@4i|iht Wu } t _gihi?|@M*i | hitTiU| |L rc |i T@h@4i|ih _iTi?_i?| t|LU@t|U @h@M*i f t t@_ |L Mi _gihi?|@M*i | hitTiU| |L r @t i** Wu } t _gihi?|@M*i T |L Lh_ih &c |i _ih@|i (kf | mkm  & Lu f | hitTiU| |L r t _i€?i_ @t

(kf ' E(k}EXc r

W? |i Thiti?| UL?|i |c *i| f '  f f2  '  iqLErci iqLErcisErc i_  c

ihi r ' E c b @?_ ihi L @?_ s @hi @t ? |i ThiLt tiU|L? Wu s @?_ L @hi _gihi?|@M*i T |L Lh_ih & ? @?_ bc |i? f t _gihi?|@M*i T |L |i t@4i Lh_ih ? r

AiLhi4 E&_{UL?ih}i?Ui @*4Lt| thi*) |L |i wAw}

wi| & : f Mi € i_c @?_ @tt4i |@| uLh @** k | mkm  &c |ihi i t|t @ ?L??i}@|i h@?_L4 @h@M*i tk  fc ?_iTi?_i?| Lu rc tU |@|

m(kfm tk @?_ .tk 4

Ai? uLh iih) Mi*iu T@h@4i|ih > 5 c @?_ uLh @?) 0 : f @?_ B : fc |ihi t @ Mf : f

tU |@|G

>i6Lh @?) M  Mf G n[  xMn& : 0j B 

A@| tc uLh M  Mfc [ @?_ xM @hic | ThLM@M*|)   Bc 0U*Lti ? |i & |LTL*L})

At |iLhi4 t|@|it |@| |i MMi*iu |)Tit t)t|i4 xM E2b UL?ih}it @*4Lt| thi*) |L

|t *@h}i |)Ti *4| [ ? E @t M |i?_t |L ?€?|) W? L|ih Lh_tc u M t *@h}i i?L}c | } ThLM@M*|) |i _)?@4U@* t)t|i4t xMc xMnc   c @?_ |i w@h}i A)Ti w4| [c

@hi 0U*Lti ? |i & _{|LTL*L}) L|i |@| |i |iLhi4 L*_t TL?|ti uLh >c |@| tc uLh}

i@U > 5 c @t M MiUL4it *@h}i |i M|)Ti t)t|i4 xME c bc i UL?ih}it @*4Lt| thi*)

|L |t wAw [E c bc >

e TT*U@M*|)

AL @| !?_ Lu t|LU@t|U @h@M*it t |t |iLhi4 @TT*U@M*iq +iU@** |@| f ' iqLc

@?_ |@| f2 ' iqLs LhiLihc @MLi | @t Mii? @tt4i_ |hL}L| |@| |i uLhi

U@t|?} h*it s @?_ |i €|?itt 4i@thit L @hi *?i@h ? |i t|LU@t|U @h@M*it i

L?t_ih @ |)TU@* ic @?_ @tt4i |@| |t ThLM@M*|) _t|hM|L? _8 Ei t Lu |i uLh4 8_{Ei _ic | 8Ei @ 4i@th@M*i u?U|L? L|i |@|}

fc f2  t ' iSiE@ n Kic

ihi @c K @?_ S U@? |@!i @?) @*it W? Lh_ih |@| ,t i t|tc i @i |i UL?_|L?G ]

iSƒiƒ_{mim8Ei _i 4}

uLh @** S Oi?Ui 8_{Ei @t |L u@** Lg u@t|ih |@? i}3ƒSƒƒiƒ _{@t mim $ 4 uLh @** TLt|i @*it}

Lu mSm ? |i L|ih @?_c u

8_{Ei  i}3&ƒiƒn

c

uLh tL4i c & : fc |i? |i UL?_|L?t Lu |i |iLhi4 @hi t@|t€i_ L|i |@| ?Lh4@**) _t|hM|i_ @h@M*itc @t i** @t @h@M*it Lti _t|hM|L? @t UL4T@U| tTTLh|c t@|tu) |iti UL?_|L?t

Ai hit| Lu |t tiU|L? t _iL|i_ |L |i ThLLu Lu |t |iLhi4

ee hi*4?@hit

W| U*i@h*) tUit |L tL |@|G

>i6Lh @** M  Mf G n  )Mn&: 0 B c

ihi |i iL*|L? 4@Tt  ? Ef @?_ )M ? E2H |@!i |i T*@Ui Lu |i _)?@4U@*

t)t|i4t [ ? E @?_ xM ? E2b

wi| 7f _i?L|i |i @ih@}i< Lih |i f ' Efc f2G

7 f ' _M M [ ' f

6?@**)c ?L|i |@| , 7f ' E,fc ,f2 ' ,iqLfc iqLfsf `| |t ?L|@|L?c UL4T@hiG

)MErc i ' _- 7 f2 7 f '  -,f2n 7f2 ,f2 ,fn 7f ,f @?_ Er '  -,f2 ,f 

L|?} |@| ,f  S : fc |i t|hL?} *@ Lu *@h}i ?4Miht tLt |@| @t M $ 4c |i

|ih4t Mi|ii? Mh@U!i|t ? |i i ThittL? Lu )M |i?_ |L f W| uL**Lt |@| )MErc i $

Er @*4Lt| thi*)c TL?|ti ? r OLiihc |t t ?L| i?L} uLh Lh ThTLtitG i ?ii_ )MErc ic |L}i|ih | |t _ih@|it T |L &<| Lh_ihc |L UL?ih}i ?uLh4*) ? r

