The Transfer Operator for Multigrid on Inverse Bioelectric Field … · 2009-04-02 · 1 The...

1

The Transfer Operator for Multigrid on Inverse

Bioelectric Field Problems

Kris Zyp

UUSCI-2003-001

Scientific Computing and Imaging InstituteUniversity of Utah

Salt Lake City, UT 84112 USA

May 2003

Abstract:

This thesis describes an accurate transfer operator for the implementation of multigrid on theinverse bioelectric field problem. The traditional computational methods that apply to bioelectricfield problems often lead to inaccurate and inefficient solutions due to the ill-posed nature of theinverse problem.Multigrid is a computational technique that researchers have effectively applied to a large numberof computational simulations. It has an inherent regularization property and can achieve linear ornear-linear convergence. When applied to the inverse bioelectric field problem, multigrid rapidlycalculates internal bioelectric fields. The ill-posed nature of the inverse problem causes inaccuraciesto infiltrate the multigrid coarse grid correction scheme, significantly challenging this application ofmultigrid. The complexity of accurately modeling the body also adds to this level of difficulty. How-ever, with proper implementation, multigrid’s fast convergence improves the efficiency of solvingthis problem.The research in this thesis examines the accuracy of several methods for determining the transferoperator that drives the multigrid coarse grid correction. Also included is a proposal for a semi-coarsening strategy, called multistep, that facilitates accurate coarse grid correction, necessary formultigrid application to the inverse bioelectric problem. This thesis also contains tests of thesemethods on several datasets and a comparison and review of these test results, showing how mul-tistep yields the greatest accuracy. The final section includes suggestions for an appropriate set ofmethods for future inverse bioelectric multigrid implementations.

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O � i L > 5 ; 5 >Z; e � R = T P � DaBb> 5 � `9;SGWO�BUG 1 B ;4> 5 ; 5 � � � � � � � � � � � � � � � � � � � � � � ��O @O �Q@ L > 5 ;(`9>Z; e � R = TVP � DaBb> 5 � : ? � 3QK6K G 1 . ;4> 5 ; 5N?b543 Ob] cLK � J F[D 1 ;=<�> T OUG K5 D K P > �� OVO

O �SO L > 5 ; 5 >Z; i F[D 1 �VG 1 B 8 1 D - K > A � R = TVP � D9B�> 5 � � � � � � � � � � � � � � � � � � � � � � ��OVRO �UP L > 5 ; 5 >Z; @ � ihghg � DaB�> 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��O TO �SR L > 5 ; 5 >Z; O � =V=�� O � DaBb> 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��O �O �UT L > 5 ; 5 >Z; P � e P � e � DaBb> 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � P =O � � L > 5 ; 5 >Z; R � @ R T � � DaBb> 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � P e

O � = g L > 5 ; 5 >Z; T � = O P R e T � D9B�> 5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � P i

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e � = W 3 GJ] 1 G A DJFX;4<�>2;=D 1@5 DEF[D 1 5 D ?�1 IZ> F[D 1 A ?�K GW; 3 DhO � � � � � � � � � � � � � � � � � � � � � Te � e > 365@? G KQ3 � G ; 3 DJO�DJF�;=<�> 3 O/;=> 1@3 D 1 A > 5 <&F[D 1 ;=f;4> 5 ; 5 >Z; e 8 1 D - K > A � M�;SGW<;=D 1@5 D�� R @��

e � i L <�> 8 1 Dh] 1 > 5@543 DhO�DWFXF ?�KQK A ?�K ; 3 ] 143 B ;=< 1 D ? ]J< ;4<�>\ICD/G 1@5 >\] 1@3 B K > P > K65 � � � � � � = Te �Q@ J �bG Ad8 K > DJF IZD/G 1@5 > ] 143 B 5 > K >CI ; 3 DhO � L <�> K G 1 ]h> 8 D 3 O/; 5 G 1 > ;4<�> IZD/G 1@5 > ] 143 B8 D 3 O/; 5 GJO�Bf;= 5 A G K6K > 1 8 D 3 O/; 5 G 1 > ;= T O�>\] 143 B 8 D 3 O"; 5 � � � � � � � � � � � � � � =��e �SO : 5 G Ad8 K > 8 1 D - K > A GW; K > P > K = � ICDhG 145 > 5 ; K > P > K � ?�5 > 5 G i � i ] 143 B*GJO�B 3655 D K P >CB B 3Q1 >CI ; K . � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � =��

e �UP : 5 G Ad8 K > 8 1 D - K > A G ; K > P > K e ?�5 > 5 G O � O ] 143 B � L <�>\] 1 G 8 < 5 <bD�� 5VP G KQ? > 5- > F[D 1 > 5 A D9DJ;=< 3 O�] � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � eJge �SR : 5 G Ad8 K > 8 1 D - K > A G ; K > P > K e ?�5 > 5 G O � O ] 143 B � L <�> ] 1 G 8 <(GWF ;=> 1 5 A D9DJ;=< 3 O�] � eJge �UT : 5 G Ad8 K > 8 1 D - K > A G ; K > P > K i ?�5 > 5 G � � � ] 143 B � L <�>\] 1 G 8 < 5 <bD�� 5VP G KQ? > 5- > F[D 1 > 5 A D9DJ;=< 3 O�] � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � e =e � � : 5 G Ad8 K > 8 1 D - K > A G ; K > P > K i ?�5 > 5 G � � � ] 143 B � L <�>\] 1 G 8 < 5 <bD�� 5VP G KQ? > 5GWF ;=> 1 5 A DaDJ;4< 3 Ob] �� e =e � = g : 5 G A 8 K > 8 1 D - K > A GW; K > P > K @ ?�5 > 5 G = R � = R ] 143 B � L <�> ] 1 G 8 < 5 <�D�� 5P G K6? > 5 - > F[D 1 > 5 A D9DJ;=< 3 O�] � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ehee � =V= : 5 G A 8 K > 8 1 D - K > A GW; K > P > K @ ?�5 > 5 G = R � = R ] 143 B � L <�> ] 1 G 8 < 5 <�D�� 5P G K6? > 5 GWF ;=> 1�5 A D9DJ;4< 3 O�] � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ehee � = e : 5 G A 8 K > 8 1 D - K > A GW; K > P > K O ?�5 > 5 G ihi � iJi ] 143 B � L <�> ] 1 G 8 < 5 <�D�� 5P G K6? > 5 GWF ;=> 1�5 A D9DJ;4< 3 O�] � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � eJie � = i : 5 G A 8 K > 8 1 D - K > A GW; K > P > K O ?�5 > 5 G ihi � ihi ] 143 B � L ] 1 G 8 < 365 ;=<�>B 361 >CIZ; K . 5 D K P >CB 5 D K6? ; 3 DhO � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � eJii � = _ > 5 <'DJF ;=<�> O @ = ObDaB�> 5 G A 8 K > 8 1 D - K > A � � � � � � � � � � � � � � � � � � � � � � � � � i =i � e L <�> 1 > 54?�K ; DJF�G ICD/G 145 > ] 143 B 5 D KQP > DhO�;= F[D 1 �VG 1 B*;=> 5 ; 8 1 D - K > A � L � � G � 365 3Q5 8 D 5@3 ; 3 DhO�DhOf;= G 1 ; b. � G�� 3Q5�365 8 DJ;=>ZO"; 3 G K � � � � � � � � � � � � � � � � � i/ei � i L <�> 1 > 5@?�K ;dDJF G ICD/G 145 > ] 1@3 B 5 D KQP >fDhO�;= 3 O P > 1@5 >f;=> 5 ; 8 1 D - K > A � L � � G � 365 3Q5 8 D 5@3 ; 3 DhO�DhOf;= G 1 ; b. � G�� 3Q5�365 8 DJ;=>ZO"; 3 G K � � � � � � � � � � � � � � � � � ihii �Q@ � D9B�> 5 G 1 > 1 >ZB ? IZ>CB,D P > 1(5 > P > 1 G K 5 ;=> 8 5 � 3 ;=< 5 > A 3 ICDhG 145 >CO 3 O�] F 1 D A O @ =O�DaBb> 5 ;=D i � � O�D9B�> 5 ;4D ihe T O�DaBb> 5 ;=D e T i O�D9B�> 5 � L < 365�3Q5 ;=<�> 3 O 3 ; 3 G K ] 143 B � i R

i �SO `a> A 3 IZD/G 145 >CO 3 O�] 1 >ZB ? I ; 3 DJO'GWF ;4> 1 DhOb> 5 ;=> 8 � � � � � � � � � � � � � � � � � � � � � � � � i R

i �UP `a> A 3 IZD/G 145 >CO 3 O�] 1 >ZB ? I ; 3 DJO'GWF ;4> 1 ; � D 5 ;=> 8 5 � � � � � � � � � � � � � � � � � � � � � � � i Ti �SR `a> A 3 IZD/G 145 >CO 3 O�] 1 >ZB ? I ; 3 DJO'GWF ;4> 1 ;4< 1 >Z> 5 ;=> 8 5 � � � � � � � � � � � � � � � � � � � � � � i Ti �UT J �bG Ad8 K > @ ObDaB�> � 5@? - I 361 I ?�3 ;�� 3 ;4< 3 OfG A > 5 < � � � � � � � � � � � � � � � � � � � � � i �i � � J �bG Ad8 K > i O�D9B�> � 54? - I 361 I ?�3 ;�� 3 ;=< 3 O�G A > 5 < � L 3 O�O�> 1 O�D9B�> � ObDaB�>g ��<UG 5 - >C>CO 1 > A D P >CB GJO�B�>CY ?�3QP G K >CO/; 1 > 5@365 ;=GJO�IZ>�F[D 1 ;4<�> 1 > A G 3 O 3 O�]1 > 5@365 ;=D 1@5 ICGJO - >\ICD A 8 ? ;=>CB � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � i �

@ � = L <�> O ? A - > 1 DWF\O�DhO � > 1 D 5 � . � G � 3Q5 �(G ; ;= ICD/G 145 > 5 ; K > P > K P > 1@54?�5 � > G XICDhO�Ob>CIZ; 3 DhOf;=D K > 1 GJO�IZ> K > P > K � � � G � 365 � F[D 1 ;=> 5 ; 5 >Z; e � � � � � � � � � � � � � � � � � � @ O@ � e L <�> � >CG X ICDJO�O�>CI ; 3 DhO;4D K > 1 GJObIC> K > P > K � 5 >�� >CIZ; DhO 8 > 1 F[D 1 A GJO�IZ> � L 5 >Z; ? 8 ; 3 A >EGJO�B�;=<�> 5 D KQP >(; 3 A > � . � G�� 3Q5 � 8 K DJ;4;4>CB P > 1454?b5 ;= � > G X ICDhO �O�>CI ; 3 DJOf;4D K > 1 GJObIC> K > P > K DJOf;4<�> � � G � 365 F[D 1 ;4> 5 ; 5 >Z; e � � � � � � � � � � � � � � � � � @ P

@ � i L <�> � > G X IZDhO�O�>ZIZ; 3 DhO�;4D K > 1 GJObIC> K > P > K � 5 >�� >CI ;NDhO�GJICI ?�1 GWI . � L <�>d> 1@1 D 13 O�;4<�> 5 D KQ? ; 3 DhO � . � G � 365 � 8 K DJ;@;=>CB P > 1454?b5 ;=<�> � >CG X ICDhO�Ob>CIZ; 3 DhO ;=D K > 1 GJO�IC>K > P > K DhOf;= � � G � 365 F[D 1 ;4> 5 ; 5 >Z; e �� @ R

@ �Q@ B Ob>+DJF�;=<�> 1 GJO�B�D A P >CIZ;4D 145(?�5 >CB,G 5 ;4<�> F[D 1 > 8 3 ICG 1 B 3 G K 8 DW;=>CO/; 3 G KQ5 F[D 1;=> 5 ; 5 > ; @ � L <�> 1 > A G 3 O 3 O�] IZD A 8 ? ;=>ZB 8 DJ;4>CO/; 3 G K65 G 1 > ;=CO - G 5 >CB ? 8 DJO;=< 3Q5 ;4> 5 ; P >ZIZ;4D 1 � L <�> � � G � 365 1 > 8 1 > 5 >CO/; 5 8 D 5@3 ; 3 DhO DhO�;=<�>d<�> G 1 ; . � G � 3651 > 8 1 > 5 >CO/; 5 8 DW;=>CO/; 3 G KQ5 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � @ �O � = _ > 5 < ?�5 >CB�F[D 1 ;=> 5 ; 5 >Z; = � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��O eO � e � O";4> 1@3 D 1VP93 >��$DJF ;= A D9B�> K F[D 1 ;=> 5 ; 5 >Z; e � � � � � � � � � � � � � � � � � � � � � � � ��O PO � i _ > 5 <'ICDJO 5 ; 14? I ;=>CB F[D 1 ;=> 5 ; 5 > ; @ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��O TO �Q@ _ > 5 <'ICDJO 5 ; 14? I ;=>CB F[D 1 ;=> 5 ; 5 > ; P 8 1 D - K > A � � � � � � � � � � � � � � � � � � � � � � � � P gO �SO N > 1 F[D 1 A GJO�IZ> 5 I G K G - 36KQ3 ; . F[D 1 A ?bK ; 3Q5 ;4> 8 A ?�K ; 3 ] 1@3 B � _'?�K ; 3 ] 143 B 5 >Z; ? 8 ; 3 A >� . � G � 3Q5 � 3 O 5 >ZICDhO�B 5 3Q5 8 K DJ;4;4>CB P > 145@?�5 ;=<�> O ? A - > 1 DWF ObDaB�> 5 DhO ;= � � G � 365F[D 1 8 1 D - K > A 5 5 D KQP >CB ?�543 O�]E;=<�> A ?�K ; 3Q5 ;=> 8 G K ]hD 143 ;4< A DhOf;=> 5 ; 5 >Z; 5 @ � R � � � � P @

O �UP L > 5 ; 5 >Z; = GWF ;4> 1 DhO�>dI . I K > � O�D 5 A DaDJ;4< 3 Ob]�� L <�> IZD K D 145\1 > 8 1 > 5 >CO/; 8 D �;=>CO/; 3 G KQ5 ;=< 1 D ? ]h<�D ? ; ;=<�>2;4D 145 D �� P OO �SR L > 5 ; 5 >Z; = GWF ;4> 1 DhO�>dI . I K > � O�D 5 A D9DJ;=< 3 O�]�� L <�>dICD K D 1@5^1 > 8 1 > 5 >ZO/; ;=<�>> 141 D 1 3 O�;4<�>\ICD Ad8 ? ;=GW; 3 DhO � = O � � _ `�> 141 D 1 � � � � � � � � � � � � � � � � � � � � � � � PVPO �UT L > 5 ; 5 >Z; = GWF ;=> 1 DJO�> I . I K > GJO�B 8 D 5 ; 5 A DaDW;=< 3 O�] � � 3 ;4<�;4< 1 >Z> 5 A DaDW;=< 5 � �L <�>\ICD K D 145 1 > 8 1 > 5 >ZO/; 8 DJ;=>ZO"; 3 G KQ5 ;=< 1 D ? ]J<�D ? ;�;=\;4D 145 D �� PVPO � � L > 5 ; 5 >Z; = GWF ;=> 1 DJO�> I . I K > GJO�B 8 D 5 ; 5 A DaDW;=< 3 O�] � � 3 ;4<�;4< 1 >Z> 5 A DaDW;=< 5 � �L <�>\ICD K D 145 1 > 8 1 > 5 >ZO/; ;= > 141 D 1 3 O�;= IZD Ad8 ? ;SG ; 3 DJO � = i � � _ `+> 141 D 1 � � � P R

O � = g L > 5 ; 5 > ; = GWF ;4> 1 ;=< 1 >C>fI . I K > 5 � ;=< 1 >C> 5 A DaDW;=< 5 8 > 1 I . I K > � � L <�> ICD K D 1451 > 8 1 > 5 >CO/; 8 DJ;4>CO/; 3 G K65 ;4< 1 D ? ]h<�D ? ; ;=<�>2;=D 145 D � � � � � � � � � � � � � � � � � � � � � � � P RO � =V= L > 5 ; 5 > ; = GWF ;4> 1 ;=< 1 >C>fI . I K > 5 � ;=< 1 >C> 5 A DaDW;=< 5 8 > 1 I . I K > � � L <�> ICD K D 1451 > 8 1 > 5 >CO/; 1 > 8 1 > 5 >CO/; ;4<�>\> 1@1 D 1 3 Of;4<�>\ICD Ad8 ? ;=GW; 3 DhO � O �UP � � _ `�> 1@1 D 1 � � � � PVT

3 �

O � = e L > 5 ; 5 >Z; = ICD 1@1 >ZIZ; 5 D K6? ; 3 DJO � L ICD K D 1@5X1 > 8 1 > 5 >ZO/; 8 DJ;4>CO/; 3 G K65 ;4< 1 D ? ]h<�D ? ;;=<�>2;=D 145 D � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � PVTO � = i L <�>+; 1 GJB�>CD � - >Z; � >C>CO�GJIZI ?�1 GJI . GWO�B 8 > 1 F[D 1 A GWO�IC>+DWF�;4<�>+B 3 � > 1 >ZO";dG K �]hD 143 ;=< A 5 � `a> ; ? 8 ; 3 A >EGWO�B 5 D K P > ; 3 A > 3 O 5 >ZICDhObB 5 � . � G � 365 � G 1 > 8 K DJ;@;=>CBP > 1@54?�5 ;4<�> 8 > 1 IZ>CO/;SGW]h> > 1@1 D 1 3 O ;4<�> 5 D KQP > DhO+;= � � G � 365 F[D 1 ;4<�> B 3 � > 1 >ZO";

G K ]hD 143 ;4< A 5 G 8�8 K63 >ZB+;=DE;=> 5 ; 5 > ; R � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��R gO � = @ N > 1 F[D 1 A GJO�IZ> 5 I G K G - 3QK63 ; . F[D 1�5 ;=GJO�BUG 1 B A ?�K ; 3 ] 1@3 B � _�?�K ; 3 ] 1@3 B 5 > ; ? 8 ; 3 A >3 O 5 >ZICDhO�B 5 � . � G � 365 � 3Q5 8 K DJ;@;=>ZB P > 1@54?�5 ;=<�>\O ? A - > 1 DJF O�DaBb> 5 � � � G�� 3Q5 � F[D 1

8 1 D - K > A 525 D KQP >ZB ?b543 Ob]f;4<�> A ?�K ; 3 ] 143 B 5 ;=GJO�BUG 1 B�G K ]hD 1@3 ;4< A DhO�;4> 5 ; 5 >Z; 5

@ � R � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��R =O � = O L <�> 5 D K P >�; 3 A > � . � G � 365 � P > 1@54?�5 ;=<�>fO ? A - > 1 DWF O�D9B�> 5 � � � G � 365 � 3 O&;=<�>8 1 D - K > A ?�543 O�](;=<�>\ICDJO � ? ]/GW;4>2] 1 GWB 3 >ZO";�G K ]hD 1@3 ;4< A F[D 1 ;=> 5 ; 5 >Z; 5 @ � R � � � � ��R eO � = P L <�>2O ? A - > 1 DJF O�D9B�> 5 GWO�B+;=<�>2O ? AN- > 1 DJF O�DhO � > 1 D 5 � . � G�� 3Q5 � P > 1@54?�5 ;=<�>B�> 8 ;4< � � � G � 365 � B ?�143 O�] ;= IZD/G 1@5 >CO 3 O�] 5 ;4> 8 5 F[D 1 ;=> 5 ; 5 > ; T � � � � � � � � � � � ��R iO � = R L <�> >�� >CI ;�DWF 8 1 D - K > A 543�� > DhOGJIZI ?�1 GJI . � L <�> > 141 D 1+3 O ;4<�> 5 D K6? ; 3 DhO� . � G � 3Q5 � 365 8 K DJ;@;=>CB P > 145@?�5 ;4<�>\O ? A - > 1 DJFXO�DaBb> 5 � � � G�� 3Q5 � F[D 1 ;4> 5 ; 5 >Z; 5 @ � R RVO

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� � D ?�K B KQ3 X >d;4D�;=<�GJO X AN. GJB P9365 D 1 c < 143Q5�� Dh<bO 5 DhO F[D 1 G K6K < 3Q5N5@? 8�8 D 1 ; >CO�IZD ?�1 �GJ]h> A >ZO/; GJB P93 IC> GJO�B 3 B�>CG 5 F[D 1 ]h> ;4; 3 O�] A > ;4< 1 D ? ]h< AN.�A G 5 ;4> 1 � 5 B�>Z] 1 >Z> � � IZ> 1 ;=G 3 O K .G KQ5 D G 8�8 1 >ZI 3 GW;=>�;=<�> IZD ? O/; K > 5@5 <�D ?�1@5 <�> 5 8 >CO/; 1 > P936543 O�] AN.dA GJO . B 1 GWF ; 5 GJObB+>CO�B ?�143 O�]

AN. ICDhO 5 ;SGWO";�O�GJ]h] 3 O�] � � 365 K 8 <�G 5 - >Z>CO 3 O P G KQ? G - K >�;4D AN. 5@? ICIZ> 5@5 � � � GJO/; ;=DN;4<UGJO XW G P > � > 3 O 5 ;=> 3 O�F[D 1 < 365 <�> K 8 GJO�B�; ? ;4D 143 O�] ;4<UGW; 3 O/; 1 DaB ? IC>CB A >(;=D 3 O P > 1@5 > 8 1 D - K > A5 D KQP93 O�] � � >NG K65 D ] 1 > GW; K . G 5@543Q5 ;=>ZB A > � 3 ;=<�< 365�3 B�>CG 5 GJO�B -/. ] 3 Pa3 O�] A > 8 1 D - K > A 5 >Z; 5;=D � D 1YX � 3 ;=< �

� � GJO/; ;=D\;=<UGJO X � D 545 � < 3 ;=G X > 1 GJO�B � D - _ I�� >CD9B F[D 1 ;4<�> 3Q1 GJB P93 IZ>�GJO�B G 545@365 ;SGJO�IZ>DhO 3 Ad8 1 D P93 O�] AN. ;= 543Q5 G 5 � > K6K � � G A P > 1 . ] 1 GW;4>ZF ?�K F[D 1 G K6K DWF F K . ;4<�> � D - K > A GWO�� 51 > P936543 DhO 5 GJObB IZD 141 >CIZ; 3 DhO 5 DJO A^. 8 G 8 > 1 � L <�> ` c � GWB A 3 O 365 ; 1 GW; 3 P > 5 ;SG � � > 3 B 3 : K6K . O�> � GJ> K . ObO GJO�B�;= 1 > 5 ; <�G P >NG K � G . 5 - >C>CO � DJO�B�> 1 F ?�K6K . <�> K 8 F ?bK ;4DaD �

� � GJO/; ;=D2;=<UGWO XE_ G 1 I ?�5 _ DJ< 1 GJO�B M KQ143 IS< ��? B�>VF[D 1 ;=<�> 361 8 G 1 ;=O�> 145 < 3 8 3 O(G 8b8 K . 3 Ob]A ?�K ; 3 ] 143 B ;=D^;4<�> 3 O P > 1@5 > - 3 D9> K >CIZ; 143 I T > K B 8 1 D - K > A � � G K65 D � GJO/;V;4DNGJI X O�D�� K >CB�]h> c 1 G 3 ]W D ? ] K G 5 � 5 - 3 - K63 Dh] 1 G 8 < . � e P � �

� �VGWO"; ;=D^;4<UGJO X AN.d8 G 1 >CO/; 5 GJO�B 5@365 ;=> 1 F[D 1 G K6K ;=<�> 361 K D P > 5@? 8�8 D 1 ; GJObB 8 1 G . > 145 G 5� <UG P > - >Z>CO � D 1YX"3 Ob] DJO A^.'A G 5 ;4> 1 � 5 B�>Z] 1 >Z> � H 3 OUG KQK . � �VGWO";2;4D�;=<UGJO X K DaB F[D 1 G K6K� >2<�G 5 B�DhO�> F[D 1 A > GWO�B�F[D 1 ] 3 Pa3 O�] A > ;4<�>\G - 3QK63 ; . GJObB 5 ; 1 >CO�]W;=<�;=D A G X > 3 ; ;4< 1 D ? ]h<;=< 365 ] 1 > GW;�IS<UG KQK >ZO�]h> �

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] 1@3 B G 8�8 1 D � 3 A G ; 3 DJO 5 DJF ;4<�> 3 O P > 145 > 8 1 D - K > A � 3 ;4<'GWO'G 8b8 1 D 8 143 G ;=>2; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 �L <�D ? ]h<�B 3 � > 1 >CO/;�; 1 GJO 5 F[> 1 D 8 > 1 G ;=D 1 G K ]hD 1@3 ;4< A 5 8 1 D P > - > ;4;=> 1 GJBUG 8 ;=>CB ;4D,B 3 � > 1 >ZO/;543 ; ? G ; 3 DJO 5 ;4<�> K63 O�> G 1 ICDhO P > 1 ]h>ZO�IC>�DJF A ?�K ; 3 ] 1@3 B 5 <�D�� 5 ] 1 > GW; 5 I G K G - 3QK63 ; . GJO�B ;=A ?�K ; 3Q5 ;=> 8 IZD/G 1@5 >CO 3 O�]2G K ]hD 1@3 ;4< A 3Q5 ;4<�> DhO K . ; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 � 3 ;=< 54? � I 3 >CO/; GJIZI ?�1 GJI .;=D 8 > 1 F[D 1 A ;=<�> 5 D KQP > 5 � � < 3QK > ;=<�> A ?�K ; 3 ] 1@3 BG K ]hD 143 ;=< A ;=<UG ; � 3 Ad8 K > A >CO/;=>ZB�B 3 BO�DJ; <UG P > G - 36K63 ; . ;4D 1 > KQ3 G - K .'8 > 1 F[D 1 A GJICI ?�1 GW;4> K G 1 ]J> � 5 I G K > F ?�K6K 3 O P > 145 > 5 D KQP > 5 B ? >d;4D3 Ob>�� >CIZ; 3QP > 1 > K G��G ; 3 DJO A >Z;4<�DaB 5 ;=<�>^BUGW;=GdF 1 D A ;=<�> 3 O/;=> 1 A >CB 3 GW;=> 5 ;=> 8 5 1 > P >CG K >ZB ICDhO �I KQ?�543 P > 3 ObF[D 1 A GW; 3 DhO � L <�> ;=> 5 ; 1 > 54?�K ; 5 5 <�D�� >CBN;4<UGW;XG A ?�K ; 365 ;4> 8 ICDhG 145 >CO 3 O�] G 8b8 1 D/GWIS< 3Q5O�>ZIC> 5@5 G 1 . ;=D 8 1 D P93 B�> ;4<�> ICD/G 1@5 > ] 1@3 B\ICD 1@1 >ZIZ; 3 DhO^GJICI ?�1 GJI . O�>CIZ> 5@5 G 1 . ;4D A G X > A ?�K ; 3 ] 1@3 B> � I 3 >CO/; K . 5 D KQP >\;4<�> 3 O P > 145 > - 3 Da> K >ZIZ; 1@3 I T > K B 8 1 D - K > A �

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L <�> 8 1 DaIZ> 5@5 DJF B�> ;=> 1 A 3 O 3 Ob]^;= 5 > - 3 D9> K >CIZ; 143 I T > K B 5 - G 5 >CB ? 8 DhO 5@?�1 FHGJIZ> A > G 5@?�1 > �A >CO/; 5�365 GJO 3 O P > 145 > 8 1 D - K > A � L <�> 1 > <UG 5 - >Z>CO'G 5@? - 5 ;=GJO/; 3 G K G A D ? O/;�DJF � D 1YX DJO�;=?�5 > DJF IZD Ad8 ? ;=> 1 5@3 A ?�K GW; 3 DhO ;=D 5 D K P >�;=< 3Q5 8 1 D - K > A � = O P Se � =i = =i/e @ e�� @ @ O e O i O T P = � P i P P RVO R � TVP � T T � � = ghg = g/e = g P =V= i =V=�� = e = = e @ � � : 8�8 K63 >CB ;4D�;4<�> - 1 G 3 O ;=2]hD/G K DJFX;4<�> 3 O P > 145 > 8 1 D - K > A 365 ;4D K D9I GW;4> ;= 8 D 3 O/; 5 D ?b1 IC> 5 � 3 ;=< 3 O+;= - 1 G 3 O+;=<UG ;B�> K63QP > 1 > K >ZIZ; 143 I^I ?�1@1 >ZO"; -/. ?�543 O�] J�J K BUG ;SG � H D 1 ;= <�> G 1 ; ;=<�> 8 1 D - K > A 3Q5 543 A 3QK G 1

O; 1 . 3 O�] ;=D B�> ;=> 1 A 3 O�>+;4<�>�; 365@54? > �� 1 > > K >CI ; 143 I G K I ?�1@1 >CO/; 5 D 1@3 ] 3 OUGW;4> - G 5 >CB,DhO J cLKBUGW;=G � : O ? A - > 1 DJF � G . 5 ;=D B�> ;=> 1 A 3 O�>+;4<�> 5 > 3 O/;=> 1 OUG K > K >ZIZ; 1@3 ICG KV5 D ?�1 IZ> 5 G 1 > A D 1 >3 O P G 5@3QP > b- ? ; 3 O P > 145 >\GJOUG K . 54365 5 >Z> X"5 ;=DEG P D 3 B ;4<�> 5 > 3 O/; 14?�5@3 DhO 5 � L <�> 5 >\G 8�8 1 D/GJIS 5 G 1 >P > 1 . 3 Ad8 D 1 ;SGWO"; F[D 1�P > 143 T I G ; 3 DJO'DJFR;4<�> O�DhO 3 O P G 5@3QP > A >Z;=<bDaB 5 � c ?�141 >CO/; K .� ;=<�>^I K63 O 3 ICG K?�5 >�DJF J cLK 365 - G 5 >CB A D 1 >�DhO�> A 8 36143 I G K 8 GW;4;4> 1 O 1 >CICDJ]hO 3 ; 3 DhO&;4<UGJO,DhO - 3 D 8 < . 543 I G KA DaB�> K63 O�] � L <�>f]hD/G K DJF 3 O P > 145 > J cLK 8 1 D - K > A 5 D K Pa3 O�] 365 ;=D 3 Ad8 1 D P > ;=<�> GJIZI ?�1 GJI .DJF - 3 D 8 < . 543 I G K A D9B�> K63 Ob] F[D 1 I KQ3 O 3 I G K ?b5 GJ]h> � � > 5 >CG 1 IS<�<UG 5 B�> A DhO 5 ; 1 GW;=>ZB�;=<UG ; > K >CI �; 1 DaICG 1 B 3 Dh] 1 G 8 < . ICGJO K 8 IS<UG 1 GJIZ;4> 143�� > GJO�BdB�>Z;4>CI ; AN. DaICG 1 B 3 G K�3 ObFHG 1 I ; 3 DhO � e = Sehe � GWO�BAN. DaICG 1 B 3 G K 1 > 8 D K G 1@3 � GW; 3 DhO+G - O�D 1 A G KQ3 ; 3 > 5 � eJg � �M 5 > DJF2;= 3 O P > 145 > J cLK 8 1 D - K > A <UG 5 ObDJ; . >Z;fGJIS< 3 > P >CB ;4<�> GJB�>ZY ? GW;=> K > P > K DJF

5 8 GW; 3 G K 1 > 5 D KQ? ; 3 DhO F[D 1 � 3 B�> 5 8 1 >CGJB I KQ3 O 3 I G K ?�5 > � � > 5 D K6? ; 3 DJO 3 O ;4<�> 1 GJO�]h> DJF O � = g(A A� 3 ;4< K > 545 ;=<�>ZO = g � > 1@1 D 1 365 1 >CY ?�3Q1 >ZB ;=D - > ?b5 >ZF ?bK F[D 1 G 8�8 KQ3 I G ; 3 DJO 5 54? IS<fG 5 B�> 5 I 1@3 - 3 O�]1 >Z>CO/; 1 GJO/;�;SGJIS< . I G 1 B 3 G 5 > P G K6? GW; 3 O�] AN. DaICG 1 B 3 G K�365 IS A 3 G D 1+K DaICG K63��C3 O�] P >CO/; 143 I ?�K G 1G 1@1 . ;=< A 3 G 5 � R e RVO � � ` ? IS< 5 8 GW; 3 G K 1 > 5 D K6? ; 3 DhO 365 B 3 � I ?�K ;�;4DdGJIS< 3 > P > - >ZI G ?�5 >NG ? O 3 Y ? >5 D K6? ; 3 DhO F[D 1 I ?�141 >CO/; 5 D ?b1 IC> 5 /- G 5 >CB ? 8 DhO 5@?�1 FHGWIC> A > G 5@?�1 > A >ZO"; 5 B�D9> 5 O�DJ;R> � 365 ; � L < 3Q5<UG 5 K >ZB ;=DNGNO ? A - > 1 DJF B 3 � > 1 >CO/; G 8�8 1 D/GJIS<�> 5 F[D 1 A D9B�> K63 Ob]\;4<�> > K >ZIZ; 1@3 ICG K 5 D ?�1 IC> 5 � @ @�� L <�> 1 D9DJ; 1 > G 5 DhOfF[D 1 ;=<�> K GWI X DJF GWB�>CY ? GW;4> 5 8 GW; 3 G K 1 > 5 D K6? ; 3 DhO 365 ;4<�> B 365@543 8 GW; 3 DhO�DJF

;=N> K >CI ; 143 I G K 5@3 ]hO�G K G 5 3 ; A D P > 5 ;4< 1 D ? ]h<�;4<�> - D9B .� ��< 3 IS< K > GWB 5 ;4D G ;4;=>ZO ? GW; 3 DhO GWO�B5 8 GW; 3 G K 5 A DaDJ;4< 3 Ob] � F DJ;=<'DJF ;=<�> 5 > A ?�5 ; - > 1 > P > 1@5 >CB ;4D 1 >ZICD P > 1 ;=<�> 3 O/;=> 1 OUG K 543 ]hOUG KQ5 �L < 3Q5�1 > P > 1@5 G K 8 1 DaIZ> 545 A G X > 5 ;4<�> 5 D K6? ; 3 DhO P > 1 . 5 >CO 5@3 ; 3QP > ;4D,ObD 365 > IZD Ad8 ? ;SG ; 3 DJOUG K8 1 >CI 3Q543 DhO K D 5@5 GJObB A DaBb> K 3 OUGJICI ?�1 GWI 3 > 5 �D�; D�; : � �� 8�� : � > KQK � 8 D 5 >CB 8 1 D - K > A G 5 B�> T O�>ZB -". � GJBUG A G 1 B � @ T � 365 DhO�> 3 O ��< 3 IS<�G K6K ;=

F[D KQK D�� 3 O�]NI 143 ;=> 143 GEG 1 > A >Z; �

= � HUD 1 >CGJIS< 5 >Z;�DJF BUGW;SG ;=<�> 1 >\>�� 3Q5 ; 5 G 5 D KQ? ; 3 DhO �e � L <�> 5 D K6? ; 3 DhO 3Q5�? O 3 Y ? > �i � L <�> 5 D K6? ; 3 DhO�Bb> 8 >CO�B 5 ICDhO/; 3 O ? D ?�5@K . DJOf;4<�>\BUGW;=G �

