Pooled Mean Group Estimation of Dynamic Heterogeneous Panels

26
LL*i_ i@? BhLT ,t|4@|L? Lu #)?@4U Oi|ihL}i?iLt @?i*t O@ti4 it@h@? Ah?|) L**i}ic @4Mh_}ic @?_ N?iht|) Lu 5L|ih? @*uLh?@ vL?}UiL* 5? #iT@h|4i?| Lu ,UL?L4Utc N?iht|) Lu ,_?Mh} +L? 54| h!MiU! L**i}ic wL?_L? }t| bb. +iti_ Li4Mih bbH a,w *@ttU@|L?G c 2c Sc ,2 ki) Lh_tG Oi|ihL}i?iLt _)?@4U T@?i*tc TLL*i_ 4i@? }hLT it|4@|Lhc U Ef @?_ U E hi}hittLhtc UL?t4T|L? u?U|L?tc i?ih}) _i4@?_

Transcript of Pooled Mean Group Estimation of Dynamic Heterogeneous Panels

�LL*i_ �i@? BhL�T ,t|�4@|�L? Lu #)?@4�U

Oi|ihL}i?iL�t �@?i*t�

�� O@t�i4 �it@h@?Ah�?�|) �L**i}ic �@4Mh�_}ic @?_ N?��iht�|) Lu 5L�|�ih? �@*�uLh?�@

vL?}U�iL* 5��?#iT@h|4i?| Lu ,UL?L4�Utc N?��iht�|) Lu ,_�?M�h}�

+L? �� 54�|���h!MiU! �L**i}ic wL?_L?

��}�t| �bb.+i��ti_ �L�i4Mih �bbH

Devwudfw

Lw lv qrz txlwh frpprq wr kdyh sdqhov lq zklfk erwk W> wkh qxpehu ri wlph vhulhv

revhuydwlrqv/ dqg Q> wkh qxpehu ri jurxsv/ duh txlwh odujh dqg ri wkh vdph rughu

ri pdjqlwxgh1 Wkh xvxdo sudfwlfh lv hlwkhu wr hvwlpdwh Q vhsdudwh uhjuhvvlrqv dqg

fdofxodwh wkh frh�flhqw phdqv/ zklfk zh fdoo wkh Phdq Jurxs +PJ, hvwlpdwru/ ru wr

srro wkh gdwd dqg dvvxph wkdw wkh vorsh frh�flhqwv dqg huuru yduldqfhv duh lghqwlfdo1

Lq wklv sdshu/ zh sursrvh dq lqwhuphgldwh surfhgxuh/ uhihuuhg wr dv wkh Srrohg Phdq

Jurxs +SPJ, hvwlpdwru/ zklfk frqvwudlqv wkh orqj uxq frh�flhqwv wr eh lghqwlfdo/

exw doorzv wkh vkruw uxq frh�flhqwv dqg huuru yduldqfhv wr gl�hu dfurvv jurxsv1 Zh

frqvlghu erwk wkh fdvh zkhuh wkh uhjuhvvruv duh vwdwlrqdu| dqg wkh fdvh zkhuh wkh|

iroorz xqlw urrw surfhvvhv/ dqg iru erwk fdvhv ghulyh wkh dv|pswrwlf glvwulexwlrq ri wkh

SPJ hvwlpdwruv dv W whqgv wr lq�qlw|1 Zh dovr surylgh wzr hpslulfdo dssolfdwlrqv=

djjuhjdwh frqvxpswlrq ixqfwlrqv iru 57 RHFG hfrqrplhv ryhu wkh shulrg 4<950<6/ dqg

hqhuj| ghpdqg ixqfwlrqv iru 43 Dvldq ghyhorslqj hfrqrplhv ryhu wkh shulrg 4<:70<31

a,w �*@tt��U@|�L?G ���c �2�c �S�c ,2��ki) �Lh_tG Oi|ihL}i?iL�t _)?@4�U T@?i*tc TLL*i_ 4i@? }hL�T it|�4@|Lhc UEf� @?_ UE��hi}hittLhtc UL?t�4T|�L? u�?U|�L?tc i?ih}) _i4@?_�

�Sduwldo �qdqfldo vxssruw iurp wkh HVUF +Judqw Qr1 K84<588336, dqg wkh Lvddf Qhzwrq Wuxvw ri Wulqlw|Froohjh/ Fdpeulgjh lv judwhixoo| dfnqrzohgjhg1 Wkh �uvw dxwkru dovr dfnqrzohgjhv wkh krvslwdolw| ri wkh LPI

Uhvhdufk Ghsduwphqw zkloh vrph ri wkh lghdv ehklqg wklv sdshu zhuh irupdol}hg1 Zh duh dovr judwhixo iru

wkh h�ruwv ri Vxqlo Vkdupd dqg Pdqvrxu Jloo lq frpslolqj wkh RHFG gdwd vhw> iru khosixo glvfxvvlrqv zlwkPlfkdho Elqghu/ Qdghhp X1 Kdtxh/ Urehuw PdfNd|/ Vxqlo Vkdupd/ dqg Ulfkdug Vplwk> dqg iru ydoxdeoh

frpphqwv rq dq hduolhu yhuvlrq iurp wkh hglwruv dqg d uhihuhh1

� W?|hL_�U|�L?

W? hiUi?| )i@ht |�ihi �@t Mii? �?Uhi@t�?} �?|ihit| �? _)?@4�U T@?i* _@|@ 4L_i*tc ��ihi |�i?�4Mih Lu |�4i tih�it LMtih�@|�L?tc A c �t hi*@|��i*) *@h}i @?_ Lu |�i t@4i Lh_ih Lu 4@}?�|�_i@t �c |�i ?�4Mih Lu }hL�Tt� 5�U� T@?i*t @h�ti T@h|�U�*@h*) �? UhLtt�UL�?|h) @?@*)tit� W?4Lt| @TT*�U@|�L?t Lu |��t |)Tic |�i T@h@4i|iht Lu �?|ihit| @hi |�i *L?} h�? igiU|t @?_ |�itTii_ Lu @_��t|4i?| |L |�i *L?} h�?� �? i @4T*i �t |�i *@h}i *�|ih@|�hi L? |it|�?} T�hU�@t�?}TL�ih T@h�|) �? T@?i*tc ��ihi @UULh_�?} |L iUL?L4�U |�iLh) |�i *L?} h�? ULi�U�i?|t Lu |�i*L}@h�|�4t Lu _L4it|�U Th�Uitc uLhi�}? Th�Uit @?_ i U�@?}i h@|it t�L�*_ Mi E�c��c���c ��|�|�i tTii_ Lu @_��t|4i?| Mi�?} Lu Ui?|h@* TL*�U) UL?Uih?�� �?L|�ih ThL4�?i?| i @4T*i �t|�i 6�t�ih i^�@|�L? ���U� TLt|�*@|it @ �?�| ULi�U�i?| uLh |�i *L?}�h�? igiU| Lu Ei TiU|i_��?�@|�L? L? |�i ?L4�?@* h@|i Lu �?|ihit|c M�| �t t�*i?| @t |L |�i 4@}?�|�_i Lu |�i t�Lh|�h�?igiU|t Lu U�@?}it �? �?�@|�L? L? �?|ihit| h@|it�

A�ihi @hi |�L ThLUi_�hit UL44L?*) �ti_ uLh t�U� T@?i*t� �| L?i i |hi4ic L?i U@?it|�4@|i tiT@h@|i i^�@|�L?t uLh i@U� }hL�T @?_ i @4�?i |�i _�t|h�M�|�L? Lu |�i it|�4@|i_ULi�U�i?|t @UhLtt }hL�Tt� �u T@h|�U�*@h �?|ihit| ��** Mi |�i 4i@? Lu |�i it|�4@|itc ���U� �iU@** |�i �i@? BhL�T E�B� it|�4@|Lh� �it@h@? @?_ 54�|� E�bbD� t�L� |�@| |�i �B it|�4@|Lh��** ThL_�Ui UL?t�t|i?| it|�4@|it Lu |�i @�ih@}i Lu |�i T@h@4i|iht� A��t it|�4@|Lhc �L�i�ihc_Lit ?L| |@!i @UUL�?| Lu |�i u@U| |�@| Uih|@�? T@h@4i|iht 4@) Mi |�i t@4i @UhLtt }hL�Tt� �||�i L|�ih i |hi4i @hi |�i |h@_�|�L?@* TLL*i_ it|�4@|Lhtc t�U� @t |�i � i_ @?_ h@?_L4 igiU|tit|�4@|Lhtc ��ihi |�i �?|ihUiT|t @hi @**L�i_ |L _�gih @UhLtt }hL�Tt ���*i @** L|�ih ULi�U�i?|t@?_ ihhLh �@h�@?Uit @hi UL?t|h@�?i_ |L Mi |�i t@4i� W? |��t T@Tihc �i UL?t�_ih @? �?|ih4i_�@|iit|�4@|Lhc ���U� �i U@** |�i �LL*i_ �i@? BhL�T E��B� it|�4@|Lh MiU@�ti �| �?�L*�it ML|�TLL*�?} @?_ @�ih@}�?}� A��t it|�4@|Lh @**L�t |�i �?|ihUiT|tc t�Lh|�h�? ULi�U�i?|t @?_ ihhLh�@h�@?Uit |L _�gih uhii*) @UhLtt }hL�Ttc M�| |�i *L?}�h�? ULi�U�i?|t @hi UL?t|h@�?i_ |L Mi|�i t@4i� A�ihi @hi Lu|i? }LL_ hi@tL?t |L i TiU| |�i *L?}�h�? i^��*�Mh��4 hi*@|�L?t��TtMi|�ii? �@h�@M*it |L Mi t�4�*@h @UhLtt }hL�Ttc _�i |L M�_}i| Lh tL*�i?U) UL?t|h@�?|tc @hM�|h@}iUL?_�|�L?t Lh UL44L? |iU�?L*L}�it �?��i?U�?} @** }hL�Tt �? @ t�4�*@h �@)� A�i hi@tL?t uLh@tt�4�?} |�@| t�Lh|�h�? _)?@4�Ut @?_ ihhLh �@h�@?Uit t�L�*_ Mi |�i t@4i |i?_ |L Mi *ittUL4Ti**�?}� �L| �4TLt�?} i^�@*�|) Lu t�Lh|�h�? t*LTi ULi�U�i?|t @*tL @**L�t |�i _)?@4�UtTiU��U@|�L?c i�}� |�i ?�4Mih Lu *@}t �?U*�_i_c |L _�gih @UhLtt }hL�Tt�

i �ti |�L �4TLh|@?| i4T�h�U@* i @4T*it |L UL4T@hi |�i �Bc ��B @?_ #)?@4�U 6� i_,giU| E#6,� it|�4@|Lht� A�i �ht| �t |�i UL?t�4T|�L? u�?U|�L? �? �,�# UL�?|h�it� A�i_i|ih4�?@|�L? Lu t@��?} h@|it �t @? �4TLh|@?| TL*�U) �tt�i @?_c @t ��|� |�i i @4T*i LuT�hU�@t�?} TL�ih T@h�|) }��i? @ML�ic |�i |�iLh) 4@!it t|hL?} Thi_�U|�L?tG |�@| |�i *L?} h�?�?UL4i i*@t|�U�|) Lu UL?t�4T|�L? t�L�*_ Mi �?�|) �? @** UL�?|h�itc _itT�|i |�i�h �4TLh|@?|�?t|�|�|�L?@* @?_ U�*|�h@* _�gihi?Uit� �|�ih��tic ?@|�L?@* ETh��@|i� t@��?} h@|it ��** Mih�t�?} Lh u@**�?} �?_i�?�|i*)� A�i ��B it|�4@|Lh @**L�t �t |L it|�4@|i |��t UL44L? *L?}�h�? ULi�U�i?| ��|�L�| 4@!�?} |�i *itt T*@�t�M*i @tt�4T|�L? Lu �_i?|�U@* _)?@4�Ut �? i@U�UL�?|h)� W? |��t @TT*�U@|�L?c ML|� � ' 2e @?_ A ' �2 @hi ^��|i *@h}i� A�i tiUL?_ i @4T*i�t i?ih}) _i4@?_ �? _i�i*LT�?} �t�@? iUL?L4�it� �h�Lh |L |�i �?@?U�@* Uh�tit Lu |�i t�44ihLu �bb.c |��t �@t |�i u@t|it| }hL��?} hi}�L? Lu |�i �Lh*_ @?_ |�i }hL�|� �? �|t i?ih})

4D uhfhqw uhylhz ri wklv olwhudwxuh lv surylghg lq Urjr� +4<<9,1 Vrph ri wkh uhodwhg hfrqrphwulf lvvxhv

duh glvfxvvhg lq Er|g dqg Vplwk +4<<;,1

d�o

_i4@?_ ��** �@�i tih�L�t �4T*�U@|�L?t ML|� uLh �Lh*_ i?ih}) 4@h!i|t @?_ }hii?�L�ti }@ti4�tt�L?t� �t ��|� |�i UL?t�4T|�L? u�?U|�L? i @4T*ic *L?}�h�? hitTL?tit Lu i?ih}) _i4@?_|L �?UL4i @?_ hi*@|��i i?ih}) Th�Uit @hi *�!i*) |L Mi t�4�*@h @UhLtt UL�?|h�itc @*|�L�}� t�Lh|�h�? @_��t|4i?|t �? i?ih}) _i4@?_c _iTi?_�?} L? T@||ih?t Lu �?�it|4i?| �? i?ih}) �t�?}i^��T4i?| @?_ t�TT*) UL?t|h@�?|tc �t �?*�!i*) |L Mi �L4L}i?iL�t @UhLtt UL�?|h�it� �}@�? |�i��B it|�4@|Lh @**L�t �t |L �?�it|�}@|i *L?}�h�? �L4L}i?i�|) ��|�L�| �4TLt�?} T@h@4i|ih�L4L}i?i�|) �? |�i t�Lh| h�?� W? |��t i @4T*ic ML|� � ' �f @?_ A ' �. @hi ^��|i t4@**�A��t |�ihi �t @ UL?|h@t| �? |�i T@?i* _�4i?t�L?t �? |�i |�L i @4T*it�

A�i T*@? Lu |�i T@Tih �t @t uL**L�tG 5iU|�L? 2 ThL��_it @ Mh�iu hi��i� Lu @*|ih?@|��i T@?i*_@|@ it|�4@|Lht @?_ _�tU�ttit �L� |�i ��B it|�4@|Lh �t hi*@|i_ |L |�i4� 5iU|�L? � ti|t L�||�i 4L_i* @?_ �|t �?_ih*)�?} @tt�4T|�L?tc @?_ _ih��it |�i *L}�*�!i*��LL_ u�?U|�L?� 5iU|�L?e _i�i*LTt |�i }i?ih@* |�iLh) Lu ��B it|�4@|�L?c ML|� �? |�i U@ti Lu t|@|�L?@h) hi}hittLht@?_ ��i? |�i) uL**L� �?�| hLL| ThLUittit� 5iU|�L? D _�tU�ttit @ ?�4Mih Lu 4L_i**�?} �t�t�it @?_ Thiti?|t |�i i4T�h�U@* @TT*�U@|�L?t� 5iU|�L? S UL?|@�?t tL4i UL?U*�_�?} hi4@h!t��@|�i4@|�U@* ThLLut @hi ThL��_i_ �? @? @TTi?_� �

A�i uL**L��?} ?L|@|�L?t ��** Mi �ti_ |�hL�}�L�|G |�i t)4ML*R$ t�}?��it UL?�ih}i?Ui �?

ThLM@M�*�|)c , �i@! UL?�ih}i?Ui �? ThLM@M�*�|) 4i@t�hic@� @t)4T|L|�U i^�@*�|) �? _�t|h�M��

|�L?tc �� 4� |�hi ?Lh4@* _�t|h�M�|�L?c W6 @? �_i?|�|) 4@|h� Lu Lh_ih 6c _�@}d�o @ _�@}L?@*4@|h� c @?_ UE_� @? �?|i}h@|i_ �@h�@M*i Lu Lh_ih _�

2 �*|ih?@|��i ,t|�4@|Lht Lu #)?@4�U �@?i*t

A�ihi @hi @*hi@_) @ *@h}i ?�4Mih Lu _)?@4�U T@?i* _@|@ it|�4@|Lht� AL tii |�i hi*@|�L?t��TLu |�i ��B it|�4@|Lh @_�@?Ui_ �? |��t T@Tih |L |�i L?it ThLTLti_ �? |�i *�|ih@|�hic �| �tUL?�i?�i?| |L _���_i |�i *@||ih �?|L |�hii U@|i}Lh�itc _�gih�?} �? |�i�h @tt�4T|�L?t @ML�| |�ihi*@|��i 4@}?�|�_it Lu � @?_ A � 6�ht|c |�ihi �t |�i Rt4@** � c *@h}i A� |�4i�tih�it *�|ih@|�hi_i�L|i_ |L it|�4@|�?} *L?} h�? igiU|t� W? |�i U@ti Lu �?_���_�@* |�4i�tih�it ��ihi � ' �c |�i|h@_�|�L?@* @TThL@U� �@t |L it|�4@|i @? @�|Lhi}hitt��i _�t|h�M�|i_ *@} E�+#w� 4L_i*� W?hiUi?| )i@htc |�i i4T�@t�t �@t t��u|i_ |L it|�4@|�?} UL�?|i}h@|�?} hi*@|�L?t��Tt uhL4 @ t�?}*i|�4i�tih�it� A�i hi*@|�L? Mi|�ii? |�iti |�L @TThL@U�it �t _�tU�tti_ �? �it@h@? @?_ 5��?E�bbH�� 6Lh � : �c uL**L��?} ~i**?ih E�bS2� |�i 5ii4�?}*) N?hi*@|i_ +i}hitt�L? ,^�@|�L?E5N+,� ThLUi_�hi �t Lu|i? �ti_� A�i 4@�? @||h@U|�L? Lu |�i 5N+, ThLUi_�hi *�it �? |�iu@U| |�@| �| @**L�t |�i UL?|i4TLh@?iL�t ihhLh UL�@h�@?Uit |L Mi uhii*) it|�4@|i_� OL�i�ihc|��t �t TLtt�M*i L?*) ��i? � �t hi@tL?@M*) t4@** hi*@|��i |L A � `�i? � �t Lu |�i t@4i Lh_ihLu 4@}?�|�_i @t A c |�i U@ti �i @hi �?|ihit|i_ �?c 5N+, �t ?L| ui@t�M*i�2 �|�ih @TThL@U�it4�t| Mi tL�}�|� W| �t Lu|i? *�!i*) |�@| |�i U@�ti Lu ?L?�3ihL ihhLh UL�@h�@?Uit 4@) Mi_�i |L L4�||i_ UL44L? igiU|t ���U� �4T@U| @** }hL�Tt( @? �?_�U@|�L? Lu 4�t�tTiU��U@|�L?h@|�ih |�@? ihhLh ULhhi*@|�L?� W? t�U� U@tit �| �t 4Lhi @TThLTh�@|i |L 4L_i* |�i igiU|t���U� @UUL�?| uLh Mi|�ii? }hL�T ?L?�3ihL ihhLh UL�@h�@?Uit i T*�U�|*)� A��t U@? Mi _L?i �? @?�4Mih Lu �@)t� �?i TLtt�M�*�|) �t |L �?U*�_i UhLtt�tiU|�L?@* 4i@?t Lu |�i �?U*�_i_ hi}hittLht