W? |i ?i | tMtiU|L?c @ ?uLh4 *@ Lu *@h}i ?4Miht t ^L|i_c U i*Tt t |L it|@M*t ThiUti*) @| i @?|

eD N?uLh4 *@ Lu *@h}i ?4Miht

Ai uL**L?} |iLhi4c | U@?}i_ ?L|@|L?c t ^L|i_ uhL4 ai??hU EbSbc TSSc |iLhi4 2

AiLhi4

wi| }Erc i Mi _i€?i_ L? V  Hc ihi H t @ ,U*_i@? tT@Uic @?_ ihi V t @ UL4T@U| tMti| Lu @? ,U*_i@? tT@Ui wi| } Mi UL?|?Lt ? r uLh i@U ic @?_ 4i@th@M*i ? i uLh i@U r tt4i |@| m}Erc im  Ei uLh @** r @?_ ic ihi  t ?|i}h@M*i | hitTiU| |L @ ThLM@M*|) _t|hM|L? 8 L? H Wu ic i2c   c t @ h@?_L4 t@4T*i uhL4 8 c |i? uLh

@*4Lt| iih) ti^i?Ui iijc  M M [ ' }Eic r $ ]

}Eic r _8 Ei @*4Lt| thi*)c ?uLh4*) ? r

L|i |@| u mkm  &c |i )TL|itt Lu |t |iLhi4 t t@|t€i_ uLh (kf t?Ui |iti

t|LU@t|U @h@M*it @hi _L4?@|i_ M) tk At tLt @*hi@_) |@| )M $  @*4Lt| thi*)

? |i f _|LTL*L})

`i @i |@|

(kf $ ,(7 kf @rc E2

?uLh4*) ? r LhiLihc @}@? MiU@ti Lu _L4?@|L? ,(kf ' (k,f

Ai _ih@|i (k)M t UL4T|i_ uLh mkm ' G

(k)M '  (k,f2n(kf72 ,(kf2 ,fn 7f ,f ,f2n 7f2 ,f2 (k,fn(kf7 ,(kf  ,fn 7f  ,f2

iU@ti Lu |i ?uLh4 UL?ih}i?Ui Lu |i _ih@|it E2c | uL**Lt |@| u mkm  c (k)MEic r $ (kEr @rc

?uLh4*) ? r Ai U@ti Lu }ih Lh_ih _ih@|it t *iu| |L |i hi@_ih At €?tit |i ThLLu Lu |i |iLhi4

D #)?@4U@* UL?ti^i?Uit

W? @| ti?ti t |i *@h}i |)Ti *4| @ }LL_< @TThL 4@|L? Lu |i t)t|i4 | @ *@h}i M| €?|i ?4Mih Lu Mi*iutq At ^it|L? *i@_t |L |L !i) UL?UiT|t ? |i |iLh) Lu _)?@4U@* t)t|i4tc t|hU|h@* t|@M*|) @?_ Tihtt|i?Ui Aiti @hi _tUtti_ ? |i ?i | tMtiU|L?c @?_ @TT*i_ |L Lh iL*|L?@h) t)t|i4 ? tMtiU|L? D2 W| ** Mi @h}i_ |@| @** }i?ihU @?_ Tihtt|i?| ThLTih|it Lu |i wAw iL*|L? 4@T [c | ThLM@M*|) @hM|h@h*) U*Lti |L  @*tL LUUh uLh |i iL*|L? 4@T xM u |i ?4Mih Lu |h@_ih |)Tit

M t tUi?|*) *@h}i

D 5|hU|h@* t|@M*|) @?_ Tihtt|i?Ui

W? |t tMtiU|L? [ @?_ x _i?L|i }i?ih@* _)?@4U@* t)t|i4t  _)?@4U@* t)t|i4 [ t U@**i_ &_{t|hU|h@**) t|@M*ic u iih) t)t|i4 x tUi?|*) U*Lti |L [ ? |i}&_{?Lh4 nn}

&

t UL?}@|i_ |L [( |@| tc M) @ t|@M*i U@?}i Lu @h@M*it @?_ T@h@4i|ihtc x U@? Mi |h@?tuLh4i_ ?|L [

5|hU|h@* t|@M*|) Lu @ t)t|i4 t t@**) @h_ |L ThLi OLiihc u |i UL?UiT| t hi t|hU|i_ |L Uih|@? ThLTih|it Lu |i t)t|i4  *!i @?} @? @||h@U|?} € i_ TL?|c Lh ?_ih}L?} @ t@__*i?L_i MuhU@|L?  tL4i|4it | U@? Mi tL? |@| @** t)t|i4t x tUi?|*) &_{U*Lti @*tL @i |i t@4i ThLTih|)c U t |i? U@**i_ @}&_Tihtt|i?|