P: 5 A >ZO"; 3 DhOb>CB >CG 14KQ3 > 1 ;=<�> 3 O P > 1@5 > - 3 D9> K >ZIZ; 143 I T > K B 8 1 D - K > A B�D9> 5 ObDJ; <UG P >(G ? O 3 Y ? >5 D K6? ; 3 DhO � � O(DJ;= 1 � D 1 B 5 B 3 � > 1 >CO/; ICD AN- 3 OUG ; 3 DJO 5 DJF 3 O/;4> 1 O�G K I ?�141 >CO/; 5 D ?�1 IC> 5 ICGJO K > GWB;=D\;= 5 G A >�D - 5 > 1 P >ZB+>��9;=> 1 OUG K 8 DJ;4>CO/; 3 G K65 � L < 3Q5 A > GJO 5 ;4<UGW; ;= 8 1 D - K > A 3Q5 36K6K � 8 D 5 >ZB �: KQ5 D K G 1 ]J>VIS<UGJO�]J> 5 3 O ;= 3 O/;=> 1 OUG K�5 D ?�1 IC> 5 I GWO K > GJB ;4D DJO K . >��9; 1 > A > K . 5 A G K6K IS<UGJO�]h> 53 O ;4<�> >��9;=> 1 OUG K 8 DJ;4>CO/; 3 G K65 5 D&;=<�> 5 D K6? ; 3 DhO�B�Da> 5 O�DJ;fB�> 8 >ZO�B�IZDhO/; 3 O ? D ?�54K . DhO ;=BUGW;=G � L < 365 < 3 ]J< 5 >CO 5@3 ; 3 P93 ; .\A > GJO 5 ;= B 3Q5 I 1 >Z;4> F 1 D A DJFa;=<�> 8 1 D - K > A 365 36KQK � IZDhO�B 3 ; 3 DhO�>CB �L <�> 1 >ZF[D 1 > 3 ; 365 O�>CIZ> 545 G 1 . ;=D ICDhO 5 ; 1 G 3 O^;=<�> 8 1 D - K > A� GJO�BN;4<�> 5 D K6? ; 3 DJO A ?b5 ; - > K63 A 3 ;4>CB;=D�G 54? - 5 8 GWIC> � � > ICGJO K63 A 3 ;^;4<�> 54? - 5 8 GJIZ> 3 O 5@? IS< G � G . ;=<UGW;E;4<�> 1 > 365 DhO K . DhOb>5 D K6? ; 3 DhO � 3 ;=< 3 O ;=<UG ; 5 8 GWIC> � � > ICGJO 543 A 8 KQ3 F . ;4<�> A D9B�> K � > ?b5 > ;=D&Bb> 5 I 143 - > ;=I ?b141 >ZO/; 5 D ?�1 IZ> 5 � 3 ;=< 3 O&;=<�> - DaB . ;=D�GJIS< 3 > P >f;=< 365(K63 A 3 ;=>CB 54? - 5 8 GJIZ> � @ = � � : K65 D � >A ?�5 ;EICDJO 5 ; 1 G 3 O*;=<�>+BbD A G 3 O 5 D ;=<UGW;N;=<�> 5 D K6? ; 3 DJO � 36KQK Bb> 8 >CO�B�ICDJO"; 3 O ? D ?b54K . DhO*;=BUGW;=G � L <UGW; 3Q5 ;4<�> 5 D KQ? ; 3 DhO A ?�5 ; - > 1 >Z] ?�K G 143 � >CB �D�; D�; D 2 � ��

B O�> G 8b8 1 D/GWIS<�F[D 1 ;4<�> A D9B�> KQ3 O�] DJF2> K >ZIZ; 1@3 ICG K�5 D ?�1 IC> 5+365 ;=D K DaICG K63�� >+;4<�> 5 D ?�1 IZ>B 3 8 D K > 5 � : 543 A 8 K > GJOUG K . 54365 DJF ;4<�> 5 ;SGJO�B�G 1 B > K >ZIZ; 1 DaICG 1 B 3 Dh] 1 G A 3Q5 - G 5 >CB DJO G 5@3 Ad8 K >I ?b141 >ZO/;2B 3 8 D K > P >CI ;=D 1 A D9B�> K DJF ;=<�>^<�> G 1 ; � 5 > K >CI ; 143 I G K GJI ; 3 Pa3 ; . � W 3 8 D K > A D9B�> KQ3 O�](ICGJO- > 8 > 1 F[D 1 A >CB � 3 ;=<�;4< 365d543 A 8 K > 543 O�] K > B 3 8 D K > G 8�8 1 D/GJIS< D 1d?�5@3 O�] A ?�K ; 3 8 K >�B 3 8 D K > 5 �� D�� > P > 1 � 3 ;=<�D ? ; IZDhO 5 ; 1 G 3 O/; 5 DJO K . G F[>�� B 3 8 D K > 5 ICGJO - > 1 > K63 G - K . > 5 ; 3 A GW;=>ZB � : K ;4> 1 �OUGW; 3QP > K . G A D 1 > 1 >CG K63Q5 ; 3 I /- ? ; IZD A 8 ? ;SGW; 3 DhO�G K6K . B 3 � I ?�K ; G 8�8 1 DhGJIS< 3 O P D KQP > 5 A D9B�> KQ3 O�];=d G 1 ; G 5 G 5@?�1 FHGWIC>(DJF B 3 8 D K > 5 � eJi O e O i � ��<�> 1 >E;=<�> - D ? O�B�G 1 . - >Z; � >C>ZO�> �bI 3 ;4>CBGJO�B 1 > 5 ; 3 O�](IC> K6KQ5 1 > 8 1 > 5 >CO/; 5 ;=<�> 5@?�1 FHGJIZ> �L < 365�1 > 5 >CG 1 IS< � 3QK6K F[D9I ?b5 DJO GJO�DW;=<�> 1 G 8�8 1 DhGJIS<�;4<UGW; GW;4;4> Ad8 ; 5 ;4D I 1 > G ;=>^G A G 8 DJF

;= 8 DW;=>CO/; 3 G KQ5 DhO^;=<�>V> 8 3 ICG 1 B 36? A - G 5 >CB ? 8 DhO 5@?�1 FHGWIC> P G KQ? > 5 � � T = e @�� L < 365 G 8�8 1 DhGJIS<B�D9> 5 O�DJ; G ;4;=> A 8 ;R;=D\B�> ;=> 1 A 3 O�>V;= K DaICG K63 ; . DJF ;=<�> 5 D ?�1 IZ> 5 � 3 ;=< 3 O ;= <�> G 1 ; "- ? ; DJO K .B�> ;=> 1 A 3 O�> 5 ;4<�> 54?�1 FHGJIC> 8 DJ;=>ZO"; 3 G KQ5 DJFX;=<�>\<�>CG 1 ; �D�; D�; Z �(� � � �� [� � �� L <�> - 3 D9> K >ZIZ; 143 I T > K B 8 1 D - K > A A ?�5 ; - > A G ;=<�> A GW; 3 ICG K6K . F[D 1 A ?�K GW;=>ZB - > F[D 1 > 3 ;�ICGJO

- > 5 D KQP >CB � L D - >C] 3 O � > G 5@54? A >dG Y ? G 5@365 ;SGW; 3 IEICDJO�B 3 ; 3 DhO ;=<UGW; 3Q5 > P >CO�;4<�D ? ]h< ;=8 DJ;=>ZO"; 3 G KQ5 GJO�B�I ?�1@1 >CO/; 5 G 1 > IS<�GJO�] 3 O�] � 3 ;=<�; 3 A > � >'G 5@54? A >�GW;d> P > 1 . 3 O 5 ;SGJObIC>fDJF

R; 3 A >^;=<UGW; > K >CI ; 1@3 I G K GJIZ; 3QP93 ; . 365 IZDhO 5 ;=GJO/;^GJO�B � >dI GJO�G 8�8 K . B 361 >ZIZ; I ?b141 >ZO/; GJO�G K . 543Q5 �L <�> > K >ZIZ; 143 ICG K GJIZ; 3QP93 ; . I GJO - > B�> 5 I 143 - >ZB A GW;=<�> A G ; 3 ICG K6K . � 3 ;=<^G ]h>ZO�> 1 G K63�� >ZB�N D 36545 DhO�� 5>CY ? G ; 3 DJOf;4D 5 D KQP > 3 O+;=> 1 A 5 DJFX;4<�> 8 143 A G 1 . I ?�1@1 >CO/; 5 D ?b1 IC> 5��

�� e � = �

?�5@3 O�]E;= - D ? ObBUG 1 . ICDhO�B 3 ; 3 DhO 5��

�� DJO�� e � e �

��<�> 1 > � G 1 >�;4<�> > K >ZIZ; 1 D 5 ;=GW; 3 I 8 DJ;4>CO/; 3 G K65 �� G 1 >�;=<�> I G 1 B 3 GWI I ?�141 >CO/; 5 D ?�1 IZ> 5 �'3Q5 ;=ICDJO�B ? I ; 3QP93 ; . ;4>CO 5 D 1 GJO�B�� 1 > 8 1 > 5 >CO/; 5 ;=<�> 54?�1 FHGJIC> DJF ;=�;4D 145 D � � > G 5@54? A > I ?�141 >CO/;5 D ?�1 IZ> 5 >�� 365 ;�DhO K . DhO+;4<�> 54?b1 FHGJIZ>2DJF ;=<�>2<�>CG 1 ; 5 D5N D 3Q545 DhO�� 5 >ZY ? GW; 3 DhO�I GWO - > 1 >CB ? IZ>CB;=D � G 8 K GJIC> � 5 >ZY ? GW; 3 DhO �

�� g � � e � i �� 3 ;4<�;=<�> c G ? IS< . - D ? O�BUG 1 . IZDhO�B 3 ; 3 DJO 5��

��! DhO#"�$%�� e �Q@ ��&� � �'� DhO#�(� � � e �SO �

L < 3Q5 F[D 1 A ?�K GW; 3 DhO 1 > 8 1 > 5 >CO/; 5 ;=<�> 54?b1 FHGJIZ> � ;4D � 5@?�1 FHGWIC> 3 O P > 145 > - 3 D9> K >CI ; 143 I T > K B 8 1 D - K > AG 5�1 > 8 1 > 5 >ZO";4>CB 3 O9H 3 ] ?b1 > e � = �

� < 36K > � >+O�D�� <UG P >fG ? O 3 Y ? > 5 D K6? ; 3 DJO ;4<�> 8 1 D - K > A 365N5 ; 3QK6K < 3 ]J< K . 5 >CO 5@3 ; 3 P > ;4D3 O 3 ; 3 G K ICDhO�B 3 ; 3 DhO 5 GJO�B�;=< ?�5 ;= 8 1 D - K > A 365 5 ; 36KQK 36KQK � ICDhO�B 3 ; 3 DhO�>ZB �D�; D�; E 2 � ��

� O&D 1 Bb> 1 ;4D 5 D KQP > F[D 1 ;4<�> > 8 3 ICG 1 B 3 G K 8 DW;=>CO/; 3 G KQ5 � > A ?�5 ; IZDhO 5 ; 14? I ;(G A DaBb> K -".A > G 5@?�143 O�]2GJO�BEB 365 I 1 > ; 3 �Z3 O�]�;=<�>VGJOUGW;4D AN. � : O�DhO 3 O P G 543 P > A >Z;4<�DaBNDJF A >CG 54?b1 > A >CO/;RF[D 1K63 P93 O�] - > 3 Ob] 5 365 ]h>CO�> 1 G KQK .E8 1 >ZF[> 1 G - K > � _ D 5 ; A DaB�> K65 G 1 > - G 5 >CB DhO A GJ]hO�> ; 3 I 1 > 5 DhOUGJO�IZ>3 A GJ] 3 O�] � _ � � � D 1 IZD Ad8 ? ;=>ZB�;=D A Dh] 1 G 8 < . � c L � 3 A GJ]J> 5 � =V= e � �

� > �a; ;= 5 ICGJO�O�>ZB 3 A GJ]h> 5 A ?b5 ; - > 5 >C] A >CO/;4>CB � M ObF[D 1 ; ? O�GW;=> K .� F ?�KQK . G ? ;4D A GW;=>ZB5 >Z] A >CO/;SGW; 3 DhO�BbDa> 5 O�DJ; G K �VG . 5 8 1 D9B ? IZ>�GJICIZ> 8 ;=G - K > 1 > 5@?�K ; 5 5 D ;=<�> 5 >C] A >CO/;SG ; 3 DJO8 1 DaIZ> 545 DJF ;4>CO 1 >ZY ?b361 > 5^?b5 > 1 ] ?b3 BUGJObIC> � K >COb> 1 G K6K . ?�5 > 145 A ?�5 ;\IS<�DaD 5 >dICDhO/; 1 D K 8 D 3 O/; 5

T

�� D�; : ��W 3 GJ] 1 G A DWFX;4<�>2;=D 1@5 D(F[D 1 5 D ?b1 IC>2F[D 1 A ?�K GW; 3 DhO �

D ? ; K63 O 3 O�]+;4<�> 3 O�B 3QP93 B ? G K D - � >ZIZ; 5 DJF 3 O/;=> 1 > 5 ; � 3 ;=< 3 O ;=<�> - D9B . � L <�> 1 > G 1 >dG�O ? AN- > 1DJF�;=>ZIS<�O 3 Y ? > 5 F[D 1 GW;4;4> Ad8 ; 3 O�]';=D�G ? ;=D A GW; 3 I G KQK . 5 >C] A >CO/;(;=<�> 3 A GW]h> 5 GWO�B,G 545@365 ; 3 OA GJO ? G K 5 >C] A >CO/;SG ; 3 DJO � O � � � L <�> 5 > 3 O�I KQ? B�> >ZB�]h>�B�>Z;4>CIZ; 3 DhO � =V=V= � ;4< 1 > 5 <�D K B � = g T � >CBb]h> � - G 5 >ZB 5 >C] A >CO/;SG ; 3 DJO � R = � GJObB 1 >C] 3 DhO�] 1 D�� 3 O�] � = e O � �

H 1 D A ;=<�> 5 > 5 >C] A >CO/;SG ; 3 DJO 5 � > A ?b5 ;2I 1 > G ;=> 54?b1 FHGJIZ> - D ? O�BUG 1@3 > 5 � :�; 1@3 GJOb] ?�K G ;=>CB54?b1 FHGJIZ> 3Q52?�54? G K6K . 8 1 >ZF[> 1 G - K > F[D 1 B�> 5 I 1@3 - 3 O�]�;=<�> 361@1 >Z] ?�K G 1 54?�1 FHGJIC> 5 DJF ;4<�> - D9B . � : K �;=<bD ? ]h< 3 ; 3Q5 B 3 � I ?�K ; ;=D I 1 >CGW;=> 54?�1 FHGJIC> 5 F 1 D A GJO 3Q141 >C] ?�K G 1 5 > ; DJF 8 D 3 O/; 5 JA D 5 ; 5 ICGJO�O 3 O�];=>ZIS<�O 3 Y ? > 5 . 3 > K B 8 D 3 O/; 5 ;4<UGW; G 1 >^IZDhO 5 ; 1 G 3 O�>CBf;=D 8 K GJO�> 5 GJO�B � > I GJO ?�5 >^G 1 > K GW; 3 P > K .543 A 8 K > K GJI 3 O�] ;=>ZIS<�O 3 Y ? >\;=D(I 1 > G ;=> - D ? O�BUG 1 . 54?b1 FHGJIZ> 5 � R P � �D�; D�; � 2 � �� ! � ��

B O�IC> G 5@?�1 FHGJIZ> 3Q5 I 1 >CGW;=>ZB � > A ?�5 ; ]h>ZO�> 1 GW;=> G A > 5 <�F[D 1 ;4<�> P D K6? A > �� O�D 1 B�> 1;=D 5 D K P > F[D 1 ;=<�> > 8 3 ICG 1 B 3 G K 8 DW;=>CO/; 3 G KQ5 ;=<�> 8 G 1 ; 3 G K B 3 � > 1 >CO/; 3 G K >CY ? GW; 3 DhO 5 � N W J � A ?�5 ;- > G 8�8 1 D � 3 A GW;=>ZB O ? A > 143 I G KQK . DJO�GN] 1@3 B � H 361@5 ; � > A ?�5 ;VIS<�D9D 5 > ;=<�> B 365 I 1 > ; 3�� GW; 3 DhOdDJF;=2]h>CD A >Z; 1 . F 1 D A 5 ICGJO�O�>ZB 3 A GJ]h> 5 � � >2I 1 > GW;4>\G A > 5 <fDJF O�D9B�> 5 ;=<�GW;�G 1 >2ICDhO�Ob>CIZ;4>CB;=D�> GJIS< DJ;4<�> 1 ;=D�F[D 1 A ;=<�>�ICDhO�Ob>CIZ; 3 DhO 5 GJO�B > K > A >CO/; 5 G 5 B 365 8 K G . >ZB 3 O H 3 ] ?�1 > e � e �_ > 5 <+]h>ZO�> 1 GW; 3 DhO 365 G K G 1 ]h> T > K B 3 O 3 ; 5 > K F /- ? ; ;=<�> 1 > G 1 >�G F[>�� 8 1 >CB�D A 3 O�GJO/; 5 ; 1 GW;=>Z] 3 > 5F[D 1 ;4<�>(]h>CO�> 1 GW; 3 DhO DJF O�D9B�> 5 GJO�B > K > A >CO/; 5 � `9; 1@? IZ; ?�1 >ZB 8 G 1 ; 3 ; 3 DhO 3 Ob] 365 ;4<�> 543 Ad8 K > 5 ;

�

�� D�; D � > 365@? G K63�� GW; 3 DhO DWFV;=<�> 3 O/;=> 143 D 1 A > 5 <�F[D 1 ;=<�>d;=> 5 ; 5 >Z; e 8 1 D - K > A � M�;=GJ<;=D 145 D �� R @ � �

A >Z;=<bDaB,DJF2]h>ZO�> 1 GW; 3 DhO � i O R g � � L < 3Q5 5 ; 1 G ;=>C] .�- >Z] 3 O 5 � 3 ;4< G ] 3QP >CO - D ? O�BUG 1 . GWO�B1 >ZI ?�1@543 P > K . B 3QP93 Bb> 5 3 ; � L <�> B 3 P936543 DhO 5 G 1 > ;=CO 5@? - B 3QP93 B�>ZB 1 > 8 > GW;4>CB K . 3 O G B 3QP93 B�> GWO�BICDJO�Y ? > 1 A GJO�Ob> 1 ? O"; 36K � >\GWIS< 3 > P >2GJO+G 8�8 1 D 8 143 GW;=> K > P > K DJF B 3 P936543 DhO 5 � `9; 1 G 3 ]J<";@F[D 1 � G 1 B8 1 Dh] 1 G A A 3 O�] 365 ;=^GWB P GJO/;SGJ]h>2DWFX;4< 365 ;=>ZIS<�O 3 Y ? > �

W > K G ? OUG . ; 143 GJO�] ?�K GW; 3 DhO 3Q5 G A D 1 > T O�> K . IZDhO/; 1 D K6K >ZB A > ;=<�D9B&F[D 1 ;=<�> - 3 Da> K >ZIZ; 1@3 IT > K B 8 1 D - K > A � i O =V= P � � L < 3Q5 A > ;=<�D9B - >C] 3 O 5 � 3 ;4< G ] 3 P >CO 5 >Z;2DJF 8 D 3 O/; 5 ;=<UG ;2B�> T O�>;= O�D9B�> 5 � L <�> O�D9B�> 5 G 1 > ;=<�>ZO ICDhObO�>CI ;=>CB ;4D F[D 1 A GJO'D 8 ; 3 A G K A > 5 < DJF ;4>Z; 1 GJ<�>ZB 1 G �L < 3Q5 A >Z;4<�D9B�G K6K D�� 5 ;4<�> A > 5 <f;=D - >\]h>ZO�> 1 GW;=>ZB ;4D IZDhObF[D 1 A ;4Dd;4<�>\] 3QP >CO 1 >C] 3 DhO 5 GWO�B- D ? O�BUG 143 > 5 � 3 ;4< ;=<�> A D9B�> K GJO�B 8 1 D P93 B�> 3 Ad8 1 D P >CB 5 8 GJI 3 O�] � L <�> B 365 GWB P GJO/;SGJ]h> DJF ;=< 3Q5A >Z;=<bDaB 3Q5 ;=<�GW; 3 ; 365 A D 1 >NB 3 � I ?�K ; ;=D 8 1 Dh] 1 G A � B ;=<�> 1 A > 5 < ]h>ZO�> 1 GW; 3 DhO';=>ZIS<�O 3 Y ? > 53 ObI K6? B�> A G 8b8 3 O�] A >Z;=<bDaB 5 DaI ; 1 >Z> A >Z;4<�DaB 5 � = g � =V= g � GJO�B 8 G P93 O�] � GJB P GJObI 3 Ob]dF 1 DhO/;A >Z;=<bDaB 5 �� i O =i R � �

J K > A >CO/; 5 8 GWI 3 Ob] 365 GJObDJ;=<�> 1N3 A 8 D 1 ;=GJO/;\B�>CI 365@3 DhO 3 O A > 5 <*]J>CO�> 1 GW; 3 DhO � : K ;4<�D ? ]J<;= 543 Ad8 K > 5 ;VG 8�8 1 D/GJIS< 365 ;=D ?�5 >\GJOfG 8�8 1 D � 3 A G ;=> K . ICDhO 5 ;SGJO/;�B 3Q5 ;=GJO�IC> - >Z; � >C>ZO�ObDaB�> 53 O�;=<�> A > 5 < ]h>COb> 1 G ; 3 DJO ;=<�> A > 5 1 - > 3 Ad8 1 D P >CB -/. GWBUG 8 ; 3QP > K . 1 > T O 3 O�];= A > 5 < - G 5 >CB DhO'G 5 D K6? ; 3 DJO�> 5 ; 3 A G ;=> � P e = gJi � � : O G K ]hD 1@3 ;4< A ICG K6K >CB �� F ?�1 ;=<�> 1 1 > T Ob> 5 ;=<�> A > 5 < ;4<UGW; 365 I 1 > GW;4> 5 A D 1 >EO�D9B�> 5\3 O�G 1 > G 5 DJF ] 1 > GW;4> 1 8 DW;=>CO/; 3 G K

= g

] 1 GJB 3 >ZO/; 5 � : K ;4> 1 O�GW; 3 P > K .� �� 54? - 5 ; 3 ; ? ;4> 5 < 3 ]h<�> 1 D 1 B�> 1 > K > A >ZO/; 5\3 O < 3 ]h<�> 1] 1 GJB 3 >ZO/; G 1 > G 5 � � �� IZD A - 3 O�> 5 ;=<�> 5 > ;=>CIS<bO 3 Y ? > 5 F[D 1�3 Ad8 1 D P >ZB GJB�G 8 ;SG ; 3 DJO� e O TVO � O � �

� > �a; � > A ?�5 ; B�> 5 I 1@3 - >�;4<�> 8 < . 543 I 5 DJF ;=<�> 8 1 D - K > A 3 O(G2O ? A > 143 ICG K B 365 I 1 > ; 3 � GW; 3 DhO �_ > ;=<�D9B 5 F[D 1 ;4< 365 B 3Q5 I 1 >Z; 3 � GW; 3 DhO 3 ObI K6? B�>N;= T O 3 ;4> B 3 � > 1 >CO�IZ> A > ;=<�D9B � H W _ � T O 3 ;4>> K > A >CO/; A > ;=<�D9B � H J _ � D 1 - D ? O�BUG 1 . > K > A >CO/; A >Z;=<bDaB � F J _ � � L <�> T O 3 ;4> B 3 � > 1 >CO�IZ>A >Z;=<bDaB 365 - G 5 >CB ? 8 DhO'G 8�8 1 D�� 3 A GW; 3 O�](B�> 143 P G ; 3QP > 5 DhO G ? O 3 F[D 1 A K . 5 8 GJIZ>CB ] 1@3 B � L <�>A > 5 5 ]h>COb> 1 G ;=>CB F[D 1 ;4<�> - 3 D9> K >CIZ; 143 I T > K B 8 1 D - K > A I GWO - > ? O 5 ; 14? IZ; ?b1 >CB � GJObB ;4<�> .G 1 > 3 O D ?b1 I G 5 > � GJObB 54? IS< A > 5 <�> 5 I GJO O�DW;2> G 5@36K .�- > ?�5 >CB � 3 ;4< ;=<�> T O 3 ;4> B 3 � > 1 >CO�IZ>A >Z;=<bDaB � L <�> - D ? ObBUG 1 . > K > A >ZO"; A >Z;=<bDaB 1 > K63 > 5 DhO A GW;= A GW; 3 I G KQK . ICD Ad8 ? ; 3 O�]f;=1 > K GW; 3 DhO 5 < 3 8 - > ; � >Z>CO�;4<�> O�D9B�> 5 DhO ;4<�> >��9;=> 143 D 1 DJF G P D K6? A > � L < 365 A >Z;4<�DaB�ICGJO8 1 D P93 B�>VG 543 ]JO 3QT ICGJO/; 3 A 8 1 D P > A >ZO"; 3 O^I G K I ?�K GW; 3 DhO2; 3 A > G 5 � > B�D O�DW; <UG P > ;=D ICD Ad8 ? ;4>3 O/;4> 143 D 1 ObDaB�> 5 � M�ObF[D 1 ; ? OUG ;=> K .� ;4<�> A G ;=<�> A GW; 3 I 5 ;=D2Bb>Z;=> 1 A 3 O�> ;=<�> - D ? O�B�G 1 . > K > A >ZO/;>CY ? G ; 3 DJO 5 G 1 > ?�5@? G KQK . K63 A 3 ;=>CBE;4D 365 DJ; 1 D 8 3 I P D K6? A > 5 � L <�> ;4D 145 DEGJO�B - 1 G 3 O+<UG P > A GJO .GJO 3Q5 DJ; 1 D 8 3 I^F[>CGW; ?b1 > 5 � � F � > � 365 < ;=D GJICI ?�1 G ;=> K . <UGWO�B K > ;4<�> 5 >EF[> GW; ?�1 > 5 � > A ?�5 ; K D9D X;=DdGJObDJ;=<�> 1 A > ;=<�D9B �

� O&ICD Ad8 G 1@365 DhO ;4<�> T O 3 ;=> > K > A >ZO"; A > ;=<�D9B ?�5 > 5E3 O/;4> 1 8 D K GW; 3 DhO�F ? O�IZ; 3 DhO 5N54? - 5 ; 3 �; ? ;=>CB 3 O/;=D�GJO,>CY ?�3 P G K >CO/; 3 O/;4>C] 1 G K >CY ? GW; 3 DhO�F[D 1 ;= 8 1 D - K > A � OVR � � L < 3Q5 G K6K D�� 5 F[D 1;=��U>�� 3 - 36K63 ; . ;=D*F[D 1 A ?�K G ;=>�;4<�> >CY ? G ; 3 DJO 5 F 1 D A ? O 5 ; 1@? IZ; ?�1 >ZB�] 1@3 B 5 GWO�B <UGJO�B K63 Ob]DJFNGJO 3Q5 DJ; 1 D 8 3 > 5 � L <�> 1 >ZF[D 1 > � >�IS<bDaD 5 >�;4< 365 A >Z;4<�D9B�;4D�B 365 I 1 > ; 3�� > ;=<�> IZDhO/; 3 O ? D ?�5- 3 Da> K >CI ; 1@3 I T > K B 8 1 D - K > A � � > 5 ;SG 1 ; � 3 ;=<^;4<�> >ZY ? GW; 3 DhO 5 F 1 D A G - D P > GJO�B ?�5 > G 1 - 3 ; 1 G 1 .;=> 5 ;�F ? O�I ; 3 DhO � ;=DdB�> T Ob> - D ? ObBUG 1 . ICDhO�B 3 ; 3 DhO 5��

�� &�� e �UP ��<�> 1 > ��1 > 8 1 > 5 >ZO"; 5 ;4<�> 5 D KQ? ; 3 DhO�B�D A G 3 O+;4<UGW; A ?b5 ; - >\B 3Q5 I 1 >Z; 3 � >CB �

� � �� e �SR �: B 365 I 1 >Z;=> 5@? - 5 8 GJIC> A ?�5 ; G K65 D - >\B�> T Ob>CB �

�� $ � � � � � e �UT �L <�> 8 G 1 G A > ;=> 145 DJF�;=+F ? O�IZ; 3 DhO �� G 1 >�B�> T O�>CB�GW;EO�D9B�> 8 D 3 O/; 5 ��

! � = � e � � � � �#" GJO�B�;=<�> - G 5@365 F ? O�I ; 3 DhO 365 B�> T O�>CB�G 5 G KQ3 O�>CG 1 8 3 >ZIC>�� 365 >fIZDhO/; 3 O ? D ?�5

=V=

F ? O�I ; 3 DhO � � � �� 3 ;4<&G P G KQ? > DJF = GW;EO�D9B�> 5 GJO�B g > K65 >��<�> 1 > � L < 3Q5 K >CGJB 5 ;=D ;=F[D 1 A ?�K G ; 3 DJO F[D 1 � � ��

�� " �� e � � ��<�> 1 >^G KQ3 O�>CG 1 IZD A - 3 OUGW; 3 DhO�DJF � � � �� ICGJO - > F[D ? ObB ;4DdBb> 5 I 143 - > � � �� > � GJO/;;=D T O�B � � � �� ;=D 5 GW; 3Q5 F . >CY ? GW; 3 DhO e � � GJO�B 5@3 O�IZ> � � I GJO - >EG K63 O�> G 1 ICD A - 3 O�GW; 3 DhO � > � 1@3 ;=> �

� � � " �� e � = g �J Y ? GW; 3 DhO e �QP ICGJO - > 1 >�� 143 ;4;=>ZO �

" �� = � � � � �#" � � e � =V= �

� >^O�D�� <UG P > ;=<�>^>CY ? GW; 3 DhO 3 O�;4<�>\F[D 1 A O�>ZIC> 545 G 1 . F[D 1 KQ3 O�>CG 1 5 . 5 ;4> A 5 D K P > � L <UG ;365 ;4<�> T O 3 ;4> > K > A >ZO"; G 8b8 1 D � 3 A GW; 3 DhO�<UG 5 G 5 >Z; DJF � >ZY ? GW; 3 DhO 5 � 3 ;=< � ? O X O�D��O 5ICD 141 > 5 8 DhO�B 3 O�]�;4D�;4<�> � P >ZIZ;4D 1 � L <�> >ZY ? GW; 3 DhO�ICGJO - > 8 ? ; 3 O A GW; 143 � F[D 1 A��

��<�> 1 > � 3Q5 ;4<�> 5 ; 3 � O�> 5@5 A GW; 1@3 � � 3 ;4<+> K > A >CO/; 5 �� GJObB � 3Q5 ;=5 D ?�1 IZ>2ICDhO/; 1@3 - ? ; 3 DJO 5 � 3 ;=<+> K > A >CO/; 5�� D��;=<�> F[D 1 � G 1 B 8 1 D - K > AI GWO - > >�� 8 1 > 545 >CB 3 O^;4<�> F[D 1 A � � � �� L <�> 3 O P > 1@5 > - 3 Da> K >ZIZ; 1@3 I T > K B 8 1 D - K > A 1 >ZY ?b361 > 5F ?�1 ;=<�> 1 A D9B 3QT ICGW; 3 DhO F[D 1 A ?�K ; 3 ] 1@3 B+G 8�8 K63 I GW; 3 DhO ;4D - >2B 365 I ?�5@5 >ZB K GW;4> 1 �D�; D�;��

� > �a; ;4<�>'>ZY ? GW; 3 DhO 5 A ?�5 ; - > IZDhO 5 ; 1 G 3 O�>ZB � 3 ;4< 1 >Z] ?�K G 143 � GW; 3 DhO � � 3 ;4<�B 3Q5 I 1 >Z;4>36KQK � 8 D 5 >CB 8 1 D - K > A 5 5 A G K6K IS<UGJOb]h> 5V3 O ;4<�> 3 O 8 ? ; I GJO I G ?�5 > ? O - D ? O�B�>ZB�IS<UGJO�]J> 5V3 O ;=D ? ; 8 ? ; 5 D�;=<�> 5 D K6? ; 3 DhO 5 DWF ;=>CO K GWI X 5 ;=G - 36KQ3 ; . � J 1@1 D 1@5X3 O A >CG 54?�1 > A >CO/; 5 GJO�B I G K I ?�K GW; 3 DhO 5I GWO K > GJB�;=D K G 1 ]h> > 141 D 145+3 O ;=<�> 5 D K6? ; 3 DJO � � 3 ;4< 1 >C] ?�K G 1@3 � GW; 3 DhO � > 5 >C> X ;=D A G X >;= 5 D K6? ; 3 DhO IZDhO/; 3 O ? D ?�54K . B�> 8 >ZO�B�>CO/;'DhO;4<�> 3 O 8 ? ; � � ; 3Q5 ;=<�> 1 > F[D 1 >�O�>CIZ> 5@5 G 1 . ;4DG 8�8 K . ICDJO 5 ; 1 G 3 O"; 5 3 O�D 1 B�> 1 ;4D+GJIS< 3 > P > G 1 > G K6365 ; 3 I 5 D KQ? ; 3 DhO � L < 365 I GJO - >^G 5�543 Ad8 K >^G 5A 3 O 3 A 3��C3 Ob]d;4<�>d; � D � O�D 1 A 5 D KQ? ; 3 DhO B ?�143 O�]�;=<�> 5 D KQP > - ? ; P G 143 D ?�5 DJ;4<�> 1 ICDhO 5 ; 1 G 3 O/; 5I GWO - >�G 8�8 KQ3 >CB(G 5 � > KQK 5@? IS<+G 5 ] 3 P93 O�]\G 8 1@3 D 1@3 > 5 ; 3 A GW;4> F[D 1 ;=�B�GW;SG GJObB ?b543 Ob] A D 1 >5 D 8 < 365 ; 3 I GW;4>CB A 3 O 3 A 3 � GW; 3 DhO 5 � i � RVR =V= R =V= T � �L <�> L 3 X <�DhO�D P A >Z;4<�D9B 3Q5 DhO�>EDJF ;= A D 5 ;2F 1 >CY ? >ZO/; K . ?b5 >CB A >Z;=<bDaB 5 DWF 1 >C] ?�K G 1 �

3 � GW; 3 DhO � =V= R � � � 3 ;=<d;=< 3Q5 A >Z;4<�D9B DJO�> G ;4;=> A 8 ; 5 ;4D A 3 O 3 A 3�� > ;4<�> 1 > 5@3 B ? G K � � �� GWO�B

= e

G A >CG 54?�1 G - K >dIZDhO 5 ; 1 G 3 O/; G ; ;4<�> 5 G A >d; 3 A > � : O�>��bG Ad8 K >(DJFVG�ICDJO 5 ; 1 G 3 O"; � D ?�K B - >;= 1 DaDW; A >CGJO 5 Y ? G 1 >^DJF � � L < 365 K > GJB 5 ;4DE;=<�>2F[D KQK D�� 3 O�]^F[D 1 A ?bK GW; 3 DhO �

� � � �� e � = e �

� >^ICD ?bK B G K65 D ?�5 > G < 3 ]h<�> 1 D 1 B�> 1 IZDhO 5 ; 1 G 3 O/; ;4> 1 A ;4<UGW; ?�5 > 5 ;=N] 1 GJB 3 >ZO/; D 1 ;=K G 8 K GJI 3 GJO(DJF � � : KQ5 D A ?�K ; 3 8 K > ICDhO 5 ; 1 G 3 O/; 5 I GWO - >�ICD A - 3 Ob>CB 3 O/;=D^;4<�>�ICDhO 5 ; 1 G 3 O/; ;=> 1 A�G KQK D�� 3 O�] ] 1 >CGW;=> 1 ��>�� 3 - 3QK63 ; . 3 OE<�D�� >�IZDhO 5 ; 1 G 3 Od;4<�> 8 1 D - K > A � = O = P � � J 3 ;=<�> 1 �VG . � >G 1 > O�D K DhO�]h> 1 A 3 O 3 A 3��C3 Ob]EDhO K . G 1 > 5@3 B ? G K - ? ;\G KQ5 D ;4<�> 1 > 543 B ? G K GJO�B ;4<�> IZDhO 5 ; 1 G 3 O/;;=> 1 A �: O�DW;=<�> 1 A >Z;4<�DaB�F[D 1 1 >C] ?bK G 1@3 � G ; 3 DJO 365 5@3 O�] ?bK G 1 P G KQ? >\B�>CIZD Ad8 D 5@3 ; 3 DhO � i � � � L <�> �

A GW; 1@3 � I GJO - > - 1 D X >ZO ? 8 �� e � = i �

��<�> 1 > � GJObB � G 1 > D 1 ;=<bDh]hDhOUG K A GW; 143 IC> 5 GJO�B '365 G B 3 GJ]hDhO�G K A G ; 143 � � 3 ;4<^;4<�> 5@3 O�] ?�K G 1P G K6? > 5 G 5 ;=<�>dB 3 GW]hDhOUG K >CO/; 1@3 > 5 �� F ;=<�> 5 A G K6K > 1 >ZO/; 143 > 5 3 O G 1 >d> K63 A 3 OUGW;=>ZB ;=<�>ZO � >I GWO�I 1 > G ;=> GJO : A GW; 143 � ;=<�GW; 365 - >Z;4;4> 1 ICDJO�B 3 ; 3 DhOb>CB �.B O�IZ> FHGJI ;=D 1@3 � GW; 3 DhO 365 IZD A 8 K >Z;4> ;= 5 . 5 ;=> A I GJO�;=CO - > 5 D KQP >ZB �

� � � �� e � = @ ��%� � � � � � �� e � = O �� e � = P �� e � = R �� e � = T �

� 3 A 3 ;=>ZB 3 ;4> 1 G ; 3 DJO ICDhO � ? ]/GW;4>�] 1 GJB 3 >CO/; 365 G 5@3 A 36K G 1 A >Z;4<�DaBE;4<UGW; > KQ3 A 3 OUG ;=> 5X5 A G K6K > 1

> 3 ]h>CO P G KQ? > 5 GJObBd;4<�> 3Q1 ICD 1@1 > 5 8 DhO�B 3 O�]\> 3 ]J>CO P >ZIZ;=D 145 F 1 D A ;=<�> 5 D K6? ; 3 DhO � � <�>ZO G 8b8 K . 3 Ob]G IZDhO � ? ]/G ;=>N] 1 GJB 3 >CO/; 5 D K P > 1 � > I GWO 5 ;4D 8 - >ZF[D 1 > 8 > 1 F[D 1 A 3 O�](;=<�> F ?�K6K � 3 ;=> 1 GW; 3 DhO 5 3 OD 1 B�> 1 ;=D X >C> 8 DhO K . ;= A G � D 1 > 3 ]h>ZO P >CI ;=D 1@5 GWO�B�D - ;SG 3 OfG 5 A DaDJ;4<�> 1 1 > 5@?�K ; � i � = = T � �L <�> 5 > A > ;=<�D9B 5+1 >CY ?�361 > GW; K > G 5 ;�DhO�> 8 G 1 G A >Z;4> 1 � ;=D*IS<�D9D 5 >�<bD�� A ? IS< 1 >C] ? �

K G 143 � GW; 3 DhO ;=D'G 8�8 K . � F[D 1 >��bG Ad8 K > ;= A GJ]hO 3 ; ? B�>dDJFV;4<�> A > G 54?�1 >CB&ICDJO 5 ; 1 G 3 O"; � 3 ;4<L 3 X <�DJO�D P D 1 ;=<�> A 3 O 3 A ? A G K6K D�� >CB 543 O�] ?�K G 1 P G K6? > � 3 ;=<�` > W � � L < 365 IS<�D 3 IC> 365 P > 1 .