5Lw lv dovr zruwk qrwlqj wkdw prvw ri wkh VXUH olwhudwxuh lv frqfhuqhg zlwk olqhdu furvv0htxdwlrq uh0vwulfwlrqv/ zkhuhdv rxu frqfhuq zlwk frpprq orqj0uxq frh�flhqwv/ lpsolhv qrq0olqhdu uhvwulfwlrqv dfurvv wkh

gl�huhqw htxdwlrqv1

d2o

@t @__�|�L?@* hi}hittLht �? |�i 4L_i*� 6Lh �?t|@?Uic �? �it@h@? @?_ 54�|� E�bbD� @}}hi}@|iL�|T�| �@t �?U*�_i_ �? @__�|�L? |L �?_�t|h) L�|T�| �? �?_�t|h) i4T*L)4i?| i^�@|�L?t� �tiUL?_ TLtt�M�*�|) �t |L i Thitt @** |�i �@h�@M*it @t _i��@|�L?t uhL4 |�i�h hitTiU|��i UhLtt�tiU|�L?@* 4i@?t �? i@U� Tih�L_� W? |�i tTiU�@* U@ti ��ihi |�i t*LTi ULi�U�i?|t @hi �_i?|�U@*@UhLtt }hL�Ttc |�i UL44L? |�4i�Tih�L_ igiU|t ��** Mi UL4T*i|i*) i*�4�?@|i_ M) |��t EUhLtt�tiU|�L?@*� _i4i@?�?} ThLUi_�hi� W? U@tit ��ihi |�i t*LTi ULi�U�i?|t _�gihc t�U� _i4i@?�?}��** hi_�Ui EM�| _Lit ?L| i*�4�?@|i� |�i UL44L? |�4i�tTiU��U igiU|t� � |��h_ TLtt�M�*�|) �t|L �ti i T*�U�| tT@|�@* 4L_i*t Lu |�i �?|ih@U|�L?t Mi|�ii? ?i�}�MLht� �i*L�c �i @tt�4i |�@||�i �ti Lu t�U� ThLUi_�hit �@t 4@_i �| hi@tL?@M*i |L @tt�4i |�@| |�i ihhLht @hi �?_iTi?_i?|Mi|�ii? }hL�Tt�

5iUL?_*)c |�ihi �t |�i Rt4@** A c *@h}i �� _)?@4�U T@?i* *�|ih@|�hi� W? |�i U@ti ��ihi A�t t4@** �it@h@? @?_ 54�|� E�bbD� t�L� |�@|c �?_ih Uih|@�? @tt�4T|�L?tc |�i UhLtt tiU|�L?hi}hitt�L? M@ti_ L? |�4i�@�ih@}it Lu |�i �@h�@M*it ��** ThL��_i UL?t�t|i?| it|�4@|it Lu |�i*L?}�h�? ULi�U�i?|t� OL�i�ihc |�iti @tt�4T|�L?t @hi ^��|i t|hL?}� W? T@h|�U�*@hc |�i)hi^��hi |�@| |�i }hL�T�tTiU��U T@h@4i|iht @hi _�t|h�M�|i_ �?_iTi?_i?|*) Lu |�i hi}hittLhtc@?_ |�@| |�i hi}hittLht @hi t|h�U|*) i L}i?L�t� 6Lh *@h}ih A c �it@h@? @?_ 54�|� E�bbD� t�L�|�@| |�i |h@_�|�L?@* ThLUi_�hit uLh it|�4@|�L? Lu TLL*i_ 4L_i*t t�U� @t |�i � i_ igiU|tc�?t|h�4i?|@* �@h�@M*it Lh |�i Bi?ih@*�3i_ �i|�L_ Lu �L4i?|t EB��� it|�4@|Lht ThLTLti_cuLh i @4T*ic M) �?_ihtL? @?_ Ot�@L E�bH�c �bH2�c �hi**@?L E�bHb�c �hi**@?L @?_ �L�ihE�bbD�c ki@?i @?_ +�?!*i E�bb2� @?_ ��? @?_ 5U�4�_| E�bbD� U@? ThL_�Ui �?UL?t�t|i?|c@?_ TL|i?|�@**) �ih) 4�t*i@_�?} it|�4@|it Lu |�i @�ih@}i �@*�it Lu |�i T@h@4i|iht �? _)?@4�UT@?i* _@|@ 4L_i*t �?*itt |�i t*LTi ULi�U�i?|t @hi �? u@U| �_i?|�U@*�� ��| �? 4Lt| T@?i*t Lu|��t tLh|c |it|t �?_�U@|i |�@| |�iti T@h@4i|iht _�gih t�}?��U@?|*) @UhLtt }hL�Tt� A��t @?it|�4@|Lh ���U� �4TLtit �i@!ih �L4L}i?i�|) @tt�4T|�L?t �L�*_ Mi �tiu�*�

A�i |��h_ *�|ih@|�hic @?_ |�i L?i ���U� �t U*Ltit| |L L�h UL?Uih?tc �t |�i �@)it @?_ i4�T�h�U@* �@)it it|�4@|Lht ThLTLti_ M) Ot�@L @?_ A@�4�tU�L}*� E�bb.� @?_ Ot�@Lc �it@h@? @?_A@�4�tU�L}*� E�bbH�� A�iti it|�4@|Lht M��*_ L? |�i i@h*) �Lh! Lu w�?_*i) @?_ 54�|� E�b.2�@?_ 5�@4) E�b.f�� Ot�@Lc �it@h@? @?_ A@�4�tU�L}*� E�bbH� UL?t�_ih �@)it it|�4@|�L? Lut�Lh|�h�? ULi�U�i?|t �? _)?@4�U �i|ihL}i?L�t T@?i*tc @?_ it|@M*�t� |�i @t)4T|L|�U i^���@�*i?Ui Lu |�i �@)it it|�4@|Lh @?_ |�i 4i@? }hL�T it|�4@|Lh� W? T@h|�U�*@hc |�i) t�L� |�@||�i 4i@? }hL�T it|�4@|Lh �t @t)4T|L|�U@**) ?Lh4@* uLh *@h}i � @?_ *@h}i A tL *L?} @t

s�*A

$ f @t ML|� � @?_ A $ 4� Nt�?} �L?|i �@h*L i Tih�4i?|t |�i) @*tL t�L� |�@| ���*i |�i�B it|�4@|Lh �t UL?t�t|i?|c �| �t �?*�!i*) |L Mi @ }LL_ it|�4@|Lh ��i? i�|�ih � Lh A @hit4@**� A�i 4@�? _�gihi?Ui Mi|�ii? |�i @TThL@U� @_LT|i_ �? |��t T@Tih @?_ |�i *�|ih@|�hi L?�@)it it|�4@|�L? �t ��ihi@t �i hi}@h_ |�i T@h@4i|iht @t � i_c |��t *�|ih@|�hi hi}@h_t |�i4@t h@?_L4G _h@�? uhL4 tL4i _�t|h�M�|�L? ��|� @ �?�|i ?�4Mih Lu T@h@4i|iht� B��i? |�@||�i TLtt�M�*�|) Lu h@?_L4 T@h@4i|iht �t @_4�||i_c |�i �tt�i �t ?L| Th�4@h�*) L?i Lu U*@tt�U@*�iht�t �@)it�@? @TThL@U�it t�?Ui U*@tt�U@* it|�4@|Lht U@? Mi }��i? @ �@)it�@? �?|ihThi|@�|�L?� 6Lh i @4T*ic |�i 5�@4) E�b.f� it|�4@|Lh uLh h@?_L4 ULi�U�i?| 4L_i*tc 4L|��@|i_M) U*@tt�U@* }i?ih@*�3i_ *i@t| t^�@hit @h}�4i?|tc U@? @*tL Mi ��i�i_ @t @? i4T�h�U@* �@)itit|�4@|Lh�

A�i U�L�Ui Mi|�ii? � i_ @?_ h@?_L4 igiU| uLh4�*@|�L?tc ���U� �@t Mii? i |i?t��i*) _�t�

6Wklv uhvxow krogv lq wkh fdvh ri g|qdplf udqgrp frh�flhqw prghov hyhq li lw lv dvvxphg wkdw wkh udqgrp

frh�flhqwv dqg wkh uhjuhvvruv duh lqghshqghqwo| glvwulexwhg1

d�o

U�tti_ �? |�i *�|ih@|�hic _iTi?_t L? @ ?�4Mih Lu hi*@|i_ UL?t�_ih@|�L?t� 6�ht|*)c |�i T�hTLtiLu |�i i ihU�ti 4@||ihtc t�?Ui |�i |�L @TThL@U�it |h) |L @?t�ih _�t|�?U|*) _�gihi?| ^�it|�L?t�Ot�@L E�bbSc TT�b��e� }��it @ ?�4Mih Lu i @4T*it ��ihi |�i T�hTLti Lu @?@*)t�t ��** _i|ih�4�?i |�i U�L�Ui Mi|�ii? |�i |�L uLh4�*@|�L?t @?_ 5|L!ih E�bb�c T� �HeH� TL�?|t L�| |�@|�u L?i ��t�it |L 4@!i �?uihi?Ui @ML�| 4@UhL hi*@|�L?t��Tt uhL4 4�UhL it|�4@|it M@ti_ L?@ t�Mti| Lu |�i TLT�*@|�L?c @ UL44L? ThLM*i4c |�i igiU|t �@�i |L Mi |hi@|i_ @t h@?_L4�5iUL?_*)c |�i TihUi��i_ _i}hii Lu UL44L?@*�|) �? |�i T@h@4i|iht 4@||iht� A�ihi �t @ UL?|�?���4c ��|� @| L?i i |hi4i � i_ @?_ UL44L? T@h@4i|ihtc @?_ @| |�i L|�ih i |hi4i � i_ @?_�i|ihL}i?L�t T@h@4i|ihtc ��|� |�i h@?_L4 ULi�U�i?| 4L_i* �||�?} tL4i��ihi �? Mi|�ii?Etiic uLh i @4T*ic �@__@*@ @?_ O�c �bbS�� W? Th@U|�Uic �| �t Lu|i? _��U�*| |L _i|ih4�?i��ihi L? |��t UL?|�?��4 @ T@h|�U�*@h U@ti *�it� A�i i @4T*it �i �ti @hi ?L| t@4T*it M�|@*4Lt| |�i ��L*i TLT�*@|�L? Lu UL�?|h�it �? @ T@h|�U�*@h U@|i}Lh)G 4i4Miht Lu |�i �,�# Lh�t�@? _i�i*LT�?} UL�?|h�it� A��t t�}}it|t |hi@|�?} |�i�h T@h@4i|iht @t � i_� A�i _��U�*|)Lu 4@!�?} |�i _�t|�?U|�L? ThiU�ti �t �**�t|h@|i_ �? Ot�@L i| @*� E�bbD� ��L ThLTLti @ ThLUi_�hiuLh U�LLt�?} Mi|�ii? � i_ @?_ h@?_L4 igiU|t 4L_i*tc ���U� |�i) i�@*�@|i M) �L?|i �@h*L4i|�L_t� OL�i�ihc �? |�i t�4�*@|�L?t |�i � i_ igiU|t @hi @U|�@**) }i?ih@|i_ h@?_L4*) i��|�ih @t @ 4� |�hi Lu ?Lh4@* _�t|h�M�|�L?t Lh @t @ u�?U|�L? Lu |�i hi}hittLht� `��*i |��t _it�}?igiU|��i*) U@T|�hit |�i t�|�@|�L?t ��ihi |h@_�|�L?@* h@?_L4 igiU|t it|�4@|Lht ��** _L M@_*)c|�i u@U| |�@| |�ihi �t ?L LM��L�t �@) |L }i?ih@|i � i_ igiU|t _@|@ uLh �i|ihL}i?L�t T@?i*t�?_�U@|it |�i UL?UiT|�@* _��U�*|)� A��h_*)c |�ihi @hi UL?t�_ih@|�L?t Lu it|�4@|�L?� A�i � i_igiU|t @TThL@U� �tit |�i UL?_�|�L?@* *�!i*��LL_ EUL?_�|�L?@* L? |�i T@h|�U�*@h igiU|t�c |�ih@?_L4 @TThL@U� �tit |�i �?UL?_�|�L?@* Lh 4@h}�?@* *�!i*��LL_� B��i? |�i ULhhiU| tTiU���U@|�L?c |�i *@||ih ��** Mi 4Lhi i�U�i?|� `�i? � �t *@h}i hi*@|��i |L A c |�i � i_ igiU|t@TThL@U� U@? Mi �ih) �?i�U�i?|� 6L�h|�*)c @?_ @? �4TLh|@?| Th@U|�U@* �tt�ic �t ��i|�ih |�iigiU|t @hi �?_iTi?_i?| Lu |�i hi}hittLht @?_ |��t �t |�i M@t�t Lu @ ?�4Mih Lu |it|t Mi|�ii?|�i |�L tTiU��U@|�L?t�

#)?@4�U 4L_i*t @__ u�h|�ih UL4T*�U@|�L?t� A�i �?�|�@* UL?_�|�L?t U@? @*tL Mi |hi@|i_@t � i_ Lh h@?_L4 @?_ |�i *L?}�h�? T@h@4i|iht @hi ?L?�*�?i@h u�?U|�L?t Lu |�i t�Lh|�h�?T@h@4i|iht� A��tc ��i? �t�?} |�i h@?_L4 ULi�U�i?| @TThL@U� L?i 4�t| i?t�hi |�@| |�i�L�?| _�t|h�M�|�L? uLh |�i t�Lh|�h�? T@h@4i|iht �4T*�it @ 4i@?�?}u�* �L�?| _�t|h�M�|�L? uLh |�i*L?}�h�? T@h@4i|ihtc Lh ��Ui �iht@� W? |�i U@ti �i UL?t�_ihc �L4L}i?L�t *L?}�h�? T@h@4i|ihtc|�i *L?}�h�? T@h@4i|iht @UhLtt |�i }hL�Tt �@�i @ _i}i?ih@|i _�t|h�M�|�L?c ���U� h@�tit tL4i|iU�?�U@* _��U�*|�it �? |hi@|�?} |�i �i|ihL}i?L�t t�Lh|�h�? T@h@4i|iht @t h@?_L4� `��*i|�ihi @hi @ ?�4Mih Lu �tt�it |L Mi hitL*�i_ @?_ |�ihi �t �?*�!i*) |L Mi @ t�?}*i it|�4@|Lh|�@| �t @TThLTh�@|i uLh @** _)?@4�U �i|ihL}i?L�t T@?i* ThLM*i4tc �i Mi*�i�i |�@| |�i ��Bit|�4@|Lh �i ThLTLti 4@) Mi �tiu�* �? @ ?�4Mih Lu U@tit |�@| @hi �4TLh|@?| �? Th@U|�Ui�

� A�i �L_i*

5�TTLti |�@| }��i? _@|@ L? |�4i Tih�L_tc | ' �c 2c ���c A c @?_ }hL�Ttc � ' �c 2c ���c � c �i ��t�|L it|�4@|i @? �-(u ERc ^c ^c ���c ^� 4L_i*c

+�| '

R[�'�

b��+�c|3� n

^[�'f

��

�� �c|3� n >� n 0�|c E����

deo

��ihi �| E&� �� �t |�i �iU|Lh Lu i T*@?@|Lh) �@h�@M*it Ehi}hittLht� uLh }hL�T �c >� hiThiti?||�i � i_ igiU|tc |�i ULi�U�i?|t Lu |�i *@}}i_ _iTi?_i?| �@h�@M*itc b��c @hi tU@*@htc @?_ ���@hi & � � ULi�U�i?| �iU|Lht� A 4�t| Mi *@h}i i?L�}� t�U� |�@| �i U@? it|�4@|i |�i 4L_i*uLh i@U� }hL�T tiT@h@|i*)� 6Lh ?L|@|�L?@* UL?�i?�i?Ui �i t�@** �ti @ UL44L? A @?_ R @UhLtt}hL�Tt @?_ @ UL44L? ^ @UhLtt }hL�Tt @?_ hi}hittLhtc M�| |��t �t ?L| ?iUitt@h)� 5�4�*@h*)c|�4i |hi?_t Lh L|�ih |)Tit Lu � i_ hi}hittLht t�U� @t ti@tL?@* _�44�it U@? Mi �?U*�_i_ �?E����� ��| |L !iiT |�i ?L|@|�L?t t�4T*i �i _L ?L| @**L� uLh t�U� igiU|t�

W| �t UL?�i?�i?| |L �Lh! ��|� |�i uL**L��?} hi�T@h@4i|ih�3@|�L? Lu E����G

{+�| ' ��+�c|3� n ��

� �| n

R3�[�'�

bW��{+�c|3� n

^3�[�'f

�W���{ �c|3� n >� n 0�|c E��2�

� ' �c 2c ���c�c @?_ | ' �c 2c ���c A c ��ihi �� ' � E��SR�'� b���c �� '

S^�'f ���c

bW�� ' �R[

6'�n�

b�6c � ' �c 2c ���c R� �c @?_ �W�� ' �^[

6'�n�

��6c � ' �c 2c ���c ^ � ��E����

Wu �i t|@U! |�i |�4i�tih�it LMtih�@|�L?t uLh i@U� }hL�Tc i^�@|�L? E��2� U@? Mi �h�||i? @t

{)� ' ��)�c3� nj��� n

R3�[�'�

bW��{)�c3� n

^3�[�'f

{j�c3��W

�� n >��n %�c E��e�

� ' �c 2c ���c� c ��ihi )� ' E+��c ���c +�A �� �t @ A �� �iU|Lh Lu |�i LMtih�@|�L?t L? |�i _iTi?_i?|