ThLTih|) Nt@**) |i _i}hii Lu _gihi?|@M*|) & t ?L| i T*U|*) 4i?|L?i_G Tihtt|i?|< 4i@?t &_{Tihtt|i?| | & *@h}i i?L} uLh |i ThTLti @| @?_ 5ii i} BU!i?i4ih}

@?_ OL*4it EbHS uLh @ }i?ih@* _tUttL? Lu t|hU|h@* t|@M*|) @?_ Tihtt|i?Ui , @4T*it Lu Tihtt|i?| ThLTih|it

Ai t4T*it| i @4T*i Lu @ Tihtt|i?| ThLTih|) t @ )TihML*U € i_ TL?| A@| tc u [ @t @ € i_ TL?| %fc @?_ @** i}i?@*it Lu (%[E%f @hi Lg |i ?| UhU*i ? |i UL4T*i T*@?ic

|i? %f t U@**i_ @ )TihML*U € i_ TL?| ,ih) x tUi?|*) U*Lti |L [ ? |i nn?Lh4

@*tL @t @ )TihML*U € i_ TL?|G |i) @hi _Tihtt|i?|

? 4TLh|@?| U*@tt Lu i @4T*it t uh?ti_ M) tLU@**i_ }i?ihU MuhU@|L?tc *!i |i t@__*i?L_ic OLTuc @?_ TihL__LM*?} MuhU@|L?t Lu € i_ TL?|t ,ih) }i?ihU Muh U@|L? @t @ TLt|i ?|i}ih  @ttLU@|i_ |L |c |i UL_4i?tL? Lu |i MuhU@|L?( tii i} k3?i|tL EbbH uLh @? ?|hL_U|L? |L MuhU@|L? |iLh) @?_ @ _i|@*i_ 4@|i4@| U@* |hi@|4i?| Lu MuhU@|L?t Lu UL_4i?tL?  @?_ 2 Wu [ _iTi?_t L? @ ^_4i?tL?@* T@h@4i|ih bc |i UL_4i?tL?  Lu |i MuhU@|L? UL?t_ihi_ t *itt |@? Lh i^@* |L ^c @?_ [ @t uLh b ' bf @ }i?ihU UL_4i?tL? MuhU@|L?c |i? @?) ^T@h@4i|ih t)t

|i4 x tUi?|*) U*Lti |L [ ? |i &_{?Lh4 E|i hi^hi_ _i}hii & t _i|ih4?i_ M) |i}

tTiU€U MuhU@|L? @t |i t@4i MuhU@|L?c TLttM*) uLh @ _gihi?| @*i Lu |i T@h@ 4i|ih b ' b W? tLh|G uLh @ _)?@4U@* t)t|i4 _iTi?_?} L? ^ T@h@4i|ihtc @** }i?ihU

MuhU@|L?t | UL_4i?tL? T |L @?_ ?U*_?} ^ @hi Tihtt|i?| b

W? T@h|U*@hc }i?ihU t@__*i?L_ic OLTuc @?_ TihL_ _LM*?} MuhU@|L?t @hi Tihtt |i?| uLh T@h@4i|ih u@4*it Lu _)?@4U@* t)t|i4t W? 2T@h@4i|ih t)t|i4tc UtT @?_ L}_@?LA@!i?t MuhU@|L?t E|L ?@4i @ ui Tihtt|

Aiti @hi @** i @4T*it Lu Tihtt|i?| *LU@* ThLTih|it ? 4TLh|@?| i @4T*i Lu @ Tihtt|i?| }*LM@* ThLTih|) t @ tLU@**i_ |h@?tiht@* L4LU*?U TL?|c |@| tc @ |h@?tiht@* ?|ihtiU |L? R Lu t|@M*i @?_ ?t|@M*i 4@?uL*_t Lu @ Et@__*i € i_ TL?| OL4LU*?U TL?|t @hi U@h@U|ih3i_ M) |i u@U| |@| |t |ih@|it )?_{ER @TThL@U |i € i_ TL?| uLh ? $ 4 @t}

i** @t uLh ? $ 4 Ah@?tiht@* L4LU*?U TL?|t @hi Tihtt|i?| ?_ih t4@** Tih|hM@ |L?t L|i |@| |i i t|i?Ui Lu @ |h@?tiht@* L4LU*?U TL?| 4T*it |i LUUhhi?Ui Lu LhtitLi _)?@4Ut ? |i t)t|i4