= i

3 Ad8 D 1 ;=GJO/;dGJO�B ICGJO - > G B 3�� I ?�K ; B�>CI 365@3 DhO�;=D A G X > � L <�> � � I ?�1 P > A > ;=<�D9B 3Q5 DhOb>A >Z;=<bDaBf;=D B�>Z;4> 1 A 3 Ob>^G 1 >CG 5 DJOUG - K > � � � � � P G K6? > DWF � � O = � � : O � � I ?�1@P >^] 1 G 8 < 5 ;=ICDJO 5 ; 1 G 3 O"; ;=> 1 A P > 145@?�5 ;=<�> 1 > 543 B ? G K � ;= 1 > 543 B ? G K GJObB(;4<�> ICDJO 5 ; 1 G 3 O";RIS<UGJO�]h>�� 3 ;=<E;=1 >Z] ?�K G 143�� GW; 3 DhO 8 G 1 G A >Z;=> 1 � � 3 ;=< G K Dh] � K DJ] 5 I G K > � L <�> ICD 1 O�> 1 DJF ;4<�> � � I ?�1@P > ;4<UGW; 365 ��<�> 1 > ;=<�>�I ?�1@P > - >C] 3 O 5 ;=D 1@365 > 5 <UG 1 8 K . 365 ?�5 >CB(;=D\IS<�D9D 5 > ;= 8 G 1 G A > ;=> 1 /-/. IS<�D9D 543 O�];= 8 D 3 O";�DWF A G � 3 A ? A I ?�1@P GW; ?�1 > �L <�>�B 365 I 1 > 8 GJO�I .d8 143 O�I 3 8 K > 3Q5 GJO�DJ;4<�> 1 A >Z;=<bDaBEF[D 1 IS<�D9D 5@3 O�] � � � 3 ;=<(;=< 365 A >Z;=<bDaB

� > IS<�D9D 5 > G 1 >CG 5 DJOUG - K > K > P > K F[D 1�� GJObB�ICG K6K ;4< 365�� >E;=CO A 3 O 3 A 3 � > ��< 3QK > A G 3 O/;=G 3 O 3 O�] � � � � �� : 8 D 54543 - K > IS<�D 3 IC> �'3Q5 ;=<�> A >ZB 3 GJO&DWF�;4<�>�� B 3Q5 ; 1@3 - ? ; 3 DJO �

� >�I GWO G KQ5 D ?�5 >�]h>ZO�> 1 G K63�� >CB(I 1 D 5@5 P G KQ3 BUGW; 3 DhO ;4D\B�>Z;4> 1 A 3 Ob> � � i T RVR � � HUD 1 G ] 3QP >ZO� � > TU1@5 ;2G 8�8 K . L 3 X <�DhO�D P 1 >Z] ?�K G 143 � GW; 3 DhO+;=D � � � � � ��< 3 IS< 3Q5 � � � � � � 3 ;=<�D ? ;;= ! ;=< >ZY ? GW; 3 DhO � L 1 > 5@?�K ; 3 O�]�G 8�8 1 D � 3 A GW; 3 DhO 3Q5 B�>ZO�DJ;=>ZB �� L <�>ZO � > ?�5 > �� ;=Df> 5 ; 3 A G ;=> � � � � � � �� > 5 >C> X ;=D T O�B�GJO � ;4<UGW; A 3 O 3 A 3�� > 5 ;4<�>E> 1@1 D 1 DJF ;=G - D P >\> 5 ; 3 A GW; 3 DhO �: O�DW;=<�> 1 A D 1 > 1 >ZIC>ZO"; K . Bb> P > K D 8 >CB A > ;=<�D9B 5 > K >ZIZ; 5 ;=EICD 1 O�> 1 - G 5 >CB�DhO�G A 3 O 3 �

A ? A B 365 ;SGJO�IZ>EF ? O�IZ; 3 DhO ;4<UGW; 365 T O�B 3 O�]f;=<�> 8 D 3 O/;2;=<�GW; 365 I K D 5 > 5 ;\;=Df;=dD 143 ] 3 O � R � �� ?b365YX G Ad8 � 1 DJ;=> G 8 G 8 > 1 DhO IS<�DaD 543 Ob] A D 1 > 8 < . 5@3 D K Dh] 3 I G KQK .^- G 5 >ZB�ICDhO 5 ; 1 G 3 O/; 5 1 G ;=<�> 1;=CO 543 Ad8 K > A GW]hO 3 ; ? B�> ��_ `+D 1 ] 1 GWB 3 >ZO"; - G 5 >ZB A > G 5@?�1 > A >ZO/; 5 � O @ � �: 8�8 K63 ICGW; 3 DhO�DJF�B 3 � > 1@3 O�] 8 G 1 G A >Z;=> 143�� >CB 1 >C] ?�K G 1@3 � GW; 3 DhO ;=D >CGJIS< 54? -bA GW; 143 IC> 5^365 G

1 >ZIC>ZO"; G 8�8 1 D/GJIS<�F[D 1 1 >Z] ?�K G 143�� GW; 3 DhO � P i P @�� L <�> 54? -�A GW; 143 IZ> 5 ;=<UGW;'G 1 > ?�5 >CB G 1 >B 3Q5 I ?b545 >ZB 3 O�;= A > ;=<�D9B 5+5 >CIZ; 3 DhO DWF ;4< 365 8 G 8 > 1 � J GJIS<�DJF\;4<�> 5 > 54? -�A GW; 143 IZ> 5 <UG 5� 3 Bb> K . B 3 � > 1 >ZO";+ICDhO�B 3 ; 3 DhO�O ? AN- > 145 � L 1 > F[D 1 > 3 ; 3Q5 K Dh] 3 ICG K ;=D*G 8�8 K . G�B 3 � > 1 >ZO/;G A D ? O/;�DJF 1 >Z] ?�K G 143 � GW; 3 DhO ;4Dd>CGJIS< �

� G ;=<�> 1 ;=<UGWO ?�543 O�] ;=<�> L 3 X <�DhO�D P >CY ? GW; 3 DhO ;4D A 3 O 3 A 3 � > G ICD 5 ;RF ? O�I ; 3 DJOEICDhO 5 ; 1 G 3 O �3 Ob] 5 D K6? ; 3 DhO ;=<�>+GJB A 36545@3 - K > 5 D KQ? ; 3 DhO*G 8b8 1 D/GWIS< ?�5 > 5 GJO*D 8 ; 3 A 3 � GW; 3 DhO�G K ]JD 143 ;=< A ;4DT O�B�GJO 5 D KQ? ; 3 DhO ;=<�GW; 5 GW; 365@T > 5 G 5 >Z; DJF ?�5 > 1 Bb> T O�>ZB�I 143 ;4> 1@3 G � L < 3Q5 G 8�8 1 D/GJIS<�G K6K D�� 5] 1 > GW;4> 1 �U>�� 3 - 36KQ3 ; .� G 5 A ?�K ; 3 8 K > IZDhO 5 ; 1 G 3 O/; 5 I GJO - >�> A 8 K D . >CB GJO�B(;= 5 >�ICDJO 5 ; 1 G 3 O"; 5 B�DO�DJ; <UG P >^;=D F[D K6K D��;=<�> L 3 X <�DhObD P F[D 1 A ?�K GW; 3 DhO � c DJO 5 ; 1 G 3 O"; 5 ICGJO - >NB�> T O�>ZB DhO A D 1 >8 < . 543 D K Dh] 3 I G K6K .dA > GJO 3 O�]JF ?bK A > G 5@?�1 > 5 � e � �

= @: O�DW;=<�> 1 A >Z;=<bDaB - D 1@1 D�� >CB�F 1 D A ]h>CD 8 < . 5@3 I 5 F[D 1f1 >C] ?�K G 1@3 �Z3 O�]&;= 5 D K6? ; 3 DhO 3Q5

F[D9I ?�5@3 O�] 3 O P > 145@3 DhO � T @�� L < 3Q5 A >Z;4<�DaB ?�5 > 5 A D 1 > GJB P GJO�IZ>CB IZDhO 5 ; 1 G 3 O/; 5 ;=<�GW; >CO�IZD ?�1 GW]h>K D9I G K63 � GW; 3 DhO DWFX;4<�> 5 D ?�1 IC> 5 �

H ?�1 ;4<�> 1 ��CO A ?�K ; 3 8 K > A > G 54?�1 > A >CO/; 5 G 1 > A GJBb>�GW; B 3 � > 1 >CO/; ; 3 A > 5 � >�I GJOdG 8b8 K .GV; 3 A >RBb> 8 >CO�B�>ZO/; A >Z;4<�DaB � :*; 3 A >RB�> 8 >CObB�>CO/; A > ;=<�D9B ? ; 3QK63 � > 5 ;4<�> BUGW;=G F 1 D A B 3 � > 1 >ZO/;; 3 A > 5 ;4> 8 5 ;=D2BbD A D 1 >VGJIZI ?�1 GW;=>�GJO�G K . 543Q5 � _'?�K ; 3 8 K > 5@3 ]hOUG K I K G 545@3QT ICGW; 3 DhO � _ M ` � c �X<UG 5- D 141 D�� >CB(F 1 D A 543 ]hOUG K 8 1 D9IC> 54543 O�]\;=>CIS<bO 3 Y ? > 5 ;4D B 365 ; 3 O�] ?�365 < - > ; � >Z>CO A ?bK ; 3 8 K > 5 D ?�1 IZ> 5� = g @ = g O � � : O�GJB P GJO�IZ>CB F[D 1 A DJF _ M ` � c I G KQK >CB 1 >CI ?�145@3QP > K . G 8�8 KQ3 >CB GWO�B 8 1 D � >ZIZ;4>CB

� � : N � _ M ` � c � T e � 3 ;4> 1 G ; 3QP > K . 3 A 8 1 D P > 5 DhO�;4<�> 5 D ?�1 IC> I K G 545@3QT ICGW; 3 DhO �D�; D�; \ / � � � �� 2 � ��

� <�>CO ?b543 Ob]+G B 3 8 D K > A D9B�> K ;4D > 5 ; 3 A G ;=>\;=<�> 5 D ?�1 IC> 5 ;4<�>^; .98 3 I G K G 8�8 1 D/GJIS< 3Q5 ;4D] ? > 545 ;4<�>EB 3 8 D K > 5 � K D9I G ; 3 DJO 5 GWO�B ;=<�>ZO 8 > 1 F[D 1 A G F[D 1 � G 1 B ICD A 8 ? ;SGW; 3 DhO�DJF ;=<�>N;4D 145 D54?b1 FHGJIZ> 8 DJ;=>ZO/; 3 G K65 F[D 1 ;= ] 3QP >ZO K DaICGW; 3 DhO 5 � i @�� L �> 141 D 1d3 O&;=<�> 5 D KQ? ; 3 DhO&I GWO - >I G K I ?bK GW;4>CB GJO�B�;= B 3 8 D K > 5 I GJOf;=<�>ZO - > A D P >CB�G 1 D ? O�B�;=DdD 8 ; 3 A 3�� >�;=<�> 5 D K6? ; 3 DhO �c 1 >CGW; 3 O�]dG K > GWB T > K B ICGJO 5 8 >C>ZB ;4<�> 8 1 D9IC> 545 DJF I G K I ?bK GW; 3 O�] ;=<�> 54?b1 FHGJIZ> 8 DJ;4>CO/; 3 G K65

F 1 D A ;4<�>�B 3 8 D K > K D9I G ; 3 DJO � : K >CGJB T > K B 365 G'; 1 GWO 5 F[> 1 A GW; 143 ��;4<UGW; A G 8 5N5 D ?�1 IC> 5 ;4D;= 361 1 > 54?�K ;SGJO/; 5@?�1 FHGJIZ> 8 DW;=>CO/; 3 G KQ5 � = R � = � � � L < 365VK > GJB T > K B+I GJO - > I 1 > G ;=>CB -/. BbD 3 O�]NGF[D 1 �VG 1 B 5 D K P >�DJF G2B 3 8 D K > F 1 D A > GJIS<(;=D - > 3 O�I K6? Bb>CB 3 O ;4<�> K > GWB T > K B A GW; 143 � � L < 365 ICGJO- > K63 A 3 ;4>CB ;=D2;=<�>�> 8 3 ICG 1 B 3Q? A O�DaBb> 5 ��< 3 IS< 3Q5 ?�5 > F ?�K F[D 1 > 8 3 I G 1 B 3Q? A 8 DJ;4>CO/; 3 G K ;4D\;4D 145 D54?b1 FHGJIZ> 8 DJ;=>ZO"; 3 G K A G 8�8 3 O�] D 1 ICGJO 3 O�I KQ? B�> 54?�1 FHGJIC> 8 DW;=>CO/; 3 G KQ5 F[D 1 > P > 1 . O�DaBb> � 3 ;=< 3 O;=+<�> G 1 ; � L <�> K GW;4;4> 1^365 G Bb> 543Q1 G - K > K > GJB A GW; 143 � F[D 1 ] ? > 54543 O�] GW;NB 3 8 D K > K D9I GW; 3 DhO 5 �� D�� > P > 1 a8 > 1 F[D 1 A 3 O�]2F[D 1 � G 1 B 5 D KQP > 5 F 1 D A > P > 1 . O�D9B�> � 3 ;=< 3 OE;=<�>�<�>CG 1 ; 365 > �bIZ> 5@543QP > K .; 3 A > ICDhO 54? A 3 O�] � HUD 1 ; ? OUGW;4> K . ?b543 Ob] 1 >CI 3 8 1 DaI 3 ; . ;=CD 1 . � e R � = � 3 ; 3Q5 8 D 54543 - K >�;=D DJO K .8 > 1 F[D 1 A F[D 1 � G 1 B 5 D KQP > 5 F 1 D A >CGJIS< DJF ;=<�> 54?b1 FHGJIZ> 8 D 3 O"; 5 DJF A >CG 54?�1 > A >CO/;�GJO�B 1 >CICD 1 B;= 1 > 54?bK ; 5 F[D 1 >CGJIS<�DJF 3 O/;4> 143 D 1 <�>CG 1 ; O�D9B�> 5 ;=D I 1 > GW;4>d;4<�> K >CGJB A GW; 143 � � = ehe � � ` 3 O�IZ>;=NF[D 1 � G 1 B 5 D K P > 3Q5 - > 3 O�] IZD A 8 G 1 >ZB DhO K . ;4D�GJI ; ? G K 8 D 3 O/; 5 DJF A > G 5@?�1 > A >ZO"; 5 ;4<�> 1 >G 1 > 1 > K GW; 3 P > K . F[>�� 5 D KQP > 5 O�>CIZ> 545 G 1 . �

= OD�; D�;��

� >Z]/G 1 B K > 545 DJF ��< 3 IS<'DJF ;=<�> 5 > A >Z;4<�D9B 5 DhO�> IS<�DaD 5 > 5 ;4<�> 1 > 1 > A G 3 O 5 ;4<�>NIS<�G K6K >CO�]h>DJF 5 D KQP93 O�](G K G 1 ]J> � 5 I G K > KQ3 O�>CG 1 8 1 D - K > A ;4<UGW; 3 O P D KQP > 5 GJO 3QK6K � ICDhObB 3 ; 3 DhO�>ZB A GW; 143 � � L <�>A G 3 O B 3�� I ?�K ; 3 > 5 � 3 ;=< 5 D KQP93 Ob] 5@? IS< 8 1 D - K > A 5 G 1 > A G 3 O/;SG 3 O 3 O�]dGJICI ?�1 GJI . GJO�B 5 D KQP93 Ob]Y ?�3 I X"K . � L .98 3 I G KQK . DhO�> ?�5 > 5 021 . K D P�5@? - 5 8 GJIC> A > ;=<�D9B 5 54? IS<'G 5 ICDhO � ? ]/GW;=>2] 1 GJB 3 >CO/; ;=D 5 D KQP >E;=<�> 5 > 5 . 5 ;4> A 5 - >ZI G ?�5 >(DJF ;=<�> 361 1 G 8 3 B IZDhO P > 1 ]h>ZO�IC> GJO�B 5 ;=G - 3QK63 ; . � � D�� > P > 1 ;=&ICDhO � ? ]/GW;=>�] 1 GJB 3 >CO/; A > ;=<�D9B 5 ; 36K6K 1 >ZY ?�361 > 5�� ; 3 A >�F[D 1 ICDJO P > 1 ]h>CO�IZ> � � 3 ;4<8 1 >CICDJO�B 3 ; 3 DhO 3 O�]�;4< 365 ICGJO - > K D�� > 1 >CB G K ;4<�D ? ]J< 36K6K � IZDhO�B 3 ; 3 DJO�>CB 8 1 D - K > A 5 ICGJO 5 ; 3QK6KF[D 1 IC> � � � � � ; 3 A > � � : 5 � > 8 ?b1454? >'] 1 > GW;4> 1 GJICI ?�1 GWI .� 3 ; 365 O�>ZIC> 545 G 1 . ;=D � D 1YX � 3 ;4<K G 1 ]h> 1 O ? A - > 145 DJF�O�D9B�> 5 � L <�> 5 > K G 1 ]h> 1 � 5 I G K > 8 1 D - K > A 5 - >CIZD A > 8 1 Dh< 3 - 3 ; 3QP > K . 5@K D�� 3 ;4< 54? IS< GWO�G K ]hD 1@3 ;4< A � : 5 ;=^O�>Z>CBfF[D 1�5 8 G ; 3 G K GJICI ?�1 GWI . O�>ZIC> 5@543 ;SGW;4> 5 A D 1 >2O�D9B�> 5 ;= O�>Z>CB+F[D 1 K D�� > 1 D 1 B�> 1 5 D K P93 O�] ;=<UGW; I GWO 5 ; 3QK6K <UGWO�B K > < 3 ]J< K . 3QK6K � ICDhObB 3 ; 3 DhO�>ZB 5 . 5 ;4> A 5- >CICD A > 5 ] 1 > G ;=> 1 �

� ��

_'?�K ; 3 ] 143 B 365 G A >Z;4<�D9B�F[D 1�5 D K P93 O�] K63 Ob> G 1�5 . 5 ;=> A 5 � _'?�K ; 3 ] 143 BfI 1 > G ;=> 5 K D�� > 1 1 > 5 D �K6? ; 3 DJO ] 143 B 5 GJObB�> 5 ; 3 A GW;=> 5 5 D KQ? ; 3 DhO 5 DhO ;=<�> 5 >(] 143 B 5 G 5 GJO�G 8�8 1 D�� 3 A GW; 3 DhO ;=D�< 3 ]h<�> 11 > 5 D KQ? ; 3 DhO ] 1@3 B 5 � L < 3Q5 G 8�8 1 D/GJIS<(G K6K D�� 5 F[D 1 G 5 . 5 ;=> A GW; 3 I 1 > A D P G K DJF B 3 � > 1 >CO/;RF 1 >CY ? >ZO �I 3 > 5 DJF > 1@1 D 1@5 � HUD 1 > K6KQ3 8 ; 3 I 8 1 D - K > A 5 A ?bK ; 3 ] 143 B I GJO T O�B�G 5 D K6? ; 3 DJO 3 O K63 O�> G 1 ; 3 A > GJO�B 365 >CG 543QK . 8 G 1 G K6K > K63�� >CB � � = @ = eJi � �

� O =�� P = HU>CB�D 1 >CO X D TU145 ; 3 O/; 1 D9B ? IC>ZB*;=<�> ICDhObIC> 8 ;(DJF A ?�K ; 3 ] 143 B � e T � � � ; � G 5 O�DW;? O/; 3QK = � R i ;=<UGW; F 1 GWO�Bb; 1 > G KQ3 � >ZB 3 ; 5 > � I 3 >ZO�I . � � � � � O =�� R P � GWI X - ?�5 IS< 3 O�Bb> 8 >CO�B�>ZO/; K .B�> P > K D 8 >CBE;=<�> A ?�K ; 3 ] 1@3 B A > ;=<�D9B(G 5 � > KQK � @ R � � ` 3 O�IC> ;=<�>ZO /A ?�K ; 3 ] 143 B <UG 5 - >Z>COdG 8�8 KQ3 >ZB;=D G P G 5 ;RG 141 G . DJF G 8�8 K63 I GW; 3 DhO 5 � 3 ;=< � ?�5 ; G�F[>�� 1 >ZIC>ZO"; 8 G 8 > 145 I 3 ;4>CB <�> 1 > F[D 1 > �bG A 8 K > �� G P93 > 1 � `9;=D X > 5 � O O � 1 GJB 3 GW; 3 DhO � ; 1 GJO 5 8 D 1 ; B 3 � ?�5@3 DhO � @�� VG P > 8 1 D 8 GJ]/GW; 3 DhO GJO�B 3 A GJ]h>5 >Z] A >CO/;SGW; 3 DhO � = g R � � M ObF[D 1 ; ? O�GW;=> K .� A ?�K ; 3 ] 143 BfICGJO - >NG B 3 � I ?�K ; ;=D 3 A 8 K > A >CO/; GJO�B F[D 1 IC> 1 ;=G 3 O 8 1 D - K > A 5 1 >ZY ?�361 > 5 I ?�5 ;=D A 3 � GW; 3 DhO � F >CICG ?�5 >�DJF ;4<�> 36K6K � 8 D 5 >ZB&OUGW; ?�1 > DJF;= 3 O P > 145 > - 3 D9> K >CI ; 143 I T > K B 8 1 D - K > A� ;=< 3Q5 8 1 D - K > A 1 >ZY ?b361 > 5 I ?b5 ;=D A 3�� GW; 3 DhO,DJF2;=G K ]hD 143 ;=< A �L <�> - G 543 I A > ;=<�D9B�D K Dh] . DJF A ?�K ; 3 ] 1@3 B 3Q5 G 5 F[D K6K D�� 5��

= P= � � > K G � � � � � �� DhO�;4<�> T O�> ] 143 B+;=D(D - ;=G 3 O � �e � c D Ad8 ? ;4> 1 > 5@3 B ? G K�� i � L 1 GJO 5 F[> 1 � 1 > 5 ; 1@3 IZ; � 1 > 5@3 B ? G K ;=D(IZD/G 145 >^] 143 B � ��@ � � > K G ��DhO 1 > 543 B ? G K >ZY ? GW; 3 DhO � ��&� � DhOfICD/G 1@5 >\] 1@3 B

O � L 1 GJO 5 F[> 1 � 3 O";4> 1 8 D K GW;=> � G 8�8 1 D � 3 A G ; 3 DJO DWF > 1@1 D 1 DhO'IZD/G 1@5 >N] 143 B �� ;=D T O�>] 1@3 BfGJObB�IZD 141 >CIZ; 5 D K6? ; 3 DhO � � � � � � ��

��<�> 1 >�� B�>CO�DW;=> 5 ;=<�> T O�> ] 1@3 B^GJO�B�� B�>ZO�DJ;=> 5 ;4<�> ICD/G 1@5 > ] 143 B � � > K G �bGW; 3 DhO 1 > 5 ; 143 IZ; 3 DhO GJO�B 3 O/;4> 1 8 D K GW; 3 DhO�G 1 > ;=<�> 3 Ad8 D 1 ;=GJO/; 8 1 D9IC>ZB ?�1 > 5�3 O P D K P >ZB 3 Of;4<�> A ?�K ; 3 ] 143 B 8 1 D9IC> 545 �L <�> 1 > K G �bGW; 3 DhO � G K65 D X O�D��O G 5 5 A DaDJ;4< 3 Ob]�� 5 ;=> 8 1 >ZB ? IC> 5 ;4<�>�< 3 ]J< F 1 >CY ? >ZO�I . IZD A �

8 DhO�>CO/; DJF ;4<�> > 1@1 D 1 � L < 365 3Q5 O�D 1 A G K6K .\8 > 1 F[D 1 A >CB � 3 ;=<(G F[>�� 3 ;4> 1 GW; 3 DhO 5 DWF GWO 3 ;=> 1 GW; 3QP >5 D KQP > 1 � � GJIZD - 3 GJO�B K G ?�5@5 � `a> 3 B�> K G 1 > >��bG Ad8 K > 5 DJF 5 D KQP > 1@5 ;=<UG ; � D 1YX -/. T�145 ; 1 >CB ? I 3 O�];= < 3 ]h<�F 1 >CY ? >ZO�I . > 1@1 D 1 GJO�B�;4<�> 1 >ZF[D 1 >d;4<�> .�A G X >d>�� >CI ; 3QP > 5 A D9DJ;= 145 � L <�> A D 5 ;F 1 >ZY ? >CO/; K . ?�5 >ZB 5 A D9DJ;= 145 F[D 1 A ?�K ; 3 ] 1@3 BEG 1 > P G 143 G ; 3 DJO 5 DhO(;=<�> K G ?�5@5 � `9> 3 Bb> K A >Z;=<bDaB 54? IS<�G 5 54? ICIC> 545@3QP >\D P > 1 � 1 > K G �bGW; 3 DhO GJO�B+B 3 � > 1 >ZO/; ICD K D 143 O�] 5 IS<�> A > 5 � : OfG 8b8 1 D � 3 A GW;=>3 O P > 145 > 5 A DaDJ;4<�> 1 <UG 5 G KQ5 D 5 <bD��O 8 1 D A 3Q543 O�] 1 > 54?�K ; 5 � = eJg � � � D�� > P > 1 021 . K D P 54? - 5 8 GWIC>A >Z;=<bDaB 5 K63 X >(ICDJO � ? ]/GW;4>(] 1 GJB 3 >CO/;NG 1 >(O�DW;^; .98 3 I G KQK . ?b5 >ZF ?bK G 5 5 A D9DJ;=<�> 145 G 5 ;=<�> . B�D

O�DJ; F[D9I ?�5 DhO�;4<�>d< 3 ]h<�F 1 >ZY ? >CO�I . IZD A 8 DhO�>ZO/; � � DJ;=> ;=< 365 365 B 3 � > 1 >CO/;NF 1 D A 1 >C] ?�K G 1 �3 � GW; 3 DhO 3 O ;=<�GW; 1 >C] ?�K G 143�� GW; 3 DhO ?b54? G KQK . 1 >CB ? IZ> 5 ;4<�> < 3 ]h<dF 1 >CY ? >ZO�I . ICD Ad8 DhO�>CO/; DJF ;=ICD A 8 ? ;=>CB 5 D KQ? ; 3 DhO ��< 36K > 1 > K G �bGW; 3 DhO 1 >ZB ? IZ> 5 ;4<�> < 3 ]h< F 1 >ZY ? >CO�I . IZD Ad8 DhOb>CO/; DJFV;=> 1@1 D 1 � ;=<�>\B 3 � > 1 >ZO�IC> - > ; � >Z>CO ;=<�>\ICD A 8 ? ;=>CB�GJO�Bf; 1@? > 5 D KQ? ; 3 DhO � �: F ;4> 1 1 > K G �bGW; 3 DhO ;4<�> 1 > 5 ; 1@3 I ; 3 DJO 5 ;4> 8 GW;4;4> Ad8 ; 5 ;4D A G X >2GJO GJIZI ?�1 GW;=>\G 8�8 1 D � 3 A G �

; 3 DhO�DWF ;=<�> T O�>+] 1@3 B 1 > 5@3 B ? G K DhO�;4<�>+IZD/G 145 >+] 1@3 B � L <�> 1 > 543 B ? G K F 1 D A ;4<�> T O�> ] 143 BA ?�5 ; - > 5 D K P >ZB�DhO�;=<�>dICD/G 145 >d] 1@3 B 3 O�D 1 Bb> 1 ;=D A G X >dG�ICDhG 145 > ] 1@3 B�G 8�8 1 D � 3 A GW; 3 DhO �L <�> 1 >^G 1 > 543 B ? G K P >CI ;=D 1 ICD 1@1 > 5 8 DhO�B 3 O�]E;=D(;=<�>\ICDhG 145 >^] 1@3 B 8 D 3 O/; 5 A ?�5 ; - > ]J>CO�> 1 GW;4>CB

F 1 D A ;4<�> T O�>2] 1@3 B 1 > 543 B ? G K � L < 3Q5 365 8 > 1 F[D 1 A >CB -/. ;=G X"3 O�](G � > 3 ]h</; 3 O�](G P > 1 GJ]h>2DJF ;=P G K6? > 5 DJFX;=<�> T O�>\] 1@3 B 8 D 3 O/; 5 ;4<UGW;�G 1 >2ICDhObO�>CI ;=>CB�;=DdGE] 3QP >CO ICD/G 1@5 >\] 1@3 B 8 D 3 O/; �

� > �a; G 5 D KQP > D 1 G 8b8 1 D � 3 A GW; 3 DhO 365 8 > 1 F[D 1 A >ZB^DJO^;= ICDhG 145 > ] 1@3 B K > P > K ;=D I 1 > GW;4> ;=ICDhG 145 > ] 1@3 B+G 8�8 1 D � 3 A GW; 3 DhOEF[D 1 ICD 1@1 >ZIZ; 3 DhO � :�F ;=> 1 ;=< 365 ;= ICDhG 145 > ] 1@3 B G 8�8 1 D�� 3 A GW; 3 DhO

= R365X3 O/;=> 1 8 D K G ;=>CB � D 1 8 1 D K DhO�]h>ZB � DhO/;=D ;= T O�>V] 143 B^;=D 8 1 D Pa3 B�> ;4<�>V> 1@1 D 1 ICD 1@1 >ZIZ; 3 DhO � L <�>3 O/;4> 1 8 D K GW; 3 DhO 5 ;=> 8 1 > P > 1@5 > 5 ;4<�> 1 > 5 ; 143 IZ; 3 DhO 5 ;=> 8 ;=D'; 1 GJO 5 F[D 1 A ;4<�>+ICDhG 145 >+] 143 B�> 141 D 1

ICD 141 >ZIZ; 3 DhO DJO";4D+;=<�> T O�>E] 1@3 B � L <�> 3 O";4> 1 8 D K GW; 3 DhO�G K ]hD 143 ;4< A G KQ5 D ? ; 36KQ3 � > 5 G � > 3 ]h</;4>CBG P > 1 GJ]h> � L <�> G K ]hD 143 ;4< A B�> ;=> 1 A 3 O�> 5 >CGJIS 3 O+;=<�>2> 141 D 1 ICD 141 >ZIZ; 3 DhO P >CIZ;4D 1 GW; ;=T O�>2] 143 B -/. ;=G X"3 O�](G � > 3 ]h</;=>ZB'G P > 1 GJ]J> DWF ;4<�>2ICDhG 145 > ] 143 B 8 D 3 O"; 5 ;=<�GW;�G 1 >2ICDhO�Ob>CIZ;4>CB;=D ;=<�> ] 3QP >ZO T O�>N] 143 B 8 D 3 O/; � K >ZO�> 1 G K6K .� ;=<�> 1 > 5 ; 1@3 IZ; 3 DhO GJO�B 8 1 D K DJO�]/GW; 3 DhO D 8 > 1 G ;=D 1@5G 1 > ; 1 GJO 5 8 D 5 > 5 DJF > GWIS< DW;=<�> 1 � L <�> 1 > 5 ; 143 IZ; 3 DhO � GJO�B 3 O";4> 1 8 D K GW; 3 DhO � D 8 > 1 GW;=D 145 � D 1YXG 5 F[D KQK D�� 5��

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level 3

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5 <bD��O 3 O�H 3 ] ?b1 > e � i � L <�>ZD 1 > ; 3 I G KQK .� F ?�KQK A ?�K ; 3 ] 143 B 365 O�>CIZ> 5@5 G 1 . ;4D GJIS< 3 > P >�; 14? > K63 Ob> G 1ICDJO P > 1 ]h>CO�IZ> DJ;=<�> 1 � 3Q5 >�ICDhO P > 1 ]J>CO�IZ> ; 3 A > 365 � � �� - >CI G ?�5 >�DJF ;=<�>�] 1 D�� ;4<DJF ;=<�>\B�> 8 ;=< DJFX;=<�>\I . I K > 5 �

F >ZF[D 1 >�;=<�> A ?bK ; 3 ] 143 B�I . I K >fI GWO - >C] 3 O ;= IZD/G 1@5 >f] 143 B 8 D 3 O/; 5 A ?b5 ; - >�IS<bD 5 >ZO �L .a8 3 I G K6K . ;=<�>�O�D9B�> 5 IS<bD 5 >ZO�F[D 1 ;= ICD/G 145 >�] 143 B 5 G 1 > - G 5 >ZB ? 8 DhO�;=<�> ? O�B�> 14K . 3 O�]]h>ZD A > ; 1 . � c D/G 1@5 > ] 143 B 8 D 3 O/; 5 G 1 > 8 1 > F[> 1 G - K . > P >ZO K . 5 8 GJIZ>CB GWO�B�IS<bD 5 >ZO 5 D G 5 O�DJ; ;4D1 > A D P >VGJO . T O�>V] 143 B 8 D 3 O/; 5 ;=<�GW; G 1 > ObDJ;RIZDhO�O�>ZIZ;=>ZB ;=D GW; K > G 5 ;X; � D2ICDhG 145 > ] 1@3 B 8 D 3 O/; 5 �L <�> ]hD/G K 3Q5 ;=<UGW;(;4<�>�IZD/G 1@5 > ] 143 B 5 <�D ?�K B�GWICI ?b1 GW;4> K . 1 > �U>ZIZ;d;=<�> D 1@3 ] 3 OUG K ]J>CD A >Z; 1 . �H 3 ] ?�1 > e �Q@ B�> A DhO 5 ; 1 GW;=> 5 G ? O 3 F[D 1 A ; � D � B 3 A >CO 5@3 DhOUG K ] 1@3 B � 3 ;4<�GEO 3 O�> � 8 D 3 O/; 5 ;4>CO�I 36K �L D^B�> A DhO 5 ; 1 GW;=>�;=<�> A ?�K ; 3 ] 143 B 8 1 D9IC> 545 � > K DaD X GW; G 5@3 Ad8 K > > K6K63 8 ; 3 I 8 1 D - K > A � 3 ;4<

G 8 D 3 O/; 5 D ?b1 IC>^GJO�B � >�� A GJO�O - D ? O�BUG 1 . ICDhObB 3 ; 3 DhO � � >\<UG P > � G 8 K GJIC> � 5 >CY ? G ; 3 DJO �

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�� D�; � � : 5 G Ad8 K > 8 1 D - K > A GW; K > P > K = � IZD/G 1@5 > 5 ; K > P > K � ?�5 > 5 G i � i ] 143 B�GWO�B 3Q55 D KQP >ZB�B 361 >ZIZ; K . �

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�� D�; : Z � : 5 G Ad8 K > 8 1 D - K > A GW; K > P > K O ?�5 > 5 G ihi � ihi ] 143 B � L +] 1 G 8 < 3Q5 ;=B 3Q1 >CI ; K . 5 D KQP >ZB 5 D K6? ; 3 DJO �

e @� G ;=<�> 1 ;4<UGJO - > 3 O�] ?�5 >ZB G K DhO�> UA ?�K ; 3 ] 1@3 B 365 G KQ5 DdDJF ;=>ZO ?b5 >CB G 5 G 8 1 >ZICDhObB 3 ; 3 DhO�> 1 �

L < 3Q5 I GWO�;SG X >&GJB P GWO";=GJ]h>�DJF 021 . K D P5@? - 5 8 GJIC>*IZDhO P > 1 ]h>ZO�IC> A >Z;4<�DaB 5'K63 X > 8 1 >ZICDhO �B 3 ; 3 DJO�>CB�ICDhO � ? ]/GW;=>�] 1 GJB 3 >CO/; G K DhO�] � 3 ;4<�;=<�> 8 D�� > 1 DJF A ?�K ; 3 ] 1@3 B 3 O�;4<�>�F[D 1 A DJF8 1 >CICDJO�B 3 ; 3 DhOb> 1 � � 3 ;=< 8 1 >CIZDhO�B 3 ; 3 DhO 3 Ob] GJO G 8b8 1 D � 3 A GW;=> A GW; 1@3 � 3 O P > 1@543 DJO 365 G 8�8 KQ3 >ZB;=D ;4<�> 1 > 543 B ? G K GW;E> GWIS< 3 ;=> 1 GW; 3 DhO�;4D 3 Ad8 1 D P > ;=<�>�IZDhO�B 3 ; 3 DhO 3 Ob]'DJF�;= 5 . 5 ;4> A � � >I GWO ?�5 > A ?�K ; 3 ] 1@3 B�;=D+]J>CO�> 1 GW;4> G IZD/G 145 > ] 1@3 B'IZD 141 >CI ; 3 DJO'F 1 D A ;4<�> 1 > 543 B ? G K G 5 GdF[D 1 A

DJF 8 1 >CICDJO�B 3 ; 3 DhO 3 O�]N;4D 3 Ad8 1 D P > ;=<�>2IZDhO�B 3 ; 3 DJO 3 O�]^DJF ;=<�> 8 1 D - K > A G 5 � > KQK � J 3 ]h>CO P G K6? >GJOUG K . 543Q5X5 <�D�� 5 A ?�K ; 3 ] 143 B 8 1 >CIZDhO�B 3 ; 3 DJO 3 O�] . 3 > K B 5 > 3 ]h>CO P G K6? > 5 A D 5 ; K . I K6?b5 ;=> 1 >ZB(G 1 D ? O�BDhO�> GJO�BdICDhO 5 >CY ? >ZO"; K . K D�� > 1@5 ;4<�>�ICDhObB 3 ; 3 DhOEO ? A - > 1 � : K ;=<�D ? ]h< A ?�K ; 3 ] 143 BNG K65 D2;=>CObB 5;=D 8 1 D9B ? IZ> G�F[>�� > 3 ]J>CO P G K6? > 5 O�>CG 1� > 1 D ;=<�>�ICDhO � ? ]/GW;4>'] 1 GJB 3 >ZO/; > K63 A 3 O�GW;=> 5 ;4<�> 5 >

Y ?�3 I X"K . � =V= O � � L < ?�5 X-/. 3 A 8 1 D Pa3 O�] ;4<�>EICDhObB 3 ; 3 DhO O ? A - > 1 DWF ;4<�> 5 . 5 ;4> A A ?�K ; 3 ] 1@3 BI GWO�GJICIZ> K > 1 GW;4> ;=+ICDhO � ? ]/GW;4>+] 1 GWB 3 >ZO"; 8 1 D9IC> 545 � : K65 D 543 ObIC> 3 ;=> 1 GW; 3 P > A > ;=<�D9B 5 KQ3 X >ICDJO � ? ]/GW;4>2] 1 GWB 3 >ZO"; G ? ;=D A GW; 3 ICG K6K . 5 ICG K >2>CGJISCI ;=D 1 IZD 141 >CIZ; 3 DhO ;=< 3Q5 G KQK D�� 5 F[D 1 G ? ;=D �A GW; 3 I 5 ICG K63 O�]\DJF ;4<�>�ICD/G 145 >�] 1@3 BEICD 141 >ZIZ; 3 DhO ��< 3 IS< ICGJO 5 D A >Z; 3 A > 5 - >�;4DaD K G 1 ]h> D 1 ;=D9D5 A G KQK �D�; Z�; : � � � �� 2 � � � � � � � : K ]h> - 1 G 3 I _'?�K ; 3 ] 143 B � : _ K � 1 >ZF[> 145 ;4D ?�543 O�] A ?�K ; 3 ] 143 B,DhO A GW; 1@3 IC> 5 ��<�> 1 > ;=

? O�Bb> 14K . 3 O�]�]h>CD A > ; 1 . 365 O�DJ;d] 3 P >ZO � = g = e = i � � L <�> ICD/G 145 > O�D9B�> 5 G 1 >f;4<�>CO,IS<�D 5 >CO8 ?�1 > K . DhO;4<�>�] 3QP >COB 365 I 1 > ; 3�� GW; 3 DhO A GW; 1@3 � � L < 365 A > ;=<�D9BI GJO�GJIZ; ? G K6K . - > A ? IS<543 A 8 K > 1 3 O ;4<�>EI G 5 >EDJF ? O 5 ; 14? IZ; ?b1 >CB A > 5 5 � M O 5 ; 14? IZ; ?b1 >CB A > 5 5 I GWO - >EB 3 � I ?�K ;;=D � D 1YX � 3 ;=< ��<�>CO,; 1 . 3 O�]�;4D�IS<bDaD 5 >'G 5 > ; DWF ICDhG 145 >�] 1@3 B 5 - G 5 >CB ? 8 DhO�]J>CD A >Z; 1 .�- ? ;^;=<�> G K ]JD 143 ;=< A 5 F[D 1 : _ K G 1 > DJF ;4>CO A D 1 > 1 D - ?�5 ; 3 O�<UGJObB K63 O�] ;4<�> 3Q141 >C] ?�K G 143 ; 3 > 5DJF 54? IS< A > 5 5 � � ; 3Q5 B 3�� I ?bK ;2;=D 8 > 1 F[D 1 A A > 5 < ]h>COb> 1 G ; 3 DJO�DJO�IZD Ad8 K > � ]h>ZD A > ; 1@3 > 5GW;\B 3 � > 1 >ZO"; 1 > 5 D K6? ; 3 DhO 5 GWO�B�>ZO 54?b1 >(;=<UGW; >CGJIS< A > 5 < 3Q5 G 8 1 D 8 > 1@K . 1 >C] 3Q5 ;4> 1 >ZB 5@? - 5 >Z;DJF2;4<�> T O�> 1 A > 5 <�> 5 � L <�> IZD/G 145 > ] 143 B�I 1 > G ; 3 DJO 365 <�GJO�B K >CB -/. : _ K � 3 ;=<�D ? ;+;=B 3 � I ?�K ; . DJF 1 >CB ? I 3 O�] ? O 5 ; 1@? IZ; ?�1 >ZB+] 143 B 5 � B O�> B 365 GWB P GJO/;SGJ]h>�DJF : _ K 365 ;=<UG ; 3 ; DJF ;=>ZO1 >ZY ?�361 > 5 A D 1 > 5 > ; ? 8 ; 3 A > ��<�>ZO+;=<�> ]h>CD A >Z; 1 . 3 OaF[D 1 A GW; 3 DhO(ICD ?bK B+DJ;4<�> 1 � 365 > K >CGJB ;4DEGY ?�3 I X B�> ;=> 1 A 3 OUGW; 3 DhO DJF G 8�8 1 D 8 143 GW;=> ICD/G 145 >^O�D9B�> 5 � L <�>NIS<�D 3 IZ>NDJFRICD/G 1@5 >^] 143 B 8 D 3 O/; 5365d5 ; 36KQK�P > 1 . 3 A 8 D 1 ;=GJO/; � 3 ;=<�: _ K > 5 8 >CI 3 G KQK . 3 O A D 1 > B 3�� I ?�K ; 8 1 D - K > A 5d54? IS<�G 5

e O? O 5 ; 1@? IZ; ?�1 >ZB A > 5 <�> 5 GJO�B�GJO 365 DJ; 1 D 8 3 I 8 1 D - K > A 5 � T � � c DhG 145 >�] 1@3 B 5 > K >ZIZ; 3 DhO,I GJO - >- G 5 >CB 8 ?b1 > K . DhO�;= ] 1 G 8 < DJF ;4<�> A GW; 1@3 � � � D�� > P > 1 < 3 ]h 1 Y ? G K63 ; . IZD/G 1@5 > ] 1@3 B 5I GWO - >�]h>ZO�> 1 GW;=>ZB -/. ?�543 O�] ;=<�> ICDhObO�>CI ; 3 DJO 5 ; 1 >ZO�]J;=< 5 G 5 � > K6K G 5 ;=<�> ] 1 G 8 <,DJF ;=A GW; 1@3 � G K ;=<�D ? ]h< 3 O�ICD 1 8 D 1 GW; 3 O�]�IZDhO�O�>ZIZ; 3 DhO 5 ; 1 >ZO�]J;4< 5 I GWO - > 54K D�� > 1 � K >ZO�> 1 G K6K .�3 ; 3Q5 GJB P GWO";=GJ]h>ZD ?�5 ;4D�IS<bDaD 5 >�IZD/G 145 >�] 1@3 B 8 D 3 O/; 5 ;=<UG ;�� 3QK6K ICDhG 145 >CO�GJI 1 D 5@5'5 ; 1 DJO�]ICDJO�O�>CI ; 3 DhO 5 G P D 3 B 3 O�](ICD/G 145 >ZO 3 Ob] GWI 1 D 545�3 O/;=> 1 FHGJIZ> 5 � = = PVT � �: _ K G K65 D ?�5 > 5 ;4<�> A G ; 143 �,;=D 8 1 D9B ? IZ> ;=<�> ; 1 GJO 5 F[> 1 D 8 > 1 GW;=D 145 � L <�> ; 1 GWO 5 F[> 1

D 8 > 1 GW;=D 1@5 G 1 > ;=<�> 1 > 5 ; 143 I ; 3 DhOEGJO�B 3 O";4> 1 8 D K GW; 3 DhO � G K65 D 1 > F[> 141 >CB(;=D\G 5 ;4<�> 8 1 D K DhO�]hGW; 3 DhO �D 8 > 1 GW;=D 1@5 ;=<UG ; G 1 > ?�5 >CB(;=D 1 > 5 ; 1@3 I ; GWO�B 3 O/;=> 1 8 D K GW;4> ;= A GW; 143 � G 5 � > KQK G 5 ;=<�> P >CIZ;4D 145 �M 5@3 O�] ;4<�> A G ; 143 �d;=D(I 1 > GW;4> ;=<�> 5 >\D 8 > 1 G ;=D 1@5 I GJO - > 543 Ad8 K > 1 GWO�B A D 1 >2GJIZI ?�1 GW;=>2;=<�GJOGW;@;=> Ad8 ; 3 O�] ;4DdI 1 >CGW;=>2;= A F 1 D A ]h>ZD A > ; 1@3 > 5 � 3 ;=<fICD A 8 K >�� ? O 5 ; 14? I ; ?�1 >CB 8 1 D - K > A 5 �D�; Z�; D � � �� 2 �� , � � �

L <�> 1 > <�G 5 - >C>ZO � D 1 X DhO G 8�8 K . 3 O�] A ?�K ; 3 ] 143 B^;=D\DJ;= 1 B 3�� I ?�K ; GJObB 3QK6K � 8 D 5 >CB 8 1 D - �K > A 5 �5B O�>E> ��G A 8 K > 365 ;=<�>dG 8�8 K63 ICGW; 3 DhO'DWF A ?�K ; 3 ] 1@3 B�;4Df< 3 ]h< K . GJO 3Q5 DJ; 1 D 8 3 I 8 1 D - K > A 5� O P P � = g = � � L < 365 365 O�DJ;�GJO 36KQK � 8 D 5 >CB 8 1 D - K > A b- ? ;�GJO 365 DJ; 1 D 8 3 > 5 I 1 > G ;=> 8 1 D - K > A 5 F[D 1A ?�K ; 3 ] 143 B G ]J>CD A >Z; 143 ICG K6K . - G 5 >CB,G K ]hD 143 ;=< A GJO�B�GJO 3Q5 DJ; 1 D 8 3 > 5 B 365 ;=D 1 ;N;4<�>�>�� >CI ; 3QP >]h>ZD A > ; 1 . � L <�> GJO 365 DJ; 1 D 8 3 > 5 ;4>CO�B ;=D I 1 > G ;=> 3QK6K � ICDhObB 3 ; 3 DhO�>ZB 5 . 5 ;4> A 5 � L <�> 5 > 8 1 D - K > A 5G 1 >�;=GJI X"K >ZB ?b543 Ob] KQ3 O�> 1 > K G �bGW; 3 DhO � ?�5@3 O�]\B 3 � > 143 O�]2B�>C] 1 >C> 5 DWF 5 A D9DJ;=< 3 O�] 3 O(> GJISCI �; 3 DhO � GJObBNGJO^G 8�8 1 D/GJIS< ;=<UG ; 3 O P D K P > 5 ICDhG 145 >CO 3 O�] 3 O2;=<�> 5 G A > B 3Q1 >CI ; 3 DhO G 5 GWO 365 DJ; 1 D 8 3 > 5 �L < 3Q5 IZD/G 145 >CO 3 O�] 5 ; 1 GW;=>Z] . 1 > F[> 141 >CB�;=D�G 5�� 3Q5\543 A 36K G 1 ;4D ;4<�>+G 8�8 1 DhGJIS<;=<�GW; � � 3QK6K B�> 5 I 1@3 - > K GW;=> 1 ;=<�D ? ]h< 3 ; B�D9> 5 5 >C] A >CO/; ;4<�> 5 ;=> 8 5�? 8 3 O+;4<�> 5 G A > A GJO�O�> 1;=<�GW; � BbD � : 8 G 8 > 1 -/. : X IC> KQ3 X GJO�B K <�GW;4;=G 5 B 365 I ?�545 > 5 G 8b8 K . 3 Ob] A ?bK ; 3 ] 143 B*;=D�GJO3 O P > 145 > 8 1 D - K > A � i � � � D�� > P > 1 ;= 361 � D 1 X 365 � 3 ;=< 3 O P > 145 > � G P > 8 1 D 8 GW]/GW; 3 DhO GWO�BE;=< 3Q5365 G A ? IS 1 >CO/; 8 1 D - K > A ;=<UGWOd;4<�> 8 1 D - K > A � > G 1 > 5 D KQP93 Ob] � L <�> 1 > 365 G KQ5 D 1 > 5 >CG 1 IS<GW; � > 3 � A GWO�O � O 5 ; 3 ; ? ;=>�DJF `9I 3 >ZO�IC> 3 O � 5@1 GJ> K -/. : IS< 3 F 1 GJObBb; DJO G 8b8 K . 3 Ob] A ?�K ; 3 ] 1@3 BN;4D5 D KQP93 O�]�;4<�> 3 O P > 1@5 > 8 1 D - K > A DJFV> K >CI ; 1@3 I G K 3 Ad8 >ZBUGJO�IZ>(;4D A Dh] 1 G 8 < . � J � L � G K ;=<�D ? ]h< DhO�IZ> GJ]hG 3 O ;=<�> J � L 8 1 D - K > A 365 Y ?�3 ;4>'B 3 � > 1 >CO/; F 1 D A ;= 3 O P > 145 > - 3 Da> K >CI ; 1@3 I T > K B8 1 D - K > A - >CI G ?�5 >(;=<�> J � L 8 1 D - K > A 5 D KQP > 5 F[D 1 ;=<�>(IZDhO�B ? I ; 3 Pa3 ; 3 > 5\3 O 5 ;=>CGJB�DWF 5 D KQP93 Ob]F[D 1 ;4<�> 8 DJ;4>CO/; 3 G K65 �

B O�]hD 3 O�] 1 > 5 > G 1 IS< 8 1 D � >CIZ; 5 ;4<UGW;^G 8�8 K . A ?�K ; 3 ] 143 B ;4D ;4<�> 3 O P > 145 > - 3 D9> K >CI ; 143 I T > K B

e P8 1 D - K > A ?b5 > B 3 8 D K > K D9I G KQ3 � G ; 3 DJO � B Ob>EG 8�8 1 D/GJIS< ?�5 > 52K D�� > 1 1 > 5 D K6? ; 3 DhO�] 143 B 5 ;4D�> 5 ; 3 �A GW;=> 5 D ?�1 IZ> K DaICG K63 ; . KQ3 A 3 ; 5 � ihi � � L 5 > K63 A 3 ; 5 G 1 > ;=<�>ZO ?�5 >CB�G 5 ICDJO 5 ; 1 G 3 O"; 5 DhO 5 D ?�1 IZ>K D9I G K63 � GW; 3 DhO GW; G < 3 ]h<�> 1 1 > 5 D K6? ; 3 DhON;4D K D9I G ;=> ;4<�>VB 3 8 D K > 5 Y ?�3 I X > 1 GJO�B A D 1 >VGJIZI ?�1 GW;=> K . �: KQ5 D GW; ;=<�> M O 3 P > 1@543 ; . DJF J 1@K GJOb]h>CO _ Dh< 1 GJO�B ��? B�> G 1 > 3 Ad8 K > A >CO/; 3 O�] A ?�K ; 3 ] 1@3 B;=D 8 > 1 F[D 1 A ;= F[D 1 �VG 1 B 5 D K P > 5 F[D 1(K >CGJB T > K B,ICDJO 5 ; 14? I ; 3 DJO � P O T g � � : O�GJB P GJO/;SGJ]J>DJF ?�543 O�] A ?�K ; 3 ] 143 B�F[D 1 ;=< 365 G 8�8 KQ3 ICGW; 3 DhO 3Q5 ;=<UGW; ��< 3QK >N;4<�>EF[D 1 � G 1 B 8 1 D - K > A A ?�5 ; - >5 D KQP >ZB A GWO . ; 3 A > 5 ;= A ?�K ; 3 ] 143 B 5 >Z; ? 8 Ob>C>CB 5 DhO K .d- > 8 > 1 F[D 1 A >CB+DJO�IC> ;4D <UGJObB K > G K6K;= 5 D KQP > 5 �

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L D F[D 1 A ?�K GW;=> ;4<�> 3 O P > 145 > J cLK 54?b1 FHGJIZ> � ;4D � 5@?�1 FHGWIC> 8 1 D - K > A F[D 1 G K ]h> - 1 G 3 I A ?�K ; 3 ] 1@3 B� : _ K �� > O�>C>ZB ;=<�> 8 1 D - K > A 3 O';=<�>^F[D 1 A DJF � � � � � � 365 B�> T O�>CB 3 O J Y ? GW; 3 DhO i �QPGJO�B 365 B 365 ; 3 O�] ?�365 <�>CBEF 1 D A ;= 5 ; 3 � O�> 545 A GW; 1@3 � � � 3 O(D 1 B�> 1 ;4DÎCG 141 . D ? ; ;4<�> A ?�K ; 3 ] 1@3 B8 1 DaIZ>CB ?�1 > 5 � = e � � L <�> 1 >�G 1 > B 3 � > 1 >CO/; � G . 5 ;=D�G 141 GWO�]h>';4<�> 8 1 D - K > A 3 O/;4D&G K63 Ob> G 1A GW; 1@3 � 5 D KQP > � � 3 ;=< : _ K 3 ; 365�3 A 8 D 1 ;=GJO/; ;=<UG ;�;4< 365 >ZY ? GW; 3 DhO A >C> ; IZ> 1 ;SG 3 O�I 143 ;4> 1@3 G �H 3Q145 ; : _ K 365 1 > KQ3 GJO/; ? 8 DhO 3 ;=> 1 GW; 3 P > 5 A D9DJ;= 145 3 OfD 1 Bb> 1 ;=D F ? O�IZ; 3 DhO 8 1 D 8 > 14K . � L < 3Q55 A D9DJ;=<�> 1 I GJO - > GJO 3 ;4> 1 GW; 3 P > A > ;=<�D9B K63 X > � GJICD - 3 K G ?�545 � à> 3 B�> K � 3 O,D ?�1 ICG 5 > � D 1DhO�> DJFR;4<�> A GJO . DJ;4<�> 1 A >Z;=<bDaB 5 - ? ; ;4<�> 5 A D9DJ;4<�> 1 A ?�5 ; > �a< 3 - 3 ; 5 D A >ÎZDhO P > 1 ]h>ZO�IC>DhO � � � � � ` 8 >CI 3 T I G K6K . ;= 3 ;=> 1 GW; 3QP > A >Z;4<�D9B A ?�5 ; - >�G - K >*;4DB 3 A 3 O 3Q5 <$;=< 3 ]h< � F 1 >CY ? >ZO�I . > 141 D 123 O�Gf] 3QP >ZO�] ? > 5@5 �� ; 3Q5 O�DJ;^G K � G . 5 Ob>CIC> 545 G 1 . F[D 1 ;4<�> 3 ;=> 1 GW; 3QP >A >Z;=<bDaB+;4D 1 >CB ? IC> K D�� F 1 >CY ? >ZO�I . > 141 D 1 543 O�IC> ;4<�>2ICDhG 145 > K > P > K 8 G 1 ;�DJF : _ K >��aIZ> K65 G ;;=< 365 � : O�DJ;= 1 3 A 8 D 1 ;=GJO/; 1 >CY ?�361 > A >CO/;2DJF ;4<�> � � � �N5 > ; ? 8 365 ;4<UGW; � A ?�5 ;2<�G P >(G]h>ZD A > ; 1@3 I 3 O/;=> 1 8 1 >Z;=GW; 3 DhO 5 D ;4<UGW;�;=<�>^G K ]JD 143 ;=< A I GJO GWICI ?b1 GW;4> K .f8 > 1 F[D 1 A IZD/G 1@5 >CO 3 O�] �L < 3Q5 3Q5454? > 1 >CY ?�361 > 5 GJO G K ;=> 1 GW; 3 DhO 3 Od;4<�> 3 A 8 K > A >CO/;=GW; 3 DhON;=<�GW; � 3QK6K - >�B 365 I ?�5@5 >CB K GW;=> 1 �: 5 A >ZO"; 3 DhOb>CB > G 1@K63 > 1 ;4<�> 8 < . 543 I 5 DJF ;4<�> - 3 Da> K >ZIZ; 1@3 I T > K B 8 1 D - K > A G 1 > B�> 5 I 1@3 - >CB

� 3 ;4< G B 365 I 1 > ; 3 � GW; 3 DhOf;=<UGW; 1 > K GW;4> 5 ;4<�>NI ?�141 >CO/; 5 D ?�1 IZ> 5 ;4D ;= 8 DJ;=>ZO"; 3 G KQ5 ;4< 1 D ? ]h<�D ? ;;= - D9B . � L <�> >CY ? G ; 3 DJOf;4<UGW;�B�> 5 I 1@3 - > 5 ;=< 365 1 > K GW; 3 DhO�ICGJO - > � 143 ;4;4>CO 3 O�;=\F[D 1 A �

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LX1 GJB 3 ; 3 DJOUG K6K .� � >2ICD Ad8 ? ;4> ;=<�> K > GJB T > K B A GW; 143 �d;4<UGW; B 3Q1 >ZIZ; K . 1 > K GW;=> 5 ;=<�>2> 8 3 ICG 1 �B 3 G K 8 DJ;=>ZO/; 3 G K65 ;4D ;4<�> 54?�1 FHGJIC> 8 DJ;4>CO/; 3 G K65 ��< 36K > 3 ]hO�D 1@3 O�]�;=<�> 1 > 5 ;dDJF�;= 8 DJ;4>CO/; 3 G K65� ObDaB�> 5 - >Z; � >C>ZO ;4<�>N G 1 ; GJObB 54?�1 FHGJIC> � � = R � = � � � � D�� > P > 1 -/. B 3Q5 ICG 1 B 3 O�](;=<�> P G K6? > 5� > K D 5 >^;4<�> ]h>ZD A > ; 1@3 I B�> 5 I 143 8 ; 3 P >ZO�> 5@5 DJF ;=<�> F ?�K6K 5 D K6? ; 3 DhO � � >Z;=G 3 O 3 O�] ;4<�>N> 5 ; 3 A GW;=> 5DJF ;4<�> 5 > 8 DJ;4>CO/; 3 G K65 F 1 D A IZD/G 145 >�] 143 B*ICD 141 >ZIZ; 3 DhO 5^365 I 143 ; 3 ICG K ;=D 8 > 1 F[D 1 A 3 O�]f;=�]h>CD �A >Z; 1@3 ICG K6K . ICD Ad8 K >Z;=> ICD 1@1 >CI ; 3 DhO 5 � _�?�K ; 3 ] 1@3 B�� 5 5 8 >ZIZ; 1 G K A >CIS<�GJO 365 A 1 > KQ3 > 5 DhO+;=<�> K D9I G K1 > K GW; 3 DhO 5 DJF G ]h>ZD A > ; 1@3 I G K6K .�- G 5 >CB 5 . 5 ;4> A � L <�> 1 > F[D 1 > VAN. G 8b8 1 D/GWIS< K >CGJB 5 ;=D ;=F[D 1 A ?�K G ; 3 DJO - > K D�� OfGWB�B 3 ; 3 DhO ;4< 365 A > ;=<�D9B 3 Ob<�> 1 >CO/; K . 5 D KQP > 5 F[D 1 G K6K ;=<�> 8 DJ;4>CO/; 3 G K65- >Z; � >C>COf;= ;=D 1@5 D(GJO�Bf> 8 3 ICG 1 B 3Q? A � L <�> 5 >^GJB�B 3 ; 3 DJOUG K 8 DW;=>CO/; 3 G KQ5 ] 3 P > ?�5 3 O 543 ]h</; 3 O/;4D;= - 3 ]h]h> 1 8 3 I ; ?�1 >2DJF ;=<�> 3 O/;4> 143 D 1 > K >CI ; 1@3 I\GJI ; 3QP93 ; . �

H 1 D A ;=< 365 K Dh] 3 I � >2I 1 >CGW;=>2G F[D 1 A ?bK GW; 3 DhO � J K >ZIZ; 1 DaICG 1 B 3 Dh] 1 G A 5 8 1 D Pa3 B�> A > G 54?�1 >CB;=D 145 D 5@?�1 FHGWIC> 8 DW;=>CO/; 3 G KQ5 �� ;4<�> A >CG 54?b1 >CB O�D9B�> 5 I GJO - >(G 54? - 5 >Z; DJF ;= �� O�D9B�> 5 - ? ; ;4<�> >ZO/; 361 > 54?�1 FHGJIC>�I GJO - >�> 5 ; 3 A GW;=>ZB(;4< 1 D ? ]h< 3 O/;=> 1 8 D K GW; 3 DhO D 1 ;= O�DJO � A > G 5@?�1 >ZB;=D 145 D�ObDaB�> 5 I GJO - > ; 1 > GW;4>CB G 5 P D K6? A >^O�DaBb> 5 � GWO�B � > 5 >C> X ;=D�B�> ;=> 1 A 3 O�> > 8 3 ICG 1 B 3 G K8 DJ;=>ZO"; 3 G KQ5 �� O';4< 365�1 > 5 >CG 1 IS< ;=<�>^>CO/; 3Q1 > 5@?�1 FHGWIC> 3Q5 ; 1 > G ;=>CB G 5 X O�D��O ;=D 145 D O�D9B�> 5 �� > G 5@54? A > O�D I ?�141 >CO/; 5 D ?�1 IZ> 5 D ? ; 543 B�> DWF ;=<�> <�> G 1 ; 5 D ;4<�> - D ? O�B�G 1 . ICDJO�B 3 ; 3 DhO 5 ;=> K6K?�5 ;4<UGW; � � GWO�B � � ��< 3 IS< 1 > 8 1 > 5 >CO/; ;=D 1@5 D2GWO�B P D K6? A > I ?�141 >CO/; 5 D ?�1 IZ> 5 5 <�D ?�K B - > >CY ? G K;=D � > 1 D � : KQ5 D �� 5 <�D ?bK BE>CY ? G K ;=<�> A > G 5@?�1 >ZB 54?�1 FHGJIC> 8 DJ;=>ZO/; 3 G K65 �� 1 > 8 1 > 5 >CO/; 5 ;=I ?b141 >ZO/; 3 O � ? ��GJI 1 D 545 ;=<�> > 8 3 I G 1 B 36? A GJO�B 5@3 O�IZ> ;4< 365 365 ? O X O�D��O,GJO�B ? O�O�>ZIC> 5@5 G 1 .� >2I GJO�B 3Q5 ICG 1 B+;4< 365 8 G 1 ;VDJF ;=<�> 8 1 D - K > A K > G P93 Ob] � > 1 D F[D 1 ;4<�> 1@3 ]h</;V<�GJO�B 543 B�> � ` 3 O�IZ>� >2G 1 > 5 D K P93 O�] F[D 1 � a- ? ; �� 365 G K61 > GJB . X O�D��O � > ICGJO 54? - ; 1 GJIZ; �� F 1 D A ;4<�> 8 1 D - K > AGJO�B > KQ3 A 3 OUG ;=>�;=<�> 5 > O�DaBb> 5 F 1 D A ;=<�> 8 1 D - K > A G 5 � > KQK � � > ObD��<UG P > �

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ihg

Z�; : ; : � �� ]��

L D 3QK6KQ?�5 ; 1 GW;4>�;4<�> IS<�G K6K >CO�]h> DJF G 8�8 K . 3 O�] A ?�K ; 3 ] 143 BE;4DN;=<�> 3 O P > 145 > 8 1 D - K > A � > � 3QK6K>��bG A 3 Ob> G e W 8 1 D - K > A � 3 ;=< O @ = O�D9B�> 5 � 5 <bD��O 3 O[H 3 ] ?�1 > i � = � �-B F ;=<�> 5 > ;=<�> 1 >(G 1 >P g > 8 3 ICG 1 B 3 G K O�D9B�> 5 �i R P P D K6? A > O�D9B�> 5 GWO�B = g O ;=D 1@5 D O�D9B�> 5 � L <�> 8 DJ;=>ZO/; 3 G K65 DhO+;=<�>CG 1 ;^G 1 > G 54? - 5 > ; DJF 1 >CG K A >CG 54?b1 >CB P G K6? > 5 ;SG X >CO�F 1 D A G�;=< 1 >C> � B 3 A >ZO 543 DhOUG K A D9B�> K� R @�� L <�> ;=D 145 D P G KQ? > 5 G 1 > ICG K I ?�K G ;=>CB2F 1 D A ;= F[D 1 � G 1 B 8 1 D - K > A GJO�B <UG P > O�D 3Q5 > GJB�Bb>CB;=D ;4<�> A 3 O D 1 B�> 1 ;4D 543 A ?�K GW;4> ;=D 145 D A > G 5@?�1 >ZB P G KQ? > 5 � L <�> 5 > 543 A ?�K GW;4>CB ;4D 145 D A > G 54?�1 >CBP G K6? > 5 �� G 1 > ;4<�> 3 O 8 ? ; GJO�B�;4<�>^G K ]hD 143 ;4< A GW;4;4> Ad8 ; 5 ;=DdB�> ;=> 1 A 3 O�> <�> G 1 ; 8 DJ;4>CO/; 3 G K65�� > I GWO�ICD Ad8 G 1 > ;= I G K I ?�K GW;=>ZB <�>CG 1 ; 8 DJ;4>CO/; 3 G K65 � 3 ;4< ;= 1 >CG K A > G 54?�1 >CB P G K6? > 5 �W ?�1@3 O�] ;4< 365 ;4> 5 ; ;=<�>�IZD/G 145 >CO 3 O�] 365 DJO�> K > P > K Bb>C> 8 ;=D 5@3 Ad8 K . 36KQK6?�5 ; 1 GW;=> ;=<�>�>�� >CI ; DJF GJO36KQK � ICDhO�B 3 ; 3 DhO�>ZB A GW; 143 � � L <�> 3 O";4> 1 8 D K GW; 3 DhO GWO�B 1 > 5 ; 1@3 I ; 3 DJO 5 ;4> 8 5\?�5 > 543 Ad8 K > - 3QK63 Ob> G 1G 8�8 1 D � 3 A GW; 3 DhO � F DJ;4< ;4<�> F[D 1 �VG 1 B 8 1 D - K > A GJO�B ;= 3 O P > 145 > 8 1 D - K > A G 1 > 5 D KQP >ZB DhO;=< 365 ;=> 5 ; �

H 1 D A ;4< 365 ;4> 5 ; � >�I GJO 5 >Z> ;=<�GW; GJICI ?�1 GJI . 365 B 3 � I ?�K ; ;4D A G 3 O";=G 3 O � 3 ;=<(;=<�> 3 O P > 145 >8 1 D - K > A � L <�> A G 3 O 1 > G 5 DhO F[D 1 ;=< 3Q5 3 OUGJIZI ?�1 GJI . 3Q5 - >ZI G ?b5 > ;=<�> 3 O P > 145 > 8 1 D - K > A 3Q5 Y ?�3 ;4>36KQK � ICDhO�B 3 ; 3 DhO�>ZBNGJObBdBbDa> 5 ObDJ; ICDJO"; 3 O ? D ?b54K . B�> 8 >CO�BdDhOE;= BUGW;SG � ` A G K6K IS<UGJO�]J> 5 3 OE;=;=D 145 D 5@?�1 FHGWIC> 8 DJ;=>ZO/; 3 G K A > G 5@?�1 > A >ZO/; 5 GJO�B*G K65 D 5 A G K6K IS<UGJOb]h> 5E3 O�;=�ICDhO�B ? IZ; 3QP93 ; .