�@h�@M*i Lu |�i ��|� }hL�Tc j� ' E ��c ���c �A �� @ A�& 4@|h� Lu LMtih�@|�L?t L? |�i hi}hittLht

|�@| �@h) ML|� @UhLtt }hL�Tt @?_ |�4i Tih�L_tc � ' E�c ���c ��� @ A � � �iU|Lh Lu L?itc )�c3�@?_ j�c3� @hi � Tih�L_ *@}}i_ �@*�it Lu )� @?_ j�c {)� ' )� � )�c3�c {j� ' j� � j�c3�c{)�c3� @?_ {j�c3� @hi � Tih�L_ *@}}i_ �@*�it Lu {)� @?_ {j�c @?_ %� ' E0��c ���c 0�A �

��

i 4@!i |�i uL**L��?} @tt�4T|�L?tG

�tt�4T|�L? ��� A�i _�t|�hM@?Uit 0�|c � ' �c 2c ���c� c | ' �c 2c ���c Ac �? E���� @hi �?_iTi?�_i?|*) _�t|h�M�|i_ @UhLtt � @?_ |c ��|� 3ihL 4i@?tc �@h�@?Uit j2� : fc @?_ �?�|i uL�h|��Lh_ih4L4i?|t� A�i) @hi @*tL _�t|h�M�|i_ �?_iTi?_i?|*) Lu |�i hi}hittLhtc �|�

A�i @tt�4T|�L? |�@| |�i _�t|�hM@?Uit 0�| @hi _�t|h�M�|i_ �?_iTi?_i?|*) @UhLtt }hL�Tt�@t _�tU�tti_ �? 5iU|�L? 2c |�i @tt�4T|�L? |�@| |�i) @hi �?_iTi?_i?| @UhLtt |�4i �t @*tL ?L|�ih) hit|h�U|��ic @?_ U@? Mi t@|�t�i_ �? 4Lt| @TT*�U@|�L?t M) �?Uhi@t�?} |�i _�t|h�M�|i_ *@}Lh_iht L? +�| @?_ �|� A�i �?_iTi?_i?Ui Lu |�i _�t|�hM@?Uit @?_ |�i hi}hittLht �t ?ii_i_ uLh|�i UL?t�t|i?| it|�4@|�L? Lu |�i t�Lh|�h�? ULi�U�i?|tc M�| @t t�L�? �? �it@h@? E�bb.� �| �thi*@|��i*) t|h@�}�|uLh�@h_ |L @**L� uLh |�i TLtt�M*i _iTi?_i?Ui Lu �| L? %�| ��i? it|�4@|�?}|�i *L?}�h�? ULi�U�i?|tc tL *L?} @t �| �@�i �?�|i�Lh_ih @�|Lhi}hitt��i hiThiti?|@|�L?t�

�tt�4T|�L? ��2 A�i �-(uERc ^c ^c ���c ^� 4L_i* E���� �t t|@M*i �? |�@| |�i hLL|t Lu

R[�'�

b��5� ' �c � ' �c 2c ���c�c

*�i L�|t�_i |�i �?�| U�hU*i�

dDo

A��t @tt�4T|�L? i?t�hit |�@| �� fc @?_ �i?Ui |�ihi i �t|t @ *L?}�h�? hi*@|�L?t��TMi|�ii? +�| @?_ �| _i�?i_ M)

+�| ' �E��

�*��� �| n #�|c

uLh i@U� � ' �c 2c ���c � c ��ihi #�| �t @ t|@|�L?@h) ThLUitt�e �tt�4T|�L? ��2 @*tL i?t�hit |�@||�i Lh_ih Lu �?|i}h@|�L? Lu +| �t @| 4Lt| i^�@* |L |�@| Lu �|�

�tt�4T|�L? ��� EwL?}�h�? �L4L}i?i�|)� A�i *L?}�h�? ULi�U�i?|t L? j�c _i�?i_ M) �� '���*��c @hi |�i t@4i @UhLtt |�i }hL�Ttc ?@4i*)

�� ' �c � ' �c 2c ���c �� E��D�

N?_ih �tt�4T|�L?t ��2 @?_ ���c hi*@|�L? E��e� U@? Mi �h�||i? 4Lhi UL4T@U|*) @t

{)� ' ����E�� n`��� n %�c � ' �c 2c ���c �c E��S�

��ihi

��E�� ' )�c3� �j��c � ' �c 2c ���c�c E��.�

�t |�i ihhLh ULhhiU|�L? UL4TL?i?|c `� ' E{)�c3�c ���c{)�c3Rn�c {j�c{j�c3�c ���c{j�c3^n�c ��c@?_ �� ' EbW��c ���c b

W

�cR3�c �W�

�fc �W�

��c ���c �W�

�c^3�c >���� A�i }hL�T�tTiU��U i^�@|�L?t �? |�i T@?i*

E��S� @hi ?L?�*�?i@h �? �� @?_ �c @?_ t�?Ui � �t UL44L? @UhLtt }hL�Tt |�i T@?i* �t t�M�iU||L UhLtt�i^�@|�L? T@h@4i|ih hit|h�U|�L?t� W? ��@| uL**L�t �i @*tL @**L� |�i ihhLh �@h�@?UitcT @oE0�|� ' j2� c |L _�gih @UhLtt }hL�Tt�

AL it|�4@|i |�i 4L_i*c �i @_LT| @ *�!i*��LL_ @TThL@U� @?_ �?�|�@**) @tt�4i |�@| |�i_�t|�hM@?Uit 0�| @hi ?Lh4@**) _�t|h�M�|i_c |�L�}� |��t @tt�4T|�L? �t ?L| hi^��hi_ uLh |�i@t)4T|L|�U hit�*|t� N?_ih �tt�4T|�L? ��� |�i *�!i*��LL_ Lu |�i T@?i* _@|@ 4L_i* U@? Mi�h�||i? @t |�i ThL_�U| Lu |�i *�!i*��LL_t uLh i@U� }hL�T� 5�?Ui |�i T@h@4i|iht Lu �?|ihit|@hi |�i *L?}�h�? igiU|t @?_ @_��t|4i?| ULi�U�i?|tc �i _�hiU|*) �Lh! ��|� |�i UL?Ui?|h@|i_*L}�*�!i*��LL_ u�?U|�L?� B��i? ?Lh4@*�|) �i �@�i

�A E*� ' �A

2

�[�'�

*? 2Zj2� ��

2

�[�'�

�

j2�E{)� � ����E���

�O�E{)� � ����E���c E��H�

��ihi O� ' WA � `�E`�

�`��3�`�

�c * ' E��c!�c����c ! ' E��c �2c ���c ����c @?_ � '

Ej2�c j22c ���c j

2��

��6Lh |�i ThLLu Lu UL?t�t|i?U) @?_ @t)4T|L|�U ?Lh4@*�|) Lu |�i TLL*i_ 4i@? }hL�T it|�4@�

|Lht �i @*tL hi^��hi |�i uL**L��?} @__�|�L?@* @tt�4T|�L?tG

�tt�4T|�L? ��e * 5 X) ' Xw � X� � Xjc ��ihi X) �t @ UL4T@U| t�Mti| Lu U?) ��|�

?) ' &n2� � A�i |h�i �@*�i Lu *c _i?L|i_ M) *f ' E��

fc!�

fc��

f��c �t @? �?|ih�Lh TL�?| Lu X)�

7Shvdudq/ Vklq dqg Ulfkdug Vplwk +4<<9, surylgh d jhqhudo iudphzrun iru whvwlqj Dvvxpswlrq 615/ luuh0vshfwlyh ri zkhwkhu wkh uhjuhvvruv/ {lw> duh L+4, ru L+3,1

dSo

�tt�4T|�L? ��D E�� 6Lh @ }��i? t@4T*i t�3ic A c @?_ @** �@*�it Lu * 5 X) |�i hi�_i�?i_

LMtih�@|�L? 4@|h� ~E*� 'k�jE!c��c��E�c��c � E��

l�@t @ u�** UL*�4? h@?!c ��ihi

�jE!c�� ' � dE��*j��j�

�c E�2*j2�j�

2c ���c E��*j��j�

��o�

c

@?_ � E�� @?_ ��E�c�� @hi M*LU! _�@}L?@* 4@|h�Uit ��|� |�i�h ��|� M*LU!t }��i? M) `�*j� @?_��E��*j�c hitTiU|��i*)� E��� `�i? �| @hi t|@|�L?@h)c A3�~�E*�~E*� UL?�ih}it �? ThLM@M�*�|)|L @ TLt�|��i _i�?�|i 4@|h� @t A $ 4� E���� `�i? �| @hi UE��c @t A $ 4c k5~

�E*�~E*�k5

�i@!*) UL?�ih}it �? ThLM@M�*�|) |L @ TLt�|��i _i�?�|i h@?_L4 4@|h� ��|� ThLM@M�*�|) �c ��ihik5 ' _�@}EA3�W&c A

3�*2W�Rc A3�*2W�ERn&^nr���

�tt�4T|�L? ��D ti|t L�| t|@?_@h_ �_i?|��U@|�L? UL?_�|�L?t @?_ h�*it L�| |�i TLtt�M�*�|) Lui @U| 4�*|��UL**�?i@h�|)� W? |�i U@ti ��ihi �| @hi UE��c T@h| E���� Lu |��t @tt�4T|�L? i?t�hit|�@| �| @hi ?L| |�i4ti*�it UL�?|i}h@|i_� �L|�Ui @*tL |�@| |��t @tt�4T|�L? �t �i@!ih |�@?�t ?ii_i_ uLh �_i?|��U@|�L? Lu |�i }hL�T�tTiU��U *L?}�h�? ULi�U�i?|tc ��c �u |�i *L?}�h�?�L4L}i?i�|) �tt�4T|�L? ��� �t ?L| �4TLti_�

�iUitt@h) UL?_�|�L?t uLh T@h|t E��� @?_ E���� Lu �tt�4T|�L? ��D |L �L*_ @hi }��i? �?|�i �TTi?_� c 5iU|�L? ���� W? |�i U@ti ��ihi �| @hi UEf�c |�i TLL*i_ UhLtt�ThL_�U| LM�tih�@|�L? 4@|h� L? |�i hi}hittLhtc �3�

S�

�'�E�2� *j

2� �A

3�j�

�O�j�c 4�t| UL?�ih}i �? ThLM�@M�*�|) |L @ � i_ TLt�|��i _i�?�|i 4@|h� @t A $ 4� W? |�i U@ti ��ihi �| @hi UE��c�3�

S�

�'�E�2� *j

2� �A

32j�

�O�j� 4�t| �i@!*) UL?�ih}i |L @ h@?_L4 TLt�|��i _i�?�|i 4@|h� ��|� ThLM@M�*�|) � @t A $ 4�D A�iti UL?_�|�L?t t�L�*_ �L*_ uLh @** ui@t�M*i �@*�it Lu �� @?_j2� �

e A�i �LL*i_ �i@? BhL�T ,t|�4@|Lh

A�i 4@ �4�4 *�!i*��LL_ E�w� it|�4@|�L? Lu |�i *L?}�h�? ULi�U�i?|tc �c @?_ |�i }hL�T�tTiU��U ihhLh�ULhhiU|�L? ULi�U�i?|tc ��c U@? Mi UL4T�|i_ M) 4@ �4�3�?} E��H� ��|� hitTiU||L *� A�iti �w it|�4@|Lht ��** Mi hiuihhi_ |L @t |�i RTLL*i_ 4i@? }hL�T� E��B� it|�4@|Lht�? Lh_ih |L ��}�*�}�| ML|� |�i TLL*�?} �4T*�i_ M) |�i �L4L}i?i�|) hit|h�U|�L?t L? |�i *L?}�h�? ULi�U�i?|t @?_ |�i @�ih@}�?} @UhLtt }hL�Tt �ti_ |L LM|@�? 4i@?t Lu |�i it|�4@|i_ihhLh�ULhhiU|�L? ULi�U�i?|t @?_ |�i L|�ih t�Lh|�h�? T@h@4i|iht Lu |�i 4L_i*�

A�i ��B it|�4@|Lht U@? Mi UL4T�|i_ M) |�i u@4�*�@h �i�|L?�+@T�tL? @*}Lh�|�4 ���U�4@!it �ti Lu ML|� |�i �ht| @?_ |�i tiUL?_ _ih��@|��it� �*|ih?@|��i*)c |�i) U@? Mi UL4T�|i_M) @ RM@U!�t�Mt|�|�|�L?� @*}Lh�|�4 |�@| L?*) 4@!it �ti Lu |�i �ht| _ih��@|��it Lu E��H�� W?|��t U@tic ti||�?} |�i �ht| _ih��@|��it Lu |�i UL?Ui?|h@|i_ *L}�*�!i*��LL_ u�?U|�L? ��|� hitTiU||L * |L f )�i*_t |�i uL**L��?} hi*@|�L?t �? �c ��c @?_ j2� ���U� ?ii_ |L Mi tL*�i_ �|ih@|��i*)GS

� ' �+

�[�'�

�2�j2�j�

�O�j�

,3�+ �[

�'�

��j2�j�

�O�

�{)� � ��)�c3�

�,c Ee���

8Wkhvh frqglwlrqv dovr fryhu wkh fdvh zkhuh erwk W dqg Q duh odujh19Wr vlpsoli| wkh qrwdwlrqv zh duh ghqrwlqj �

l+a�, e| a�

l1

d.o

�� '���

�O���

�3���

�O�{)�c � ' �c 2c ���c �c Ee�2�

j2� ' A3�E{)� � �����

�O�E{)� � �����c � ' �c 2c ���c�c Ee���

��ihi �� ' )�c3� �j��� 5|@h|�?} ��|� @? �?�|�@* it|�4@|i Lu �c t@) �

Ef�c it|�4@|it Lu �� @?_

j2� U@? Mi UL4T�|i_ �t�?} Ee�2� @?_ Ee���c ���U� U@? |�i? Mi t�Mt|�|�|i_ �? Ee��� |L LM|@�?

@ ?i� it|�4@|i Lu �c t@) �E��c @?_ tL L? �?|�* UL?�ih}i?Ui �t @U��i�i_�

W? Lh_ih |L _ih��i |�i @t)4T|L|�U _�t|h�M�|�L? Lu |�i ��B it|�4@|Lht �i _�t|�?}��t�Mi|�ii? |�i U@tit Lu t|@|�L?@h) @?_ ?L?�t|@|�L?@h) hi}hittLhtc �|� �*|�L�}� �? Th�?U�T*i|�i t@4i @*}Lh�|�4 U@? Mi �ti_ |L UL4T�|i |�i ��B it|�4@|Lht �hhitTiU|��i Lu ��i|�ih|�i hi}hittLht @hi UEf� Lh UE��c |�i �?_ih*)�?} @t)4T|L|�U |�iLh�it uLh |�iti |�L U@tit @hiu�?_@4i?|@**) _�gihi?| @?_ |�i�h _ih��@|�L?t hi^��hi tiT@h@|i |hi@|4i?|t�

e�� A�i �@ti Lu 5|@|�L?@h) +i}hittLht

W? |��t U@ti �?_ih u@�h*) t|@?_@h_ UL?_�|�L?t |�i UL?t�t|i?U) @?_ |�i @t)4T|L|�U ?Lh4@*�|)Lu |�i �w it|�4@|Lht Lu |�i T@h@4i|iht �? E��H� U@? Mi i@t�*) it|@M*�t�i_� i ti| L�||�i UL?t�t|i?U) @?_ |�i @t)4T|L|�U _�t|h�M�|�L? Lu |�i �w it|�4@|Lht Lu *c _i?L|i_ M)

* ' E��

c !�

c ����c �? |�i uL**L��?} |�iLhi4G

A�iLhi4 e�� N?_ih �tt�4T|�L?t ��� � ��ec ��D E�� @?_ E���c @?_ @tt�4�?} |�@| |�i hi�}hittLht �| @hi t|@|�L?@h)c |�i �w it|�4@|Lh Lu * �? |�i _)?@4�U �i|ihL}i?iL�t T@?i* _@|@4L_i* E��S� �t UL?t�t|i?|� 6�h|�ih4Lhic @t A $ 4 uLh @ � i_ � c |�i ��B it|�4@|Lh Lu# ' E��c!���c �@t |�i uL**L��?} @t)4T|L|�U _�t|h�M�|�L?G

sA E# �#f�

@� ��fca3�E#f�

�c Ee�e�

��ihi aE#f� �t |�i E& n��� E& n�� �?uLh4@|�L? 4@|h� }��i? M)

aE#f� �

599997

S��'�

�2�f

j2�f

"f�f����f

j2�f

"f�1�f � � � ���f

j2�f

"f� 1�f

���fj2�f

"�

f�1�f�j2�f

^1�f1�f � � � f���

������

���

���f

j2�f

"�

f� 1�ff � � � �

j2�f

^1�f1�f

6::::8 c Ee�D�

��|� "f�f�c "f�1�fc @?_ ^1�f1�f Mi�?} |�i ThLM@M�*�|) *�4�|t Lu A3�j�

�O�j�c A3�j�

�O���fc @?_A3����fO���fc hitTiU|��i*)�

�hLLu� W? |��t U@ti |�i ThLLu U@? Mi it|@M*�t�i_ �t�?} u@4�*�@h hit�*|t� #i|@�*t U@? Mi uL�?_�? |�i �TTi?_� |L �it@h@?c 5��? @?_ 54�|� E�bb.��

+i4@h! e�� 6LU�t�?} L? |�i *L?}�h�? ULi�U�i?|tc uLh @ � i_ � @t A $ 4 |�i TLL*i_ �wit|�4@|Lh �c _i�?i_ M) Ee���c �t @t)4T|L|�U@**) _�t|h�M�|i_ @t

sA E� � �f�

@� �

;?=fc

%�[�'�

�2�fj2�f

�"f�f�

�"f�1�f^3�1�f1�f

"�

f�1�f

�&3�<@> � Ee�S�

dHo

e�2 A�i �@ti Lu �L?�5|@|�L?@h) +i}hittLht

Oihi |�i �?_ih*)�?} hi}hittLht @hi @tt�4i_ |L uL**L� �?|i}h@|i_ ThLUittit Lu Lh_ih �c ?@4i*)UE��� A�i @t)4T|L|�U @?@*)t�t �? |��t U@ti �t 4Lhi UL4T*�U@|i_ _�i |L |�i u@U| |�@| |�i�w it|�4@|Lht Lu |�i *L?}�h�? @?_ |�i t�Lh|�h�? T@h@4i|ihtc � @?_ E!�c����c hitTiU|��i*)cUL?�ih}i |L |�i�h |h�i �@*�it @| _�gihi?| h@|itc @?_ |�@| |�i 4ihi UL?t�t|i?U) Lu |�i �wit|�4@|Lht �t ?L| t��U�i?| |L }�@h@?|ii |�i �i@! UL?�ih}i?Ui Lu |�i t@4T*i �?uLh4@|�L?4@|h� |L �|t |h�i �@*�i� W? T@h|�U�*@hc |L i?t�hi t�U� @ UL?�ih}i?Ui |�i t@4T*i �?uLh4@|�L?4@|h� t�L�*_ t@|�tu) |�i t|LU�@t|�U i^���UL?|�?��|) UL?_�|�L?� 6Lh @ }i?ih@* |hi@|4i?| Lu|�iti �tt�it tii 5@�!!L?i? E�bbD� @?_ �it@h@? @?_ 5��? E�bb.��

A�i uL**L��?} |�iLhi4 it|@M*�t�it |�i UL?t�t|i?U)c |�i hi*@|��i h@|it Lu UL?�ih}i?Uic @?_|�i @t)4T|L|�U _�t|h�M�|�L? Lu |�i �w it|�4@|Lh Lu *G

A�iLhi4 e�2 N?_ih �tt�4T|�L?t ��� � ��ec ��D E�� @?_ E����c @?_ @tt�4�?} |�@| �| @hiUE��c |�i �w it|�4@|Lh Lu |�i t�Lh|�h�? ULi�U�i?|t ! @?_ � �? |�i _)?@4�U �i|ihL}i?iL�tT@?i* _@|@ 4L_i* E��S� @hi

sA�UL?t�t|i?|c @?_ |�i �w it|�4@|Lh Lu � �t A�UL?t�t|i?|c

?@4i*)

� � �f ' JREA3

�

2 �c !� !f ' JRE�� @?_ � � �f ' JRE��� Ee�.�

6�h|�ih4Lhic uLh @ � i_ � @?_ @t A $ 4c |�i �w it|�4@|Lh Lu # ' E��c!��� @t)4T|L|�U@**)�@t |�i 4� |�hi�?Lh4@* _�t|h�M�|�L?