Ai }i?itt Lu |h@?tiht@* L4LU*?U ?|ihtiU|L?t M) @ L4LU*?U |@?}i?U) MuhU@|L? ? L?iT@h@4i|ih u@4*it t @?L|ih }*LM@* i @4T*i Lu @ Tihtt|i?| ThLTih|) W? t)t|i4t | |L_4i?tL?@* T@ti tT@Uic tU @ MuhU@|L? 4T*it E?_ih tL4i 4*_ UL?_|L?t |i i t|i?Ui Lu t|h@?}i @||h@U|Lht uLh @ ti| Lu T@h@4i|iht Lu TLt|i 4i@thi 5ii @*t @?_ A@!i?t Ebb uLh @ hiUi?| 4@|i4@|U@* |hi@|4i?| Lu L4LU*?U MuhU@|L? |iLh) #i V*_ih EbbS UL?|@?t @ t|4*@|?} ?|hL_U|L? Lu Ti?L4i?@ @ttLU@|i_ |L L4LU*?U MuhU@|L?t @?_ @TT*U@|L? |L @ |L_4i?tL?@* ihtL? Lu |i Lih*@TT?} }i?ih@|L?t 4L_i*

?L|ih i @4T*i t uh?ti_ M) |i iLti+i**iA@!i?t Ti?L4i?L?G |i) tLi_ |@| uLh @ u@4*) Lu 4@TT?}tc @?} @? ?@h@?| ^@tTihL_U UhU*i MuhU@|?} |L @? ?@h@?| 2|Lht E@ tLU@**i_ ^@tTihL_U OLTu MuhU@|L?c M) @ 2_{t4@** Tih|hM@}

|L?c @ t)t|i4 | @ t|h@?}i @||h@U|Lh ?t|i@_ Lu @ ^@tTihL_U 2|Lht U@? Mi LM|@?i_ E+i**i @?_ A@!i?t Eb. @?_ iLtic +i**i @?_ A@!i?t Eb.H Oi?Ui iih) t)t |i4 _tT*@)?} @ ^@tTihL_U OLTu MuhU@|L? t 2_{?i@h |L @ t)t|i4 | @ t|h@?}i}

@||h@U|Lh L|i |@| ^@tTihL_U OLTu MuhU@|L?t LUUh }i?ihU@**) ? |LT@h@4i|ih u@4*it E|L} L?*) L? T@h@4i|ih ti|t Lu TLt|i 4i@thic M| i4T|) ?|ihLhc tii hLih i| @* Ebbf

, @4T*it Lu ?L?Tihtt|i?| ThLTih|it

 ?L?Tihtt|?} i @4T*i t uh?ti_ M) |i T|UuLh! MuhU@|L? W| ** Mi tiu* |L _tUtt |t i @4T*i ihic t?Ui | ** T*@) tL4i hL*i ? |i t4T*i wAw t|_i_ ? tiU|L? S  t4T*i i @4T*i i M|?} @ T|UuLh! MuhU@|L? t |i T@h@4i|ih u@4*) _)?@4U@* t)t|i4 [E%c b uLh b ' fc ihi [ t }i? M)G

[E%c b ' % n b%  %_{c m%m} 

c mbm 2

 E

6Lh b : f |ihi @hi |L t|@M*i € i_ TL?|t % ' sb @?_ L?i ?t|@M*i € i_ TL?| % ' fc U UL@*itUi @| b ' f 6Lh b f |ihi t L?*) L?i t|@M*i € i_ TL?| % ' f

) @__?} @ t4@** UL?t|@?| 0 : f |L [c |i TU|hi _t?|i}h@|it Ai t)t|i4 [0c |G

[0E%c b ' % n b%  %n 0 c Ee

−1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1 lambda x PF

6}hi G uhU@|L? _@}h@4 uLh |i T|UuLh! MuhU@|L? Lu [ ? E W? |t E>c % T*L|c |i T@ti tT@Ui t T*L||i_ ih|U@**) uLh iih) T@h@4i|ih > #h@? *?it ?_U@|i |i TLt|L? Lu € i_ TL?|t Ai _L| E6 ?_U@|it |i T|UuLh! MuhU@|L? TL?|

@t @ }i?ihU t@__*i ?L_i MuhU@|L? Lu @ t|@M*i @?_ @? ?t|@M*i € i_ TL?|c |L}i|ih | @ t|@M*i E)TihML*U € i_ TL?| U i t|t uLh @** b Oi?Ui |i T|UuLh! MuhU@|L? t ?L| }i?ihU W? u@U|c |i T|UuLh! MuhU@|L? L?*) LUUht ? t)t|i4t | @ hiiU|L?@* t)44i|h) 6Lh i @4T*ic |i t)t|i4 E t t)44i|hU h| |L % ' fc t?Ui [E%c b ' [E%c b __?} @ Tih|hM@|L? T@h@4i|ih " ? Ee 4i@?t @ Mhi@!?} Lu |i t)44i|h) ? |i t)t|i4 @?_ |i T|UuLh! MuhU@|L? _t@TTi@ht W| tL*_ Mi ?L|i_ Liih |@|c uLh t4@** " |i MuhU@|L? _@}h@4 Lu |i Tih|hMi_ T|UuLh! ? €}hi 2 t U*Lti |L |i MuhU@|L? _@}h@4 Lu |i T|UuLh! ? €}hi 

−1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1 lambda x SN

6}hi 2G uhU@|L? _@}h@4 uLh |i Tih|hMi_ T|UuLh! MuhU@|L? ? Ee wi}i?_ @t ? €}hi  Ai T|UuLh! MuhU@|L? _Lit ?L| Tihtt| L|i |i LUUhhi?Ui Lu @ t@__*i?L_i MuhU@|L? E5c U t ? UL?|h@t| |L |i T|UuLh! @ }i?ihU UL_4i?tL? MuhU@|L?