A DaB�> K ICG ?�5 > K G 1 ]J>'> 1@1 D 1@5�3 O�;4<�> I G K I ?bK GW;4>CB > 8 3 I G 1 B 3 G K 8 DJ;4>CO/; 3 G K65 � M ObF[D 1 ; ? O�GW;=> K .�;=2ICD/G 1@5 >ZO 3 O�](DJF A GW; 1@3 � � B�D9> 5 3 ObB�>C>ZB�ICG ?�5 > 5 A G KQK B 365 ;4D 1 ; 3 DhO 5V3 O+;4<�>\ICDhO�B ? IZ; 3QP93 ; .A DaB�> K � L < 365 A > GJO 5 ;=<UG ;+;=<�> 5 D KQ? ; 3 DhO�;=D�;=<�> IZD/G 145 >CO�>ZB K > P > K >ZY ? GW; 3 DhO 5+3Q5 O�DW;fG8 1 >CI 3Q5 > A GW;=IS< ;4D ;= 5 D KQ? ; 3 DhO DhO ;4<�> T O�> K > P > K � : O GJICI ?�1 GW;4>EICD/G 145 > A GW; 143 � 5 <�D ?�K B>��bGJI ; K . ICD Ad8 ? ;4>dG 1 > 5 ; 143 IZ;=>ZB 5 D K6? ; 3 DJO P >CI ;=D 1 F 1 D A ;=<�> 1 > 5 ; 143 IZ;=>ZB 3 O 3 ; 3 G K ICDhObB 3 ; 3 DhO 5P >ZIZ;4D 1 � L <�> 8 1 D - K > A DJF ICD/G 145 > A GW; 143 � 3 OUGJIZI ?�1 GJI . B�D9> 5 O�DW; A GJO 3 F[> 5 ; 3 ; 5 > K F 3 O A D 1 >� > K6K � IZDhO�B 3 ; 3 DJO�>CB 8 1 D - K > A 5 � eWi � R � �c DhO 5@3 B�> 1 ;4<�> 5 > ] 1 G 8 < 5 � 3 ;4<�;4<�> ; 1@? > 5 D K6? ; 3 DhO�GJObB�;4<�> ICDhG 145 >�] 143 B IZD Ad8 ? ;=>ZB

5 D K6? ; 3 DhO � H 3 ] ?�1 > i � e 5 <�D�� 5 ;=<�> � > KQK � 8 D 5 >CB F[D 1 �VG 1 B J cLK ;4> 5 ; 8 1 D - K > A �� 1 >CG 5H 3 ] ?�1 > i � i 5 <bD�� 5 ;= 3QK6K � 8 D 5 >ZB 3 O P > 145 > J cLK ;=> 5 ; 8 1 D - K > A �

� ? GJO/; 3 ;SGW; 3QP > K . 5 8 >CG X"3 O�] ;=<�> 3 O P > 145 > 8 1 D - K > A ICGJO - > >�� 8 1 > 545 >CB�G 5 A D 1 > B 3 � I ?�K ;- >CI G ?�5 > ;4<�>NIZDhO�B 3 ; 3 DJO'O ? A - > 1 F[D 1 ;4<�> A GW; 1@3 �f;=D 5 D K P > 3Q5 A ? IS< < 3 ]h 1 ;4<UGJO'F[D 1 ;=F[D 1 �VG 1 B 8 1 D - K > A � HUD 1^3 O 5 ;SGJO�IZ> � 3 ;=< L > 5 ; `9>Z; e GJObB R � `a>ZIZ; 3 DhO O � = � ;4<�>+F[D 1 �VG 1 B

i =

−200 −150 −100 −50 0 50 100 150 200−150

−100

−50

0

50

100

150

�� Z�; : � _ > 5 <�DJF ;=<�> O @ = O�D9B�> 5 G A 8 K > 8 1 D - K > A �

8 1 D - K > A <�G 5 G+ICDhObB 3 ; 3 DhO O ? AN- > 1 DJF G 8�8 1 D�� 3 A GW;4> K . = � = g � GJO�B ;= 3 O P > 145 > 8 1 D - K > A<UG 5 G ICDJO�B 3 ; 3 DhO�O ? A - > 1 DJF G 8�8 1 D � 3 A GW;4> K . = � = g �� L <�>f] 1 G 8 < 5 G - D P > � > 1 >f;SG X >COF 1 D A L > 5 ;\`9>Z; = � HUD 1 ;=< 3Q5 B�GW;SG 5 >Z; ;4<�> F[D 1 � G 1 B 8 1 D - K > A <�G 5 GdICDhObB 3 ; 3 DhOfO ? A - > 1 DJFG 8�8 1 D � 3 A GW;=> K . = � = g � GJObB ;=<�> 3 O P > 1@5 > 8 1 D - K > A <UG 5 G+IZDhO�B 3 ; 3 DJO'O ? A - > 1 DWF G 8�8 1 D � 3 �A GW;=> K . = � = g �� L <�> 3QK6K � 8 D 5 >ZB�O�> 5@5 DJF ;4<�> 3 O P > 1@5 > 8 1 D - K > A G KQ5 D A G X > 5 ;= 5 A D9DJ;=< 3 O�] 8 1 DaIZ> 545 DJF

A ?�K ; 3 ] 143 B A ? IS< K > 5@5 >�� >ZIZ; 3 P > � � ;4> 1 GW; 3 P > 5 D K P > 1@5 ]h>ZO�> 1 G K6K . ICDJO P > 1 ]h> A ? IS< 54K D�� > 1 � 3 ;4<36KQK � 8 D 5 >CB 8 1 D - K > A 5 GJObB ;=<�> B�> 5@361 >CB�ICDJO P > 1 ]h>CO�IZ> 3 O ;4<�> < 3 ]h< F 1 >CY ? >ZO�I . 1 GJO�]h> 54? � > 1@5G 5 � > K6K � L <�> 1 > G 1 > G�O ? A - > 1 DJF 5 A D9DJ;4<�> 1@5 ;=<�GW; 3 A 8 1 D P > ? 8 DJO�;=<�> - G 5@3 I � GWICD - 3D 1 K G ?�545 � `a> 3 B�> K G K ]hD 143 ;4< A � @ O @ P P R � � : A D 1 > 1 >ZIC>CO/; G 8�8 1 D/GJIS< ��< 3 IS< ?�5 > 5 GJOG 8�8 1 D � 3 A GW;=> 3 O P > 1@5 > 5 A DaDJ;4<�> 1 <UG 5 8 > 1 F[D 1 A >ZB P > 1 . � > K6K DhO 36KQK � ICDhO�B 3 ; 3 DhO�>ZB 8 1 D - K > A 5� = eJg � � � D�� > P > 1 � � 36KQK O�DJ; - > B�D 3 Ob] G IZD Ad8 G 143Q5 DhO DJF�;4<�> 3 ;=> 1 GW; 3QP > 5 D KQP > 145 >�� >CI ; 3QP >CO�> 545� 3 ;4<fB 3 � > 1 >CO/; 5 A DaDJ;4< 3 Ob] 8 1 D9IC> 545 > 5 �

i/e

0 20 40 60 80 100 120−20

−15

−10

−5

0

5

10truecoarse grid computed

�� Z�; D � L 1 > 54?bK ;^DJF GfICD/G 145 >d] 1@3 B 5 D K P >dDhO�;4<�>(F[D 1 � G 1 B�;=> 5 ; 8 1 D - K > A � L <�>� � G � 3Q5 365 8 D 543 ; 3 DJO�DhO ;4<�>\<�> G 1 ; �. � G � 365 365 8 DJ;4>CO/; 3 G K �

�� ) � � � ��

L <�> 8 1 D - K > A DJF 3 O�GJICI ?�1 GW;4>NIZD/G 145 >N] 1@3 B�ICD 1@1 >CI ; 3 DhO 3 O/; 1 D9B ? IC>ZB -/. 3QK6K � ICDJO�B 3 ; 3 DhOb>CB8 1 D - K > A 5 A ?b5 ; - >�GJB�B 1 > 5@5 >CB -/. ?�5 >�DJF A D 1 >�GJICI ?�1 G ;=>�IZD/G 1@5 >CO 3 O�] 5 IS<�> A > 5 ;=<�GJO

;=<bD 5 > ; 1 GJB 3 ; 3 DhOUG KQK . ?b5 >CB�F[D 1 � > K6K � ICDhObB 3 ; 3 DhO�>ZB A ?bK ; 3 ] 143 B 8 1 D - K > A 5 � : O�DJ;4<�> 1 8 1 D - K > A� 3 ;4<�Bb>C> 8 > 1 O�> 5 ; 3 O�]fDJFVIZD/G 1@5 >d] 143 B 52365 ;4<UGW; � 3 ;4<�G 5 A G KQK BUG ;SG 5 >Z; ;=d;4D 145 D ObDaB�> 5G 1 >'DhO K . ;=< 1 >C> ;=D 5@3 � K G . > 145 DJF2O�D9B�> 5 G �VG . F 1 D A ;4<�>'> 8 3 ICG 1 B 3 G K O�D9B�> 5 3 O 8 K GJIZ> 5 �:V;4;4> Ad8 ; 3 O�]�G 5 >ZICDhObB K > P > K DJF9ICD/G 145 >ZO 3 Ob]�D - P93 D ?�54K . I 1 >CGW;=> 5 5 D A > G - O�D 1 A G K ]h>ZD A > ; 1@3 > 5

� 3 ;4<$;=<�>�;=D 1@5 D O�D9B�> 5 > 3 ;4<�> 1 ;=D ? IS< 3 O�] D 1 DJO K . <UG P93 O�] DJO K . DhO�> K G . > 1 DJF(O�D9B�> 5 - >Z; � >C>CO�> 8 3 I G 1 B 3 G K GJO�Bf;=D 145 D(O�D9B�> 5 � L < 365 ICD ? 8 K >ZB � 3 ;=<+;4<�>\ICD/G 1@5 >ZO 3 O�](>�� >ZIZ;�DJF GJO36KQK � ICDhO�B 3 ; 3 DhO�>ZB A GW; 1@3 � I 1 > GW;4> 5 8 1 D - K > A 5 � 3 ;4< A G 3 O";=G 3 O 3 O�]'GJO�GWICI ?b1 GW;4> ]J>CD A >Z; 1 . �B O�>^G 8�8 1 D/GJIS<�;4D G K6K > P93 GW;4> ;=< 3Q5 8 1 D - K > A 3Q5 ;=DdICD/G 1@5 >ZO'DhO K . G K DhO�] K G . > 145 � 1 >ZB ? IZ>^;=O�D9B�> 5\3 O�>CGJIS< K G . > 1 - ? ; O�DJ;\;=D 1 >CB ? IZ>d;4<�>(O ? A - > 1 DJF K G . > 145 � 3 O ;4<�>dIC> 1 ;SG 3 O K > P > KQ5

ihi

0 10 20 30 40 50 60−50

−40

−30

−20

−10

0

10

20

30truecoarse grid computed

�� Z�; Z � L <�> 1 > 54?bK ; DWF�G'ICD/G 145 >�] 143 B 5 D K P >+DJO�;=<�> 3 O P > 145 >+;4> 5 ; 8 1 D - K > A � L <�>� � G � 3Q5 365 8 D 543 ; 3 DJO�DhO ;4<�>\<�> G 1 ; �. � G � 365 365 8 DJ;4>CO/; 3 G K �

DJF�IZD/G 145 >CO 3 O�] � L < 3Q5 8 1 D - K > A 5 <�D ?�K B&O�DJ; - > A GJO 3 F[> 5 ;4>CB 3 O*> G 14K . 5 ;=GJ]h> 5 DJF�O�> 5 ; 3 O�]3 O K G 1 ]h> 1 BUGW;=G 5 > ; 5 � � O,BUGW;=G 5 > ; 5 ��<�> 1 >�;=<�> 1 >�G 1 > eJg D 1 A D 1 > K G . > 145 - > ; � >Z>CO�;4D 145 DGJO�B�> 8 3 I G 1 B 3 G K O�D9B�> 5 ;=<�>(O�> 5 ;=>ZB�IZD/G 145 >CO 3 O�] 5 <�D ?bK B 8 1 DJ] 1 > 545 A ? IS< K DhO�]J> 1 � 3 ;=<�D ? ;8 1 D - K > A 5 �L < 365d1 > 5 >CG 1 IS< <UG 5 A D 5 ; K . F[D9I ?b5 >CB�DhO�I 1 > G ; 3 Ob] A D 1 > GJIZI ?�1 GW;=> 5 IS<�> A > 5 F[D 1 ;=

3 O/;4> 1 8 D K GW; 3 DhO(GJO�B 1 > 5 ; 1@3 IZ; 3 DhOdDJF IZD/G 1@5 >COb>CB+] 1@3 B 5 F[D 1 ?�5 > 3 O 5 D KQP93 O�] 3 O P > 1@5 > - 3 Da> K >ZIZ; 1@3 I

T > K B 8 1 D - K > A 5 � L 1 > <UG 5 - >C>ZO�G K G 1 ]h> F[D9I ?�5 DhO ;= IS<�D 3 IC> DWF ;=<�> ICD/G 145 > ] 143 B 8 D 3 O/; 53 O A ?�K ; 3 ] 1@3 B G 8�8 KQ3 ICGW; 3 DhO 5 "- ? ; > P >CO GWF ;=> 1 ;4<�>2IS<�D 3 IC> <UG 5 - >Z>CO A GJB�>�;=<�> 1 > 365 5 ; 36K6K ;=Y ? > 5 ; 3 DhO DJF >��bGJIZ; K . <�D��;=D 3 ObICD 1 8 D 1 GW;=>\;= 3 ObF[D 1 A GW; 3 DhOfG - D ? ;�;= T Ob>N] 1@3 B 8 D 3 O/; 5 �� >+I GJO&B 365 ICG 1 B�;=<�> P G KQ? > 5 F[D 1 ;4<�> T Ob>+] 143 B 8 D 3 O/; 5 GJO�B X >C> 8 DJO K . ;=+ICD/G 145 > ] 143 B3 OaF[D 1 A GW; 3 DhO � : K ;=> 1 OUGW; 3QP > K . GWO G 1@3 ;=< A > ; 3 I+G 8�8 1 D/GJIS<�ICGJO - > ?�5 >ZB�;=D�ICD AN- 3 O�>f;=ICDhG 145 > GWO�B T O�>E] 1@3 B 8 D 3 O/; P G KQ? > 5 � � > A ?�5 ;2;4<�>CO B�>ZI 3 Bb>d<bD�� ;=D � > 3 ]h</;2;=<�>EIZD/G 145 >

i @GJO�B T O�> 8 D 3 O/; 5 � L <�> TU145 ; 5@3 Ad8 K > � > 3 ]J<"; 3 O�]�G 8�8 1 D/GJIS<�;=D I G K I ?�K GW; 3 O�]fG�Ob>�� IZD/G 145 >] 1@3 B 8 D 3 O/; 3Q5 - 36KQ3 O�>CG 1 G 8�8 1 D � 3 A G ; 3 DJO � � 3 ;=<(;=< 3Q5 A >Z;4<�D9B � > ] 3QP >�;4<�> D K BdICD/G 1@5 > ] 143 B8 D 3 O/; G ? O 3 ; � > 3 ]h</; GJObB+> GJIS<�DWF ;=<�> ICDhObO�>CI ;=>CB T Ob> ] 1@3 B 8 D 3 O"; 5 GWO+>CY ? G K � > 3 ]J<"; ;=<UG ;54? A 5 ;=DE;4<�> ? O 3 ; � > 3 ]h</; �L <�> 5 >CIZDhO�B � > 3 ]h</; 3 O�],G 8�8 1 D/GJIS< IZDhO�O�>ZIZ; 3 DhO - G 5 >ZB � > 3 ]h</; 3 Ob] � c F � � A G X > 5

> GWIS<�DJF ;=<�> � > 3 ]h</; 5 8 1 D 8 D 1 ; 3 DhOUG K ;=D�;=<�> P G KQ? >EDJF ;=<�>(ICDJO�O�>CI ; 3 DhO � = @�� L < 3Q5 5 <�D ?�K B3 Ad8 1 D P > ;=fG - 36KQ3 ; . ;4D A G 3 O/;SG 3 O�;=�D 8 > 1 GW; 3 DhO�DJF�;=<�> � A GW; 143 � � � D�� > P > 1 ;= �A GW; 1@3 � 365 O�DJ; ;4<�>\DhO K . 5 > ;�DJF 3 ObF[D 1 A GW; 3 DhO ;=<UGW; A ?�5 ; - >\GJICI ?�1 GW;4> K . > 5 ; 3 A GW;4>CB 3 O�;=ICDhG 145 > ] 1@3 B � L - P >CIZ;4D 1 � ;=<�> 1 > 543 B ? G K 3 O�ICD/G 1@5 > 1 ] 1@3 B 5 � A ?�5 ; G K65 D - >+GJIZI ?�1 GW;=> K .ICDhG 145 >CO�>ZB � � O�GWB�B 3 ; 3 DhO 3 ; 365 ?�5 > F ?�K ;=DE<�G P > 5 D A > ; .98 >2DJF A >ZIS<UGJO 3Q5 A ;4<UGW;�� 3QK6K G K6K D�� > G X ICDhObO�>CI ; 3 DJO 5 ;4D - > B 1 D 8�8 >CB DJ;= 1 � 3Q5 >d;=<�> ICD/G 1@5 >ZO 3 O�] 8 1 D9B ? IZ> 5 D P > 1@K . B�>CO 5 >A GW; 1@3 IC> 5 �L <�> ;=< 361 B�G 8�8 1 DhGJIS< ��< 3 IS< 3Q5 ;=<�> 5 ;SGJObBUG 1 B A >Z;4<�D9B ?�5 >ZB � 3 ;=< : _ K ?�5 > 5 G

;=D K > 1 GJO�IZ> K > P > K F[D 1 ;4<�>fICDhObO�>CI ; 3 DJO 5 � � F�;=<�> 5 ; 1 >ZO�]J;=<,DJF�;=<�>fIZDhO�O�>ZIZ; 3 DhO 365 - > K D�� G;=D K > 1 GJO�IZ> K > P > K ;=<�>\IZDhO�O�>ZIZ; 3 DhO 365 O�DW; F ?�K6K . IZD A 8 ? ;=>ZB 3 O+;=<�> � > 3 ]J<"; 3 O�](ICG K I ?�K GW; 3 DhO 5 �: K D�� > 1 ;=D K > 1 GJO�IC> K > P > K A >CGJO 5 ] 1 > GW;4> 1 GJICI ?�1 GJI .�U- ? ;VB�>ZO 5 > 1 A GW; 143 IZ> 5 � L <�> >ZY ? GW; 3 DhOF[D 1 B�> ;=> 1 A 3 O 3 O�] � > 3 ]h</; 5 - >C] 3 O 5 � 3 ;4<�;=<�> 5 A D9DJ;=< � > 1@1 D 1 G 8�8 1 D � 3 A GW;4> 1 > K GW; 3 DhO �

� � � � � �� " �� " �� " �� i � = O �

��<�> 1 >��G 1 > ;=<�>2IZD/G 1@5 >2] 1@3 B 8 D 3 O/; 5 �� G 1 > ;=<�> 5 ; 1 DJO�] K . ICDJO�O�>CI ;=>ZB T O�>2] 143 B 8 D 3 O/; 5 GJO�B �� G 1 > ;=<�> � > G X"K . ICDhO�Ob>CIZ;4>CB T O�B ] 143 B 8 D 3 O/; 5 � HUD 1 �� > G 8�8 1 D � 3 A G ;=> � �� HUD 1 � � � > � � -/. G � > 3 ]h</;=>ZB G P > 1 GJ]J> DWF ��23 O�;4<�>\ICD/G 1@5 > 3 O/;4> 1 8 D K GW;=D 1 . 5 >Z;��

� �� " � �� !� ��" � ��

� � i � = P �

H 3 OUG K6K .� � >\G 8�8 1 D � 3 A G ;=> GJO�B 54? - 5 ; 3 ; ? ;=> ;4D ]h>Z; ;=<�> 5 ;SGJObBUG 1 B >CY ? GW; 3 DhO ?�5 >CB 3 O+: _ KF[D 1 B�> ;=> 1 A 3 O 3 O�] � > 3 ]h</; 3 O�] �

� � � �� ! � #"�%$'&�( � � $

� � � ��) �� ) � � i � = R �

��<�> 1 > � G 1 >d;4<�> � > 3 ]h</; 5 � L < 3Q5 � 3QK6K - > 1 >ZF[> 1@1 >ZB�;=D�G 5 ;=<�> 5 ;=GJO�BUG 1 B A >Z;4<�DaB � L < 3Q5>CY ? G ; 3 DJO � 3QK6K - 1 > G X BbD��O ;=D ;=<�> 543 A 8 K > � > 3 ]h</;=>CB ICDhObO�>CI ; 3 DJO A >Z;4<�DaB ��<�>ZO�;=

i O;=D K > 1 GJO�IZ> K > P > K 365 5 > ;VGW; � > 1 DNGJO�Bd> P > 1 . ICDhObO�>CI ; 3 DJO 365 IZDhO 543 B�> 1 >CB�G 5 ; 1 DhOb]NICDJO�O�>CI ; 3 DhO� = @�� L <�> F[D ?b1 ;=<*G 8�8 1 D/GJIS< 3Q5 A ?bK ; 3Q5 ;4> 8� ��< 3 IS< � <�G P >+B�> P > K D 8 >CB�;4D 5 8 >CI 3QT ICG K6K . B�> G K

� 3 ;4<�;=<�> 3 OUGJICI ?�1 GWI . DJFdIZD/G 145 >�] 143 B�ICD 1@1 >CI ; 3 DhO � 3 ;4< ;4<�> 3 O P > 145 > - 3 D9> K >ZIZ; 143 I T > K B8 1 D - K > A � L < 3Q5 A > ;=<�D9B\> 5 ;=G - KQ365 5 5 > P > 1 G K93 O/;=> 1 A >CB 3 GW;=> 5 > A 3 IZD/G 1@5 >COb>CB ] 143 B 5 - > ; � >Z>CO;= T O�> ] 143 B^GWO�B\ICD/G 1@5 > ] 1@3 B � L <�> 3 O/;=> 1 8 D K G ; 3 DJO D 8 > 1 G ;=D 1 3Q5 ;=<�>ZO - ?b36K ; -". 5@? ICIZ> 5@543QP > K .A D P93 O�] - >Z; � >C>CO ;4<�> 5 > 3 O/;=> 1 A >CB 3 GW;=>^] 143 B 5 � L O�>��9; 5 >CIZ; 3 DhO � _'?�K ; 365 ;=> 8 : 8�8 1 D/GJIS ;SG 3QK �L <�> T F ;4< G 8�8 1 D/GJIS< 3Q5 ;=D ?�5 > GWO G 8�8 1 D � 3 A G ;=> 3 O P > 145 > � L < 365 I GJO 1 >ZF[> 1 ;=D&GWO .

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� <�>CO � >�BbD2>CObF[D 1 IC>V;4<�> 14?�K >VDJF O�DJ; 1 > A D Pa3 O�]2ICDJO�O�>CI ;=>ZB O�D9B�> 5 3 O ;=< 3Q5R5 > A 3 ICD/G 145 �>CO 3 O�] G 8�8 1 D/GJIS< 8 1 > 5 I 143 - >CB -/. ;=<�> A ?bK ; 3Q5 ;4> 8 A > ;=<�D9B � > 5 >C> G ] 1 > G ; 3 Ad8 1 D P > A >ZO/;3 O GJICI ?�1 GJI . � ` 3 O�IC>';4< 365 B�D9> 5 O�DW; 1 > A D P > P > 1 . A GJO . ObDaB�> 5 GW;�DJO�IC> 3 O�D 1 B�> 1 ;4DI 1 > GW;4> ICD/G 1@5 >ZO�>CB] 143 B 5 ;=<�GW; G 1 > GWB�>CY ? GW;4> K . 5 8 GJIC>ZB � > A ?b5 ;fICD A - 3 Ob> 5 > P > 1 G K DJF;= 5 > 5 > A 3 ICD/G 145 >ZO 3 Ob]dD 8 > 1 GW;4D 145 3 O";4D(DhO�>\D 8 > 1 G ;=D 1 G 5 Bb> 5 I 143 - >ZB 8 1 > P93 D ?b54K . �

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� O ;= 3 O P > 5 ; 3 ]/G ; 3 DJO � > P G KQ? GW;=>ZB 5 > P > 1 G K B 3 � > 1 >CO/; � > 3 ]h</; 3 O�] 5 IS<�> A > 5 F[D 1 3 O";4> 1 8 D �K G ; 3 DJOfGJO�B 1 > 5 ; 143 IZ; 3 DhOfDJF IZD/G 1@5 >COb>CB'] 143 B 5 � L ^; 1 GJO 5 F[> 1 D 8 > 1 G ;=D 1 � > 3 ]J<"; 3 O�] 5 IS A > 5� ;=> 5 ;=>ZB 3 O�I KQ? B�>CB - 36K63 O�> G 1 IZDhO�O�>ZIZ; 3 DhO - G 5 >CB � > 3 ]h</; 3 O�] � c F � � IZDhO�O�>ZIZ; 3 DhO - G 5 >CB� > 3 ]J<"; 3 O�] � 3 ;=<*;4D K > 1 GJO�IZ> K > P > K � 5 ;=GJO�BUG 1 B � A ?�K ; 365 ;4> 8� G 8�8 1 D � 3 A GW;4> 3 O P > 145 > GJO�B,G< .9- 143 B �L < 365 3 O P > 5 ; 3 ]/G ; 3 DJO�� 3QK6K O�DW;N> P G K6? GW;4>(DJ;=<�> 1 G 5 8 >CIZ; 5 DJF A ?�K ; 3 ] 1@3 B 54? IS<&G 5 IZD/G 145 >

] 1@3 B 5 > K >ZIZ; 3 DhO 1 > K G �bGW; 3 DhO A >Z;4<�D9B 5 GJO�B 5 ;4D 8�8 3 O�]�I 1@3 ;=> 143 G � L < 365 1 > 5 >CG 1 IS< 365 F[D9I ?�5 >CB DhO��< 3 IS< ; 1 GJO 5 F[> 1 D 8 > 1 GW;=D 1@5 G 1 > A D 5 ;V> � I 3 >CO/; 3 O+;=< 3Q5 8 G 1 ; 3 I ?�K G 1 G 8�8 KQ3 ICGW; 3 DhO A ?�K ; 3 ] 143 B �L < 3Q5 3Q5 O�DJ;^GJO�GW;4;4> Ad8 ;\;=DfF ?�K6K . 3 A 8 K > A >CO/;2;= A ?�K ; 3 ] 1@3 B G K ]hD 1@3 ;=< A F[D 1\1 > G K � D 14K BK G 1 ]h> 5 ICG K > 8 1 D - K > A 5 >Z; 5 3 O G I K63 O 3 ICG K6K . ?�5 G - K > G 8�8 K63 ICGW; 3 DhO � : K ;4<�D ? ]J< 5 > P > 1 G K DJFR;=BUGW;=G 5 > ; 5 G 1 > F 1 D A 1 > G K 8 GW; 3 >CO/; 5 ;= 3 Ad8 D 1 ;SGJObIC> DJF ;4< 365 1 > 5 > G 1 IS< 3Q5 ;=<�>E> P G K6? GW; 3 DhODJF B 3 � > 1 >ZO"; G K ]JD 143 ;=< A 5 F[D 1 Bb>Z;=> 1 A 3 O 3 O�] ;4<�>^; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 F[D 1 : _ K IZD/G 1@5 >CO 3 O�] �L < 3Q5 � 3QK6K 8 DJ;4>CO/; 3 G K6K . G K6K D�� F ? ; ?�1 > 1 > 5 >CG 1 IS<�> 145 ;=D 3 Ad8 K > A >ZO/;N;= A ?bK ; 3 ] 143 B�DhO�;=3 O P > 145 > - 3 D9> K >CIZ; 143 I T > K B � GWO�B DJ;=<�> 1 � 8 1 D - K > A GJO�B > G 5@36K . 5 > K >ZIZ; G 8 1 D 8 > 1 ICDhG 145 >CO 3 O�]G K ]hD 143 ;=< A F[D 1 ;4<�> 3Q1 G 8�8 KQ3 ICGW; 3 DhO �L <�> ; � D A G 3 O A > ; 143 I 5 ;=<UG ; � >+ICDhO 543 Bb> 1 G 1 >+GWICI ?b1 GJI . GJObB 5 8 >C>ZB � : ICI ?b1 GJI . 3Q5

A > G 5@?�1 >ZB+G 5 ;=<�> 1 D9DJ; A > GJO 5 Y ? G 1 > � � _ ` �R> 141 D 1 - >Z; � >C>ZO+;=<�> A ?�K ; 3 ] 143 B 5 D K6? ; 3 DJO GWO�B; 1@? > 5 D K6? ; 3 DhO � � G KQ5 D A >CG 54?�1 >CB ;4<�> 5 8 >C>ZB DJF ;= 8 1 D9IC> 545 1 > 8 D 1 ;=>ZB -". ;= K >ZO�]J;=<�DJF; 3 A > > GJIS< 5 ;=> 8 ;=G X > 5 �L <�> 1 >�G 1 >�G KQ5 D B 3 � > 1 >ZO/; G 5 8 >CI ; 5 DJF ;=<�> A ?�K ; 3 ] 1@3 B 8 1 D9IC> 545 ;=<UG ; I GJO - > 3 O�B 3QP93 B ? G K6K .

A > G 5@?�1 >ZB � L D ;4> 5 ; ;= 3 O";4>C] 1@3 ; . DWF ;= B 3Q5 I 1 >Z; 3 � GW; 3 DhO A GW; 143 � GW;^GfICD/G 1@5 >ZO�>CB K > P > K � >�IZD/G 145 >CO,;=D F[>�� > 1 ObDaB�> 5 � ?�5@3 O�]�DhO�> DJF�;=<�> ] 3QP >CO A > ;=<�D9B 5 � > 3 ]h</; 3 O�] 5 IS A > 5 � GJO�B�;=<�>ZO 5 D K P >'DJO�;=<�>'ICD/G 1@5 >�] 143 B � L 5 D KQ? ; 3 DhO A GW; 143 � 365 G K65 D 1 > 5 ; 1@3 I ;=>CB ?�543 O�];= 5 G A > � > 3 ]h</; 3 O�] 5 IS<�> A > � L <�>CO � > ICD Ad8 G 1 > ;4<�> IZD/G 145 >CO�>ZB 5 D KQ? ; 3 DhO�GJO�B ;=

@V@5 D K6? ; 3 DhO�F 1 D A ;=<�>+IZD/G 1@5 > 8 1 D - K > A F[D 1 GJICI ?�1 GWI . � L < 3Q5 ;=> 5 ;(> KQ3 A 3 OUG ;=> 5 3 O�GJICI ?�1 GJI 3 > 5B ? >�;=D 3 O/;=> 1 8 D K GW; 3 DhO(GJObB ;=<�> GJICI ?�1 GWI . DJF ;= 1 > 5 ; 143 I ; 3 DhO D 8 > 1 GW;=D 1 3Q5 A > G 5@?�1 >ZB � L < 3Q5365 G ?�5 > F ?�K A >Z; 143 I\F[D 1 IZD A 8 G 143 O�]E;=<�>NGJICI ?�1 GJI . DJF Gd] 3QP >CO'IZD/G 1@5 >CO 3 O�] 5 IS<�> A > DJO�;=

A GW; 1@3 � P > 1@54?�5 ;=<�> P >CIZ;4D 1 � L < 3Q5 ;=> 5 ; 365 1 > F[> 1@1 >CB ;=DdG 5 ;= �� L D^;=> 5 ; ;4<�>2GJIZI ?�1 GJI . DJF G ICD/G 1@5 >ZO 3 O�] 5 IS<�> A > DJO ;=<�> P >ZIZ;=D 1 G K DhO�> � > 1 > 5 ; 1@3 I ; ;=

5 D K6? ; 3 DhO P >CI ;=D 1 GJO�B ;=CO 3 O/;4> 1 8 D K GW;=> - GJI X ;=D 3 ; 5 D 143 ] 3 OUG K/5@3 � > � L CO ;4<�> 3 O/;4> 1 8 D K GW;=>ZBP > 145@3 DhO 365 IZD A 8 G 1 >ZBd;4D\;4<�>�D 143 ] 3 O�G K F[D 1 GWICI ?b1 GJI . � L < 3Q5 A > ; 143 I 1 > P > G K65 1 > 5 ; 1@3 I ; 3 DJO GWO�B3 O/;4> 1 8 D K GW; 3 DhO�GJIZI ?�1 GJI . DhO�;4<�> P >CI ;=D 1 � L < 365 ;=> 5 ; 365 1 >ZF[> 1@1 >ZB ;4D G 5 ;4<�>��

� D�� > P > 1 ICD 141 >ZIZ; K . 8 > 1 F[D 1 A 3 O�] A ?�K ; 3 ] 1@3 B 3 O P D KQP > 5 A D 1 > ;=<�GJO � ?�5 ; 5 D K P93 O�] G ICDhG 145 �>COb>CB P > 1@543 DJO�DJF ;=dD 143 ] 3 OUG K 8 1 D - K > A� - ? ; 1 GW;4<�> 1\5 D KQP93 O�]+F[D 1 ;=<�> 1 > 543 B ? G K F 1 D A ;=T O�>�] 143 B � � � � � � � CO ;= 1 > 543 B ? G K�365 ICDhG 145 >CO�>ZB ;=<�>'GJICI ?�1 GJI . DJF2ICDhG 145 >CO 3 O�]- DJ;=<(;=<�> P >CIZ;4D 1 GJO�B A GW; 143 �EICDJO"; 143 - ? ;=> ;4D ;4<�>�D P > 1 G K6K GJIZI ?�1 GJI . � � A > G 5@?�1 >ZB - DJ;=<(;=GJIZI ?�1 GJI . GWO�Bd;4<�> 5 8 >C>ZB DWF ;4<�> 5 > A >Z;4<�DaB 5 DhO(DhO�> A ?�K ; 3 ] 143 BNI . I K > � H D 1 ; 14? > A ?�K ; 3 ] 1@3 B> P G KQ? GW; 3 DhO ;=< 3Q5 ;=> 5 ; �VG 5 8 > 1 F[D 1 A >CBfDhO 5 > P > 1 G K I . I K > 5 G 5 � > K6K �

� G K65 D A > G 5@?�1 >ZB A ?�K ; 3Q5 ;=> 8�A ?�K ; 3 ] 1@3 B GJ]/G 3 O 5 ;�;4<�> 5 D K6? ; 3 DhOfF 1 D A GWO'>��bGJI ; 3 O P > 145 >5 D KQP > ?b543 Ob]2ICDhO � ? ]/GW;=> ] 1 GJB 3 >CO/; � � 3 ;4 1 GW; 3 DhO 5 ��<�> 1 > � 365 ;4<�> O ? A - > 1 DWF ObDaB�> 5 � �L < 3Q5 ;4> 5 ; B�> A DJO 5 ; 1 GW;4> 5 ;=<�> 1 GW;=> GW; ��< 3 IS< ;4<�> A ?�K ; 3 ] 1@3 B�G K ]hD 1@3 ;4< A IZDhO P > 1 ]h> 5 ;=D(;=A D 5 ; 8 1 >CI 3Q5 > 5 D KQ? ; 3 DhO G P G 36K G - K > F 1 D A 3 O P > 145 > 5 D KQP93 Ob] � L < 365 ;=> 5 ; � G 5 8 > 1 F[D 1 A >ZB�DJO K .DhO�;=> 5 ; 5 > ; = �L < 365 3 O P > 5 ; 3 ]/GW; 3 DhO(G KQ5 D IZD A 8 G 1 > 5 ;=<�> >�� >ZIZ; DJF P G 1 . 3 Ob] K > P > KQ5 DJF 3 O 8 ? ; O�D 365 > GJB�Bb>CB