#3�� E# �#f�

@� ���fc/3�E#f�

�c Ee�H�

��ihi #� ' _�@}EA3�W&c A3�*2W�� @?_ /E#f� �t |�i h@?_L4 �?uLh4@|�L? 4@|h� _i�?i_ M)

E��2f��

�hLLu� 5ii |�i �TTi?_� c 5iU|�L? ��2�

+i4@h! e�2 �Lhi tTiU��U@**)c |�i TLL*i_ �w it|�4@|Lh �c _i�?i_ M) Ee���c �@t |�i uL**L��?}*@h}i A @t)4T|L|�U _�t|h�M�|�L?G

A E� � �f�@� ��

;?=fc

#�[�'�

�2�f

j2�f

+f�f�

$3�<@> c Ee�b�

��ihi +f�f�c � ' �c 2c ���c � c @hi |�i h@?_L4 ThLM@M�*�|) *�4�|t _i�?i_ M) E����� �L|�Ui |�@|

�| �t ?L| hi^��hi_ |�@| @** |�i 4@|h�Uit +f�f�t�L�*_ Mi TLt�|��i _i�?�|i� W| �tc �L�i�ihc i@t�*)

tii? |�@| M) T@h| E���� Lu �tt�4T|�L? ��DS�

�'�

�2�f

j2�f

+f�f��t @ TLt�|��i _i�?�|i 4@|h� ��|�

ThLM@M�*�|) �� �*tL ?L|i |�@| �? |�i U@ti Lu UE�� hi}hittLht |�i �w it|�4@|Lht Lu |�i *L?}�h�? @?_ |�i t�Lh|�h�? T@h@4i|iht @hi @t)4T|L|�U@**) _�t|h�M�|i_ �?_iTi?_i?|*) Lu i@U� L|�ih�E6Lh @ ThLLu Lu Ee�b� tii 5iU|�L? ��� �? |�i �TTi?_� ��

dbo

�?Ui |�i TLL*i_ �w it|�4@|Lh Lu |�i *L?} h�? T@h@4i|ihtc �c �t t�UUittu�**) UL4T�|i_c|�i t�Lh| h�? ULi�U�i?|tc �?U*�_�?} |�i }hL�T�tTiU��U ihhLh ULhhiU|�L? ULi�U�i?|tc �� U@?Mi UL?t�t|i?|*) it|�4@|i_ M) h�??�?} |�i �?_���_�@* �w5 hi}hitt�L?t Lu {)� L? E��c`��c� ' �c ���c� c ��ihi �� ' )�c3� � j�

�� A�i UL�@h�@?Ui 4@|h� Lu |�i �w it|�4@|Lhtc

E��

c ��c ���c �� c ��

�c ���c ��

��� �t |�i? UL?t�t|i?|*) it|�4@|i_ M) |�i �?�ihti Lu

599999999999997

S��'�

�2�j

�

�j

�

�

j2�

3��j

�

���

j2�

� � � 3��j

�

���

j2�

3��j

�

�`�

j2�

� � � 3��j

�

�`�

j2�

��

���

j2�

� � � f�

�

�`�

j2�

� � � f���

������

����

�

���

j2�

f � � � ��

�`�

j2�

`�

�`�

j2�

� � � f���

���`

�

�`�

j2�

6:::::::::::::8

e�� A�i �@ti Lu w@h}i A @?_ w@h}i �

W? |��t U@ti |�i 4i@? Lu |�i ihhLh ULhhiU|�L? ULi�U�i?|t @?_ |�i L|�ih t�Lh| h�? T@h@4i|ihtU@? Mi it|�4@|i_ UL?t�t|i?|*) M) |�i �?�i�}�|i_ @�ih@}i Lu |�i �?_���_�@* ULi�U�i?|t ELh|�i �B it|�4@|Lht�G

��C ' �3�

�[�'�

��c ��C ' �3�

�[�'�

���

A�i �@h�@?Ui Lu |�iti it|�4@|Lht U@? Mi UL?t�t|i?|*) it|�4@|i_ @*L?} |�i *�?it t�}}it|i_ M)�it@h@?c 54�|� @?_ W4 E�bbS�� 6Lh i @4T*ic �? |�i U@ti Lu ��Cc @ UL?t�t|i?| it|�4@|Lh Lu|�i �@h�@?Ui Lu ��C �t }��i? M)

{� '�

� � �

�[�'�

E�� � ��C�2�

�*|ih?@|��i*)c L?i U@? �ti |�i �i�}�|i_ it|�4@|Lh ThLTLti_ M) 5�@4) E�b.f�c �? |�i UL?|i |Lu |�i t|@|�U h@?_L4 ULi�U�i?| 4L_i*t� ��| @t �| �t t�L�? �? Ot�@Lc �it@h@? @?_ A@�4�t�U�L}*� E�bbH� @?_ �@t ?L|i_ @ML�ic |�i 5�@4) it|�4@|Lh E@*tL !?L�? @t |�i i4T�h�U@* �@)itit|�4@|Lh� @?_ |�i �B it|�4@|Lh @hi @t)4T|L|�U@**) i^���@*i?| @t A $ 4 @?_ � $ 4 t�U�|�@|

s�*A $ f� N?_ih |�iti UL?_�|�L?t |�i @t)4T|L|�U _�t|h�M�|�L? Lu ��Cc uLh i @4T*ic

�t }��i? M)

s�

���C � �

�@y � Efc{�� c

��ihi � ' .E��� @?_ {� ' T @oE����6Lh |�i UL44L? *L?}�h�? ULi�U�i?|tc �c |�i TLL*i_ �w it|�4@|Lh �t UL?t�t|i?| tL *L?}

@t A $ 4c �hhitTiU|��i Lu ��i|�ih � �t *@h}i Lh ?L|� AL LM|@�? |�i @t)4T|L|�U _�t|h�M�|�L?Lu � ��i? � �t *@h}i �i ?ii_ |L @tt�4i |�@| � �t @ 4L?L|L?�U u�?U|�L? Lu A Et@) � EA ��c

d�fo

t�U� |�@| � $ 4 L?*) @t A $ 4� W? |��t ti||�?} |�i h@|i Lu UL?�ih}i?Ui Lu � |L�@h_t �|t|h�i �@*�i ��** Mi }��i? M)

s�A �? |�i U@ti ��ihi |�i hi}hittLht @hi UEf�� 6Lh |��t hit�*|

|L �L*_ �| �t ?iUitt@h) |�@| |�i *�4�| Lu

�3�

�[�'�

�2�f

j2�f

�"f�f�

�"f�1�f^3�1�f1�f

"�

f�1�f

�

@t � $ 4 �t @ TLt�|��i _i�?�|i 4@|h� Etii Ee�S��� `�i? |�i hi}hittLht @hi UE�� |�i h@|i LuUL?�ih}i?Ui Lu � �t }��i? M) A

s� tL *L?} @t

�3�

�[�'�

�2�f

j2�f

+f�f�

|i?_t |L @ TLt�|��i _i�?�|i 4@|h� ��|� ThLM@M�*�|) �c @t � $ 4 Etii Ee�b��� �L|�Ui |�@| ���** ?L| Mi UL?t�t|i?| uLh �?�|i A c i�i? �u � $ 4�

D ,4T�h�U@* �TT*�U@|�L?t

�iuLhi UL?t�_ih�?} |�i |�L i @4T*itc �i Mh�i�) _�tU�tt |�hii 4L_i**�?} �tt�it� A�i �ht| �tt�i�t |�@| ���*i |�i |�iLh) @ML�i @tt�4i_ |�@| @** *L?}�h�? ULi�U�i?|t �ihi |�i t@4i @UhLtt}hL�Ttc �| �t t|h@�}�|uLh�@h_ |L @_@T| |�i ��B it|�4@|Lh |L @**L� L?*) @ t�M ti| Lu |�i *L?}�h�? ULi�U�i?|t |L Mi |�i t@4i ���*i |�i L|�iht _�gih� #i|@�*t @hi }��i? �? |�i i@h*�ih �iht�L?Lu |�i T@Tih E�it@h@?c 5��? @?_ 54�|�c �bb.�� A�i tiUL?_ �tt�i �t |�@| �i ?ii_ |L U�LLtiMi|�ii? |�i @*|ih?@|��i tTiU��U@|�L?t� Ait|t Lu �L4L}i?i�|) Lu ihhLh �@h�@?Uit @?_%Lh t�Lh|�Lh *L?}�h�? t*LTi ULi�U�i?|t U@? Mi i@t�*) U@hh�i_ L�| �t�?} w�!i*��LL_ +@|�L @?_ L|�ihU*@tt�U@* t|@|�t|�U@* |it|tc t�?Ui |�i ��B @?_ � i_ igiU|t it|�4@|Lht @hi hit|h�U|i_ �iht�L?tLu |�i ti| Lu �?_���_�@* }hL�T i^�@|�L?t� �*|�L�}� �| �t UL44L? |L �ti TLL*i_ it|�4@|Lht��|�L�| |it|�?} |�i �4T*�i_ hit|h�U|�L?tc �? |�i U@ti Lu UhLtt�UL�?|h) t|�_�it |�i w�!i*��LL_+@|�L |it|t �t�@**) hi�iU| i^�@*�|) Lu ihhLh �@h�@?Uit @?_%Lh t*LTit Et�Lh|�h�? Lh *L?}�h�?� @|UL?�i?|�L?@* t�}?��U@?Ui *i�i*t� A��t �t |�i U@ti �? ML|� L�h i @4T*it� A�i �?|ihThi|@|�L?Lu |��t ui@|�hi �t _�tU�tti_ i |i?t��i*) �? �it@h@?c 54�|� @?_ �!�)@4@ E�bbH� @?_ �i hi|�h?|L �| �? |�i UL?U*�t�L?� �? @*|ih?@|��i |L w�!i*��LL_ +@|�L |it|t �L�*_ Mi |L �ti O@�t4@?E�b.H� |)Ti |it|t� A�i �B it|�4@|Lh ThL��_it UL?t�t|i?| it|�4@|it Lu |�i 4i@? Lu |�i *L?}�h�? ULi�U�i?|tc |�L�}� |�iti ��** Mi �?i�U�i?| �u t*LTi �L4L}i?i�|) �L*_t� N?_ih *L?}�h�?t*LTi �L4L}i?i�|) |�i TLL*i_ it|�4@|Lht @hi UL?t�t|i?| @?_ i�U�i?|� A�ihiuLhic |�i igiU|Lu �i|ihL}i?i�|) L? |�i 4i@?t Lu |�i ULi�U�i?|t U@? Mi _i|ih4�?i_ M) @ O@�t4@? |)Ti|it| @TT*�i_ |L |�i _�gihi?Ui Mi|�ii? |�i �B @?_ |�i ��B Lh |�i � i_ igiU|t it|�4@|Lht�A�i _i|@�*t Lu t�U� |it|t @hi _�tU�tti_ �? �it@h@?c 54�|� @?_ W4 E�bbS�� A�i |��h_ �tt�i�t |�@| @*|�L�}� |�i �i@? BhL�T it|�4@|Lh �t UL?t�t|i?|c uLh *@h}i � @?_ A c uLh t4@** A|�i u@4�*�@h *@}}i_ _iTi?_i?| �@h�@M*i M�@t U@�tit |�i it|�4@|it Lu b� @?_ �� ' Eb� � ��|L �?_ihit|�4@|i |�i�h |h�i �@*�it� w@h}i � _Lit ?L| �i*T ��|� |��t ThLM*i4c t�?Ui @** |�iit|�4@|it @hi M�@ti_ �? |�i t@4i _�hiU|�L?� �it@h@? @?_ ~�@L E�bbH� ThLTLti @ M�@t ULhhiU|i_�i@? BhL�T ,t|�4@|Lhc ���U� _�hiU|*) @_��t|t |�i *L?}�h�? ULi�U�i?| M) @? it|�4@|i Lu �|tM�@t� W? |�i U@ti Lu |�i TLL*i_ it|�4@|Lhtc |�i _L�?�@h_ *@}}i_ _iTi?_i?| �@h�@M*i M�@tc

d��o

���U� |�i) @*tL t�gihc 4@) Lgti| |�i �T�@h_ �i|ihL}i?i�|) M�@t _�tU�tti_ �? �it@h@? @?_54�|� E�bbD�� W? i4T�h�U@* @TT*�U@|�L?t �| 4@) Mi _��U�*| |L ��_}i |�i hi*@|��i igiU| Lu |�i|�L M�@titc 4@!�?} �?uihi?Ui @ML�| |�i tTii_ Lu @_��t|4i?| _��U�*|� A��t �t @ ui@|�hi LuML|� L�h i @4T*it�

D�� A�i �L?t�4T|�L? 6�?U|�L? �? |�i �,�#

A�i �ht| i @4T*i �i i @4�?i �t @ t|@?_@h_ UL?t�4T|�L? u�?U|�L? Lu |�i #@��_tL? i| @*�E�b.H� |)Ti uLh @ t@4T*i Lu �,�# UL�?|h�it� 5�4�*@h tTiU��U@|�L?t �@�i @*tL Mii? it|�4@|i_uLh @ ?�4Mih Lu _i�i*LT�?} UL�?|h�it M) O@^�i @?_ �L?|�i* E�bHb�� i @tt�4i |�@| |�i*L?}�h�? UL?t�4T|�L? u�?U|�L? �t }��i? M)

S�| ' wf� n w��+_�| n w2�Z�| n ��|c � ' �c 2c ����c | ' �c 2c ���c Ac

��ihi S�| �t |�i *L}@h�|�4 Lu hi@* UL?t�4T|�L? Tih U@T�|@c +_�| �t |�i *L}@h�|�4 Lu hi@* Tih U@T�|@_�tTLt@M*i �?UL4ic @?_ Z�| �t |�i h@|i Lu �?�@|�L?� �Lt| |�iLh�it Lu @}}hi}@|i UL?t�4T|�L?�L�*_ t�}}it| |�@| w�� ' �� A�i ��B it|�4@|�L? ThLUi_�hi @**L�t �t |L it|�4@|i @ UL44L?*L?}�h�? ULi�U�i?| @?_ |it| �u �| �t �?�|)� A�i �?�@|�L? �@h�@M*ic Z�|c �t @ ThL ) uLh �@h�L�t�i@*|� igiU|t @?_ �i �L�*_ i TiU| w2� f� i @tt�4i |�@| @** Lu |�iti �@h�@M*it @hi UE�� @?_UL�?|i}h@|i_c 4@!�?} ��| @? UEf� ThLUitt uLh @** �� W? |��t @TT*�U@|�L? �i |@!i |�i 4@ �4�4*@} @t Mi�?} L?ic |��t |�i �+#wE�c�c�� i^�@|�L? �t

S�| ' >� n B�f�+_�| n B���+

_�c|3� n B2f�Z�| n B2��Z�c|3� n b�S�c|3� n 0�|c

@?_ |�i ihhLh ULhhiU|�L? i^�@|�L? �tG

{S�| ' ��ES�c|3� � wf� � w��+�| � w2�Z�|�� B���{+_�| � B2��{Z�| n 0�|c

��ihi

wf� '>�

�� b�c w�� '

B�f� n B����� b�

c w2� 'B2f� n B2���� b�

c �� ' �E�� b���

A�i @ML�i ihhLh ULhhiU|�L? i^�@|�L?t @hi �h�||i? �? |ih4t Lu U�hhi?|c h@|�ih |�@? *@}}i_*i�i*t Lu |�i i L}i?L�t hi}hittLhtc t�?Ui |��t @**L�t @? �+#wE�cfcf� @t @ tTiU�@* U@ti�

i 4i@t�hi UL?t�4T|�L? M) |�i *L}@h�|�4 Lu |L|@* hi@* Th��@|i UL?t�4T|�L? Tih U@T�|@@?_ �?�@|�L? M) |�i U�@?}i �? |�i *L}@h�|�4 Lu |�i UL?t�4T|�L? _i�@|Lh� A�i �?�|�@* 4i@t�hiLu �?UL4i �i �ti �t ?@|�L?@* _�tTLt@M*i �?UL4i Tih�U@T�|@ _i�@|i_ M) |�i UL?t�4T|�L?_i�@|Lhc �#W�. Nt�?} �bSf @?_ �bS� |L Uhi@|i *@}t �i �@�i _@|@ uLh �2 )i@htc �bS2�b�c uLh2� UL�?|h�it @?_ �� )i@htc �bS2��bb2c uLh �i*}��4�

6�ht| @ UL44L? �+#wE�c�c�� �@t h�? uLh i@U� UL�?|h) tiT@h@|i*)� A�i hit�*|t @hi }��i?�? |�i i@h*�ih �iht�L? Lu |��t T@Tih� 6Lh @ *L?}�h�? hi*@|�L?t��T |L i �t| �i hi^��hi �� 9' f� W|�t U*i@h |�@| �? @ ?�4Mih Lu UL�?|h�itc |�i �)TL|�it�t Lu ?L *L?}�h�? hi*@|�L? �L�*_ ?L| Mihi�iU|i_�H A�i *L?}�h�? �?UL4i i*@t|�U�|�it h@?}i uhL4 f�S2 �? 5��|3ih*@?_ |L ���b �? |�i N5

:Wkh gdwd duh wdnhq iurp wkh RHFG Qdwlrqdo Dffrxqwv Vwdwlvwlfv dqg zhuh froohfwhg dv sduw ri dq LPI

surmhfw rq lqwhuqdwlrqdo vdylqj udwhv1;Vhh Shvdudq/ Vklq dqg Ulfkdug Vplwk +4<<9,/ zkr ghyhors d whvw iru wkh h{lvwhqfh ri d orqj0uxq uhodwlrq0

vkls lq DUGO*v ri wklv irup1

d�2o

@?_ @hi t�}?��U@?|*) *itt |�@? �?�|) �? ?�?i UL�?|h�it @?_ t�}?��U@?|*) }hi@|ih |�@? �?�|)�? |�hii EW|@*)c |�i Nk @?_ |�i N5�� A�i *L?}�h�? �?�@|�L? ULi�U�i?| �t 4Lhi _�tTihti_ch@?}�?} Mi|�ii? ��eS �? Bih4@?) @?_ ���2D �? �@?@_@� OL�i�ihc �| �t ?i}@|��i �? @** M�|uL�h UL�?|h�it� ��ih Sf Tih Ui?| Lu |�i U�@?}i �? |�i *L}@h�|�4 Lu Tih U@T�|@ UL?t�4T|�L? �ti T*@�?i_ �? @** M�| |�hii UL�?|h�itG w� i4ML�h}c �Lh�@) @?_ ��t|h�@� A�i t|@?_@h_ ihhLhLu hi}hitt�L? �@h�it uhL4 f�DI �? 6h@?Ui |L ���I �? A�h!i)c @?_ |�i i^�@*�|) Lu ihhLh �@h�@?Uit_Lit ?L| tii4 |L Mi @? @TThLTh�@|i @tt�4T|�L?c @ hit�*| MLh? L�| M) uLh4@* t|@|�t|�U@* |it|t��| |�i DI *i�i*c |�ihi �t i��_i?Ui Lu tih�@* ULhhi*@|�L? �? |�i i^�@|�L?t uLh |�L L�| Lu |�i2e UL�?|h�itc @?_ Lu u�?U|�L?@* uLh4 4�ttTiU��U@|�L? �? |�hiic ?L?�?Lh4@* ihhLht �? |�Lc@?_ �i|ihLt!i_@t|�U�|) �? L?i� A�i |it|t @hi _itUh�Mi_ �? �it@h@? @?_ �it@h@? E�bb.�c |�i+,5,A |it|t uLh u�?U|�L?@* uLh4 @?_ |�i |it| Lu �i|ihLt!i_@t|�U�|) @hi M@ti_ L? |�i �||i_�@*�it uLh |�i U�@?}it �? |�i *L}@h�|�4 Lu Tih U@T�|@ UL?t�4T|�L?� A�i u@U| |�@| �. Lu |�i2e UL�?|h)�tTiU��U i^�@|�L?t t�L� ?L i��_i?Ui Lu 4�ttTiU��U@|�L? �t hi@tt�h�?}�

A@M*i � Thiti?|t |�i @*|ih?@|��i TLL*i_ it|�4@|itG �i@? BhL�T E�B�c ���U� �4TLtit?L hit|h�U|�L?tc �LL*i_ �i@? BhL�T E��B�c ���U� �4TLtit UL44L? *L?}�h�? igiU|t @?_#)?@4�U 6� i_ ,giU|t E#6,� ���U� UL?t|h@�?t @** |�i t*LTi ULi�U�i?|t @?_ ihhLh �@h�@?Uit|L Mi |�i t@4i�b A�i #6, t|@?_@h_ ihhLht @hi ULhhiU|i_ uLh |�i �i|ihLt!i_@t|�U�|) Lu ih�hLh �@h�@?Uit @UhLtt UL�?|h�itc |�i �?ULhhiU|i_ L?it @hi t�Mt|@?|�@**) t4@**ih��f A�i |�hiiit|�4@|it Lu |�i *L?}�h�? �?UL4i i*@t|�U�|�it @hi �ih) t�4�*@hc U*Lti |L f�b� @?_ t�}?��U@?|*)*itt |�@? �?�|)� A�i *L?}�h�? �?�@|�L? ULi�U�i?|t @hi @** t�}?��U@?|*) ?i}@|��ic |�L�}� |�iit|�4@|it _�gih tL4i��@|� �t |�i iUL?L4i|h�U |�iLh) t�}}it|t �4TLt�?} �L4L}i?i�|) U@�tit@? �T�@h_ M�@t �? |�i ULi�U�i?| Lu |�i *@}}i_ _iTi?_i?| �@h�@M*i @?_ |�i �B it|�4@|i t�}�}it|t 4�U� u@t|ih @_��t|4i?| |�@? |�i ��B Lh #6,� A�i �B it|�4@|i Lu |�i @_��t|4i?|ULi�U�i?| @*tL �@t |�i t4@**it| t|@?_@h_ ihhLh�

W4TLt�?} *L?}�h�? �L4L}i?i�|) hi_�Uit |�i t|@?_@h_ ihhLht Lu |�i *L?}�h�? ULi�U�i?|tcM�| _Lit ?L| U�@?}i |�i it|�4@|it �ih) 4�U�� A��t �t UL?�h4i_ M) |�i O@�t4@? |it| t|@|�t|�ULu ���bc ���U� �t �2E2� �?_ih |�i ?�** �)TL|�it�t Lu ?L _�gihi?Ui Mi|�ii? |�i �B @?_ ��Bit|�4@|Lht� �t �t U*i@h uhL4 A@M*i �c w�!i*��LL_ +@|�L |it|t @| UL?�i?|�L?@* t�}?��U@?Ui*i�i*tc L? |�i L|�ih �@?_c �L�*_ t|hL?}*) hi�iU| @** |�i hit|h�U|�L?tc �?U*�_�?} �L4L}i?i�|)Lu *L?}�h�? ULi�U�i?|t� A��t �t |h�i uLh ML|� �?UL4i @?_ �?�@|�L?� Wu �L4L}i?i�|) Lu ��t||�i *L?}�h�? �?UL4i i*@t|�U�|�it �t �4TLti_ E2� hit|h�U|�L?t� |�i �@ �4�ti_ wL}�*�!i*��LL_E�ww� u@**t uhL4 2�bf |L 22.f� Wu �L4L}i?i�|) Lu ML|� �?UL4i @?_ �?�@|�L? *L?}�h�? igiU|t�t �4TLti_ EeS hit|h�U|�L?t�c |�i �ww u@**t |L 22e.�

�?i @_�@?|@}i Lu |�i ��B L�ih |�i |h@_�|�L?@* #6, 4L_i* �t |�@| �| U@? @**L� |�i t�Lh|�h�?�_)?@4�U tTiU��U@|�L? |L _�gih uhL4 UL�?|h) |L UL�?|h)� A�i *@} Lh_ih �@t �ht| U�Lti?�? i@U� UL�?|h) L? |�i �?hit|h�U|i_ 4L_i* M) |�i 5U��@h3 �@)it�@? �h�|ih�L? E5���c t�M�iU|

<Wkh SPJ frpsxwdwlrqv zhuh fduulhg rxw xvlqj wkh Qhzwrq0Udskvrq dojrulwkp lq d surjudp zulwwhq lq

JDXVV1 Wkh surjudp dqg gdwd duh dydlodeoh rq kwws=22zzz1hfrq1fdp1df1xn2idfxow|2shvdudq1 Wkh surjudp

doorzv wkh xvhu wr vwduw wkh lwhudwlrqv zlwk gl�huhqw vhwv ri lqlwldo ydoxhv/ ghshqglqj rq wkh qdwxuh ri wkhDUGO vshfl�fdwlrq dfurvv wkh jurxsv1 Zkhq wkh vdph DUGO lv hvwlpdwhg dfurvv wkh frxqwulhv wkh PJ dqg

wkh GIH hvwlpdwhv ri wkh orqj0uxq frh�flhqwv fdq eh xvhg dv lqlwldo ydoxhv1 Lq wkh h{dpsohv frqvlghuhg khuh/wkhvh uhvxowhg lq wkh vdph pd{lpxp iru wkh srrohg orj0olnholkrrg ixqfwlrq1 Wklv kdv qrw ehhq wkh fdvh lq

vrph rwkhu h{dpsohv143Wkh khwhurvnhgdvwlflw| urexvw vwdqgdug huuruv duh frpsxwhg doorzlqj iru d jhqhudo fryduldqfh pdwul{ ri

wkh glvwxuedqfhv %lw dfurvv l1 Vhh/ iru h{dpsoh/ Edowdjl +4<<8/ ss1 45046,1

d��o

|L @ 4@ �4�4 *@} Lu L?i� A�i? �t�?} |�iti 5�� _i|ih4�?i_ *@} Lh_iht �L4L}i?i�|) �@t�4TLti_� A�i 4Lt| UL44L? U�L�Uic �? �@*u |�i UL�?|h�itc �@t @? �-(u E�c �c f�c L?i *@}Lu UL?t�4T|�L? @?_ �?UL4i M�| L?*) U�hhi?| �?�@|�L?� �ihuLh4@?Ui L? |�i 4�ttTiU��U@|�L?|it|t @?_ it|�4@|it Lu |�i *L?}�h�? igiU|t �ihi �ih) t�4�*@h |L |�Lti LM|@�?i_ �t�?} @?�-(u E�c �c �� 4L_i*� �}@�? |�i O@�t4@? |it| t|@|�t|�U _Lit ?L| hi�iU| i^�@*�|) Mi|�ii?|�i �B @?_ ��B it|�4@|it ���*i |�i w+ |it| t|@|�t|�U Lu 2H� hi�iU|t i^�@*�|) Lu @** |�i*L?}�h�? ULi�U�i?|t� �L|�Ui |�@| �?_ih |�i ?�** �)TL|�it�t |��t t|@|�t|�U �t @t)4T|L|�U@**)_�t|h�M�|i_ @t �2EeS�� W? |��t i @4T*ic it|�4@|it Lu |�i *L?}�h�? ULi�U�i?|t @hi hLM�t| |L|�i Lh_ih Lu |�i �+#w� A��t �t T@h|*) MiU@�ti A �t *@h}i( @t ��** Mi tii? �? |�i ?i | i @4T*ic��i? A �t t4@**c U�L�Ui Lu *@} Lh_ih �t 4Lhi �4TLh|@?|�

`��*i _@|@ uLh ?@|�L?@* _�tTLt@M*i �?UL4i �t ��_i*) @�@�*@M*ic �| �t ?L| |�i 4Lt| @TThLTh��@|i |�iLhi|�U@* 4i@t�hi Lu �?UL4ic tL �i @*tL it|�4@|i_ @? i^�@|�L? �t�?} @ Mi||ih 4i@t�hicTh��@|i _�tTLt@M*i *@ML�h �?UL4i E�?|ihit| @?_ _���_i?_ �?UL4i @hi i U*�_i_�� #@|@ @�@�*�@M�*�|) hi_�Uit |�i t@4T*i |L �D UL�?|h�itc ��|� tL4i UL�?|h�it �@��?} @t ui� @t H LMtih�@|�L?tE|�i �i|�ih*@?_t�� A�i U�@h@U|ih�t|�Ut Lu |��t _@|@ @**L� �t |L �?�it|�}@|i |�i ti?t�|���|) Lu|�i it|�4@|Lht |L @ ?�4Mih Lu �?|ihit|�?} ui@|�hit� A�i T@?i* �t �ih) �?M@*@?Ui_ ��|� A �ih)t4@** �? tL4i U@tit( �? |�iti U@tit U�LLt�?} *@} Lh_ih M) |�i 5�� �t 4Lhi hi*�@M*i |�@? �t�?}@ UL44L? �-(u E�c �c �� ���U� |i?_t |L t�L� 4�ttTiU��U@|�L?� A�ihi �t @*tL @? i |hi4iL�|*�ih� W? 5�i_i?c ��ihi |�i 5�� U�Lti �-(u E�c �c f�c |�i tTii_ Lu @_��t|4i?| �@t �f�f�Ef��De�c |�i *L?}�h�? �?UL4i i*@t|�U�|) �@t ���.e E2D�22� @?_ |�i *L?}�h�? �?�@|�L? ULi�U�i?|�@t �.�.SH Eef��S�� �*|�L�}� |��t i^�@|�L? T@ttit |�i uL�h 4�ttTiU��U@|�L? |it|tc |�i �| �t�ih) TLLh @?_ �| _�t|Lh|t |�i �B it|�4@|it�

A@M*i 2 Thiti?|t |�i @*|ih?@|��i TLL*i_ it|�4@|it Lu |�i *L?}�h�? �?UL4i i*@t|�U�|) uLh|�hii }hL�Tt Lu UL�?|h�it E� ' �Dc �ec @?_ b�c uLh |�hii �+#w tTiU��U@|�L?t� A�i � ' �D}hL�T �?U*�_it @** |�i UL�?|h�it uLh ���U� |�ihi �t _@|@ L? Th��@|i _�tTLt@M*i *@ML�h �?UL4i�A�i � ' �e }hL�T i U*�_it 5�i_i?� A�i � ' b }hL�T @*tL i U*�_it UL�?|h�it uLh ���U� A�t �� Lh *itt EW|@*)c �i|�ih*@?_tc �i� ~i@*@?_c �Lh|�}@*c 5T@�?�� A�i igiU| Lu 5�i_i? L?|�i �B it|�4@|Lh �? |�i � ' �D }hL�T �t �ih) LM��L�tc UL4T*i|i*) _�t|Lh|�?} |�i �-(uE�c �c �� it|�4@|i @?_ ti�ihi*) M�@t�?} |�i 5�� it|�4@|i� A�i ��B it|�4@|it @hi 4�U� *ittti?t�|��ic @t L?i �L�*_ i TiU|c }��i? |�i *@h}i t|@?_@h_ ihhLht L? |�i 5�i_�t� it|�4@|it�#hLTT�?} 5�i_i? uhL4 |�i t@4T*i �@h_*) U�@?}it |�i ��B it|�4@|ic M�| U�@?}it |�i �Bt�Mt|@?|�@**)� �}@�? |�i O@�t4@? |it| t|@|�t|�U _Lit ?L| hi�iU| i^�@*�|) Mi|�ii? |�i �B@?_ ��Bc ���*i |�i w+ |it| t|@|�t|�U hi�iU|t i^�@*�|) Lu @** |�i *L?}�h�? ULi�U�i?|t�

A�iti hit�*|t �?_�U@|i |�@| |�i ��B tii4t ^��|i hLM�t| |L L�|*�iht @?_ |L U�L�Ui Lu *@}Lh_ih� ��ih@** |�i it|�4@|it t�}}it| |�@| |�i @�ih@}i *L?}�h�? �?UL4i i*@t|�U�|) �t h@|�ih*@h}ih |�@? f�bc M�| t�}?��U@?|*) *itt |�@? �?�|) L? ��B t|@?_@h_ ihhLht� OL�i�ihc |�itit|@?_@h_ ihhLht 4@) Mi �?_ihit|�4@|it� A�i @�ih@}i *L?}�h�? �?�@|�L? igiU| �t t�}?��U@?|*)*itt |�@? 3ihL� A�iti }i?ih@* UL?U*�t�L?t tii4 hLM�t| |L *@} Lh_ihc t@4T*i @?_ it|�4@|�L?4i|�L_� A�i @�ih@}i @_��t|4i?| ULi�U�i?| tii4t |L Mi t�}?��U@?|*) *itt |�@? 3ihL @?_}hi@|ih |�@? �f�Dc M�| |�i it|�4@|it Lu |�i @_��t|4i?| ULi�U�i?|t |i?_ |L t�L� 4Lhi ti?�t�|���|) |L |�i U�L�Ui Lu |�i it|�4@|�L? 4i|�L_� A�i i @4T*i Lu |�i UL?t�4T|�L? u�?U|�L?�@t U�Lti? |L _i4L?t|h@|i |�i ��B it|�4@|Lh MiU@�ti Lu �|t u@4�*�@h�|) @?_ �4TLh|@?Ui�OL�i�ihc �| t�L�*_ Mi hiUL}?�3i_ |�@| 4L_i**�?} UL?t�4T|�L? h@�tit 4@?) _��U�*| �tt�it?L| U@T|�hi_ M) |��t t�4T*i 4L_i*� �*i@h*)c |�ihi @hi �4TLh|@?| L4�||i_ �@h�@M*itc �?U*�_�

d�eo

�?} �?�|�@* �i@*|�c hi@* �?|ihit| h@|i igiU|tc Uhi_�| hi}�*@|�L?tc }L�ih?4i?| M�_}i| t�hT*�titE_i�U�|t� @?_ _i4L}h@T��Ut� A��t |)Ti Lu i^�@|�L? �@t ThL�i_ t|h�U|�h@**) �?t|@M*i �? @?�4Mih Lu |�i UL�?|h�it �? L�h t@4T*i� W? 4@?) Lu |�i UL�?|h�it L?i �L�*_ ?L| Mi @M*i |Lhi�iU| |�i ?�** �)TL|�it�t Lu ?L *L?}�h�? hi*@|�L?t��Tc |�L�}� |�iti |it|t �@�i *L� TL�ih�A�i �B it|�4@|it @hi @*tL t�M�iU| |L t4@** A M�@t MiU@�ti Lu |�i u@4�*�@h *@}}i_ _iTi?_i?|�@h�@M*i ThLM*i4�

D�2 ,?ih}) #i4@?_ �? �t�@? #i�i*LT�?} �L�?|h�it

��h tiUL?_ i @4T*i �t i T*@�?�?} |�i *L}@h�|�4 Lu i?ih}) UL?t�4T|�L? E4i@t�hi_ �? AL?tLu ��* ,^���@*i?|tc A�,c Tih U@T�|@�c e�|c M) |�i *L}@h�|�4 Lu hi@* Tih U@T�|@ L�|T�| �?�?|ih?@|�L?@* Th�Uit |@!i? uhL4 |�i �i?? Lh*_ A@M*itc +�|c @?_ M) |�i *L}@h�|�4 Lu hi@*i?ih}) Th�Uit E@�ih@}i i?ih}) Th�Uit Tih A�, �? *LU@* U�hhi?U)c _i�@|i_ M) |�i UL?t�4ihTh�Ui �?_i �c R�|� A�i _@|@ @hi uLh |i? �t�@? _i�i*LT�?} UL�?|h�it uLh |�i )i@ht �b.e��bbf(|��t ML|� � @?_ A @hi t4@**� A��t i @4T*i �t _h@�? uhL4 �it@h@?c 54�|� @?_ �!�)@4@E�bbH� ���U� _�tU�ttit |�i _@|@ �? 4Lhi _i|@�* @?_ �?�it|�}@|it u�?U|�L?@* uLh4c _)?@4�Utc_�t@}}hi}@|�L? @?_ �@h�L�t L|�ih �tt�it�

A�i �?�|�@* �?hit|h�U|i_ 4L_i* �t @ T@h|�@* @_��t|4i?| E�+#wE�cfcf�� 4L_i*G

{e�| ' ��Ee�|3� � wf� � w��+�| � w2�R�|� n 0�|c � ' �c 2c ���c �f�

�@h|�@* @_��t|4i?| @?_ �L4L}i?i�|) Lu _i}hii 3ihL �? Th�Uit �ihi ?L| hi�iU|i_ �? @** M�|L?i Lu |�i |i? UL�?|h�it EA@��@?�� W? |�i UL�?|h)�tTiU��U hi}hitt�L?tc |�i *L?}�h�? �?UL4i@?_ Th�Ui i*@t|�U�|) it|�4@|it uLh �@*@)t�@c 5h� w@?!@ @?_ �@?}*@_it� @hi �4T*@�t�M*ic ���U�UL�*_ Mi _�i |L _@|@ �?@_i^�@U�it @?_ |�i ��}� *i�i* Lu @}}hi}@|�L?� �T@h| uhL4 |�itic |�iit|�4@|it @hi hi@tL?@M*i� A�i *L?}�h�? �?UL4i i*@t|�U�|) h@?}it uhL4 f�H�D |L ��DSe ��|� @?@�ih@}i Lu ���2c @?_ |�i *L?}�h�? Th�Ui i*@t|�U�|�it h@?}i uhL4 f�fD |L �f�eHH ��|� @? @�ih@}iit|�4@|i Lu �f�22� �** |�i it|�4@|it Lu |�i @_��t|4i?| ULi�U�i?|tc ��c @hi ?i}@|��i @?_ u@**�? |�i h@?}i E�f���2 |L �f�H2D�� A�i t|@?_@h_ ihhLh Lu |�i hi}hitt�L? �@h�it uhL4 ��. Tih Ui?|�? |�i U@ti Lu A�@�*@?_ |L S�� Tih Ui?| �? |�i U@ti Lu 5h� w@?!@( tL @}@�? |�i @tt�4T|�L?Lu UL?t|@?| ihhLh �@h�@?Uit @UhLtt UL�?|h�it tii4t �?@TThLTh�@|i� #�@}?Lt|�U |it|t hi�i@* ui�ThLM*i4tG @| |�i DI *i�i* L?i u@�*�hi uLh tih�@* ULhhi*@|�L? @?_ L?i uLh ?Lh4@*�|)� `�i? |�iLh_ih Lu i@U� *@} �t U�Lti? M) |�i 5�� uLh i@U� UL�?|h)c t|@h|�?} ��|� @ }i?ih@* �+#wE�c�c��tTiU��U@|�L?c |�i �+#wE�cfcf� �t U�Lti? uLh ti�i? UL�?|h�itc @ t|@|�U 4L_i* �t U�Lti? uLh W?_�@@?_ 5h� w@?!@c @?_ @? �?t|@M*i �+#wE�cfc�� �t U�Lti? uLh A@��@?�

A�i @*|ih?@|��i TLL*i_ it|�4@|Lht uLh |�i �+#wE�cfcf� tTiU��U@|�L? @hi Thiti?|i_ �?A@M*i �� A�i |@M*i Thiti?|t it|�4@|it Lu |�i *L?}�h�? L�|T�| @?_ Th�Ui i*@t|�U�|�it @?_ |�i@_��t|4i?| ULi�U�i?|tc |L}i|�ih ��|� |�i �@ �4�ti_ wL}�w�!i*��LL_ E�ww�c |�i ?�4Mih LuLMtih�@|�L?t @?_ |�i ?�4Mih Lu T@h@4i|iht it|�4@|i_ E�?U*�_�?} |�i ihhLh �@h�@?Uit�� �t�? |�i Thi��L�t i @4T*ic w�!i*��LL_ +@|�L Ew+� |it|t hi�iU| |�i �)TL|�it�t Lu i^�@*�|) Lu*L?}�h�? ULi�U�i?|t ��ihi@t O@�t4@? |it|t _L ?L| hi�iU| |��t �)TL|�it�t ��i? |�i ��B@?_ �B it|�4@|Lht @hi UL4T@hi_� 5�?Ui |�i �B it|�4@|it �@�i *@h}i t|@?_@h_ ihhLhtc |�iO@�t4@? |it| �t *�!i*) |L �@�i *L� TL�ih� Wu |�i uLU�t Lu |�i @?@*)t�t �t L? @�ih@}i E@UhLttUL�?|h�it� �?UL4i @?_ Th�Ui i*@t|�U�|�itc |�i? |�i ��B it|�4@|it @hi ThLM@M*) Thiuih@M*i |L|�i �B it|�4@|it L? |�i }hL�?_t Lu |�i�h Mi||ih ThiU�t�L? @?_ |�i u@U| |�@| |�i) @hi *itt

d�Do

ti?t�|��i |L L�|*�ih it|�4@|it� W? |��t UL?|i | |�i O@�t4@? |it| U@? Mi tii? @t ThL��_�?}uLh4@* t|@|�t|�U@* i��_i?Ui |�@| �i @hi ?L| �? }hLtt ��L*@|�L? Lu |�i _@|@ M) hi*)�?} L? ��Bit|�4@|it h@|�ih |�@? |�i �B it|�4@|it� A�i it|�4@|it t�}}it| @ *L?}�h�? �?UL4i i*@t|�U�|)Lu ���H Ef�f�b� @?_ @ Th�Ui i*@t|�U�|) Lu �f��e Ef�f���� A�i ��B it|�4@|it @hi U*Lti |L |�i�B it|�4@|itc @?_ |�i #6, it|�4@|it @hi h@|�ih *@h}ih� A�i _)?@4�Ut U*i@h*) 4@||ih @?_|�i t|@|�U � i_ igiU|t it|�4@|Lh �@t @? �?t�}?��U@?| Th�Ui igiU|� A�i t|@?_@h_ ihhLht Lu ML|�|�i ��B @?_ |�i #6, @hi �ih) 4�U� t4@**ih |�@? |�Lti Lu |�i �B( TLL*�?} t�@hTi?t |�iit|�4@|it UL?t�_ih@M*)� �t MiuLhi TLL*�?} @*tL *i@_t |L @ 4�U� t4@**ih it|�4@|i_ tTii_ Lu@_��t|4i?|( |�i �B it|�4@|it t�}}it| tTii_t Lu UL?�ih}i?Ui |L i^��*�Mh��4 Lu @hL�?_ DfTih Ui?| @ )i@hc |�i ��B �f Tih Ui?|c |�i #6, @ML�| 2f Tih Ui?|�

A@M*i e }��it �B @?_ ��B it|�4@|it ��i? |�i Lh_ih Lu |�i tTiU��U@|�L? �? |�i �?_����_�@* UL�?|h�it �t U�Lti? M) |�i 5��� A��t ThLUi_�hi U@??L| Mi �ti_ ��|� |�i � i_ igiU|it|�4@|Lh @?_ |�i �+#wE�c�c�� it|�4@|it @hi }��i? �?t|i@_� �}@�? |�i ��B it|�4@|it Lu |�i*L?}�h�? Th�Ui @?_ �?UL4i i*@t|�U�|�it �@h_*) U�@?}ic |�L�}� |�i it|�4@|i_ tTii_ Lu @_��t|�4i?| �t h@|�ih ��}�ihc T@h|*) MiU@�ti |�i 5�� U�LLtit |�i t|@|�U 4L_i*c ��|� �?t|@?|@?iL�t@_��t|4i?|c �? |�i U@ti Lu tL4i UL�?|h�it� Nt�?} |�i 5�� }��it @ t�Mt|@?|�@* �4ThL�i4i?|�? |�i �ww uLh |�i �B it|�4@|Lh E@| �D. �| �t U*Lti |L |�i �+#wE�c�c�� �ww Lu �S2c ��|� u@hui�ih T@h@4i|iht� M�| *itt uLh |�i ��Bc ��ihi |�i 5�� �ww �t �Lhti |�@? |�i �+#wE�cfcf��ww� W| �t U*i@h |�@| �L4L}i?i�|) hit|h�U|�L?t @?_ _)?@4�U tTiU��U@|�L? �?|ih@U| �? @ UL4�T*i �@)� `�@| 4�}�| Mi |�i LT|�4@* Lh_ih uLh |�i UL�?|h)�tTiU��U it|�4@|it 4@) ?L| Mi |�iLT|�4@* Lh_ih ��i? UhLtt�UL�?|h) �L4L}i?i�|) hit|h�U|�L?t @hi �4TLti_� A�i h@|�ih tih�L�tTL*�U) �4T*�U@|�L?t Lu @? �?UL4i i*@t|�U�|) @hL�?_ ��2 @?_ @ Th�Ui i*@t|�U�|) @hL�?_ �f�� @hi_�tU�tti_ �? �it@h@?c 54�|� @?_ �!�)@4@ E�bbH��

S �L?U*�_�?} +i4@h!t

A�i �LL*i_ �i@? BhL�T it|�4@|Lh ���U� @tt�4it �L4L}i?iL�t *L?}�h�? ULi�U�i?|t ThL���_it @ �tiu�* �?|ih4i_�@|i @*|ih?@|��i Mi|�ii? it|�4@|�?} tiT@h@|i hi}hitt�L?tc ���U� @**L�t@** ULi�U�i?|t @?_ ihhLh �@h�@?Uit |L _�gih @UhLtt |�i }hL�Ttc @?_ UL?�i?|�L?@* � i_ igiU|tit|�4@|Lhtc ���U� @tt�4i |�@| @** t*LTi ULi�U�i?|t @?_ ihhLh �@h�@?Uit @hi |�i t@4i� W|�@t |�i Th@U|�U@* @_�@?|@}i |�@| |�i t�Lh|�h�? _)?@4�Ut U@? Mi _@|@ _i|ih4�?i_ uLh i@U�UL�?|h)c |@!�?} @UUL�?| Lu |�i ?�4Mih Lu |�4i tih�it LMtih�@|�L?t @�@�*@M*i �? i@U� U@ti�A�ihi @hic �L�i�ihc @ ?�4Mih Lu �?hitL*�i_ �tt�it� 6Lh t4@** A @** |�i it|�4@|Lht E}hL�T�tTiU��Uc �i@? BhL�Tc �LL*i_ �i@? BhL�T @?_ � i_ igiU|t� ��** Mi t�M�iU| |L |�i u@4�*�@h_L�?�@h_ M�@t L? |�i ULi�U�i?| Lu |�i *@}}i_ _iTi?_i?| �@h�@M*i� 5�?Ui |�i M�@t �t �? |�it@4i _�hiU|�L? uLh i@U� }hL�Tc @�ih@}�?} Lh TLL*�?} _Lit ?L| hi_�Ui |��t M�@t� A�ihi @hiM�@t ULhhiU|�L?t @�@�*@M*i �? |�i *�|ih@|�hi Ei�}� k���i| @?_ ���**�Ttc�bb��c M�| |�iti @TT*)|L |�i t�Lh|�h�? ULi�U�i?|t� �iU@�ti |�i *L?}�h�? ULi�U�i?| �t @ ?L?�*�?i@h u�?U|�L? Lu |�it�Lh|�h�? ULi�U�i?|tc ThLUi_�hit ���U� hi4L�i |�i M�@t �? |�i t�Lh|�h�? ULi�U�i?|t U@?*i@�i |�i *L?}�h�? ULi�U�i?| M�@ti_� �it@h@? @?_ ~�@L E�bbH� _�tU�tt �L� |�i M�@t �? |�i*L?}�h�? ULi�U�i?| U@? Mi hi_�Ui_� A�i �i@? BhL�T it|�4@|Lh �ti_ �? |��t T@Tih �t @t�4T*i �?�i�}�|i_ 4i@? Lu |�i ULi�U�i?|t� i�}�|i_ 4i@?t @hi @? LM��L�t @*|ih?@|��i @?_Ot�@Lc �it@h@? @?_ A@�4�tU�L}*� E�bbH� UL?t�_ih �@)it it|�4@|�L? Lu |�i 4i@?t Lu t�Lh|�h�?ULi�U�i?|t �? _)?@4�U T@?i* _@|@ 4L_i*t� ,t|�4@|�L? �? |��t T@Tih �@t UL?_�U|i_ �?_ih

d�So

|�i @tt�4T|�L? |�@| |�ihi i �t|i_ @ *L?}�h�? hi*@|�L?t��T� W| �L�*_ Mi �tiu�* |L �@�i @ T@?i*|it| uLh |�i i �t|i?Ui Lu @ *L?}�h�? hi*@|�L?t��T ��i? |�i �@h�@M*it @hi UE��c t�4�*@h |L |�iT@?i* �?�| hLL| |it| t�}}it|i_ �? W4c �it@h@? @?_ 5��? E�bb.��

�ih�@Tt |�i 4Lt| �4TLh|@?| �tt�i �t |�i �?|ihThi|@|�L? Lu |�i �i|ihL}i?i�|)� �Lt| t|�_�it���U� it|�4@|i tiT@h@|i hi*@|�L?t��Tt uLh @ ?�4Mih Lu }hL�Tt �?_ _�gihi?Uit �? ULi�U�i?|t���U� @hi ?L| L?*) t|@|�t|�U@**) t�}?��U@?|c M�| iUL?L4�U@**) �4T*@�t�M*i� W? L�h i4T�h�U@*i @4T*it |�i �?UL4i i*@t|�U�|) Lu UL?t�4T|�L? L�| Lu *@ML�h �?UL4i �? 5�i_i? @?_ |�i�?UL4i i*@t|�U�|) Lu _i4@?_ uLh i?ih}) �? 5h� w@?!@ �ihi t�U� U@tit� #itT�|i |��t |�i 4i@?}hL�T Lh TLL*i_ it|�4@|it Lu |�i *L?}�h�? ULi�U�i?|t |i?_ |L Mi ti?t�M*i� �?i i T*@?@|�L?�t |�@| |�i }hL�T tTiU��U it|�4@|it @hi M�@ti_ MiU@�ti Lu t@4T*i�tTiU��U L4�||i_ �@h�@M*itLh 4i@t�hi4i?| ihhLht |�@| @hi ULhhi*@|i_ ��|� |�i hi}hittLht� Wu L?i �@t it|�4@|�?} @?i^�@|�L? uLh @ t�?}*i }hL�Tc L?i 4�}�| i Tih�4i?| ��|� _�gihi?| tTiU��U@|�L?t Lh @*|ih?@|��i_@|@ �?|�* T*@�t�M*i it|�4@|it @hi LM|@�?i_� `�i? it|�4@|�?} i^�@|�L?t uLh *@h}i ?�4MihtLu }hL�Ttc ��ihi ?L L|�ih _@|@ �t @�@�*@M*i �? 4@?) U@titc |��t �t ?L| @? LT|�L?� Wu |�iULi�U�i?|t hi@**) @hi |�i t@4i @?_ |�i M�@t �?_�U�?} ULhhi*@|�L?t @hi ?L| t)t|i4@|�U E��i�|�i) @�ih@}i |L 3ihL L�ih }hL�Tt�c |�i? TLL*i_ it|�4@|�L? ��** Mi @TThLTh�@|i _itT�|i |�i�L4L}i?i�|) hit|h�U|�L?t Mi�?} hi�iU|i_� OL�i�ihc |�ihi �t ?L LM��L�t �@) Lu _i|ih4�?�?}uhL4 |�i _@|@ |�@| |��t �t |�i U@ti� A��t h@�tit LM��L�t ThLM*i4t uLh �?uihi?Ui ���U� hi^��hiu�h|�ih @?@*)t�t�

d�.o

Wdeoh 4= Dowhuqdwlyh srrohg hvwlpdwhv iru DUGO+4/4/4, frqvxpswlrq ixqfwlrqv

iru RHFG frxqwulhv ryhu wkh shulrg 4<950<6 xvlqj qdwlrqdo glvsrvdeoh lqfrph

Phdq Jurxs Srrohg Phdq Jurxs G|qdplf Il{hg H�hfw

Lqfrph hodvwlflw|/ �4 31<4; +3135:, 31<37 +31343, 31<45 +31378,

Lq�dwlrq h�hfw/ �5 031686 +3144:, 031799 +31396, 031599 +313<<,

Vshhg ri Dgmxvwphqw/ ! 031639 +31363, 031533+31365, 0314:< +31375,

Pd{lplvhg Orj Olnholkrrg 56<3 557: 4<<<

Qxpehu ri Sdudphwhuv Hvwlpdwhg 49; 455 63

Wdeoh 5=Dowhuqdwlyh srrohg hvwlpdwhv ri wkh orqj0uxq frqvxpswlrq lqfrph hodvwlflw|

xvlqj shufdslwd uhdo sulydwh glvsrvdeoh oderxu lqfrph

Q DUGO Phdq Jurxs Srrohg Phdq Jurxs G|qdplf Il{hg H�hfwv

48 4/3/3 3=<7; +=3:3, 3=<66 +=343, 3=<69 +=355,

48 4/4/4 �45=; +46=;, 3=<4; +=349, 3=<68 +=356,

48 VEF 3=99< +=64<, 3=<6; +=346, Q@D

47 4/3/3 3=<<< +=385, 3=<67 +=343, 3=<7 +=345,

47 4/4/4 3=<4; +=399, 3=<4< +=349, 3=<76 +=354,

47 VEF 3=<;8 +=387, 3=<6< +=346, Q@D

< 4/3/3 3=<<6 +=393, 3=<59 +=344, 3=<64 +=347,

< 4/4/4 3=<49 +=433, 3=<5: +=348, 3=<58 +=358,

< VEF 3=<<8 +=38<, 3=<74 +=346, Q@D

A@M*i �G �*|ih?@|��i TLL*i_ it|�4@|Lht uLh �+#wE�cfcf� i?ih}) _i4@?_ u�?U|�L?

uLh |i? �t�@? iUL?L4�it L�ih |�i Tih�L_ �b.e��bbf

�i@? BhL�T �LL*i_ �i@? #)?@4�U 6� i_ 5|@|�U 6� i_

,t|�4@|Lht BhL�T ,t|�4@|Lht ,giU|t ,t|�4@|Lht ,giU|t ,t|�4@|Lht

Rxwsxw 4155; 414;7 41634 4133<Hodvwlflw| Ew�� +314;6, +3136<, +3143<, +3136:,

Sulfh 031594 03166< 031698 03139:Hodvwlflw| Ew2� +3144;, +31366, +313<:, +31363,Dgmxvwphqw 031857 0315<; 031568 04Frh�flhqw Ee�� +313:3, +31396, +31373, +Q2D,Orj0olnholkrrg 67:145 6551:< 5;;169 4;91<8

� f A 4:3 4:3 4:3 4:3Qr1 ri Hvwlpdwhg 83 65 48 46

Sdudphwhuv

A@M*i eG �*|ih?@|��i TLL*i_ it|�4@|Lht uLh �+#w�5�� i?ih}) _i4@?_ u�?U|�L?