D2 TT*U@|L? |L *@h}i |)Ti *4|t

Ai @MLi UL?t_ih@|L?t U@? Mi @TT*i_ |L |i U@ti Lu €?|i Mi*iu t)t|i4t @?_ |ih ULhhitTL?_?} *@h}i |)Ti *4|t

ihtt|i?Ui Lu MuhU@|L?t ? ThLM@M*|)<

wi| xME%c bc i uLh M ' c 2c  Mi @ MMi*iu |)Tit t)t|i4 @t ? E2bc _iTi?_?} L? @

^_4i?tL?@* t|hU|h@* T@h@4i|ih b wi| [E%c bc > Mi |i *@h}i |)Ti *4| @t ? Ec U _iTi?_t L? b @t i** @t L? |i Mi*iu T@h@4i|ih > Ai |iLhi4 Lu tiU|L? e t|@|it |@| |i t)t|i4t xMc |L}i|ih | |ih _ih@|it T |L Lh_ih &c UL?ih}i ? ThLM@M*|)

|L |ih *@h}i |)Ti *4| @t M |i?_t |L ?€?|)

wi| 0 5 Efc  @?_ > 5  Mi € i_ 5?Ui }i?ihU UL_4i?tL? MuhU@|L?t Tihtt| u   ^c | uL**Lt |@| @?) }i?ihU UL_4i?tL?  MuhU@|L? | hitTiU| |L |i t|hU|h@* T@h@4i|ih b uLh [ E> t € i_ LUUht | ThLM@M*|) @| *i@t|   0 uLh xMc uLh M *@h}i

Ai hL*i Lu Mi*iu T@h@4i|iht

L|i |i _t|?U|L? Mi|ii? t|hU|h@* T@h@4i|iht b @?_ Mi*iu T@h@4i|iht > At t hL}*) _i |L |i u@U| |@| uLh xM @?_ [c L?*) MuhU@|L?t ? b U@? Mi UL4T@hi_ |

i@U L|ihc t?Ui xM _Lit ?L| _iTi?_ ? @ _hiU| @) L? > Ai uL**L?} i @4T*i 4@)

**t|h@|i |t TL?| uh|ih 5TTLti xME%c i _i?L|it |i uL**L?} _)?@4U@* t)t|i4G

xME%c i ' _M M

[

'

in %  %2c

| i WW#c ,>i ' > @?_ V@h i ' j2 Ai T@h@4i|iht > @?_ j @hi Mi*iu T@h@4i|iht

Ai *@h}i |)Ti *4| [ Lu xM t }i? M)G

[E%c > ' > n %  %2_

6Lh > : fc |t t)t|i4 @t |L )TihML*U € i_ TL?|t( uLh > fc |ihi @hi ?L?i | > ' fc |ihi t L?i ?L?)TihML*U € i_ TL?|

Lc *i| @}@? 0 5 Efc  @?_ > : f Mi € i_ 5i| B ' >

2 Ai? M) |i |iLhi4 Lu tiU|L? ec

|ihi t @ Mf : fc tU |@| uLh @** M  MfG

n[  xMn&'    M [ ' i >    B c

| ThLM@M*|) @| *i@t|   0 Eu ULhtic |i t@4i hit*| U@? Mi uL?_ _hiU|*) M) AtUiM)Uig<t ?i^@*|) Oi?Uic | |t ThLM@M*|)G

M

[

'

i  >₂ : f c

@?_ |i t)t|i4 xME%c i @t |L € i_ TL?|t

? |i L|ih @?_c u > t ti| |L fc |i? @t)4T|L|U@**)G 

M [

i  Efc j2*M c

ihi Efc j2_{*M _i?L|it |i ?Lh4@* _t|hM|L? @hL?_ f Oi?Ui |i ThLM@M*|it}

Lu  M

S

i : f @?_ _M Si f @hi ML| @TThL 4@|i*) ₂ Ai *@h}i |)Ti *4| uh

?tit ?L ?uLh4@|L? @ML| |i ?4Mih Lu t|i@_) t|@|it Lu |i €?|i Mi*iu t)t|i4t ? |t U@ti

`i t44@h3i |t @t uL**LtG MuhU@|L?t ? |i *@h}i |)Ti *4| t)t|i4 4@) Mi uL?_ t?} Mi*iu T@h@4i|ihtc M| |i) @i |L Mi @?@*)3i_ ? |ih4t Lu t|hU|h@* T@h@4i|iht

LhL**@h) Lu *@h}i |)Ti *4| UL?ih}i?Ui |iLhi4

Ai _tUttL? ? |i Thiti?| tiU|L? t t44@h3i_ ? |i uL**L?} ULhL**@h)c *t|?} tL4i 4TLh|@?| Tihtt|i?| ThLTih|it Uc u |i) LUUh uLh |i wAwc | } ThLM@M*|) @*tL LUUh uLh |i M Mi*iu |)Ti t)t|i4 i? M t *@h}i

LhL**@h) Lu wAw UL?ih}i?Ui |iLhi4

tt4i |@| xM ? E2b t @ t)t|i4 | M Mi*iu |)Tit @?_ ^ t|hU|h@* T@h@4i|ihtc @?_ [

t |t w@h}i A)Ti w4| ? E @t M |i?_t |L ?€?|) Ai? uLh iih) & @?_ iih) &

Tihtt|i?| ThLTih|) Lu [ @?_ uLh iih) 0c |ihi i t|t @ ?4Mih Mf Lu Mi*iu |)Titc tU

|@| uLh iih) M  Mfc | ThLM@M*|)    0 |i t)t|i4 xM }i?ihU@**) @t |i t@4i

ThLTih|)

W? T@h|U*@hc |t 4i@?t |@| u [ @t  )TihML*U € i_ Lh TihL_U TL?|tc

2 |h@?tiht@* L4LU*?U ?|ihtiU|L?t Lu t|@M*i @?_ ?t|@M*i 4@?uL*_t Lu @ TihL_U TL?|c

 LhtitLitc

e *LU@* Lh }*LM@* MuhU@|L?t T |L UL_4i?tL? ^c

D LTi? ?i}MLhLL_t ? u?U|L? tT@Ui | t|h@?}i @||h@U|Lht EiLti+i**i A@!i?t Ti?L4i?L?c

|i? xM ** @i |iti |LL | ThLM@M*|)    0 u M  Mf

S ,L*|L?@h) _)?@4Ut ? @ t4T*i wAw

W? |t tiU|L? i ?it|}@|i |i _)?@4U@* Mi@Lhc uLUt?} L? }i?ihU @?_ Tihtt|i?| ThLTih|itc Lu @ t4T*i i @4T*i Lu @? wAwc ihi |h@_iht< uLhiU@t|?} h*it @hi *?i@h u?U|L?t Lu T@t| ThUi _i@|L?tc i

s| ' s|Ei ' ifn i%|3n    n i_%|3_c ED

| t|LU@t|U Mi*iu @h@M*it i _t|hM|i_ 4*|@h@|i ?Lh4@* `i U@*U*@|i wAw<t

uLh |i t4T*i @?_ |h@U|@M*i U@ti ihi €|?itt t *@t| TihL_<t hi@*3i_ ThL€|tc |@| tc L| ' E%| -%|3n @j25rn B|Esc|3 -%|3n @j

2₅r

@j2  ES

W?U*_?} 4Lhi 4i4Lh) ? |i €|?itt 4i@thi t t|h@}|uLh@h_c M| *i@_t |L @ } _4i?tL?@* wAw._{ +iU@** |@| iB}

|j t |i @h|?}@*i #gihi?Ui 5i^i?Ui UL4TL?i?| ?

|i _iUL4TLt|L? Lu |i i Uitt hi|h?t ThLUitt i-|j ? E2 `i ti| B| ' fc tL |@| €|?itt

MiUL4it

L|' E%| -%|3n @j25rEsc|3 -%|3n @j 2₅r

@j2 c E.

|L }i| @| i t@** U@** R|i _i|ih4?t|U t!i*i|L? Lu |i t|LU@t|U _)?@4U@* t)t|i4 `i t |L ?ULih t|@M*3?} @?_ _it|@M*3?} iUL?L4U uLhUit M) t|_)?} |i t!i*i|L? Ai _i|ih4?t|U t!i*i|L? ULhhitTL?_t |L |i U@ti ihi |i €|?itt 4i@thi i^@*t |i UL?_|L?@* i TiU|@|L? Lu ThL€|t

Ai uh@U|L?t ?| Lu |h@_ih |)Ti c @t }i? M) |i _tUhi|i ULUi ThLM@M*|it E2c

U@? Mi t4T*€i_ M) ?L|?} |@| |i) @hi ?L| @giU|i_ i? tM|h@U|?} |i t@4i |ih4c ?_iTi?_i?| Lu c uhL4 @** €|?ittit Lc|3 AihiuLhic i U@? }?Lhi |i |ih4 E-%|3n

@j2₅r_E%

|  -%|3 n @j25r ? |i ?L4?@|Lh Lu |i tiUL?_ T@h| Lu E. |L LM|@? |i

i^@*i?| €|?itt

Lc|3' E%|3 -%|32n @j25rs_@jc|32₂  EH

Nt?} Efc |i wAw uLh *?i@h uLhiU@t|?} h*it ED t |i? }i? M) %|' _- .ke#E%|33-%|32n@j25rs|32Eifs |Eif l . de#E%|33-%|32n@j25rs|32Eifo c Eb ihi #  q*E@j2_{@?_} s|Eif ' iffn if%|3n    n if_%|3_c Eef