�i@? BhL�T �LL*i_ �i@? #)?@4�U 6� i_

,t|�4@|Lht BhL�T ,t|�4@|Lht ,giU|t ,t|�4@|Lht �+#wE�c�c��

Rxwsxw 415:: 414:4 414;4Hodvwlflw| Ew�� +314;5, +31369, +3147:,

Sulfh 031493 031634 031657Hodvwlflw| Ew2� +31497, +3135;, +31346:,Dgmxvwphqw 031835 03174: 031486Frh�flhqw Ee�� +31446, +31454, +31375,Orj0olnholkrrg 6891;4 648174 63315:

� f A 4:3 4:3 4:3Qr1 ri Hvwlpdwhg 84 66 4:

Sdudphwhuv

W? @** |�i @ML�i |@M*it �}�hit �? T@hi?|�itit @hi @t)4T|L|�U t|@?_@h_ ihhLht� W? |�i U@ti Lu |�i _)?@4�U � i_ igiU|t

it|�4@|it |�i t|@?_@h_ ihhLht @hi ULhhiU|i_ uLh TLtt�M*i �i|ihLt!i_@t|�U�|) �? |�i UhLtt�tiU|�L?@* ihhLh �@h�@?Uit�

dA��o

� �TTi?_� G �@|�i4@|�U@* �hLLutWr vdyh vsdfh zh jlyh wkh surriv rqo| iru fdvh zkhuh wkh uhjuhvvruv duh L+4,1 Surri iru wkh L+3, fdvh lv jlyhq

lq wkh Dsshqgl{ wr wkh hduolhu yhuvlrq ri wkh sdshu +Shvdudq/ Vklq/ dqg Vplwk/ 4<<:,1

��� �hi*�4�?@h) +it�*|t

����� 5L4i �tiu�* ThLM@M�*�|) *�4�|t

Wr vlpsoli| wkh qrwdwlrqv lq zkdw iroorzv zh ghqrwh �l+�, e| �

ldqg �

l+�3, e| �

l31 Zkhq {lw duh doo L+4,/

wkh iroorzlqj suredelolw| olplwv h{lvw dv W $4/ iru hdfk l=

W�5[3

lKl[l , U[l[l

> W�4[3

lKl�l3 , U[l�l3 > W�4[3

lKl%l @ Rs+4,> +D14,

zkhuh U[l[ldqg U[l�l3 duh Rs+4, udqgrp pdwulfhv1 Zh dovr kdyh

W�4

5 �3l3Kl%l @ Rs+4,> W�4�3l3Kl�l3s$ t�l3�l3 > dqg W�4%3lKl%l @ �5l3 . rs+4,> l @ 4> ===> Q=

+D15,

����2 #iUL4TLt�|�L? Lu |�i *L}�*�!i*��LL_ h@|�L

Xvlqj +61;, lw lv hdvlo| vhhq wkdw

W�4 ^cW +*3,� cW +*,` @

4

5+DW . EW ,> +D16,

zkhuh

DW @ D� . FW > +D17,

D� @

Q[l@4

��5l3

�5l� oq

�5l3

�5l� 4

�> FW @

Q[l@4

�4

�5l�

4

�5l3

��%3lKl%l

W� �5l3

�> +D18,

EW @ W�4

Q[l@4

4

�5l^+�|l � !l�l,

3Kl+�|l � !l�l,� %3

lKl%l` = +D19,

Dovr xvlqj wkh uhvxow

!l�l @ +!l � !l3 . !l3,+�l � �l3 . �l3, @ �!l[l+� � �3, . +!l � !l3,�l3 . !l3�l3>

dqg qrwlqj wkdw �|l @ !l3�l3 .Zl�l3 . %l/ zh kdyh44

�|l � !l�l @ %l .Zl�l3 . !l[l+� � �3,� +!l � !l3,�l3= +D1:,

Vxevwlwxwlqj +D1:, lq +D19,/ dqg diwhu vrph dojheud zh kdyh=

EW @ +� � �3,3

#Q[l@4

!5l�5l

[3

lKl[l

W

$+� � �

3, .

Q[l@4

�+!l � !l3,

5

�5l

���3l3Kl�l3

W

�

�5

Q[l@4

�!l+!l � !l3,

�5l

���3l3Kl[l+� � �3,

W

�. 5+� � �3,

3

#Q[l@4

!l

�5l

[3

lKl%l

W

$

�5

Q[l@4

�+!l � !l3,

�5l

���3l3Kl%l

W

�> +D1;,

44Vhh +619,/ dqg qrwh wkdw xqghu wkh gdwd jhqhudwlqj surfhvv * @ *31

dA�2o

zklfk fdq dovr eh zulwwhq pruh frpsdfwo| dv +uhfdoo wkdw # @ +�3>!3,3,

EW @ +# �#3,3JW +# �#3

, . 5+# �#3,3iW > +D1<,

zkhuh

JW @

59999999999997

SQ

l@4

!5l

�5l

[3

lKl[l

W�

!4�54

[3

4K4�43W

� � � �

!Q�5Q

[3

QKQ�

Q3

W

�

!4�54

�3

43K4[4

W4

�54

�3

43K4�43W

� � � 3

�

!5�55

�3

53K5[5

W3 � � � 3

111111

111111

�

!Q�5Q

�3

Q3KQ[Q

W3 � � �

4

�5Q

�3

Q3KQ�

Q3

W

6::::::::::::8

> iW @

599999997

SQ

l@4!l�5l

[3

lKl%lW

�

4

�54

�3

43K4%4W

111

�

4

�5Q

�3

Q3KQ%QW

6:::::::8=

+D143,

Lq whupv ri wkh pdwul{ qrwdwlrqv xvhg lq Vhfwlrq 6/ JW fdq dovr eh zulwwhq dv

JW @ ]3

4+*,

kL� �Z+�,

��Z

3+�, �Z+�,��4

�Z3+�,

l]4+*, +D144,

zkhuh ]4+*, @

��[+!>�,

111��+�>�,

�/ �[+!>�, @ � ^+!4@�4,[

3

4> +!5@�5,[

3

5> ===> +!Q@�Q ,[3

Q ,`3

/ dqg �Z+�, dqg

��+�>�, duh eorfn gldjrqdo pdwulfhv zlwk wkhlu l0wk eorfnv jlyhq e| Zl@�l dqg �l+�,@�l/ uhvshfwlyho|/ zlwk

� @ �31 Wkhuhiruh/ JW lv wkh sduwlwlrqhg lqyhuvh ri wkh xsshu0ohiw kdqg fruqhu ri

]3+*,]+*, @

�]3

4+*,]4+*, ]34+*,�Z+�,

�Z3+�,]4+*,�Z3+�, �Z+�,

�>

zlwk * @ *31 Khqfh/ xqghu Dvvxpswlrq 618 JW lv dovr d srvlwlyh gh�qlwh pdwul{1

��2 �hLLu Lu A�iLhi4 e�2 � A�i �@ti Lu WE�� +i}hittLht

Sduwlwlrq * @ +�3>�3,3 lqwr wkh orqj0uxq sdudphwhuv/ �> dqg wkh vkruw0uxq sdudphwhuv/ � @ +!3>�3,31 Gh�qh

wkh rshq edoo E+�3> ��, @ i� 5 �� = n� � �3n ? ��j/ dqg lwv frpsohphqw E+�3> ��, @ i� 5 �� = n� � �3n ���j1

Wr suryh wkh frqvlvwhqf| ri wkh PO hvwlpdwru ri � +ghqrwhg e| a�,/ lw lv vx�flhqw wr vkrz wkdw iru dooydoxhv ri � 5 �� @ �! ��

�dqg iru hyhu| �� A 3> +vhh/ iru h{dpsoh/ Vdlnnrqhq +4<<8/ s1<36,,/

olpW$4

Su

�lqi

*5 �E+�3>��,���

W�4 ^cW +*3,� cW +*,` A 3

�@ 4= +D145,

Xvlqj wkh uhvxowv lq +D14, dqg +D15, dqg xqghu Dvvxpswlrq 617 lw lv hdvlo| vhhq wkdw h{fhsw iru wkh �uvw whuplq +D1;, wkh lqi ryhu * 5 �E+�3> ��,��� ri doo wkh rwkhu whupv duh dw prvw Rs+4,1 Wkhuhiruh/

lqi*5 �E+�3>��,���

W�4 ^cW +*3,� cW +*,` � W lqi*5 �E+�3>��,���

++� � �3,

3

#Q[l@4

!5l�5l

[3

lKl[l

W 5

$+� � �3,

,.Rs+4,

� W�5��plq+UW , .Rs+4,> +D146,

zkhuh �plq+UW , lv wkh vpdoohvw hljhqydoxh ri UW @SQ

l@4!5l

�5l

[3

lKl[l

W5 gh�qhg ryhu ��1 Dv W $ 4/ UW

frqyhujhv wr U @SQ

l@4!5l

�5l

U[l[lzlwk suredelolw| 4/ zkhuh U[l[l

lv jlyhq e| +D14,1 Exw xqghu Dvvxpswlrqv

617 dqg 618/SQ

l@4!5l

�5l

U[l[llv d srvlwlyh gh�qlwh pdwul{ zlwk suredelolw| 4 iru doo ydoxhv ri � 5 ��1 Khqfh/

dA��o

dv W $4> �plq+UW , dovr zhdno| frqyhujhv wr �plq+U, A 3/ dqg wkh uljkw kdqg vlgh ri +D146, zloo lqfuhdvh

zlwkrxw erxqgv zlwk suredelolw| 4/ zklfk hvwdeolvkhv wkh frqvlvwhqf| ri a�1

Wr suryh wkh vxshu0frqvlvwhqf| ri a�/ dqg wkh frqvlvwhqf| ri wkh PO hvwlpdwruv ri wkh rwkhu sdudphwhuv

zh gh�qh E+�3> ��, @ i� 5 �� = n�� �3n ? ��j/ E+!3> �!, @ i! 5 �! = n!� !

3n ? �!j/ E+�3> ��, @ i� 5�� = n� � �3n ? ��j dqg wkhlu frpsohphqwv/ E+�3> ��,/ E+!3> �!,/ dqg

�E+�3> ��,> uhvshfwlyho|/ dqg iroorz

Vdlnnrqhq +4<<8, dqg gh�qh wkh rshq vkulqnlqj edoo QW +�3> �g, @ i� 5 �� = W4

5 n� � �3n ? �gj iru �/ dqg

lwv frpsohphqw QW +�3> �g, @ i� 5 �� = W4

5 n� � �3n � �gj1 Vlqfh wkh frqvlvwhqf| ri a� lv douhdg| hvwdeolvkhg

zh irfxv rxu dqdo|vlv rq ydoxhv ri � forvh wr �3 gh�qhg e| � @ �3 . W�4@5g/ zkhuh zh wdnh g wr eh d n � 4

yhfwru ri �{hg frqvwdqwv gh�qhg rq d frpsdfw vhw1 Wkh fdvh zkhuh hohphqwv ri g duh doorzhg wr lqfuhdvh

zlwkrxw erxqg lv douhdg| fryhuhg deryh1 Qrwlfh wkdw rq QW +�3> �g, zh dovr kdyh ngn � �g1

Ohw F+*3> ��> �g, @ ^�g>��

�QW +�3> �g,�E+�3> ��,

�/ zkhuh wkh xqlrq lv wdnhq ryhu doo ydoxhv ri �g dqg ��

vxfk wkdw �* @ +�5g . �5�,4@5 dqg �� @ +�5! . �5�,

4@51 Zh qrz suryh wkdw iru hyhu| �* A 3/

olpW$4

Su

�lqi

*5F+*3>��>�g,

W�4 ^cW +*3,� cW +*,` A 3

�@ 4= +D147,

Xvlqj +D17, dqg +D1<, lq +D16,/ zh �uvw qrwh wkdw

5 lqi W�4 ^cW +*3,� cW +*,` � lqi+D�, . lqi+FW , . lqi ^+# �#

3,3JW +# �#

3,`

.5 lqi ^+# �#3,3iW ` > +D148,

zkhuh lw lv qrz dvvxphg wkdw doo wkh lqi rshudwlrqv duh wdnhq ryhu wkh vhw * 5 F+*3> ��> �g,1 Exw

+# �#3,3iW @ g

3

Q[l@4

!l

�5l

[3

lKl%l

W 6@5�

Q[l@4

+!l � !l3,

�5l

�3l3Kl%l

W= +D149,

Wkhuhiruh/ xvlqj wkh uhvxowv lq +D14, dqg +D15, dqg uhfdoolqj wkdw g dqg � duh gh�qhg rq frpsdfw vhwv/ lw

wkhq iroorzv wkdw lqi ^+# �#3,3iW ` @ rs+4,= Dovr iurp +D15, lw lv hdvlo| vhhq wkdw FW @ rs+4,1 Xvlqj wkhvh

uhvxowv lq +D148,/ zh qrz kdyh

5 lqi W�4 ^cW +*3,� cW +*,` � lqi+D�, . lqi ^+# �#

3,3JW +# �#

3,` . rs+4,> +D14:,

zkhuh lw lv djdlq dvvxphg wkdw doo wkh lqi rshudwlrqv duh wdnhq ryhu wkh vhw * 5 F+*3> ��> �g,1 Exw wkh l0wk

whup lq D�/ qdpho|��5l3@�

5

l

�� oq

��5l3@�

5

l

�� 4 dwwdlqv lwv xqltxh plqlpxp dw

��5l3@�

5

l

�@ 4/ dqg lv vwulfwo|

srvlwlyh iru doo ihdvleoh ydoxhv ri �5l qrw htxdo wr �5l3/ iru doo l @ 4> 5> ===> Q 1 Khqfh/ lqi+D�, A 3 / �� A 31 Wr

hvwdeolvk +D147, lw lv wkhuhiruh vx�flhqw wr suryh wkdw hyhq li �� @ 3 wkhuh h{lvwv �* A 3 vxfk wkdw

olpW$4

Su ilqi i+# �#3,3JW +# �#

3,j A 3j @ 4=

Wr wklv hqg �uvw qrwh wkdw

+# �#3,3JW +# �#

3, @ ^N#+# �#

3,`3

JW ^N#+# �#3,` >

zkhuh N# @ gldj+W 4@5Ln> LQ ,/ N#+# �#

3, @ & @ +g3> +!� !3,

3,3> dqgJW @ N�4

# JWN�4

# 1 Khqfh

lqi i+# �#3,3JW +# �#3

,j � �5&�plq+JW ,>

zkhuh �plq

+JW , lv wkh vpdoohvw hljhqydoxh ri JW / dqg �& @ +�5g. �5!,4@5 A 3145 Dv W $4/ �

plq+JW , frqyhujhv

zhdno| wr �plq

+J, A 3/ zklfk lv wkh vpdoohvw hljhqydoxh ri J/ zkhuh

J @

599997

SQl@4

!5l

�5l

U[l[l3 � � � 3

34

�54

t�43�43 � � � 3

111111

111111

3 3 � � �4

�5Q

t�Q3�Q3

6::::8>

45Qrwlfh wkdw iru �� @ 3 zh kdyh �& @ �* A 31 Lq wkh fdvh zkhuh �� A 3/ +D14:, zloo eh vdwlv�hg hyhq li

�& @ 31

dA�eo

dqg U[l[ldqg t�l3�l3 / l @ 4> 5> ==> Q / duh gh�qhg lq +D14, dqg +D15,/ uhvshfwlyho|1 Exw xqghu Dvvxpswlrqv

614/ 617/ 618 +l, dqg +lll, J lv srvlwlyh gh�qlwh zlwk suredelolw| 4/ dqg khqfh �plq

+J, A 3 zlwk suredelolw|

41Khqfh iru vx�flhqwo| odujh W lqi i+# �#3,3JW +# �#3

,j A 31 Wklv frpsohwhv wkh surri dqg hvwdeolvkhv

wkh ghvluhg frqvlvwhqf| dqg vxshu0frqvlvwhqf| uhvxowv jlyhq e| +71:,1

Lq rughu wr ghulyh wkh dv|pswrwlf glvwulexwlrq ri wkh PO hvwlpdwruv ri � dqg !l> l @ 4> ===> Q / zh

vkrxog qrz doorz iru wkh idfw wkdw lq wklv fdvh wkh gl�huhqw frpsrqhqwv ri wkh vfruh yhfwru dqg wkh vdpsoh

lqirupdwlrq pdwul{ frqyhujh wr wkhlu wuxh ydoxhv dw gl�huhqw udwhv1 Ohw G# @ gldj+W�4Ln> W

�4

5 LQ ,/ dqg

gh�qh=

FW +#, @ G# ^CcW +*,@C#` > /W +#, @ G#

��C5cW +*,@C#C#

3�G#= +D14;,

Wkhq xvlqj vwdqgdug uhvxowv iurp wkh xqlw urrw olwhudwxuh lw fdq eh hvwdeolvkhg wkdw +vhh/ iru h{dpsoh/ Skloolsv

dqg Gxuodxi/ 4<;9,=

FW +#3,d�PQ i3> /+#3

,j > /W +#3,, /+#

3,> +D14<,

zkhuh wkh +n .Q,� +n .Q, pdwul{

/+#3, �

599997

SQ

l@4

!5l3

�5l3

U[l[l3 � � � 3

34

�543

t�43�43 � � � 3

111111

111111

3 3 � � �4

�5Q3

t�Q3�Q3

6::::8> +D153,

lv wkh udqgrp lqirupdwlrq pdwul{/ zklfk lv srvlwlyh gh�qlwh zlwk suredelolw| 41

Qrz xvlqj wkh phdq0ydoxh h{sdqvlrq ri CcW +a*,@C# durxqg #3dqg vwdqgdugl}lqj wkh uhvxow e| G#/ zh

kdyh

G�4

# +a# �#3, @ /W +�#,

�4FW +#3,> +D154,

zkhuh wkh +l> m, hohphqw ri C5cW +�*,@C#C#3 lv hydoxdwhg dw + �*l> �*m,/ dqg �*l lv d frqyh{ frpelqdwlrq ri *l3

dqg a*l1

Qrwlfh/ krzhyhu/ wkdw lq wkh fdvh ri wkh prghov zlwk xqlw urrw uhjuhvvruv wkh vdpsoh lqirupdwlrq pdwul{

/W +�#, qhhg qrw frqyhujh zhdno| wr /+#3, hyhq zkhq a# frqyhujhv wr #

31 Wr hqvxuh wkdw vxfk d frqyhujhqfh

wdnhv sodfh wkh vdpsoh lqirupdwlrq pdwul{ /W +#, vkrxog vdwlvi| wkh vwrfkdvwlf htxl0frqwlqxlw| frqglwlrq +vhh/

iru h{dpsoh/ Vdlnnrqhq /4<<8/ Frqglwlrq VHr rq s1 ;<7,1 Wklv uhvxow lv vxppdul}hg lq wkh iroorzlqj ohppd=

Ohppd D14 Xqghu Dvvxpswlrqv 6140617/ 618 +l, dqg +lll,/ dqg dvvxplqj wkdw wkh uhjuhvvruv {lw lq wkh

g|qdplf khwhurjhqhrxv sdqho gdwd prgho +619, duh L+4,/ wkh vdpsoh lqirupdwlrq pdwul{/ /W +#,> gh�qhg e|

+D14;,/ vdwlvi| wkh vwrfkdvwlf htxl0frqwlqxlw| frqglwlrq vxfk wkdw

vxs

#�5E+!