:_{Lq sduwlfxodu/ zlwk wqhvv dv lq +55, jlyhq e| d zhljkwhg dyhudjh ri doo sdvw surwv zlwk h{srqhqwldoo|}

ghfuhdvlqj zhljkwv/ wkh OWO ehfrphv lqqlwh glphqvlrqdo zlwk lqqlwho| pdq| whupv zlwk h{srqhqwldoo| ghfuhdvlqj zhljkwv dgghg1 Zkhq wqhvv lv jlyhq e| d zhljkwhg dyhudjh ri O sdvw surwv/ wkh glphqvlrq ri wkh OWO ehfrphv O . g . 41

| if ' Eiffc ifc    c if_ 4*|@h@|i ?Lh4@* W?|hL_Ui rf ' #E%|3-%|32n@j25rc

r ' #E%|3 -%|32n @j25r%|323c     _ @?_ T|

e#E%|33-%|32n@j25rs|32Eif ' erif

W? Lh_ih |L U@*U*@|i @ U*Lti_ uLh4 i ThittL? uLh |i wAw Eb i ti 4L4i?| }i?ih@|?} u?U|L? uLh4*@i uhL4 ?Lh4@* _t|hM|L? |iLh) L|i |@|

.de_{o ' e}.don 2T @odoc

uLh @ ?Lh4@* h@?_L4 @h@M*i  'Sri L|i @*tL |@|

.derifi

f&o ' _{_r}_ &.de

 rifo

tt4i |@| |i i<t @hi ?ULhhi*@|i_ Ei ?_iTi?_i?| uLh |t 4*|@h@|i ?Lh4@* U@ti uLh t4T*U|) W| t t|h@}|uLh@h_ |L i |i?_ |i 4i|L_ |L ULhhi*@|i_ i<t Nt?} |iti 4L4i?| }i?ih@|?} u?U|L? uLh4*@i uLh 4*|@h@|i ?Lh4@*t |i uL**L?} U*Lti_ uLh4 i ThittL? uLh |i wAw Eb t LM|@?i_G

-%| ' >fn >%|3n  n >_%|3_ Ee

n#E%|3 -%|32n @j25rEj2fn j2%|3%|3n j22%|32%|3e   n j2_%|3_%|3_32c

ihi >& ' .dif&oc j&2 ' T @odif&oc f  &  _ @?_ # ' q*E@j2

Ai t4T*it| tTiU@* U@ti Lu Ee |@| t|** TLttittit _)?@4Ut t LM|@?i_ i? @** if& ' fc

  &  _c |@| tc i? |i uLhiU@t|?} u?U|L? t Thi*) M@ti_c i s|Eif ' iff W?

|t t4T*it| U@tic |i wAw hi_Uit |L |i *?i@h t)t|i4 -%| ' >fn #j2f



%|3 -%|32n @j25r Ee2

At t4T*it| U@ti @*hi@_) ThL_it 4TLh|@?| iUL?L4U ?||L? @ML| |i E?t|@M*|) Lu |i Eu?_@4i?|@* t|i@_) t|@|i ? @? iL*|L?@h) t)t|i4 | 4@?) |h@_ih |)Tit `i? |ihi t ?L ?|h?tU 4i@? M@tc |@| t i? >f ' fc @?_ |i ht! Thi44 t 3ihLc

i 5r _{' fc |i t|i@_) t|@|i Lu |i wAw Ee2 UL?U_it i @U|*) | |i u?_@4i?|@*c}

i %W _{' f `i? |i 4i@? M@t @?_ ht! Thi44 @hi ML| TLt|i E?i}@|i |i}

t|i@_) t|@|i _i@|L? %W _{** Mi TLt|i E?i}@|i tL |@| |i t|i@_) t|@|i ** Mi @MLi}

EMi*L |i u?_@4i?|@* Ai ?@|h@* MuhU@|L? T@h@4i|ih |??} |i E?t|@M*|) Lu |i t)t|i4 t k ' #j2

f ' qj2f*@j2 `i tii 44i_@|i*) |@| ?t|@M*|) LUUht u @?_ L?*)

u k ?Uhi@tit Mi)L?_ |i MuhU@|L? TL?| kS'  Oi?Ui |t t4T*i U@ti @*hi@_) t}}it|t

uLhUit |@| 4@) _it|@M*3i |i iL*|L?@h) t)t|i4G @? ?Uhi@ti ? ULUi ?|i?t|) q uLh iL*|L?@h) ti*iU|L?c @ _iUhi@ti ? ht! @ihtL? R@c @ _iUhi@ti ? UL?_|L?@* @h@?Ui Lu i Uitt hi|h?t j2_{c Lh @? ?Uhi@ti ? |i _iht|) Lu Thi*) M@ti_ Mi*iut j}2

f U@? Tt k

Mi)L?_ kS @?_ ti| Lg ?t|@M*|) Lu |i Eu?_@4i?|@* t|i@_) t|@|i

Ai wAw Ee2c LM|@?i_ uLh |i t4T*it| U@ti ihi @** |h@_ih |)Tit @hi Thi*) M@ti_c t @ *?i@h t)t|i4c U t i|ih }*LM@**) t|@M*i Lh }*LM@**) ?t|@M*i , UiT| uLh |i @h*?i U@ti @| |i MLh_ih Lu t|@M*|)c k ' c ML?_i_ tL*|L?t ?L| UL?ih}?} |L |i t|i@_) t|@|i _L ?L| i t| ? |t t4T*it| U@ti `i? *@}t @hi ?U*_i_ ? |i *?i@h uLhiU@t|?} h*itc |i wAw Ee MiUL4it @ ?L?*?i@h t)t|i4 i M|?} 4U hUih _)?@4U@* Mi@Lh `i UL?t_ih @ t4T*i M| |)TU@* i @4T*ic | *?i@h uLhiU@t|?} h*it | |hii *@}tc i

s|Eif ' iffn if%|3n if2%|32n if%|3 Ee

`| |hii *@}t ? |i *?i@h uLhiU@t|?} h*ic |i ULhhitTL?_?} wAw MiUL4it @ D# ?L?*?i@h t)t|i4G