3>�,�QW +�3>�,

n.W +#�,� .W +#3,n � Rs+4,> +D155,

zkhuh E+!> �, @ i!�5 �! = n!

�� !n ? �j/ dqg QW +�> �, @ i�� 5 �� = W 4@5n�� � �n ? �j/ zlwk � ehlqj d

frpprq srvlwlyh uhdo qxpehu1

Surri1 Vhh wkh Dsshqgl{ wr wkh hduolhu yhuvlrq ri wklv sdshu/ Shvdudq/ Vklq/ dqg Vplwk +4<<:,1

Lq ylhz ri wkh uhodwlyh rughuv ri frqvlvwhqf| ri wkh PO hvwlpdwruv hvwdeolvkhg lq +71:, dqg wkh idfw wkdw

wkh vdpsoh lqirupdwlrq pdwul{ vdwlv�hv wkh vwrfkdvwlf htxl0frqwlqxlw| frqglwlrq/ +D155,/ lw dovr iroorzv wkdw

+vhh Vdlnnrqhq/ 4<<8/ Sursrvlwlrq 615,

/W +�#, @ /+#3, . rs+4,= +D156,

Xvlqj wklv uhvxow lq +D154, qrz |lhogv=

G�4

# +a# �#3, @ /W +#3

,�4FW +#3, . rs+4,= +D157,

Xvlqj +D14<, lq +D157, dqg e| wkh frqwlqxrxv pdsslqj wkhruhp/ zh rewdlq +71;,1

dA�Do

��� �t)4T|L|�U #�t|h�M�|�L? Lu |�i wL?}�+�? �Li�U�i?|t � A�i�@ti Lu WE�� +i}hittLht

Iluvw/ qrwh wkdw

a�l @ |l>�4 �[la� @ �l3 �[l+a� � �

3,> +D158,

dqg

Kl

��|l � a!l|l>�4

�@ Kl

k�[l�3!l3 � +a!l � !l3,|l>�4 . %l

l= +D159,

Xvlqj +619, dqg +D158, lq +715,/ zh kdyh

a!l � !l3 @�a�3

lKla�l

��4ka�3

lKl[l+a� � �3,!l3 . a�

3

lKl%l

l= +D15:,

Pruhryhu/ xvlqj +D159, lq +714,=

a� � �3@

+Q[l@4

a!5la�5l[3

lKl[l

,�4+Q[l@4

a!l

a�5l[3

lKl�l+a!l � !l3,�

Q[l@4

a!l

a�5l[3

lKl%l

,= +D15;,

Vxevwlwxwlqj +D15:, lq +D15;,/ dqg vroylqj iru a� � �3/ zh rewdlq

a� � �3@ V�4QW vQW > +D15<,

zkhuh

VQW @

Q[l@4

a!5la�5l[3

lKl[l �

Q[l@4

a!l!l3

a�5l[3

lKl�l3

�a�3

lKla�l

��4

a�3

lKl[l> +D163,

vQW @ �

Q[l@4

a!l

a�5l[3

lKl%l .

Q[l@4

a!l

a�5l[3

lKl�l3

�a�3

lKla�l

��4

a�3

lKl%l= +D164,

Xvlqj wkh frqvlvwhqf| ri a�> a!4> ===> a!Q > a�54> ===> a�5Q / lw lv dovr hdvlo| vhhq wkdw

W�4a�3

lKl[l , U3

[l�l3> W�4a�

3

lKla�l , t�l3�l3 > W�

4

5a�3

lKl%l , W�4

5 �3l3Kl%l> +D165,

zkhuh U[l�l3 dqg t�l3�l3 duh gh�qhg e| +D14, dqg +D15,1

Xvlqj +D14,/ +D165, dqg wkh frqvlvwhqf| ri a!l dqg a�5l / l @ 4> 5> ===> Q / lq +D163, dqg +D164,/ zh qrz kdyh

W�5VQW ,

Q[l@4

!5l3

�5l3U[l[l

> W�4vQW �PQ

+3>

Q[l@4

!5l3

�5l3

U[l[l

,>

zkhuh U[l[llv gh�qhg e| +D14,1 Xvlqj wkhvh uhvxowv lq +D15<, dqg e| wkh frqwlqxrxv pdsslqj wkhruhp/ zh

rewdlq +71<,1

dA�So

+iuihi?Uit^4` Dkq/ V1F1 dqg S1 Vfkplgw +4<<8,= _H�flhqw Hvwlpdwlrq ri Prghov iru G|qdplf Sdqho Gdwd/% Mrxuqdo

ri Hfrqrphwulfv/ 9;/ 5<0851

^5` Dqghuvrq/ W1Z1 dqg F1 Kvldr +4<;4,= _Hvwlpdwlrq ri G|qdplf Prghov zlwk Huuru Frpsrqhqwv/% Mrxu0qdo ri Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ :9/ 8<;09391

^6` Dqghuvrq/ W1Z1 dqg F1 Kvldr +4<;5,= _Irupdwlrq dqg Hvwlpdwlrq ri G|qdplf Prghov xvlqj SdqhoGdwd/% Mrxuqdo ri Hfrqrphwulfv/ 4;/ 7:0;51

^7` Duhoodqr/ P1 +4<;<,= _D Qrwh rq wkh Dqghuvrq0Kvldr Hvwlpdwru iru Sdqho Gdwd/% Hfrqrplfv Ohwwhuv/64/ 66:06741

^8` Duhoodqr/ P1 dqg R1 Eryhu +4<<8,= _Dqrwkhu Orrn dw wkh Lqvwuxphqwdo Yduldeoh Hvwlpdwlrq ri Huuru0Frpsrqhqwv Prghov/% Mrxuqdo ri Hfrqrphwulfv/ 9;/ 5<0851

^9` Edowdjl/ E1K1 +4<<8,= Hfrqrphwulf Dqdo|vlv ri Sdqho Gdwd1 Fklfkhvwhu= Mrkq Zloh| ) Vrqv1

^:` Er|g/ G1D1F1 dqg U1S1 Vplwk +4<<;,= _Whvwlqj iru Sxufkdvlqj Srzhu Sdulw|= Hfrqrphwulf Lvvxhv dqg

dq Dssolfdwlrq wr Ghyhorslqj Frxqwulhv/% Pdqfkhvwhu Vfkrro/ +iruwkfrplqj,1

^;` Gdylgvrq/ M1H1K1/ G1I1 Khqgu|/ I1 Vued dqg V1 \hr +4<:;,= _Hfrqrphwulf Prghoolqj ri wkh Djjuh0

jdwh Wlph0Vhulhv Uhodwlrqvkls ehwzhhq Frqvxphuv* H{shqglwxuh dqg Lqfrph lq wkh Xqlwhg Nlqjgrp/%

Hfrqrplf Mrxuqdo/ ;;/ 99409<51

^<` Kdtxh/ Q1X1 dqg S1 Prqwlho +4<;<,= _Frqvxpswlrq lq Ghyhorslqj Frxqwulhv= Whvwv iru Oltxlglw| Frq0

vwudlqwv dqg Ilqlwh Krul}rqv/% Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ :4/ 73;07481

^43` Kdxvpdq/ M1 +4<:;,= _Vshfl�fdwlrq Whvwv lq Hfrqrphwulfv/% Hfrqrphwulfd/ 79/ 45840:41

^44` Kvldr/ F1 +4<<9,= _Udqgrp Frh�flhqw Prghov/% Fkdswhu 8 ri P�dw|�dv dqg Vhyhvwuh +4<<9,1

^45` Kvldr/ F1 dqg D1N1 Wdkplvflrjox +4<<:,= _D Sdqho Dqdo|vlv ri Oltxlglw| Frqvwudlqwv dqg Ilup Lqyhvw0

phqw/% Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ <5/ 78807981

^46` Kvldr/ F1 E1K1 Vxq dqg M1 Oljkwzrrg +4<<8,= _Il{hg yv Udqgrp H�hfwv Vshfl�fdwlrq iru Sdqho Gdwd

Dqdo|vlv/% xqsxeolvkhg pdqxvfulsw/ Xqlyhuvlw| ri Vrxwkhuq Fdoliruqld1

^47` Kvldr/ F1/ P1K1 Shvdudq dqg D1N1 Wdkplvflrjox +4<<;,= _Ed|hv Hvwlpdwlrq ri Vkruw0Uxq Frh�flhqwv

lq G|qdplf Sdqho Gdwd Prghov/% lq Dqdo|vlv ri Sdqhov dqg Olplwhg Ghshqghqw Yduldeohv= D Yroxph

lq Krqrxu ri J1V1 Pdggdod/ hg1 e| Kvldr/ F1/ N1 Odklul/ O10I1 Ohh dqg P1K1 Shvdudq1 Fdpeulgjh=

Fdpeulgjh Xqlyhuvlw| Suhvv +iruwkfrplqj,1 kwws=22zzz1hfrq1fdp1df1xn2idfxow|2shvdudq2

^48` Lp/ N1V1/ P1K1 Shvdudq dqg \1 Vklq +4<<:,= _Whvwlqj iru Xqlw Urrwv lq Khwhurjhqhrxv Sdqhov/% xqsxe0

olvkhg pdqxvfulsw/ Xqlyhuvlw| ri Fdpeulgjh1 kwws=22zzz1hfrq1fdp1df1xn2idfxow|2shvdudq2

^49` Nhdqh/ P1 dqg G1 Uxqnoh +4<<5,= _Rq wkh Hvwlpdwlrq ri Sdqho Gdwd Prghov zlwk Vhuldo Fruuhodwlrq

Zkhq Lqvwuxphqwv Duh Qrw Vwulfwo| H{rjhqrxv/% Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 43/ 40<1

^4:` Nlylhw/ M1I1 dqg J1G1D1 Skloolsv +4<<6,= _Dowhuqdwlyh Eldv Dssur{lpdwlrqv zlwk d Odjjhg GhshqghqwYduldeoh/% Hfrqrphwulf Wkhru|/ </ 950;31

^4;` Olqgoh|/ G1Y1 dqg D1I1P1 Vplwk +4<:5,= _Ed|hv Hvwlpdwhv iru wkh Olqhdu Prgho/% Mrxuqdo ri wkh Ur|doVwdwlvwlfdo Vrflhw|/ E/ 67/ 40741

^4<` Pdggdod/ J1 V1 dqg Z1 Kx +4<<9,= _Wkh Srrolqj Sureohp/% Fkdswhu 46 ri P�dw|�dv dqg Vhyhvwuh +4<<9,1

^53` P�dw|�dv O1 dqg S1 Vhyhvwuh/ hgv +4<<9,= Wkh Hfrqrphwulfv ri Sdqho Gdwd= D Kdqgerrn ri Wkhru| zlwk

Dssolfdwlrqv/ 5qg Uhylvhg Hglwlrq/ Gruguhfkw= Noxzhu Dfdghplf Sxeolvkhuv1

^54` Shvdudq/ P1K1 +4<<:,= _Wkh Uroh ri Hfrqrplf Wkhru| lq Prghoolqj wkh Orqj0Uxq/% Wkh Hfrqrplf

Mrxuqdo/ 43:/ 4:;04<41

d+��o

^55` Shvdudq/ P1K1 dqg E1 Shvdudq +4<<:,= Plfur�w 713= Lqwhudfwlyh Hfrqrphwulf Dqdo|vlv1 R{irug= R{irugXqlyhuvlw| Suhvv1

^56` Shvdudq/ P1K1 dqg \1 Vklq +4<<:,= _Orqj0Uxq Vwuxfwxudo Prghoolqj/% xqsxeolvkhg pdqxvfulsw/ Xql0yhuvlw| ri Fdpeulgjh1 kwws=22zzz1hfrq1fdp1df1xn2idfxow|2shvdudq2

^57` Shvdudq/ P1K1 dqg \1 Vklq +4<<;,= _Dq Dxwruhjuhvvlyh Glvwulexwhg Odj Prghoolqj Dssurdfk wr Frlq0whjudwlrq Dqdo|vlv/% lq Fhqwhqqldo Yroxph ri Udjqdu Iulvfk/ Hfrqrphwulf Vrflhw| Prqrjudsk/ hg1

e| Vwurp/ V1/ D1 Kroo| dqg S1 Gldprqg1 Fdpeulgjh= Fdpeulgjh Xqlyhuvlw| Suhvv +iruwkfrplqj,1

kwws=22zzz1hfrq1fdp1df1xn2idfxow|2shvdudq2

^58` Shvdudq/ P1K1 dqg U1S1 Vplwk +4<<8,= _Hvwlpdwlqj Orqj0Uxq Uhodwlrqvklsv iurp G|qdplf Khwhurjh0

qhrxv Sdqhov/% Mrxuqdo ri Hfrqrphwulfv/ 9;/ :<04461

^59` Shvdudq/ P1K1 dqg ]1 ]kdr +4<<;,= _Eldv Uhgxfwlrq lq Hvwlpdwlqj Orqj0uxq Uhodwlrqvklsv iurp G|0

qdplf Khwhurjhqhrxv Sdqhov/% lq Dqdo|vlv ri Sdqhov dqg Olplwhg Ghshqghqw Yduldeohv= D Yroxph lq

Krqrxu ri J1V1 Pdggdod/ hg1 e| Kvldr/ F1/ N1 Odklul/ O10I1 Ohh dqg P1K1 Shvdudq1 Fdpeulgjh= Fdp0

eulgjh Xqlyhuvlw| Suhvv +iruwkfrplqj,1 kwws=22zzz1hfrq1fdp1df1xn2idfxow|2shvdudq2

^5:` Shvdudq/ P1K1/ \1 Vklq dqg U1M1 Vplwk +4<<9,= _Whvwlqj iru wkh H{lvwhqfh ri d Orqj0Uxq Uhodwlrqvkls/%

GDH Zrunlqj Sdshuv Dpdojdpdwhg Vhulhv/ Qr1 <955/ Xqlyhuvlw| ri Fdpeulgjh1

^5;` Shvdudq P1K1/ \1 Vklq dqg U1S1 Vplwk +4<<:,= _Srrohg Hvwlpdwlrq ri Orqj0uxq Uhodwlrqvklsv lq G|0qdplf Khwhurjhqrxv Sdqhov/% GDH Zrunlqj Sdshuv Dpdojdpdwhg Vhulhv/ Qr <:54/ Xqlyhuvlw| ri Fdp0

eulgjh1

^5<` Shvdudq/ P1K1/ U1S1 Vplwk dqg W1 Dnl|dpd +4<<;,= Hqhuj| Ghpdqg lq Dvldq Hfrqrplhv/ R{irug

Xqlyhuvlw| Suhvv/ +iruwkfrplqj,1

^63` Shvdudq/ P1K1/ U1S1 Vplwk dqg N1V1 Lp +4<<9,= _G|qdplf Olqhdu Prghov iru Khwhurjhqhrxv Sdqhov/%

Fkdswhu ; ri P�dw|�dv dqg Vhyhvwuh +4<<9,1

^64` Skloolsv/ S1F1E1 dqg V1 Gxuodxi +4<;9,= _Pxowlsoh Wlph Vhulhv zlwk Lqwhjudwhg Yduldeohv/% Uhylhz ri

Hfrqrplf Vwxglhv/ 86/ 7:607<91

^65` Urjr�/ N1 +4<<9,= _Wkh Sxufkdvlqj Srzhu Sdulw| Sx}}oh/% Mrxuqdo ri Hfrqrplf Olwhudwxuh/ 67/ 97:099;1

^66` Vdlnnrqhq/ S1 +4<<8,= _Sureohpv zlwk wkh Dv|pswrwlf Wkhru| ri Pd{lpxp Olnholkrrg Hvwlpdwlrq lqLqwhjudwhg dqg Frlqwhjudwhg V|vwhpv/% Hfrqrphwulf Wkhru|/ 44/ ;;;0<441

^67` Vwrnhu/ W1P1 +4<<6,= _Hpslulfdo Dssurdfkhv wr wkh Sureohp ri Djjuhjdwlrq ryhu Lqglylgxdov/% Mrxuqdo

ri Hfrqrplf Olwhudwxuh/ 64/ 7/ 4;5:04;:71

^68` Vzdp|/ S1D1Y1E1 +4<:3,= _H�flhqw Lqihuhqfh lq d Udqgrp Frh�flhqw Uhjuhvvlrq Prgho/% Hfrqrphw0

ulfd/ 6;/ 64406561

^69` ]hooqhu/ D1 +4<95,= _Dq H�flhqw Phwkrg ri Hvwlpdwlqj Vhhplqjo| Xquhodwhg Uhjuhvvlrqv dqg Whvw iru

Djjuhjdwlrq Eldv/% Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ 8:/ 67;069;1

d+�2o