-%| ' >f n >%|3n >2%|32n >%|3 Eee

n#E%|3 -%|32n @j25rEjf2n j2%|3%|3n j22%|32%|3en j2%|3%|3DEeD

`i ** _tUtt |i 4Lt| 4TLh|@?| }i?ihU @?_ Tihtt|i?| ui@|hit Lu |i _)?@4U@* Mi@Lh Lu |t D# wAw( }ih _4i?tL?@* ihtL?t Lu |i wAw i M| t4*@h _)?@4U@* Mi@Lh

6ht| i ?it|}@|i t|i@_) t|@|it @?_ |ih t|@M*|) 6}hi  tLt @ 2# MuhU@|L? _@}h@4 ? |i E#c > T@h@4i|ih T*@?ic ihi > hiThiti?|t |i 4i@? Lu |i €ht| Lh_ih

t|LU@t|U |hi?_ @h@M*i if? |i uLhiU@t|?} h*i Ee `i? |i 4i@? M@t >f ' fc |

>f |i 4i@? Lu |i UL?t|@?| iff ? |i uLhiU@t|?} h*i Eec @?_ |i ht! Thi44 t @*tL

3ihLc i @j2₅r _{' fc |i wAw t t)44i|hU h| |i u?_@4i?|@* t|i@_) t|@|i @?_ |i}

wAw t |ihiuLhi ?L?}i?ihU W? |i t)44i|hU U@ti E€}hi @c Mi|ii? |i OLTuc TihL_ _LM*?} E# @?_ T|UuLh! E6 MuhU@|L? Uhit |i u?_@4i?|@* t|i@_) t|@|i t ?^i @?_ t|@M*i t |i T@h@4i|iht UhLtt |i 6 Uhic |L @__|L?@* ?L?u?_@4i?|@* t|i@_) t|@|it @hi Uhi@|i_ |ih hL|it |L ?t|@M*|) LUUh i? UhLtt?} |i # Uhic ihi |i u?_@4i?|@* t|i@_) t|@|i MiUL4it ?t|@M*i @?_ @ Et|@M*i 2U)U*i t Uhi@|i_c Lh i? UhLtt?} |i OLTu Uhic ihi |i u?_@4i?|@* t|i@_) t|@|i MiUL4it ?t|@M*i @?_ @ Et|@M*i ?@h@?| UhU*i | TihL_U Lh ^@tTihL_U _)?@4Ut t Uhi@|i_ Ai T|UuLh! MuhU@|L? Uhi t ?L?}i?ihU @?_ L?*) LUUht ? |i t)44i|hU U@ti `i? |i t)44i|h) t MhL!i? M) @ ?L?3ihL 4i@? M@t >f 9' fc @t **t|h@|i_ ? €}hi M

uLh >f ' fc |i 6 Uhi _t@TTi@ht @?_ Mhi@!t T ?|L |L }i?ihU UL_4i?tL? L?i

MuhU@|L? Uhitc @ OLTu @?_ @ t@__*i?L_i E5 MuhU@|L? Uhi `i? UhLtt?} |i 5 Uhi uhL4 Mi*Lc |L @__|L?@* t|i@_) t|@|it @hi Uhi@|i_c L?i t|@M*i @?_ L?i ?t|@M*i L|Ui |@|c @t **t|h@|i_ ? €}hi Uc i? |i Tih|hM@|L? t t4@** @t uLh >f ' fc

|i 5 @?_ |i OLTu Uhit @hi U*Lti |L |i 6 @?_ |i OLTu Uhit ? |i t)44i|hU U@ti W? |t ti?ti |i MuhU@|L? _@}h@4 _iTi?_t UL?|?Lt*) L? |i T@h@4i|ihtc @?_ | t tiu* |L UL?t_ih |i t)44i|hU wAw @t @? RLh}@?3?} Ui?|ih |L t|_) MuhU@|L? Ti?L4i?@ ? |i }i?ihUc ?L?t)44i|hU wAw

Ai 4Lt| hi*i@?| U@ti tii4t |L Mi |i U@ti i? |i 4i@? >Lu |i €ht| Lh_ih ULiUi?|

if? |i uLhiU@t|?} h*i Ee t@|t€it f  >   W? |@| U@tic @t |i t|hU|h@* T@h@4i

|ih # ?Uhi@titc |i Eu?_@4i?|@* t|i@_) t|@|i *Ltit t|@M*|) |hL} @ OLTu MuhU@|L? 2S