;=D ;= 5@?�1 FHGJIZ> A > G 54?�1 > A >CO/; 3 O 8 ? ;dIZDhO�B 3 ; 3 DJO 5 � � A > G 5@?�1 >ZB�;= 5 D K6? ; 3 DhO�> 141 D 1 F[D 1ICDJO � ? ]/GW;4>'] 1 GJB 3 >CO/;+GWO�B A ?�K ; 3Q5 ;=> 8�A ?bK ; 3 ] 143 B,G K ]hD 143 ;4< A 5 � 3 ;=< 3 O 8 ? ;+O�D 365 > 1 GWO�] 3 Ob]F 1 D A g � ;=D eJg � � _ ` DJF 54?�1 FHGJIC> K > P > K65 � _'?�K ; 3 ] 1@3 B 8 > 1 F[D 1 A >CB T�P >(I . I K > 5 � 3 ;=< DhOb>K > P > K DJF IZD/G 1@5 >CO 3 O�](F[D 1 ;=< 365 ;=> 5 ; � L < 365 �VG 5 DJO K . 8 > 1 F[D 1 A >ZB�DhO�;4> 5 ; 5 >Z; e �L <�>2IS<�D 3 IC> DJF ;=<�> � >CG X IZDhO�O�>ZIZ; 3 DhO ;4D K > 1 GJO�IZ> � � c L � K > P > K � ;= 1 > K GW; 3QP >�ICDJO�O�>CI �

; 3 DhO 5 ; 1 >COb]J;=< ;=< 1 > 5 <�D K B F[D 125 ; 1 DJO�] P > 1@54?�5 � >CG X ICDJO�O�>CI ; 3 DhO 5 3 O ;=<�> 5 ;SGJO�B�G 1 B�: _ KG K ]hD 143 ;=< A ��G K65 D�G � >CI ; 5 ;=<�> 5 . 5 ;4> A 8 > 1 F[D 1 A GJO�IC> � `a> K >ZIZ; 3 O�]f;=<�>(;=D K > 1 GJO�IC> K > P > K 365 GICD A 8 1 D A 365 > - > ; � >Z>CO&GJIZI ?�1 GJI . GWO�B ;=<�> 5 8 GJIC> M ; 3 A >(ICDJO 5 ; 1 G 3 O"; 5 � : K D�� > 1 ;=D K > 1 GJO�IZ>K > P > K 8 1 D9B ? IC> 5 G(] 1 >CGW;=> 1 O ? A - > 1 DWFRO�DhO � > 1 D >ZO"; 143 > 5 � 5 >Z>(H 3 ] ?�1 > @ � = � � L < 365 3 O ; ?�1 O I G ?�5 > 5 54K D�� > 1 8 > 1 F[D 1 A GJO�IZ> � 5 >Z>4H 3 ] ?�1 > @ � e � � � D�� > P > 1 GWICI ?b1 GJI . B�>C] 1 GJB�> 5 � 3 ;=<,G

@ O

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

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1

1.5

2

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3

3.5

4x 10

6

Nonzeros

�� E ; : � L <�>fO ? A - > 1 DJF�O�DhO � > 1 D 5 � . � G � 3Q5 � GW;E;4<�>�ICDhG 145 > 5 ; K > P > KVP > 1454?b5 � > G XICDJO�O�>CI ; 3 DhO ;4D K > 1 GJObIC> K > P > K � � � G � 3Q5 � F[D 1 ;=> 5 ; 5 > ; e �

< 3 ]h<�> 1 ;=D K > 1 GJO�IC> K > P > K G 5 5 >Z>CO 3 O1H 3 ] ?b1 > @ � i � H D 1 ;= A G � D 143 ; . DWF ;=<�> 8 1 D - K > A 5 ;=

;=D K > 1 GJO�IZ> K > P > K �VG 5^5 > ;^;4D g � g/e - ? ;NG 5 A >ZO/; 3 DJO�>CB�G - D P > Gf] 1 > GW;4> 1 ;=D K > 1 GWO�IC> K > P > K� G 5 ?b5 >CBfF[D 1 ;4<�> K G 1 ]h> 5 ;�BUGW;SG 5 >Z; �: O�DW;=<�> 1 A >Z;=<bDaB 54? 8�8 K > A >CO/; 5 ;=<�> 5 ;=GJO�BUG 1 B A >Z;=<bDaB^DJF K63 A 3 ; 3 O�] � > G X ICDhObO�>CI ; 3 DJO 5

;=D 1 >CB ? IZ> ? O�O�>CIZ> 5@5 G 1 .^A GW; 143 � >ZO"; 143 > 5 � : F ;4> 1 > GWIS< 1 > 5 ; 143 I ; 3 DhO � > B 1 D 8 GJO . ICDJO�O�>CI ; 3 DhO3 O�;=<�> A GW; 143 � ;=<UGW;NB�D9> 5 ObDJ; A >C> ;EG'] K D - G K ;4D K > 1 GJO�IZ> K > P > K � L < 365^365 B 3 � > 1 >ZO/;N;=<�GJO;= 5 ;SGJO�B�G 1 B � c L ;4D K > 1 GJO�IZ> G 5 ;= 5 ;SGJO�B�G 1 B A > ;=<�D9B�DJO K . B 1 D 8 5 >CO/; 143 > 5 F 1 D A ;=; 1 GJO 5 F[> 1 D 8 > 1 G ;=D 1 A GW; 1@3 � �� 1 >CG 5 ;=< 3Q5 D 8 > 1 GW; 3 DhO 3Q5 G 8�8 KQ3 >CB�B 361 >ZIZ; K . ;4DE;=<�> 5 ; 3 � O�> 5@5A GW; 1@3 � GJO�B�B�D9> 5 ObDJ;�G � >CI ; ;=<�> P >CIZ;4D 145 � L < 365 A >Z;4<�DaB � G 5 ?�5 >CBfF[D 1 ;4<�> ;=> 5 ; 5 DJO+;=> 5 ;5 > ; T GWO�B�;4<�>E;=> 5 ; DhO ;=> 5 ; 5 > ; e 1 > F[> 1@1 >CB ;=D G 5 ;4<�> 5 ; 3 � O�> 5@5 A GW; 1@3 �'>CO/; 1 . ;=D K > 1 GJO�IZ>� ` _ J L ��;=> 5 ; � HUD 1 ;4> 5 ; 5 >Z; T ` _ J L DJF i � = g � � � G 52?�5 >CB�G 5 ;4<�> A GW; 1@3 � >ZO"; 143 > 5 G 1 >A ? IS< 5 A G KQK > 1 � N 1 D 8 D 1 ; 3 DhOUG KQK .� ;=< 365 � G 5 G 8�8 1 D�� 3 A GW;4> K . ;4<�> 5 G A >\G 5 ;=<�> g � g = ` _ J LP G K6? > ?�5 >CB DJON;=> 5 ; 5 >Z; e � G - D ? ; = M O ghghg DJF�;4<�>VG P > 1 GJ]J> A GW; 1@3 �\>ZO"; 1 . � � L <�> 5 > ;=> 5 ; 5 G K65 D

@ P

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.5

1

1.5

2

2.5x 10

4

Setup TimeSolve Time

�� E ; D � L <�> � >CG X ICDhO�Ob>CIZ; 3 DhO�;=D K > 1 GJO�IZ> K > P > K � 5 >�� >CI ; DhO 8 > 1 F[D 1 A GJO�IC> � L <�>5 > ; ? 8 ; 3 A >VGJO�B(;=<�> 5 D KQP >�; 3 A > � . � G � 365 � 8 K DJ;@;=>CB P > 1@54?�5 ;=<�>�� > G X IZDhO�O�>ZIZ; 3 DhOE;=D K > 1 GJO�IZ>K > P > K DhO ;4<�> � � G � 365 F[D 1 ;=> 5 ; 5 >Z; e �

ICD A 8 G 1 >CB�; 1 GJB 3 ; 3 DhOUG K 5 D K P > 145 � � 1 GJO�;4<�>2;=> 5 ; 5�5 D KQP93 O�] � 3 ;=<�IZDhO � ? ]/G ;=>\] 1 GWB 3 >ZO"; ?�543 O�]

G L 3 X <�DhO�D P�1 >C] ?�K G 1@3 � GW; 3 DhO � � 3 ;4<*GJO*G K 8 <�G DJF g � ghe � � � G KQ5 D 5 D KQP >CB ?b543 Ob] ICDhO � ? ]/GW;4>

] 1 GJB 3 >ZO/; DJO�;='O�D 1 A G K >CY ? GW; 3 DhO 5 � 3 ;4< KQ3 A 3 ;4>CB 3 ;4> 1 GW; 3 DhO 5 F[D 1(1 >Z] ?�K G 143 � GW; 3 DhO � ; � DT F ;4< 5 DJF ;=<�> > 3 ]J>CO P >ZIZ;=D 145 � > 1 >\> KQ3 A 3 OUG ;=>CB 3 O KQ3 > ? DJF ?�543 O�] L 3 X <�DJO�D P+1 >Z] ?�K G 143�� GW; 3 DhO � �� ; 5 <�D ?�K B - > O�DJ;4>CB ;4<UGW; ;4<�> A >Z;4<�D9B 5 � > 1 >VI G 1@143 >CB D ? ;RDhON;4<�> 5 . 5 ;=> A B�> 5 I 143 - >CB 3 ON;=A >Z;=<bDaB 525 >CI ; 3 DJO G K6K D�� 3 O�] G+ICDhO 5@365 ;=>CO/; ICD A 8 G 14365 DhO � 3 ;4< ;=<�> A ?�K ; 3 ] 1@3 B G K ]hD 1@3 ;4< A 5 �L D Pa3 >��,GJO(GWOUG K . 5@365 DWF <�D��IZD AdA DhO 5 D K P > 145 � D 1YX DhON; 1 GJB 3 ; 3 DhOUG K F[D 1 A ?�K GW; 3 DhO 5 8 K > G 5 >1 > F[> 1 ;=D 8 G 8 > 145 � P 4ihg P g = g P � �

� G KQ5 D A >CG 54?b1 >CBf;= 5 I G K G - 36KQ3 ; . DJF > GJIS<'G K ]hD 143 ;4< A � L <�>^GJICI ?�1 GWI . GJO�B 5 8 >C>ZB�� G 5A > G 5@?�1 >ZB DhO G 1 GJO�]h>NDJF 8 1 D - K > A 5 F 1 D A iJghg O�D9B�> 5 ;=D = O P R e T ObDaB�> 5 � L 5 > 1 > 5@?�K ; 5G 1 > I 1@? I 3 G K 3 O B�>Z;4> 1 A 3 O 3 O�]��< 3 IS<�IZD/G 145 >CO 3 O�] 5 IS<�> A > 5 G 1 > A D 5 ;�G 8�8 1 D 8 143 GW;=> GWO�B��<�> ;=<�> 1 G A 3 ��DWF 5 IS<�> A > 5�365 5@? 8 > 143 D 1 F[D 1 ;= 3 O P > 1@5 > - 3 D9> K >CI ; 143 I T > K B 8 1 D - K > A �

@ R

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3550

100

150

200

250

300solution error

�� E ; Z � L � > G X ICDhObO�>CI ; 3 DJO�;4D K > 1 GJO�IZ> K > P > K � 5 >�� >ZIZ; DhO�GJICI ?�1 GWI . � L <�>(> 141 D 13 O ;4<�> 5 D KQ? ; 3 DhO � . � G�� 3Q5 � 8 K DJ;4;4>CB P > 1454?b5 ;4<�> � >CG X ICDhObO�>CI ; 3 DJO�;4D K > 1 GJO�IZ> K > P > K DhO ;=� � G � 3Q5 F[D 1 ;=> 5 ; 5 >Z; e �

� �� HUD 1 ;=<�>2;4> 5 ; 8 1 DaIZ>CB ?�1 > ;4<�> G K ]hD 143 ;4< A 5 � > 1 > � 143 ;4;4>CO 3 O c � � GJO�B 1 GWO�DhO G(B ? G K

8 1 DaIZ> 545 D 1 � G K ;4<�D ? ]h< � B 3 B+O�DW; ?�5 > 8 G 1 G K6K > KQ3 � G ; 3 DJO � e O g _ < � M K ; 1 G/` 8 G 1 I � 3 ;4< R PVT _ FDJF A > A D 1 . � `aD A >EDJF ;=<�>E;=> 5 ; 5 � > 1 > 8 > 1 F[D 1 A >CB DJO�DW;=<�> 1 A GJIS< 3 O�> 5 - ? ;\;= 1 > 5@?�K ; 5� > 1 > 5 ICG K >ZB,;4D�;4<�> 8 > 1 F[D 1 A GJObIC>fDJF ;4<�> M K ; 1 Gh` 8 G 1 I � L <�> A GW; 143 IZ> 5 � > 1 > 5 ;4D 1 >ZB 3 OG 5 8 G 145 > A GW; 143 � F[D 1 A GW; � : O�G 141 G . ICD 1@1 > 5 8 DJO�B 3 Ob] ;=D 1 D�� 5E3 O*;=<�> A GW; 1@3 ��<�> K B&;=A GW; 1@3 � BUGW;SG � J GJIS<�> K > A >CO/;�ICDhO/;=G 3 O�>ZB'G K63Q5 ; DWF P G K6? > 5 GJO�B ICD K6? A O 8 D 5@3 ; 3 DhO+F[D 1 >CGJIS<DJF�;=<�> O�DhO � > 1 D 5 � 3 ;=< 3 O&;=<UG ; 1 D�� _ D 5 ;dDJF ;4<�> G K ]JD 143 ;=< A 5 � > 1 > TU1@5 ; � 143 ;4;=>ZO�GWO�B;=> 5 ;4>CB 3 O _ G ; K G -�- >ZF[D 1 > - > 3 O�] 3 Ad8 K > A >ZO";4>CB 3 O c � � � _ GW; K G - �VG 5 ?�5 >CB > �9;=>CO 543QP > K .;=< 1 D ? ]J<�D ? ; ;4<�>2;=> 5 ; 5 F[D 1VP >ZIZ;4D 1 A GJO 3 8 ?�K GW; 3 DhO+GJObB P9365@? G KQ3 � G ; 3 DJO �

� I 1 > GW;4>CB ;=< 1 >C>\;=> 5 ; P >CI ;=D 1@5 F[D 1 >CGJIS<�;4> 5 ; � L > 5 ; P >CIZ;4D 1 I 1 >CGW; 3 DhO - >Z] 3 O 5 -/. ]h>ZO�> 1 �GW; 3 O�] 8 5 > ? B�D <�> G 1 ;�I ?�1@1 >ZO"; 5 D ?�1 IZ> 5 � HUD 1 ;=<�>\; � D � B 3 A >ZO 543 DhOUG K 8 1 D - K > A 5 G P >CI ;=D 1 DJF1 GWO�B�D A P G K6? > 5 �VG 5 ]h>ZO�> 1 GW;=>ZB � ? O 3 F[D 1 A B�>CO 5@3 ; . 1 GJO�B�D A P G 143 G - K > � � � >��9; ;=<�> P >ZIZ;4D 1

@ T� G 5+5 A D9DJ;=<�>ZB -/. G P > 1 GW] 3 O�]�> GJIS< > 8 3 ICG 1 B 3 G K O�D9B�>�� 3 ;=< 3 ; 5 O�> 3 ]h< - D 1@5 ?�5@3 O�]�;=< 3Q5A > GJO G 5 ;4<�> Ob>�� P G K6? > � L < 3Q5 I . I K > �VG 5 >��a>ZI ? ;4>CB+; � 3 IZ> � GJO > ��G A 8 K > P >CI ;=D 1 365 5 <�D��O3 O9H 3 ] ?�1 > @ �A@ � �

HUD 1 ;=<�>V;4< 1 >Z> � B 3 A >CO 5@3 DhO�G K 8 1 D - K > A 5 ;4<�> TU145 ; ;=> 5 ; P >CI ;=D 1 � G 5 G K63 Ob> G 1 ] 1 GJB 3 >CO/; 3 O;= � B 361 >CI ; 3 DJO ;4<�> 5 >CIZDhO�B P >CI ;=D 1 � G 5 G KQ3 O�>CG 1 ] 1 GJB 3 >CO/; 3 O�;= � B 361 >CI ; 3 DJO GJO�Bf;=;=< 361 B P >ZIZ;=D 1 �VG 5 G 8 G 1 G - D K63 I ] 1 GJB 3 >CO/; 3 O � B 361 >ZIZ; 3 DhO ICD A - 3 Ob>CB � 3 ;=<EG K63 Ob> G 1 ] 1 GJB 3 >ZO/;3 O(;=

�B 361 >ZIZ; 3 DhO � L < 365 365 > G 543 > 1 ;=D 5 D KQP >�;4<UGJOd;=<�> 1 GJObB�D A 3 � >ZB P >CI ;=D 1@5 B�> 5 I 1@3 - >CB F[D 1

;=d; � D � B 3 A >CO 5@3 DhOUG K 8 1 D - K > A 5 - >CICG ?�5 >dDJF F[>�� > 1 8 >CG X"5 GJObB�G 1 > G 5 DJF < 3 ]J<�] 1 GJB 3 >CO/; G K ;=<�D ? ]h<+;=<�>2;4< 1 >Z> � B 3 A >CO 5@3 DhOUG K 8 1 D - K > A 3Q5 3 O�<�> 1 >ZO"; K . A ? IS< A D 1 > B 3 � I ?�K ; ;4D 5 D K P > �� > �9; > GJIS<&DWF�;4<�> P >CIZ;4D 145 G 1 >+O�D 1 A G K63�� >CB ;=D <�G P >fG 54? A DJF � > 1 D � 54? - ; 1 GWIZ; 3 O�] ;=A > GJO�F 1 D A >CGJIS<*DJFV;4<�> P G KQ? > 5 � � H 1 D A ;=<�> I ?�1@1 >CO/; 5 D ?�1 IC> P G KQ? > 5 ;4<�> P D K ;=GJ]h> 5 G 1 >5 D KQP >ZB*F[D 1 ;=<�>+>ZO/; 361 > 8 1 D - K > A ?�543 O�]';4<�> IZDhO � ? ]/G ;=> ] 1 GJB 3 >CO/; A >Z;4<�D9B � L < 365 ICGJO - >ICD A 8 ? ;=>CB � 3 ;=<�D ? ;2;=D9D A ? IS ;=< 3652365 G � > KQK � 8 D 5 >CB F[D 1 �VG 1 B 8 1 D - K > A �L <�> 1 > 54?bK ; 3 O�] ;=D 145 D P G KQ? > 5 G 1 > ?�5 >CB,G 5 ;4<�> A > G 5@?�1 > A >ZO"; P G KQ? > 5 F[D 1 ;= A ?�K ; 3 ] 1@3 B

8 1 D - K > A GJObB ;4<�>\> 8 3 I G 1 B 3 G K P D K ;SGJ]J> 5 G 1 > ?b5 >CB'G 5 ;= IZD 141 >CI ; 5 D K6? ; 3 DJO � 3 ;=< ��< 3 IS< ;4DA > G 5@?�1 >2;= > 141 D 1VP G K6? > 5 �

J GJIS<+;=> 5 ; 8 1 Dh] 1 G A - >Z] 3 O 5 -/. > 3 ;4<�> 1 1 > GWB 3 O�] 3 Od;=<�> G 8�8 1 D 8 143 GW;=>�;=> 5 ; A GW; 143 � F 1 D AG T�K > D 1 ]h>ZO�> 1 GW; 3 O�]�;4<�> A GW; 143 � � L <�>ZO 3 ; 1 >CGJB 5N3 O�;4<�>+G 8b8 1 D 8 143 G ;=>(;=> 5 ; P >CIZ;4D 1 �� O;=�O�> �a; 5 ;4> 8� ;= 8 1 Dh] 1 G A ]h>CO�> 1 GW;4> 5 ;=<�>�; 1 GWO 5 F[> 1 D 8 > 1 GW;=D 145 ?�543 O�]�;4<�> 5 > K >ZIZ;4>CBICDhG 145 >CO 3 O�]+G K ]hD 1@3 ;=< A � - 36K63 O�> G 1 � > 3 ]J<";4>CB >Z;4I � � � H 3 O�G K6K .� ;4<�>^IS<bD 5 >ZO A ?�K ; 3 ] 1@3 B � A G �; 1@3 � P >ZIZ;4D 1 DhO�>�I . I K > D 1 A ?�K ; 3 I . I K > � 5 ;=> 8 5 G 1 > G 8�8 K63 >ZB�;4D*GW;@;=> Ad8 ; ;=D 5 D KQP >';=3 O P > 145 > 8 1 D - K > A � :V; ;=<�>NICD/G 1@5 > 5 ; K > P > K ;= K63 O�> G 1�5 . 5 ;=> A 365 G K � G . 5 5 D KQP >CB � 3 ;=< ;=ICDJO � ? ]/GW;4> ] 1 GJB 3 >ZO/; A > ;=<�D9B � � D�� > P > 1 � 3 ;=< ;4<�> K G 1 ]h> 5 ; ;4< 1 >Z> � B 3 A >CO 5@3 DhO�G K 8 1 D - K > A;= L 3 X <�DhO�D P�5 > ; ? 8 365 O�DJ; ?�5 >CB�GJO�B 3 O 5 ;=> GWB;4<�>�IZDhO � ? ]hGW;=> ] 1 GJB 3 >ZO/;�F[D 1 O�D 1 A G K

>CY ? G ; 3 DJO 5 � 3 ;=< KQ3 A 3 ;=>ZB 3 ;=> 1 GW; 3 DhO 5 F[D 1 1 >Z] ?�K G 143 � GW; 3 DhO � O g T � � 3Q5 ?�5 >CB 3 O 5 ;=>CGJB 3 O+D 1 B�> 1;=D 1@? O�;4<�> ;=> 5 ; 5 � 3 ;=< 3 O G 1 > G 5 DhOUG - K >(G A D ? O/;\DJF ; 3 A > � L < 3Q5 A > ;=<�D9B �VG 5 G KQ5 D ?�5 >CBDhO�;=<�> 5 A G K6K > 1 ;=< 1 >C> � B 3 A >ZO 543 DhOUG K 8 1 D - K > A � ;4> 5 ; 5 > ; e � F[D 1 ;=<�> 5 G X > DJFVICD Ad8 G 1@365 DJO- >Z; � >C>CO ;4<�> K G 1 ]h> GJObB 5 A G K6K ;4< 1 >Z> � B 3 A >CO 5@3 DhOUG K 8 1 D - K > A ;4D ;=> 5 ; 5 I G K G - 3QK63 ; . � L < 3Q5 3Q5O�DJ; 3 O/;=>CObB�>CB ;=D - > GEICD A 8 G 14365 DhO�DJF 1 >C] ?�K G 1@3 � GW; 3 DhO A >Z;4<�DaB 5 �L <�> T O�G KX5 D K6? ; 3 DJO 365 ;=CO A > G 5@?�1 >ZB GJ]/G 3 O 5 ;�;=N> 8 3 I G 1 B 3 G K <�> G 1 ; P D K ;=GJ]h> P G K6? > 5

@ �

0 10 20 30 40 50 60−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

�� E ; E �9B O�>dDJF ;4<�> 1 GJO�B�D A P >CI ;=D 1@5 ?�5 >ZB&G 5 ;=<�>(F[D 1 > 8 3 I G 1 B 3 G K 8 DJ;4>CO/; 3 G K65 F[D 1;=> 5 ; 5 >Z; @ � L <�> 1 > A G 3 O 3 Ob] ICD A 8 ? ;=>CB 8 DJ;4>CO/; 3 G K65 G 1 >V;4<�>CO - G 5 >CB ? 8 DhO ;=< 365 ;4> 5 ; P >CI ;=D 1 �L <�> � � G � 365 1 > 8 1 > 5 >CO/; 5 8 D 5@3 ; 3 DhO�DhO�;4<�>\<�> G 1 ; �. � G�� 3Q5 1 > 8 1 > 5 >CO/; 5 8 DJ;=>ZO"; 3 G KQ5 �

F 1 D A ;=<�> 3 O 3 ; 3 G K 5 D KQP >^;=D B�>Z;4> 1 A 3 O�>2;=<�>NGJICI ?�1 GJI . � A > G 5@?�1 >ZB�� 3 ;4< ��_ ` > 141 D 1 � � L <�>K G 5 ;N; � D 5 ;4> 8 5 ;4<�> A ?�K ; 3 ] 143 B 5 > ; ? 8 GJObB�;4<�> A ?bK ; 3 ] 143 B 5 D KQP > G 1 >fG K65 D > GJIS<&; 3 A >CB �L <�> 1 > 5 ; 143 I ; 3 DhO�GJO�B 3 O/;=> 1 8 D K G ; 3 DJO'; 3 A > 3Q5 G KQ5 D A >CG 54?b1 >CB F[D 1 5 D A > 8 1 D - K > A 5 GJO�B 3Q5

8 G 1 ;�DJF ;=<�> 5 D KQP >2; 3 A >\GJO�B 365 ICG K I ?�K GW;4>CB -/. 54? - ; 1 GWIZ; 3 O�]E;=<�>\IZD/G 145 >\] 143 B 5 D KQP >2; 3 A > �� G K65 D 1 >CIZD 1 B�>ZB�<�D�� A GJO . K > P > K65 DJF IZD/G 145 >CO 3 O�] � > 1 > ?�5 >CB 3 O ;4<�> I . I K > � L <�>

B�>Z> 8 > 1 ;=2I . I K > � >ZO"; ;=<�> A D 1 > B 3 � I ?�K ; ;=D A G 3 O/;=G 3 O GJICI ?�1 GJI .� G 5 ;=<�>2IZD/G 145 > 1 ] 1@3 B 5� 36KQK 3 O"; 1 D9B ? IZ> A D 1 > 3 OUGJIZI ?�1 GJI 3 > 5 ;4<UGJOf;=<�> T O�>\] 1@3 B 5 �

� I G 14143 >CB�D ? ; G K6K ;4<�>\;=> 5 ; 5 ;=< 1 >C>^; 3 A > 5 GJO�B'G K6K ;4<�> 1 > 5@?�K ; 5 � > 1@1 D 1@5 GJObB�; 3 A > 5 � G 1 >G P > 1 GJ]h>ZB � � DJ;d> P > 1 .,8 D 545@3 - K >fICD A - 3 OUGW; 3 DhO&DWF ;4> 5 ; 5 ;4> 5 ; 5 >Z; 5 GJO�B A > G 5@?�1 > A >ZO"; 5G 1 > 8 > 1 F[D 1 A >CB�F[D 1 ;=<�> 5 G X >+DJF - 1 > P93 ; . � L <�> K G 1 ]h> 1 8 1 D - K > A ;=> 5 ; 5 >Z; 5 <UG P >fG A D 1 >G -�- 1 > P93 GW;=>ZB 5 >Z;�DJF > � 8 > 1@3 A >CO/; 5 B ? > ;=D&;= 361 A ? IS<�] 1 > GW;4> 1f14? O�; 3 A > � _ GJO . DJF

O g

;= ;4> 5 ; 5 B�DdO�DJ;�<UG P >^;= A ?bK ; 3 ] 143 B ; 3 A > A > G 5@?�1 > A >ZO/; - >CICG ?�5 > 3 ; � G 5�3 O 5@3 ]hO 3 T I GWO";F[D 1 G 8 1 D - K > A DJF ;4<UGW; 543 � > � : K65 D ;4<�> P >CI ;=D 1 GJO�B A G ; 143 �*;4> 5 ; 5 B�D�O�DJ;d<UG P >�; 3 A >A > G 5@?�1 > A >ZO"; 5 - >ZI G ?b5 >E;=<�> 5 >(G 1 > � ?�5 ; 54? - 5 >Z; 5 DJF ;4<�> I . I K > ��< 3 IS< 3Q5 G KQ1 > GWB .'- 1 D X >COB�D��O 3 O/;4D�B 3 � > 1 >CO/; ; 3 A > A >CG 54?�1 > A >CO/; 5 � � 3 X >�� 365 > ;4> 5 ; 5 ;=<UG ; 3 O�I KQ? B�> 5 A D9DJ;4< 3 O�]D 8 > 1 GW; 3 DhO�B�DdO�DJ;�B 3 � > 1 3 O�;=<�> 361 5 >Z; ? 8'8 1 DaIZ> 545 5 D A >CG 54?b1 > A >CO/; 5 G 1 >2O�DJ; 1 > ; 3 A >ZB �

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L < 365 5 >CIZ; 3 DhO 3 O�I KQ? B�> 5 ;4<�>�BUGW;=G 1 > 5@?�K ; 5 F 1 D A G K6K ;4<�> 543 A ?�K G ; 3 DJO 5 � L <�> 1 > � > 1 >�> 3 ]h</;;=> 5 ; 5 >Z; 5 � J GJIS< DWF ;4<�> 5 > ;=> 5 ; 5 >Z; 5 1 > 8 1 > 5 >CO/; 5 G2B 3 � > 1 >CO/; A DaB�> K DJF ;4<�> - D9B .� P G 1 . 3 O�] 3 O]h>ZD A > ; 1 . GJObB 543 � > � J GJIS<�;=> 5 ; 5 > ; 1 > 54?�K ; 3 O�I K6? Bb> 5 G B�> 5 I 143 8 ; 3 DJO+DJF ;=<�> ;4> 5 ; 5 >Z; A D9B�> KGJO�B'G(;=G - K > DWF ;= 1 > 54?bK ; 5 F 1 D A ;=<�> 543 A ?�K GW; 3 DhO 5 � ` 8 >C>ZB 365 A > G 5@?�1 >ZB 3 O 5 >CICDJO�B 5 GWO�B> 1@1 D 1 3Q5 8 > 1 IC>ZO/; ��_ `+F 1 D A ;=<�>\ICD 141 >ZIZ; P G K6? > �L <�> F[D KQK D�� 3 O�] ;SG - K > 5+5 <�D�� ;=<�>�;=> 5 ; 1 > 54?�K ; 5 � L TU145 ;�ICD KQ? A O 3 O >CGJIS< DJF\;=

;SG - K > 5 ;=> K6K65 ��<�>Z;4<�> 1 G P >ZIZ;4D 1 ;=> 5 ; A GW; 1@3 ��;=> 5 ; D 1 I . I K >+;4> 5 ; �VG 5 > �b>ZI ? ;4>CB 3 O*;=8 1 DaIZ>CB ?�1 > � � F2;=<�> 8 1 D9IC>ZB ?�1 >��VG 5 G A ?�K ; 3 I . I K >�;4> 5 ; ;=< 3Q5 IZD K6? A O�;4> KQK65 <�D�� A GJO .I . I K > 5 � > 1 > 8 > 1 F[D 1 A >CBf;=D GJIS< 3 > P >\;=<�>\] 3 P >ZO 1 > 54?bK ; 5 � L < 365 ICD KQ? A OfG K65 D 3 B�>CO/; 3 T > 5 ;=;=> 5 ; 5 8 > 1 F[D 1 A >ZB DhO 021 . K D Pd54? - 5 8 GJIZ> 3 ;4> 1 GW; 3 P > 5 D K P > 1@5 � L <�> 5 >CIZDhO�B+IZD K6? A O B�> 5 I 143 - > 5��< 3 IS<�; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 ;4<�>+;=> 5 ; ? ; 36K63�� >ZB�F[D 1 IZD/G 145 >CO 3 O�] � H ?�1 ;4<�> 1 1@3 ]h</; ;=<�>�> 141 D 1ICD K6? A O K63Q5 ; 5 > 141 D 1 P G K6? > 5 F 1 D A ;4<�> 5 D K6? ; 3 DhO^> 5 ; 3 A GW;=> DJF > GWIS<(;4> 5 ; � L <�>VF[D ?�1 ;4< ICD KQ? A O] 3 P > 5 ;=<�> > K G 8 5 >ZBN; 3 A > F[D 1 ;=<�> 5 > ; ? 8 DWFU;=<�> ; 1 GWO 5 F[> 1 D 8 > 1 GW;=D 1@5 GWO�B ICDhG 145 >CO�>ZB A GW; 143 IC> 5

GJO�B P >CI ;=D 1@5 � L <�> T F ;4< ICD KQ? A O 5 <�D�� 5 ;= 5 D K P >N; 3 A >^F[D 1 ICDhO � ? ]/GW;4> ] 1 GWB 3 >ZO"; DhO ;=

ICDhG 145 > 5 ; K > P > K GJO�B ;4<�> 543 �9;=< ICD K6? A O ] 3QP > 5 ;4<�> 8 1 DaIZ> 545@3 O�]&; 3 A >�F[D 1 G 8�8 K . 3 O�]*;=; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 ;4D ;= P >ZIZ;=D 145 � J GWIS< 5 >CI ; 3 DhO 3 O�I K6? Bb> 5 Gd<�> GWB�> 1 - 143 >�� . B�> 5 I 1@3 - 3 O�];= 8 1 >CIZ>CB 3 O�] ;4> 5 ; 5 GJObB ;4> K6KQ5 <�D�� A GJO . K > P > K65 DJFXICD/G 1@5 >ZO 3 O�](;= 8 1 D9IC>CB ?�1 >^G 8�8 KQ3 >ZB;=DE;4<�> 8 1 D - K > A 5 >Z; �L > 5 ; 5 > ; 5 F[D 1 ;=<�> 5 > 543 A ?�K G ; 3 DJO 5 3 O�I KQ? B�> �

�� :$; � D � B 3 A >CO 543 DJOUG K ;=D 1@5 D A DaBb> K � 3 ;=< O @ = O�D9B�> 5 �.B F ;4<�> 5 > ;= 1 > � > 1 >P g > 8 3 ICG 1 B 3 G K O�D9B�> 5 2i R P P D K6? A > O�D9B�> 5 GJO�B = g O ;4D 145 D,ObDaB�> 5 G 5 5 <�D��O 3 OH 3 ] ?�1 > O � = � L <�> 8 DJ;=>ZO/; 3 G K65 DhO ;4<�> G 1 ; � > 1 > 1 >CG K A > G 54?�1 >CB P G KQ? > 5 � L <�> ;4D 145 D

O e

−200 −150 −100 −50 0 50 100 150 200−150

−100

−50

0

50

100

150

�� ;&: � _ > 5 < ?b5 >CB F[D 1 ;=> 5 ; 5 > ; = �

P G KQ? > 5 � > 1 >VICG K I ?�K GW;4>CB F 1 D A ;= F[D 1 �VG 1 B 8 1 D - K > A � L <�> 3 O P > 1@5 > 8 1 D - K > A <UGJB GJOG 8b8 1 D � 3 A GW;=> ICDJO�B 3 ; 3 DhONO ? A - > 1 DJF � � = g � � � L G - K > 5 O � = � O � e 5 <�D��,;=<�> 5@3 A ?bK GW; 3 DhO1 > 54?bK ; 5 �

�� :$;4< 1 >Z> � B 3 A >CO 5@3 DhO�G K ;4D 145 D A D9B�> K ;=<UG ; �VG 5 B 3Q5 I 1 >Z; 3 � >CB�F 1 D A A GJ]hO�> ; 3 I1 > 5 DJOUGJO�IZ> BUG ;SG � R @�� ; <UGJB R = TVP ObDaB�> 5 GJO�BdDJF ;4<�> 5 > ;=<�> 1 > � > 1 > e � P > 8 3 ICG 1 B 3 G KO�D9B�> 5 P = TVT P D K6? A >�O�D9B�> 5 GJObB R ghe ;4D 145 D O�DaBb> 5 � L 5 ; 3 � O�> 545 A G ; 143 �*<�GJB� O = T � ObDhO � > 1 D 5 � L IZDhO�B 3 ; 3 DhOfO ? A - > 1 F[D 1 ;=<�> 3 O P > 1@5 > 8 1 D - K > A �VG 5�3 O�I G K I ? �K G - K >EF[D 1N_ GW; K G - � L G - K > 5 O � i � O �A@ 5 <bD�� ;4<�> 543 A ?�K GW; 3 DhO 1 > 5@?�K ; 5 � H 3 ] ?b1 > 5 e � eGJObB O � e 5 <�D��;=<�> A > 5 < �

O i

� � �� ; : � L > 5 ; 5 >Z; = � O @ = � D9B�> 5

L > 5 ; c D/G 1@5 >ZO 3 O�] A >Z;=<bDaB J 141 D 1 `a> ; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > F 3QK63 Ob> G 1 P O � g � e R 5 g �UOVO 5 � O 5@3 ] �

`9;=GJO�BUG 1 B�: _ K R @ � g � i @ 5 g �QP e 5 O 3 T I GJO/;

� > 3 ]J<";4>CB P i � g � e P 5 g �UO P 5` � : _ K � M i 5 A DaDW;=< 5 O e � g � e P 5 g �UO P 5_'?�K ; 3Q5 ;=> 8 = P � g �UR � 5 e � = T 5> >CI ;=D 1 F 3QK63 Ob> G 1 = T �c F � i R �`9;=GJO�BUG 1 B�: _ K ihi �_'?�K ; 3Q5 ;=> 8 e @ �

_ GW; 143 � F 3QK63 Ob> G 1 P R �c F � � O �`9;=GJO�BUG 1 B�: _ K � T �_'?�K ; 3Q5 ;=> 8 e O �

e � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > `9;=GJO�BUG 1 B�: _ K T = � g �A@ � 5 g �QP e 5 � O 5@3 ] �= c . I K > _'?�K ; 3Q5 ;=> 8 =�� = �UR i 5 = �UO � 5 O 3 T I GJO/;e c . I K > 5 _'?�K ; 3Q5 ;=> 8 =V= � i � eJi 5i c . I K > 5 _'?�K ; 3Q5 ;=> 8 = O � @ � � P 5@ c . I K > 5 _'?�K ; 3Q5 ;=> 8 = R � P �QP g 5O c . I K > 5 _'?�K ; 3Q5 ;=> 8 = R � T � ehec DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< O � � � R �QT R 5L 3 X <�DJO�D P�1 >Z] ?�K G 143 � GW; 3 DhOc DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4ZB 3 ;4> 1 GW; 3 DhO 5L > 5 ;�DJF ICD 1@1 >ZIZ;�ICDhO P > 1 ]J>CO�IZ> � = K > P > K B�>C> 8'A ?bK ; 3 ] 143 B A > G 5@?�1 >ZB'GW]/G 3 O 5 ;�ICD 141 >ZIZ;3 O P > 145 > 5 D KQP > � i � 3 ;=> 1 GW; 3 DhO 5 DWF IZDhO � ? ]/G ;=>\] 1 GWB 3 >ZO"; �= c . I K > _'?�K ; 3Q5 ;=> 8 = g � � �e c . I K > 5 _'?�K ; 3Q5 ;=> 8 e � i R �i c . I K > 5 _'?�K ; 3Q5 ;=> 8 = � � R �@ c . I K > 5 _'?�K ; 3Q5 ;=> 8 = � � e �O c . I K > 5 _'?�K ; 3Q5 ;=> 8 = � ��= �

O @

� � �� ; D � L > 5 ;E`a> ; = � O @ = � D9B�> 5 � L > 5 ; DJF > 1@1 D 1\1 D - ?�5 ;4O�> 5@5 � 3 ;=\GJBbB 3 ; 3 DhO �� O 8 ? ; ObD 365 >\GJB�B 3 ; 3 DJO c D/G 145 >ZO 3 Ob] A >Z;4<�DaB J 141 D 1= � > P > K W >C> 8 � O c . I K > L > 5 ; 5g � _'?bK ; 3Q5 ;4> 8 @ �QT �O � _'?bK ; 3Q5 ;4> 8 R � � �= g � _'?bK ; 3Q5 ;4> 8 = @ �= O � _'?bK ; 3Q5 ;4> 8 eJg �eJg � _'?bK ; 3Q5 ;4> 8 e P �c DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< L 3 X <�DhO�D P�1 >C] ?�K G 143�� GW; 3 DhOg � c DhO � ? ]/GW;4> ] 1 GJB 3 >CO/; @ � i �O � c DhO � ? ]/GW;4> ] 1 GJB 3 >CO/; � �UR �= g � c DhO � ? ]/GW;4> ] 1 GJB 3 >CO/; = R �= O � c DhO � ? ]/GW;4> ] 1 GJB 3 >CO/; e O �eJg � c DhO � ? ]/GW;4> ] 1 GJB 3 >CO/; ihi �

� � � � ��; Z � L > 5 ; 5 > ; e � R = TVP � D9B�> 5 � `9;=GJO�BUG 1 Bf;=> 5 ; 5L > 5 ; c D/G 1@5 >CO 3 O�] A > ;=<�D9B J 141 D 1 `a>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > `9;SGWO�BUG 1 B � � � � � ihi �A@ 5 =�� O � = 5 g � i = 5F 36KQ3 O�>CG 1 =V= gJg � e � � � O 5 =�� T �QT 5 g � i = 5

: 8�8 1 D � 3 A GW;=> 3 O P > 1@5 > PVP = � i T � i � 5 =�� P � � 5 g � i/e 5c F � = g � � e � � i R 5 =�� O � � 5 g � e � 5_'?�K ; 365 ;=> 8 O @ � = O = T 5 =V= P ihe 5 g �UO T 5

e � > P > K65 W >C> 8 L > 5 ; 5= c . I K > _'?�K ; 365 ;=> 8 O P � =�� P O i 5 e @ = eWg 5 @ �QT e 5> >CI ;=D 1 `9;SGWO�BUG 1 B i R �_'?�K ; 365 ;=> 8 eJi �

_ GW; 143 � `9;SGWO�BUG 1 B i R �_'?�K ; 365 ;=> 8 O P �

c DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< O i � P g R = 5L 3 X <�DJO�D P�1 >Z] ?�K G 143 � GW; 3 DhOc DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< T g � e R @ g 5K63 A 3 ;=>ZB 3 ;4> 1 GW; 3 DhO 5

OVO

� � �� ; E � L > 5 ; `a>Z; e � R = T P � D9B�> 5 � : ? � 3QK6K G 1 . ;4> 5 ; 5E?�543 O�] cLK � J F[D 1 ;4<�> T OUG K5 D KQP > �L > 5 ; c DhG 145 >CO 3 O�] J 141 D 1 `a>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >

A >Z;4<�D9B_'?�K ; 3 ] 143 B = c . I K >= � > P > K B�>C> 8 _�?�K ; 365 ;4> 8 R e � =�� O � e 5 O O P = 5 =V= �QT O 5e � > P > K65 B�>C> 8 _�?�K ; 365 ;4> 8 P O � e R i @ 5 R e � O 5 = T �UR e 5i � > P > K65 B�>C> 8 _�?�K ; 365 ;4> 8 T g � =V= T i O 5 O =V= @ 5 O @ � � @ 5_'?�K ; 3 ] 143 B+I . I KQ3 O�]E;4> 5 ; � e K > P > K65 B�>Z> 8 �e c . I K > 5 _�?�K ; 365 ;4> 8 O � � e R i @ 5 = ihg R � 5i c . I K > 5 _�?�K ; 365 ;4> 8 PVP � = � PVT e 5@ c . I K > 5 _�?�K ; 365 ;4> 8 � e O � e P e O i 5` A DaDW;=< 3 O�]N;=> 5 ; 5 � e W >Z> 8 �= � > P > K B�>C> 8 _�?�K ; 365 ;4> 8 RVO � e T = � i 5 R = g = 5N D 5 ; 5 A D9DJ;4< 3 O�] R g �e � > P > K65 B�>C> 8 _�?�K ; 365 ;4> 8 R e � =V=V=V= e 5 eWi @V@ � 5N D 5 ; 5 A D9DJ;4< 3 O�] R g �e � > P > K65 B�>C> 8 _�?�K ; 365 ;4> 8L > 5 ; 5 A > G 54?�1@3 O�] P G 1 . 3 O�] ;=D K > 1 GJO�IC> K > P > K65 G KQK 8 > 1 F[D 1 A >CBfDhO = I . I K > � 3 ;=<= K > P > K Bb>C> 8 � 3 ;4< A ?�K ; 365 ;4> 8� > G X IZDhO�O�>ZIZ; 3 DhOf;=D K > 1 GJO�IC> � � c L � ;=> 5 ;� c L � g � g/e R e � =V=V=V= e 5 eWi @V@ � 5� c L � g � g O RVO � O @ e R 5 = eJi @ e 5� c L � g � = P = � e P @ T 5 P ghi/e 5� c L � g � = O T g � = @ i = 5 iJi/eJi 5

� c L � g � e e T = � T R e �UO 5 = TVTVT 5� c L � g � i e R O � @ g @ 5 T =�� e 5> G 1 . 3 O�] 5 ; 3 � O�> 5@5 A GW; 143 � >CO/; 1 . ;=D K > 1 GJO�IZ> � ` _ J L � ;=> 5 ; � 3 ;4< � � c L � g � = � �` _ J L � g � ghg = PVT � e T = �QP 5 R @ i �UO 5` _ J L � g � g = PVT � = i P �UO 5 @ O g � i 5` _ J L � g � g O P � � R g � = i 5 e T = � g 5` _ J L � g � = = gJg � e � O g �UO i 5 e =�� = 5

O P

�� ; D � � O";4> 1@3 D 1VP93 >��$DJF ;= A D9B�> K F[D 1 ;=> 5 ; 5 >Z; e �

OVR�� L (F[D 1 � G 1 B - 3 Da> K >CI ; 1@3 I T > K B 8 1 D - K > A IZD Ad8 ? ;=>ZB DhO ;=<�> 5 G A > A D9B�> K?�5 >CB 3 O�;=> 5 ; 5 >Z; e � L 5 > ;=> 5 ; 5 � > 1 > - G 5 >CB DhO�G ] 3QP >CO P >CI ;=D 1 DJF > 8 3 ICG 1 B 3 G K8 DJ;=>ZO/; 3 G K65 GJO�B A >CG 54?b1 >CB�;=<�> 3 ;4> 1 G ; 3QP > 5 D K P > 1@5 > 5 ; 3 A G ;=>\DJF ;4<�> 5 D KQ? ; 3 DhO�DJO�;=

;4D 145 D GW]/G 3 O 5 ;�GEB 361 >CI ;�F[D 1 � G 1 B 5 D KQP > � L G - K > O �UO 5 <�D�� 5 ;4<�> 543 A ?�K G ; 3 DJO 1 > 54?�K ; 5 �� : ; � D � B 3 A >ZO 543 DhOUG K A D9B�> K � 3 ;4< ihghg O�DaBb> 5 �1B F ;=<�> 5 > ;4<�> 1 >� > 1 > @ g> 8 3 ICG 1 B 3 G K ObDaB�> 5 eJghg P D K6? A >EO�D9B�> 5 GWO�B P g ;=D 1@5 D O�DaBb> 5 G 525 <bD��O 3 O H 3 ] ?�1 >O � i � L < 365 8 1 D - K > A � G 5 I 1 > GW;4>CB -/. ]h>ZO�> 1 GW; 3 O�] O�D9B�> 5 3 O IZDhO�IC>ZO/; 143 I I 3Q1 I K > 5 � J GJIS<O�D9B�> <UGJB(G 1 GJO�B�D A P G K6? > 3 ObI K6? B�>CB 3 O 3 ; 5 ICG 1 ;4> 5@3 GJO IZDaD 1 B 3 OUGW;=> 5 GJObB 3 ; 5 8 D 543 ; 3 DhO

B�> ;=> 1 A 3 O�>ZBIZDhO�O�>ZIZ;4>CB�ObDaB�> 5 � � D9B�> 5 ;4<UGW; � > 1 > � 3 ;4< 3 O�G�B�> T O�>CB�B 365 ;SGJObIC> GJObB ��< 3 IS< � D ?�K B O�DJ; I G ?�5 >(ICDhO�Ob>CIZ; 3 DhO D P > 14K G 8 � > 1 >(ICDhObO�>CI ;=>CB A G 3 O";=G 3 O 3 O�]G 8 1 D 8 > 1 ; 143 GJO�] ?�K G 1 B 365 I 1 > ; 3�� GW; 3 DhO � L <�> 5 ; 3 � O�> 5@5 A G ; 143 �,<UGJB = @ ghg O�DJO � > 1 D>ZO"; 143 > 5 GJO�B+;4<�> 3 O P > 145 > 5 D K P >2<UGJBfGWO�G 8�8 1 D � 3 A GW;4> ICDJO�B 3 ; 3 DhO O ? A - > 1 DJF = � = g � �L G - K > O �UP 5 <�D�� 5 ;4<�> 543 A ?�K GW; 3 DhO 1 > 5@?�K ; 5 �

�� L <�> 5 G A > A DaBb> K G 5 ;4> 5 ; 5 >Z; @ >��aIC> 8 ; 3 ; � G 5 ICD Ad8 D 5 >CB DJF =V=�� O ObDaB�> 5 DJF��< 3 IS<d;4<�> 1 > � > 1 > = eJg > 8 3 I G 1 B 3 G K O�D9B�> 5 � � O P D K6? A > O�D9B�> 5 GWO�B T g ;=D 1@5 D\O�D9B�> 5 �L <�> 5 ; 3 � O�> 5@5 A GW; 1@3 � <�GJB P � PVP ObDhO � > 1 D�>CO/; 1@3 > 5 GJO�B�;=<�> 3 O P > 145 > 5 D K P >d<UGJB�GJOG 8b8 1 D � 3 A GW;=>�ICDhObB 3 ; 3 DhO O ? AN- > 1 DJF i � = g � � � L G - K > O �SR 5 <�D�� 5 ;=<�> 5@3 A ?bK GW; 3 DhO1 > 54?bK ; 5 �

� � �� ; � � L > 5 ; 5 > ; i F[D 1 � G 1 B 8 1 D - K > A � R = T P � DaBb> 5

L > 5 ; c D/G 1@5 >CO 3 O�] A > ;=<�D9B J 141 D 1 `9>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > F 36KQ3 O�>CG 1 =V= � i �SO = 5 e P �UP e 5 g � e � 5

`9;SGWO�BUG 1 B e = � R � � � 5 e O �SO T 5 g � e R 5: 8�8 1 D � 3 A GW;=> 3 O P > 1@5 > = g � = i � g O 5 e P �SR e 5 g � e R 5c F � i = � = i � g O 5 e P �SR e 5 g � e R 5_'?�K ; 365 ;=> 8 i � = � e R �UTVO 5 � P g � = 5 g � i @ 5

O T

−10 −8 −6 −4 −2 0 2 4 6 8 10−10

−8

−6

−4

−2

0

2

4

6

8

10

�� ; Z � _ > 5 <�ICDhO 5 ; 1@? IZ;4>CB F[D 1 ;=> 5 ; 5 >Z; @ �

� � �� ;�� L > 5 ; 5 >Z; @ � ihghg � D9B�> 5L > 5 ; c D/G 1@5 >CO 3 O�] A > ;=<�D9B J 1@1 D 1 `a>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > _'?�K ; 365 ;=> 8 � � e � g � i O 5 g �UO P 5 � O 5@3 ] �

_'?�K ; 365 ;=> 8 � M i 5 A DaDJ;4< 5 � � i � g �UO T 5 O 3 T I GJO/;c F � e � � g � = g 5 g � = g 5F 36KQ3 O�>CG 1 e = � g � = g 5 g � � 5`9;SGWO�BUG 1 B e @ � g � = O 5 g � =V= 5`9;SGWO�BUG 1 B � M i 5 A DaDJ;4< 5 ehe � g � =V= 5: 8�8 1 D � 3 A GW; 3 DhO eJg � g � eJg 5 g � =V= 5

c DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< = P � e � i O 5L 3 X <�DJO�D P�1 >Z] ?�K G 143 � GW; 3 DhOc DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4ZB 3 ;4> 1 GW; 3 DhO 5

O �

� � �� ; \ � L > 5 ; 5 >Z; O � =V=�� O � DaB�> 5

L > 5 ; c D/G 1@5 >CO 3 O�] A > ;=<�D9B J 1@1 D 1 `a>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > _'?�K ; 365 ;=> 8 = g � i � =�� 5 =�� UR i 5

_'?�K ; 365 ;=> 8 � M i 5 A DaDJ;4< 5 = g � eJg � = Tc F � eJi � g �A@ i 5 e � ghi 5F 36KQ3 O�>CG 1 eJg � g �A@ O 5 e � g P 5`9;SGWO�BUG 1 B = T � g �QPVT 5 e � g T 5`9;SGWO�BUG 1 B � M i 5 A DaDJ;4< 5 = R � e � =V= 5: 8�8 1 D � 3 A GW; 3 DhO =�� g �QT O 5 e � i/e 5 g � g @ 5> >CI ;=D 1 _'?�K ; 365 ;=> 8 = R �c F � = R �F 36KQ3 O�>CG 1 = P �`9;SGWO�BUG 1 B =�� : 8�8 1 D � 3 A GW; 3 DhO = R �

_ GW; 143 � _'?�K ; 365 ;=> 8 =�� c F � e T �F 36KQ3 O�>CG 1 eJg �`9;SGWO�BUG 1 B eJi �: 8�8 1 D � 3 A GW; 3 DhO e � �

c DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< = e � @ � �UR e 5L 3 X <�DJO�D P�1 >Z] ?�K G 143 � GW; 3 DhOc DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< i/e � = @ �UO = 5K63 A 3 ;=>ZB 3 ;4> 1 GW; 3 DhO 5

P g

�� L <�> 5 G A > A D9B�> K G 5 ;=> 5 ; 5 >Z; @ > �bIZ> 8 ; 3 ; � G 5 IZD Ad8 D 5 >CB+DWF e P � e O�D9B�> 5 DJF ��< 3 IS<';4<�> 1 > � > 1 > = T g > 8 3 I G 1 B 3 G K O�DaBb> 5 eJi � e P D KQ? A >NO�D9B�> 5 GJObB = eJg ;4D 145 DO�D9B�> 5 G 5 5 <�D��O 3 O H 3 ] ?�1 > O �Q@ � L <�> 5 ; 3 � Ob> 545 A GW; 1@3 �^<UGJB = P R @ O ObDhO � > 1 D\>CO/; 143 > 5GJObB+;=<�> 3 O P > 1@5 > 5 D KQP >2<�GJBfGJOfG 8�8 1 D � 3 A GW;=> ICDhO�B 3 ; 3 DhO+O ? A - > 1 DJF O � = g �� L G - K >O �QT 5 <�D�� 5 ;=<�> 5@3 A ?�K GW; 3 DhO 1 > 54?bK ; 5 �

�� L <�> 5 G A > A D9B�> K G 5 ;=> 5 ; 5 >Z; @ > �bIZ> 8 ; 3 ; � G 5 IZD Ad8 D 5 >CB+DWF @ R T � O�D9B�> 5 DJF ��< 3 IS<';4<�> 1 > � > 1 > e @ g > 8 3 I G 1 B 3 G K O�DaBb> 5 @ i T � P D KQ? A >NO�D9B�> 5 GJObB = P g ;4D 145 DO�D9B�> 5 � L <�> 5 ; 3 � O�> 5@5 A GW; 143 � <�GJB ihg R e @ O�DJO � > 1 Dd>CO/; 1@3 > 5 � L <�> 3 O P > 145 > 8 1 D - K > A<UGWB(GJO(G 8�8 1 D � 3 A G ;=> IZDhO�B 3 ; 3 DhONO ? A - > 1 DJF O � = g �� GJO�B ;4<�> F[D 1 �VG 1 B 8 1 D - K > A <�GJBGJO G 8�8 1 D � 3 A GW;4> ICDhObB 3 ; 3 DhO O ? AN- > 1 DWF = � = g � � L G - K > O � � 5 <�D�� 5 ;=<�> 5@3 A ?bK GW; 3 DhO1 > 54?bK ; 5 �

�� L <�> 5 G A > ;4D 145 D A DaB�> K G 5 ;=> 5 ; 5 >Z; e >��aIC> 8 ; 3 ; �VG 5 G < 3 ]h 1N1 > 5 D K6? �

−30 −20 −10 0 10 20 30−30

−20

−10

0

10

20

30

�� ; E � _ > 5 <�ICDhO 5 ; 1@? IZ;4>CB'F[D 1 ;=> 5 ; 5 >Z; P 8 1 D - K > A �

P =

� � �� ;�� L > 5 ; 5 >Z; P � e P � e � DaB�> 5L > 5 ; c D/G 1@5 >CO 3 O�] A > ;=<�D9B J 1@1 D 1 `a>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > _'?�K ; 365 ;=> 8 = T � T �UR g 5 =V= i � eJg 5

_'?�K ; 365 ;=> 8 � M i 5 A DaDJ;4< 5 = O � = e � � � O 5c F � ihg � = � = e 5 =V= �QT @ 5F 36KQ3 O�>CG 1 e O � = � g � 5 =V= � ��= 5`9;SGWO�BUG 1 B e O � = �A@ O 5 =V= �A@ O 5: 8�8 1 D � 3 A GW;=> 3 O P > 1@5 > ehe � e � ghi 5 = i � ghg 5 g � = g 5`9;SGWO�BUG 1 B � M i 5 A DaDJ;4< 5 e O � =V= �UO � 5

c DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< = O � e RVO �QT O 5L 3 X <�DJO�D P�1 >Z] ?�K G 143 � GW; 3 DhOc DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< ihg � R � �UR @ 5K63 A 3 ;=>ZB 3 ;4> 1 GW; 3 DhO 5

; 3 DhO A DaB�> K GJO�B,ICD Ad8 D 5 >ZB�DJF = O P R e T O�D9B�> 5 @ R i O DJF ��< 3 IS< � > 1 >�> 8 3 ICG 1 B 3 G KO�D9B�> 5 = @ P � i R P D KQ? A > 5 O�D9B�> 5 GWO�B ihg O P ;4D 145 D O�D9B�> 5 � L <�> 5 ; 3 � O�> 545 A GW; 1@3 �<UGWB e @ P i @ TVP O�DhO � > 1 D�>ZO/; 143 > 5 � L <�> 3 O P > 1@5 > 8 1 D - K > A � 5 ICDhO�B 3 ; 3 DhO O ? A - > 1 � G 53 O�I G K I ?�K G - K > -". _ GW; K G - � L <�> F ?�K6K 5 > ; DJF ;4> 5 ; 5 � > 1 >�ObDJ; 1@? O&DhO�;4< 365 ;=> 5 ; 5 >Z; �L D ;=> 5 ; 5 I G K G - 36KQ3 ; . � 1 GJO DhO K . G A ?�K ; 3Q5 ;=> 8 GJO�B - 36KQ3 O�>CG 1 ;=> 5 ; � � O GJBbB 3 ; 3 DhO ;=;4> 5 ; �VG 5 - 1 D X >CO 3 O/;=DN> GJIS< K > P > K ;=D 5 >C> ;4<�> 5 8 >Z>CB GJO�BfGJIZI ?�1 GJI . GW;V> P > 1 . B�> 8 ;=< �L <�> A G 3 O,;4> 5 ;� G 5 G 5 > P >CO K > P > K B�>C> 8 ;=> 5 ; � 3 ;=< >CGJIS< DJF2;4<�>'Bb>C> 8 > 1 K > P > KQ5;4> 5 ;4>CB+F[D 1 DhO�> Bb> 8 ;4<�DJF ICD/G 145 > ] 143 B ICD 141 >ZIZ; 3 DhO � L <�> K D�� > 1 Bb> 8 ;4< 5 ICD ?bK B+O�DW; - >;4> 5 ;4>CB�G 5 ;= . � D ?�K B+;SG X >\;4DaD K DhO�] � B Ob> ;=> 5 ; �VG 5 8 > 1 F[D 1 A >CB � 3 ;=<fGEICD Ad8 K >Z;=>DhOb> A ?�K ; 3 ] 143 B,I . I K > � 3 ;=<�;4< 1 >Z> K > P > KQ5 DJF\ICDhG 145 >CO 3 O�] � L G - K > O � = g 5 <�D�� 5 ;=5@3 A ?�K GW; 3 DhO 1 > 54?bK ; 5 �

� � � ! � � � �� L <�>+BUG ;SG�F 1 D A ;=< 3Q5N1 > 5 >CG 1 IS< 5 <�D�� ;4<UGW; B 3 � > 1 >ZO/;EG K ]hD 143 ;=< A 5 8 > 1 F[D 1 A - > ;4;4> 1 3 O

B 3 � > 1 >CO/; 5@3 ; ? GW; 3 DhO 5 � � D2DJO�> A >Z;=<bDaB 8 1 D P > 5 3 ; 5 > K FU;4D - > - > ;4;=> 1 ;=<UGWO ;=<�> DJ;4<�> 1@5 G KQK ;=; 3 A > � L <�> A ?bK ; 3 ] 143 B G K ]hD 1@3 ;4< A 5 � 3 ;=<fG 543 O�] K > P � I . I K > 8 > 1 F[D 1 A >CB P > 1 . ICD Ad8 >Z; 3 ; 3 P > K .� 3 ;4< ;=<�> ICDJO � ? ]/GW;4> ] 1 GJB 3 >CO/; A >Z;4<�DaB 5�3 OGJICI ?�1 GWI .� GJO�B 5 <�D�� 8 DJ;4>CO/; 3 G K F[D 1 ]hD9D9B5 ICG K G - 36KQ3 ; . G 5�5 >Z>CO 3 O9H 3 ] ?b1 > O �UO �

P e

� � �� ; � � L > 5 ; 5 >Z; R � @ R T � � DaB�> 5

L > 5 ; c D/G 1@5 >ZO 3 O�] A >Z;=<bDaB J 141 D 1 `a> ; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >= � > P > K B�>C> 8 ;=> 5 ; 5= c . I K > _'?�K ; 3Q5 ;=> 8 = O � = T � e � 5 @ R = �Q@ e 5

_'?�K ; 3Q5 ;=> 8 � M i 5 A D9DJ;=< 5 = i � @ O = � g @ 5_'?�K ; 3Q5 ;=> 8f- 36KQ3 O�>CG 1 i @ � e @ �Q@ O 5 O i � 5 g � eJi 5_'?�K ; 3Q5 ;=> 8 c F � = e � e @ � ghi 5 O @ i 5 g � i = 5c F � e @ � e � g P 5 @ = �UR � 5F 3QK63 Ob> G 1 eJi � e � ghg 5 @ = �UO e 5`9;=GJO�BUG 1 B ehe � e � ��= 5 @ g �UR � 5: 8b8 1 D � 3 A GW;=> 3 O P > 1@5 > ehe � i �QT @ 5 @V@ � eJi 5 g � = @ 5`9;=GJO�BUG 1 B � M i 5 A DaDW;=< 5 ehe � @ = � = @ 5> >CI ;=D 1 _'?�K ; 3Q5 ;=> 8 = P �_'?�K ; 3Q5 ;=> 8f- 36KQ3 O�>CG 1 = e �c F � = R �F 3QK63 Ob> G 1 = P �`9;=GJO�BUG 1 B =�� : 8b8 1 D � 3 A GW;=> 3 O P > 1@5 > = O �

_ GW; 143 � _'?�K ; 3Q5 ;=> 8 e = �c F � e � �F 3QK63 Ob> G 1 i = �`9;=GJO�BUG 1 B i = �: 8b8 1 D � 3 A GW;=> 3 O P > 1@5 > i O �

e � > P > K65 B�>C> 8 ;4> 5 ; 5= c . I K > _'?�K ; 3Q5 ;=> 8 = @ � e @ � ghi 5 OVO P 5 g � i = 5e c . I K > 5 _'?�K ; 3Q5 ;=> 8 = g � = g � g 5i c . I K > 5 _'?�K ; 3Q5 ;=> 8 � � = � = P @ e 5@ c . I K > 5 _'?�K ; 3Q5 ;=> 8 T �A@ � e =�� R 5O c . I K > 5 _'?�K ; 3Q5 ;=> 8 T � g � e RVO g 5c DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< = i � � g P � i/e 5L 3 X <�DJO�D P�1 >Z] ?�K G 143 � GW; 3 DhOc DhO � ? ]/GW;=>\] 1 GJB 3 >CO/; � 3 ;4< e � � e P e �UP � 5K63 A 3 ;=>ZB 3 ;4> 1 GW; 3 DhO 5

P i

� � �� ; : � � L > 5 ; 5 >Z; T � = O P R e T � D9B�> 5

L > 5 ; c D/G 1@5 >CO 3 O�] J 1@1 D 1 `a>Z; ? 8 ; 3 A > cLK ; 3 A > _ K ; 3 A >A > ;=<�D9B

= c . I K > _'?�K ; 365 ;=> 8 =�� e O e 5R5W >C> 8L <�>2;=> 5 ; 365 - 1 D X >ZO�BbD��O 3 O/;=D(>CGJIS< 5 ;=> 8W > 8 ;=< = @ RVO g 5W > 8 ;=< e =V= � g T 5W > 8 ;=\B�>C> 8 IZD/G 1@5 > ] 143 B�ICD 1@1 >CI ; 3 DhO � 3 ;=< ] 3 P >COfIZD/G 145 >\] 143 B 5 D KQP >\B�> 8 ;4<W > 8 ;=< @ = g P � = @ ihi R 5 = @V@ P R = 5 e R �QPVTW > 8 ;=< O T R � e @ O TVP 5 R @ TVP � 5 =�� = @ 5W > 8 ;= 8 ;=<f;=> 5 ;i W >C> 8 � = c . I K > TVT � i/e R = P = 5 = O i �SR 5= c . I K > F 36KQ3 O�>CG 1= W >C> 8 � g T � = i � � = 5 i O OVR i 5 R � � g 5e W >C> 8 = PVP � @ e P � � 5 = e R P 5 ehe 5i W >C> 8 � R � P R e �QT 5 = e � = i 5 e T �QP 5

P @

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�� ; � � N > 1 F[D 1 A GWO�IC> 5 I G K G - 3QK63 ; . F[D 1 A ?�K ; 3Q5 ;=> 8 A ?bK ; 3 ] 143 B � _'?�K ; 3 ] 1@3 B 5 > ; ? 8 ; 3 A >� . � G � 365 � 3 O 5 >CIZDhO�B 5 365 8 K DJ;@;=>CB P > 145@?�5 ;=<�>�O ? A - > 1 DJF O�D9B�> 5 DhO(;=<�>�� G�� 3Q5 F[D 1 8 1 D - K > A 55 D KQP >ZB ?b543 Ob](;4<�> A ?�K ; 365 ;=> 8 G K ]hD 1@3 ;4< A DhO ;4> 5 ; 5 >Z; 5 @ � R �

H 3 ] ?�1 > 5 O �QP � O � = e B�> 8 3 IZ; ;4<�> 8 DW;=>CO/; 3 G KQ5 ;=< 1 D ? ]J<(;4<�>V;=D 145 D\DJF ;4<�>V; � D � B 3 A >ZO 543 DhOUG K54KQ3 IZ> 3 O�;=> 5 ; 5 > ; = G 5 A ?�K ; 3 ] 1@3 B,>��a>CI ? ;=>ZB�>CGJIS GJObB ICDhO P > 1 ]h>ZB�I K D 5 > 1 ;=D*;=ICD 141 >ZIZ; 5 D KQ? ; 3 DhO � L < 365 >��bG Ad8 K > ?�5 >CB G 1 GJO�BbD A P >ZIZ;=D 1 F[D 1 > 8 3 I G 1 B 3 G K 8 DW;=>CO/; 3 G KQ5 GWO�BG F[D 1 � G 1 B 5 D KQ? ; 3 DhO(B�>Z;4> 1 A 3 Ob>CB ;4<�> 543 A ?�K GW;4>CB A > G 5@?�1 >ZB ;=D 1@5 D 8 DW;=>CO/; 3 G KQ5 3 O 8 ? ; � L < 3Q5;=> 5 ; ? ; 3QK63 � >CB(;=<�> A ?�K ; 365 ;=> 8 ; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 � L <�> > 141 D 1 B�>ZI 1 >CG 5 >ZB 543 ]hO 3QT I GJO/; K . � 3 ;4<> GWIS<+I . I K > 3 Od;4<�> 5 > T ] ?b1 > 5 GJObB+G^ICG 1 > F ?�K 3 O 5 8 >ZIZ; 3 DhO G K65 D 1 > P >CG K65 5 A DaDW;=<�> 1 > 5 ; 3 A GW;=> 5GJO�B > 141 D 145 G F ;=> 1 > GJIS< 5 A D9DJ;=< 3 O�] 5 ;=> 8 � L < 365 > �bG A 8 K > G K65 D 36K6KQ?�5 ; 1 GW;4> 5 ;=<�> 5 8 GW; 3 G K5 A D9DJ;=< 3 O�](GJO�B GW;@;=>ZO ? GW; 3 DhOfDJF 8 DJ;4>CO/; 3 G K65 ;4<UGW;�D9ICI ?b145 � 3 ;=< 3 O+;= - D9B . �: A DhO�] ;= A ?�K ; 3 ] 1@3 B$IZD/G 145 >CO 3 O�] A > ;=<�D9B 5 ;=<�> A ?�K ; 3Q5 ;=> 8�A > ;=<�D9B �VG 5 A D 5 ;

GJIZI ?�1 GW;=> ��< 36K >*;=<�> - 36KQ3 O�>CG 1 A >Z;4<�D9B � G 5 FHG 5 ;4> 5 ; � HUD 1 >��bG Ad8 K > DhO�;=> 5 ; 5 >Z; e A ?�K ; 3Q5 ;=> 8\A ?�K ; 3 ] 1@3 B � G 5 ;=<�> DhO K .2A ?�K ; 3 ] 143 B\G K ]hD 1@3 ;4< A 5@? � I 3 >CO/; K . GJICI ?�1 GW;4> ;4D GJIS< 3 > P >ICDJO P > 1 ]h>CO�IZ> � � D�� > P > 1 F[D 1 ;=<�> 5 G A >�;=> 5 ; 5 > ; - 36K63 O�> G 1NT O 3Q5 <�>ZB G 8�8 1 D � 3 A GW;=> K .*e T; 3 A > 5 FHG 5 ;4> 1 � K >ZO�> 1 G K6K .� ;= - 3QK63 O�> G 1 A > ;=<�D9B 8 > 1 F[D 1 A >CB � > K6K > 5 8 >CI 3 G KQK . DhO ;=<�> P >ZIZ;4D 1

P O

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�� ;�� L > 5 ; 5 >Z; = GWF ;4> 1 DhO�> I . I K > � O�D 5 A D9DJ;=< 3 O�]�� L �IZD K D 1@5f1 > 8 1 > 5 >CO/;8 DJ;=>ZO"; 3 G KQ5 ;=< 1 D ? ]J<�D ? ;�;=\;4D 145 D �

A GJO 3 8 ?�K GW; 3 DhO � L <�> < .9- 1@3 B A > ;=<�D9B 5 DJFRIZD A - 3 O 3 Ob]EB 3 � > 1 >CO/; � > 3 ]h</; 3 O�] 5 IS<�> A > 5 � 3 ;4<;= A ?�K ; 365 ;4> 8\A >Z;=<bDaB B 3 B\O�DW; 8 > 1 F[D 1 A G 5 � > K6K G 5 ;= B�> FHG ?�K ; IS<�D 3 IZ> DJF 5 ;SGJO�B�G 1 B : _ K� > 3 ]J<";4>CB A ?�K ; 365 ;4> 8 � L ICDJO � ? ]/GW;4> ] 1 GJB 3 >CO/; A >Z;4<�D9B � G 5N1 D - ?�5 ;EGJO�B 8 1 >ZB 3 I ;SG - K > G K - > 3 ;�� 3 ;=< G 8 > 1 F[D 1 A GJObIC> 8 >COUG K ; . ��<�>ZO ?�5 >CB � 3 ;=< K G 1 ]h> 1 8 1 D - K > A 5 �_'?�K ; 3 ] 143 B A >Z;4<�DaB 5 5 <�D�� 8 D 5@3 ; 3 P > 1 > 54?�K ; 5 > 5 8 >ZI 3 G K6K . � 3 ;4< 543 O�] K > I . I K > ;=> 5 ; 5 - ? ;

? ObF[D 1 ; ? OUGW;=> K . ;=<�> A ?�K ; 3 ] 1@3 B^G K ]hD 143 ;4< A 5 B 3 BEO�DJ; G K � G . 5 IZDhO/; 3 O ? >V;=D2ICDJO P > 1 ]h>�Y ?b3 I X"K .GJO�B F[D 1 ;= K G 1 ]h> 1 A D 1 >^B 3�� I ?�K ; 8 1 D - K > A 5 A ?�K ; 3 ] 143 B�G K ]hD 143 ;=< A 5 - >Z]/GJO ;4D�B 3QP > 1 ]J>GWF ;4> 1 G2F[>�� P � I . I K > 5 ��< 3QK >V;4<�>�ICDhO � ? ]/GW;=>�] 1 GJB 3 >CO/; ICDhO/; 3 O ? >CB(;=D\IZDhO P > 1 ]h> GWO�B 1 > A G 3 O

5 ;=G - K > � : K ;=<�D ? ]h< � 3 ;=<&;4<�> K G 1 ]J> ;=< 1 >C> � B 3 A >ZO 543 DhOUG K 8 1 D - K > A 5 G K6K ;=<�>�G K ]hD 143 ;=< A 58 > 1 F[D 1 A >CB 8 DaD 1@K . aA D 5 ; K63 X > K . B ? > 3 O 8 G 1 ;V;4Dd> �9; 1 > A > 3QK6K � ICDJO�B 3 ; 3 DhO 3 O�]2DJF ;4<�> A GW; 1@3 �� 3 ;4<�D ? ; T O�> K . ; ? Ob>CB 1 >C] ?�K G 1@3 � GW; 3 DhO �

PVP

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�� ; \ � L > 5 ; 5 >Z; = GWF ;=> 1 DhO�>(I . I K > � O�D 5 A DaDW;=< 3 O�]�� L <�>dICD K D 14521 > 8 1 > 5 >ZO/;N;=> 1@1 D 1 3 O�;=<�>\ICD A 8 ? ;SGW; 3 DhO � = O � ��_ `+> 1@1 D 1 � �

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�� ;�� L > 5 ; 5 >Z; = GWF ;=> 1 DJO�>(I . I K > GWO�B 8 D 5 ; 5 A D9DJ;=< 3 O�] � � 3 ;=< ;=< 1 >C> 5 A D9DJ;=< 5 � �L <�> ICD K D 145 1 > 8 1 > 5 >CO/; 8 DJ;4>CO/; 3 G K65 ;4< 1 D ? ]h<�D ? ;�;4<�>2;=D 1@5 D �

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�� ; � � L > 5 ; 5 >Z; = GWF ;=> 1 DJO�>(I . I K > GWO�B 8 D 5 ; 5 A D9DJ;=< 3 O�] � � 3 ;=< ;=< 1 >C> 5 A D9DJ;=< 5 � �L <�> ICD K D 145 1 > 8 1 > 5 >CO/; ;4<�>\> 1@1 D 1 3 Of;4<�>\ICD Ad8 ? ;=GW; 3 DhO � = i � ��_ `+> 141 D 1 � �

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�� ; : � � L > 5 ; 5 > ; = GWF ;4> 1 ;4< 1 >Z>(I . I K > 5 � ;4< 1 >Z> 5 A D9DJ;4< 5 8 > 1 I . I K > � � L <�>(ICD K D 1451 > 8 1 > 5 >ZO"; 8 DW;=>CO/; 3 G KQ5 ;=< 1 D ? ]h<bD ? ; ;=\;4D 145 D �

PVT

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�� ; :<: � L > 5 ; 5 > ; = GWF ;4> 1 ;4< 1 >Z>(I . I K > 5 � ;4< 1 >Z> 5 A D9DJ;4< 5 8 > 1 I . I K > � � L <�>(ICD K D 1451 > 8 1 > 5 >ZO"; 1 > 8 1 > 5 >CO/;�;=<�>\> 141 D 1�3 O+;=<�>\IZD A 8 ? ;SGW; 3 DhO � O �QP � ��_ `f> 141 D 1 � �

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�� ; : D � L > 5 ; 5 > ; = ICD 1@1 >CI ; 5 D KQ? ; 3 DhO � L 2ICD K D 145V1 > 8 1 > 5 >CO/; 8 DJ;4>CO/; 3 G K65 ;=< 1 D ? ]h< �D ? ; ;4<�>2;=D 1@5 D �

P �

� 3 ;4< ;4<�> 5 A G K6K > 1 ;=> 5 ; 5 > ; = GWF ;4> 1 ;=< 1 >C> I . I K > 5 � > <UGJB'GdI K D 5 > G 8�8 1 D�� 3 A GW; 3 DhO+;4D;= 5 D K6? ; 3 DhO 9- ? ; � 3 ;=<(;=<�> K G 1 ]h> 1 ;4> 5 ; 5 > ; e GWF ;4> 1 ;=< 1 >C> I . I K > 5 543 ]hO 3 T I GJO/; B 3QP > 1 ]h>CO�IZ>D9ICI ?b141 >ZB � L < 365 3Q5 - >ZI G ?b5 > DJF ;=<�> 3 O�G - 36KQ3 ; . DJF ;= 5 A DaDJ;4<�> 1 ;4DdG 545@365 ; 3 O�ICDhO P > 1 ]J>CO�IZ> �L <�> 5 A D9DJ;= 1 A ?b5 ; - >�G - K > ;=D 1 >CB ? IC>�< 3 ]J< � F 1 >CY ? >CObI . > 141 D 1 h- ? ; ;=<�> K G ?b545 � à> 3 B�> K G K �]hD 1@3 ;4< A ;=<�GW; � ?�5 >ZB �VG 5 3 Ob>�� >CIZ; 3QP > DhO ;=<�> P > 1 . 36K6K � IZDhO�B 3 ; 3 DJO�>CB 8 1 D - K > A 5 � L <�> 1 > 5@?�K ; 55 <bD�� ;=<�GW; ;= > 1@1 D 1 A >CG 54?�1 > A >CO/; 5 F[D 1 8 D 5 ; 5 A DaDJ;4< 3 Ob] B�D�O�DW;2>��a< 3 - 3 ; 54? - 5 ;SGJO/; 3 G KQK .K > 545 > 1@1 D 1 ;=<UGWO�;4<�> 8 1 > 5 A D9DJ;=< 3 O�]f> 1@1 D 1 � L <�> 3 Ad8 D 1 ;SGJObIC>EDJFVGJO�>�� >ZIZ; 3 P > 5 A DaDJ;4<�> 1- >CICD A > 5 ] 1 >CGW;=> 1 � 3 ;4< B�>C> 8 > 1 ICD/G 145 >ZO 3 Ob] � àD KQ? ; 3 DhO G 8b8 1 D � 3 A GW; 3 DhO 1 > KQ3 > 5 A D 5 ; K . DhO;= IZD/G 145 > ] 1@3 B 5 D KQP > � 3 ;4< 5 D KQP > 5 ;=<UGW;^B�D�O�DJ; ?�5 > A GWO . IZD/G 1@5 >d] 143 B K G . > 1@5 - ? ; G 5;=2ICD/G 1@5 >\] 1@3 B 5 ]JDdBb>C> 8 > 1 ;4<�> 5 D KQ? ; 3 DhO - >CIZD A > 5 A D 1 > B�> 8 >ZO�B�>CO/; DhO�;=<�> 5 A D9DJ;4<�> 1@5

G - 3QK63 ; . ;4D(ICDhO P > 1 ]h>\;=D�� G 1 B 5 G 5 D K6? ; 3 DhO � L < 365 3Q5 DhO�>\DJF ;=> 5 ; 5 > ; T � 5 A G � D 1 < 3 O�B 1 GJO�IC> 5

;=D�� G 1 B GJIS< 3 > P93 Ob]^< 3 ]h<dGJICI ?�1 GWI . 1 > 54?�K ; 5 � W >C> 8 ICDhG 145 >�] 143 B 5 G 1 >�G\O�>CIZ> 545@3 ; . � 3 ;4< 54? IS<K G 1 ]h>�;=> 5 ; 5 >Z; 5 GJO�B+;= 1 > F[D 1 > 3 ; 365 ? OUG P D 3 BUG - K > ;4D 3 O�I ?�1 GWO�GJICI ?�1 GWI . 8 >ZOUG K ; . � 3 ;=<�D ? ;>�� >CI ; 3 P > 5 A D9DJ;=< 3 O�] � : O�>�� >CI ; 3 P > 5 A D9DJ;=<�> 1 A ?b5 ; - >\G - K > ;=DNY ?b3 I X"K . 3 ;=> 1 GW;4> ;4D�� G 1 B 5GJO�GJICI ?�1 G ;=> > 5 ; 3 A GW;4> DJFN;4<�> 1 > K GW; 3 P > P G KQ? > 5 DJFÔ�> 3 ]h< - D 143 Ob],ObDaB�> 5 � L <UGW; 365 ;=5 A D9DJ;=<�> 1 A ?�5 ; 1 G 8 3 B K . > K63 A 3 OUGW;4> < 3 ]h< F 1 >CY ? >CObI . > 141 D 1R3 O ;4<�>V> 5 ; 3 A GW;4> � K G ?b545 � à> 3 B�> KB 3 B ObDJ;�B�D(;=< 3Q5 GJB�>CY ? G ;=> K . � 3 ;4<�;=<�> 3 O P > 145 > - 3 Da> K >ZIZ; 1@3 I T > K B 8 1 D - K > A �

� > I GJO 5 >Z> GÎ K >CG 1 ; 1 GWB�>CD � - >Z; � >C>ZOfGJICI ?�1 GJI . GJO�B IZD Ad8 ? ;SG ; 3 DJOUG K > � I 3 >ZO�I . � 3 ;4<;= A ?�K ; 365 ;4> 8 G K ]hD 143 ;=< A ICD A 8 G 1 >CB � 3 ;4<2;=<�> DJ;= 1 � > 3 ]h</;4>CB^G K ]hD 143 ;4< A 5 � H 3 ] ?�1 > O � = i � �L <�> A ?�K ; 365 ;=> 8 365 B�> T O 3 ;4> K .�A D 1 > GJIZI ?�1 GW;=> � � O]h>COb> 1 G K ;4<�> A ?�K ; 365 ;=> 8 G K ]hD 1@3 ;4< A1 D ? ]h< K . <UG K P >ZB,;4<�>f> 141 D 1E3 O&;4<�>fICD/G 1@5 >f] 1@3 B�ICD 1@1 >ZIZ; 3 DhO � � D�� > P > 1 ;=< 3Q5 GJB P GJO/;SGJ]J>I G A > � 3 ;4< 5@? - 5 ;=GJO/; 3 G K"54K D�� 3 O�] � L <�> 5 >Z; ? 8 8 1 D9IC> 545X3 O P D K P > 5 G�] 1 >CGW;=> 1 O ? A - > 1 DJF 5 ;=> 8 5;=D 8 > 1 F[D 1 A ;4<�> 3 O/;=> 1 8 D K GW; 3 DhOED 8 > 1 GW;4D 1 ��< 3 ISCBd;=< 3Q5 5 ;=> 8 ;4D\;=G X > G 8�8 1 D � 3 A GW;=> K .> 3 ]h</;+; 3 A > 5 G 5�K DhO�]�;4D&ICD Ad8 K >Z;=> � L <�> A ?�K ; 365 ;=> 8 G 8�8 1 D/GJIS<G KQ5 D*ICG ?�5 > 5 G*B 1 G 5 ; 3 I3 ObI 1 >CG 5 > 3 O\;4<�> O ? A - > 1 DJFbObDhO � > 1 D 5 3 O2;4<�> IZD/G 1@5 >COb>CB A GW; 143 IZ> 5 � L 3 O�I 1 > G 5 >CBNO ? AN- > 1DJFXO�DhO � > 1 D 5 1 G 365 >CB�;= 5 D KQP >2; 3 A > -/. G FHGJIZ;4D 1 DJF G 8�8 1 D � 3 A G ;=> K . = g �

� <�>CO 8 > 1 F[D 1 A 3 O�] ICG K I ?�K GW; 3 DhO 5 DhOE;= 5@3 Ad8 K > 1 � > KQK � ICDhO�B 3 ; 3 DhO�>ZBN; � D � B 3 A >ZO 543 DhOUG K8 1 D - K > A 5 � GJObB F[D 1 � G 1 B 8 1 D - K > A 5 G 5 ;4<�> . G 1 > A ? IS< A D 1 > � > KQK � IZDhO�B 3 ; 3 DhO�>CB �+;=54? 8 > 143 D 1+5 8 >C>ZB�DJF\;4<�> 543 O�] K > 5 ;=> 8 G 8�8 1 D/GJIS<�> 5 G 1 > IZ> 1 ;=G 3 O K .�A D 1 > B�> 54361 G - K > � L <�>G 8�8 1 D � 3 A GW;=> 3 O P > 1@5 >�GJO�B - 3QK63 O�> G 1 G 8�8 1 D/GJIS< � > 1 > ;4<�> A D 5 ;fGJIZI ?�1 GW;=> A >Z;4<�DaB 5 DhO

R g

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50Setup TimeSolve Time (scale = 10s)

�� ; :�Z � L <�> ; 1 GJB�>ZD � - >Z; � >C>ZO�GJIZI ?�1 GJI . GJO�B 8 > 1 F[D 1 A GJO�IC>�DJF\;=<�> B 3 � > 1 >ZO/;G K ]hD 143 ;=< A 5 � `a> ; ? 8 ; 3 A >(GJO�B 5 D K P >(; 3 A > 3 O 5 >ZICDhObB 5 � . � G � 365 �2G 1 > 8 K DJ;@;=>ZB P > 145@?�5 ;=8 > 1 IZ>CO/;SGW]h> > 141 D 123 O ;= 5 D KQP >(DhO ;=<�> � � G � 3Q5 F[D 1 ;=<�>(B 3 � > 1 >ZO";^G K ]hD 1@3 ;=< A 5 G 8�8 KQ3 >CB ;4D;=> 5 ; 5 > ; R �

;= � > KQK � IZDhO�B 3 ; 3 DhO�>CB 8 1 D - K > A 5 G K ;4<�D ? ]J<�;4<�> - 36KQ3 O�>CG 1 A >Z;4<�DaB � D ?�K B 8 1 D - G - K .&- >8 1 >ZF[> 1 G - K > - >ZI G ?�5 >�DWF 3 ; 5 5 8 >Z>CB � NRG 1 ;(DJF�;=<�> - 3QK63 O�> G 1 >�� >CI ; 3QP >CO�> 545 �VG 5 B ? >f;4D 3 ; 5GJIZI ?�1 GJI . � 3 ;=< ;= P >CI ;=D 1f3 O";4> 1 8 D K GW; 3 DhO � : 5 ;4<�> 8 1 D - K > A 5 ] 1 >�� 3 O B 3 � I ?�K ; . ;=5 ;=GJO�BUG 1 BEG 8b8 1 D/GWIS< - >ZICD A > P > 1 . IZD Ad8 > ; 3 ; 3QP > - ? ; - 36K63 O�> G 1 5 ; 3QK6K 8 1 D P >CB ;4D - >VG � 3 O�O�> 1F[D 1 ;4<�>\> G 5@3 > 1 8 1 D - K > A 5 � � D�� > P > 1 � 3 ;4<f;4<�> A D 1 >2B 3 � I ?�K ; 3QK6K � ICDJO�B 3 ; 3 DhOb>CB 8 1 D - K > A 5 ;= 3 A 8 1 D P >CB^GJIZI ?�1 GJI . DJF A ?�K ; 365 ;=> 8 G 8�8 1 DhGJIS< 3Q5 ;4<�> DhO K . P93 G - K > A > ;=<�D9B2F[D 1 A ?�K ; 3 ] 1@3 B

;=DEIZDhO P > 1 ]h> � L <�> 5@K D�� > 1 8 > 1 F[D 1 A GWO�IC> DWF A ?�K ; 365 ;4> 8�A ?b5 ; - > ;=D K > 1 GW;=>ZB � � < 36K > 5@K D�� > 18 > 1 F[D 1 A GJO�IC> 365 DhO�> D - 5 ;SGJI K > � >+G 1 > ; 1 . 3 Ob]�;=D�D P > 1 ICD A >� 3 ;=<�;4< 365 G K ]hD 143 ;=< A DhO�IZ>GJ]/G 3 O ObDJ;=> ;=<UG ; 3 F KQ3 O�>CG 1 � � � � ICDhO P > 1 ]J>CO�IZ>&I GJO - > A G 3 O/;SG 3 O�>CB ;=CO$> P >CO�;=< 3Q5B�>ZI 1 >CG 5 >ZB 8 > 1 F[D 1 A GJO�IZ> � 3QK6K - > FHG 5 ;=> 1 ;=<�GJO�DJ;= 1 O�DJO � A ?bK ; 3QK > P > K G K ]hD 1@3 ;=< A 5 DhO K G 1 ]h>BUGW;=G 5 > ; 5 �

R =

� �� L <�> 5 ICG K G - 36K63 ; . DJFRGEO�>CG 1 � � � � G K ]hD 1@3 ;=< A 3Q5 G 543 ]JO 3QT ICGJO/; 1 >CG 5 DJO F[D 1 ?b543 Ob] A ?�K ; 3 �

] 1@3 B � `aD�;=<�> Y ? > 5 ; 3 DhO�G 1@365 > 5 B�D9> 5 A ?bK ; 3 ] 143 B�IZDhO/; 3 O ? >';=D 5 I G K > K63 O�> G 1@K . � 3 ;=< ;=3 O P > 145 > 8 1 D - K > A � � F � > K DaD X GW; ;4<�> ]h>ZO�> 1 GW;=>ZB 8 1 D - K > A 5 � > ]h> ;\G 5 G A 8 KQ3 O�]dDJF 5@3 � > 5D P > 1 G - D ? ;�GNFHGJI ;=D 1 DWF eWi � H 3 ] ?�1 > 5 O � = @ GJO�B O �UO 5 <bD��;= 5 >Z; ? 8 ; 3 A > G 5 ;=<�>2O ? AN- > 1DJF O�D9B�> 5V3 O�I 1 >CG 5 > � H 3 ] ?b1 > O � = @ 365 � 3 ;4< ;=<�> 5 ;SGWO�BUG 1 B�: _ K G K ]JD 143 ;=< A GWO�B�H 3 ] ?�1 > O �UO365 � 3 ;4<�;=<�> A ?�K ; 365 ;=> 8 G K ]hD 143 ;4< A � F DJ;=<*DWF ;=<�> 8 K DJ; 5 DhO K . 54K63 ]h</; K . B�> P93 G ;=>CB*F 1 D A G5 ; 1 G 3 ]h</; K63 O�> ;=< 1 D ? ]J< ;4<�>\D 143 ] 3 O �

H 1 D A ;=<�> 5 > 8 K DW; 5 � >fI GJO 5 >Z>f;4<UGW;E;4<�> 5 >Z; ? 8 ; 3 A >+GWO�B,;4<�> A ?�K ; 3 ] 143 B 8 1 DaIZ> 545 �3 Ob]f; 3 A > � G 8 G 1 ;\F 1 D A ;=<�>dICDhO � ? ]/GW;4>d] 1 GJB 3 >CO/; T OUG K 5 D KQP > � � > 1 > 8 1 D 8 D 1 ; 3 DhO�G K ;4D�;=O ? A - > 1 DJF O�D9B�> 5 � HUD 1 >��bG Ad8 K > � 3 ;4< 5@3 Ad8 K > - 36KQ3 O�>CG 1 � > 3 ]h</; 3 O�]E;=<�> 5 > ; ? 8 8 1 DaIZ> 545 >CBG 8�8 1 D � 3 A GW;=> K . e O g O�D9B�> 5 8 > 125 >ZICDhObB*GJO�B ;4<�> A ?�K ; 3 ] 1@3 B 5 ;=> 8 5 � >ZO"; ;=< 1 D ? ]J<�G - D ? ;ihg ghghg O�D9B�> 5 8 > 1 5 >CIZDhO�B 8 > 1 I . I K > �%B O�;= DJ;= 1 <�GJO�B ;= ICDhO � ? ]/GW;4>'] 1 GJB 3 >ZO/;

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�� ;&: E � NX> 1 F[D 1 A GJO�IC> 5 I G K G - 36KQ3 ; . F[D 1�5 ;SGJObBUG 1 B A ?bK ; 3 ] 143 B � _'?�K ; 3 ] 143 B 5 >Z; ? 8; 3 A > 3 O 5 >ZICDhO�B 5 � . � G � 365 � 365 8 K DJ;4;4>CB P > 1454?b5 ;=�O ? AN- > 1 DJF ObDaB�> 5 � � � G � 365 � F[D 1 8 1 D - K > A 55 D KQP >ZB ?b543 Ob](;4<�> A ?�K ; 3 ] 143 B 5 ;SGWO�BUG 1 B'G K ]hD 1@3 ;=< A DJO ;4> 5 ; 5 >Z; 5 @ � R �

R e

A >Z;=<bDaB F[D K6K D�� >ZB�;4<�> > � 8 >CI ;=>ZB � � � � � ; 3 A >EF[D 1 ICDJO P > 1 ]h>CO�IZ> � 5 >C>H 3 ] ?�1 > O � = O � � HUD 1;=< 365N1 > G 5 DhO � B 3 B*O�DJ; 14? O&IZDhO � ? ]hGW;=> ] 1 GJB 3 >CO/;NDhO�;= K G 1 ]h> 5 ;^;4> 5 ; 5 > ; G 5 3 ; � D ?�K B;SG X >+G 8�8 1 D � 3 A GW;4> K . i �A@ A 36KQK63 DJO 5 >ZICDhO�B 5 D 1 @ g BUG . 5 ;=D T O 3Q5 <�� 3 ;=<�;=<�>dICD A 8 ? ;=> 1 �� G 5 ?b543 Ob] �

B O�>�B 1 G � - GJI X ;4D2;=<�> A ?�K ; 3Q5 ;=> 8 G K ]JD 143 ;=< A 365 ;4<UGW; G K G 1 ]h>VO ? AN- > 1 DWF O�DJO � > 1 D 5 G 1 >1 > ;SG 3 O�>CB D 1 GJIZI ? A ?bK GW;4>CB 3 O�;=<�> IZD/G 1@5 >COb>CB A G ; 143 ��G 5 ;4<�> ICDhG 145 >CO 3 O�]�B�>C> 8 >ZO 5 � L < 3Q5A > GJO 5 ;=<�> T OUG K 5 D K P >�GJObB 5 A DaDJ;4< 3 Ob] 5 ;4> 8 5 G 1 > 5@K D�� > 1 � � D�� > P > 1 >CGJIS< 5 ;4> 8 3 O*GJO3 ;4> 1 GW; 3 P > 5 D KQP > 1 3Q5 8 1 D 8 D 1 ; 3 DhOUG K ;4D';=<�>�ObDhO � > 1 D 5N3 O�;4<�> � A GW; 1@3 � � L <�>�O ? AN- > 1 DJFO�DhO � > 1 D 5�365 K63 O�> G 14K . 8 1 D 8 D 1 ; 3 DhOUG K ;=DE;=<�> 543�� >\DJF ;=<�> � A G ; 143 ��G 5 � > 5 I G K > ? 8� 5 D ;=1 > K G �bGW; 3 DhO 5 ;4> 8 5\5 ; 36KQK 1 >Z;=G 3 O � � � � 5 8 >C>ZB � K >COb> 1 G K6K . ;4<�> T OUG K 5 D KQP > 365 8 > 1 F[D 1 A >CB G ;;= ICD/G 145 > 5 ; K > P > K GJObB ;=<�> A ?�K ; 3 ] 1@3 B ICD/G 1@5 >ZO 52? O/; 3QK G+IZ> 1 ;=G 3 O 543 � > K63 A 3 ; 365 GWIS< 3 > P >CB �L <�> 1 >ZF[D 1 > ;4<�> T OUG K 5 D K P > 3Q5 ?�54? G K6K . 5 D KQP G - K > 3 O�IZDhO 5 ;SGJO/;�; 3 A > � � F GJO 3 ;=> 1 GW; 3QP > 5 D K P > 1365 ?�5 >ZB(F[D 1 ;=<�> T OUG K�5 D KQP > � 3 ;=< A D 5 ; DJF ;=<�>VObDhO � > 1 D 5 - > 3 O�] 1 > ;SG 3 O�>CB(G 5 ;=<�> G K ]hD 1@3 ;4< AICDhG 145 >CO 5 ;= T O�G KU5 D K P > - >ZICD A > 5 54K D�� > 1 G 5 ;= 8 1 D - K > A 5 I G K > 5 K G 1 ]h> 1 � HUD 1 ICDhO � ? ]/GW;4>

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TikhonovLimited Iterations

�� ; : � � L <�> 5 D KQP >N; 3 A > � . � G � 3Q5 � P > 145@?�5 ;=<�> O ? AN- > 1 DJF O�DaBb> 5 � � � G � 365 � 3 O ;=8 1 D - K > A ?�5@3 O�](;= IZDhO � ? ]hGW;=>2] 1 GJB 3 >CO/;�G K ]JD 143 ;=< A F[D 1 ;=> 5 ; 5 > ; 5 @ � R �

R i

] 1 GJB 3 >ZO/; ;=<�>�; 3 A > 3Q5 8 1 D 8 D 1 ; 3 DhOUG K ;=D�;=<�>&O ? A - > 1 DWF ObDhO � > 1 D 5 � 8 K6?b5 � ^- ? ; ;=ICDJO"; 143 - ? ; 3 DhO 5 DJF ObDhO � > 1 D 5 F[D 1 A ;4<�>'BbD A 3 OUGJO/;(;=> 1 A � A ?�K ; 3 8 KQ3 >CB -/. � � ;=<�> 543�� > DJF;= A GW; 1@3 � � � F ? ; � > 5 >Z> ;=<UG ; � 3 ;4< � G 5454? A >ZB*ICDhO 5 ;SGWO"; � � - > 3 O�]';4<�> 5@3 � > DJF ;=T OUG K ICD/G 1@5 >ZO�>CB A GW; 143 � 365 G 8�8 1 D � 3 A GW;=> K . IZDhO 5 ;SGJO/; G 5 K DhOb]^G 5 ;4<�> T OUG KU5 D KQP >�ICD/G 1@5 >ZO 5;=D�� 3 ;4< 3 O�G�] 3 P >ZO A G � 3 A ? A 543 � > � GJO�B�;4<�>'ObDhO � > 1 D 5 � 36KQK - > 8 1 D 8 D 1 ; 3 DhOUG K ;4D�;=3 O 3 ; 3 G K 8 1 D - K > A 543�� > - >CICG ?�5 >';=<�>'O ? A - > 1 DJF ICDhO�Ob>CIZ; 3 DhO 5 F[D 1 > GJIS< O�D9B�>�B�Da> 5 O�DW;IS<UGJOb]h> � 3 ;=<+;4<�> 8 1 D - K > A 5@3 � > � L <�> 1 >ZF[D 1 > ;4<�> 5 D K P > ; 3 A > � 36KQK 1 > A G 3 O KQ3 O�>CG 1 GJO�B � >ICDJO"; 3 O ? >2;=DdG P D 3 B�GJO . 5 ;4> 8 ;4<UGW; � D ?�K B 8 1 > P >CO/; � � � � ICDhO P > 1 ]h>ZO�IC> �

� 3 ;4<(;4<�> K G 1 ]h> 5 I G K > BUGW;SG 5 >Z; � ;=> 5 ; 5 >Z; T � � > - >C] 3 OE;=D 5 >Z>�;4<UGW; ;4<�> ; 3 A > 3Q5 O�DJ; ;=DhO K . IZD 5 ; � 3 ;=<E;=<�>�O�DJO � > 1 D GJICI ? A ?�K GW; 3 DhO h- ? ; ;=<UG ; A > A D 1 . 5 8 GJIZ> - >CIZD A > 5 GJO 365@54? > �� O H 3 ] ?�1 > O � = P � >(ICGJO 5 >C>(] 1 D�� ;=< DJF ;=<�>EO�DJO � > 1 D 5 > P >CO ;=<�D ? ]h< ;=<�>EObDaB�> 5\1 >CB ? IC> �L <�> ] 1 G 8 < 365 - G 5 >ZB(DhOdG ;=D K > 1 GWO�IC> K > P > K DJF g � i F[D 1 ;4<�> 5 ;=GJO�BUG 1 B(: _ K G K ]JD 143 ;=< A ?�5 >CB� 3 ;4<+;=<�> A ?�K ; 365 ;=> 8 G 8�8 1 D/GJIS< � L < 3Q5 ;=D K > 1 GJO�IC> K > P > K � G 5 O�>ZIC> 545 G 1 . ;=D 5 ;SG . � 3 ;=< 3 O+;=

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x 50 nonzerosnodes

�� ; : � � L +O ? A - > 1 DWF O�D9B�> 5 GWO�B�;4<�> O ? A - > 1 DJF O�DhO � > 1 D 5 � . � G � 365 � P > 145@?�5;= Bb> 8 ;4< � � � G � 365 � B ?�143 O�]E;=<�>\ICDhG 145 >CO 3 O�] 5 ;=> 8 5 F[D 1 ;=> 5 ; 5 > ; T �

R @A > A D 1 . K63 A 3 ; 5 � e K 3 ]/G -/. ;=> 5 � �L <�> A ?�K ; 3 8 K63 I GW; 3 DhO�DJF � � � 3 ;=< � - >ZF[D 1 > GJB�B 3 O�]�;4<�> L 3 X <�DJO�D P 1 >Z] ?�K G 143�� GW; 3 DhO

� F 1 D A >ZY ? GW; 3 DhO i � = e � 365 GJO�DW;=<�> 1 ; 3 A > � ICDhO 5@? A 3 O�] 5 ;=> 8 � 3 ;4< A^. 3 Ad8 K > A >ZO/;SGW; 3 DhO;=<�GW; A ?�5 ; - > 8 > 1 F[D 1 A >ZB�GW;\;=<�>(ICDhG 145 > 5 ; K > P > K - > F[D 1 > ;4<�>(ICDhO � ? ]/GW;=>(] 1 GJB 3 >CO/; 5 D K P > �L < 3Q5 5 ;4> 8 3 O P D K P > 5 G A GW; 143 � � A G ; 143 � A ?bK ; 3 8 K63 I GW; 3 DhO � L <�>+; 3 A > 1 >CY ?�361 >CB&F[D 1 5@? IS<,GA ?�K ; 3 8 K63 I GW; 3 DhO 3Q5 8 1 D 8 D 1 ; 3 DhO�G K ;=DN;4<�> O ? AN- > 1 DJF ObDhO � > 1 D 5 5 Y ? G 1 >CB�B 3 Pa3 B�>CB -/. � � ;=543�� >�DJF ;= A GW; 1@3 � � � � 3 ;=< G 5 8 G 1@5 > B 3 GJ]hDJOUG K DhO K .�A G ; 143 �&;=< 365 � D ?�K B - 1 > G X B�D��O;=D � � � � GJO�B � 3 ;4<�G�F ?bK6K . B�>ZO 5 > A GW; 1@3 ��;=< 3Q5 - >ZICD A > 5 � � � � � - >CICG ?�5 >(;4<�>(O�DhO � > 1 D 5>CY ? G K65 � � � ` 3 O�IC>\;=<�>Ô ? A - > 1 DJF O�DhO � > 1 D 5 ICGJO�O�DW; - >^] 1 > G ;=> 1 ;=<�GJO�;4<�> 5 Y ? G 1 >^DJFR;=543�� > A GW; 1@3 � � �

�365 ;4<�>\O ? A - > 1 DJFXO�DhO � > 1 D 5 GJObB � 3Q5 ;4<�> 543�� >2DJF ;=<�> A GW; 1@3 � � �

�� O � = �

àD � >ÎCGJO � 1@3 ;4> ��

��

� � �� O � e �

L <�> 1 >ZF[D 1 > 3 O�;=<�>ZD 1 . ;4<�> A GW; 1@3 � � A GW; 143 � A ?�K ; 3 8 K . � 3QK6K G K � G . 5 - >�FHG 5 ;4> 1 ;4<UGJO ;=ICDJO � ? ]/GW;4>�] 1 GJB 3 >CO/; 8 1 D9IC> 545 5 D�;= � � � �^;=> 1 A 1 > A G 3 O 5 B�D A 3 O�GJO/; � � D�� > P > 1 B ? >;=D 3 Ob> � I 3 >CO�I 3 > 5f3 O AN. 3 Ad8 K > A >ZO";=GW; 3 DhO � B 3 BO�DJ; 8 > 1 F[D 1 A ;=< 365f5 ;4> 8 � 3 ;=< K G 1 ]h> 1A GW; 1@3 IC> 5 GJObB 3 O 5 ;4> GJB ?�5 >CB�;=<�> FHG 5 ;=> 1 GWO�B A D 1 > > � I 3 >CO/; K . 3 A 8 K > A >CO/;=>ZB ICDhO � ? ]/GW;4>

] 1 GJB 3 >ZO/;�O�D 1 A G K >ZY ? GW; 3 DhO 5 D K P93 O�](G K ]hD 1@3 ;=< A �L <�> ICD Ad8 G 1@365 DhO ;=> 5 ; - > ; � >Z>CO A ?�K ; 3 ] 1@3 B GWO�B�ICDhO � ? ]/GW;=> ] 1 GJB 3 >CO/; 5 D K6? ; 3 DhO 5 DhO

;=> 5 ; 5 >Z; = B�> 8 3 I ;=>CB�<bD��I K D 5 > K . A ?�K ; 3 ] 1@3 BEICDJO P > 1 ]h>CB�;=D^;=<�> >��bGJIZ;VICDhO � ? ]/GW;=>�] 1 GJB 3 >ZO/;

L 3 X <�DJO�D Pf5 D KQ? ; 3 DhO � � 3 ;4< DJO�>^Bb>C> 8 ICD/G 145 >ZO 3 Ob] UA ?�K ; 3 ] 143 B ICDhO P > 1 ]h>ZB';=D 5 D K6? ; 3 DhO e �B 3 � > 1 >CO/; ;=<UGJO ;=<�>ÎCDhO � ? ]/GW;4>N] 1 GJB 3 >ZO/; 5 D K6? ; 3 DhO � � D�� > P > 1 ?�5@3 O�] A ?�K ; 3 ] 1@3 B � 3 ;=<�; � DB�>Z> 8 ICDhG 145 >CO 3 O�] 5 <bD�� >CB(IZDhO P > 1 ]h>CObIC>V;=D G 5 D K6? ; 3 DhONG 8�8 1 D�� 3 A GW;4> K . = O � B 3 � > 1 >CO/;XF 1 D A;= > �bGJIZ; L 3 X <�DJO�D Pf5 D KQ? ; 3 DhO �L <�>�> 1@1 D 1^3 O�;=<�> 8 1 D - K > A 5N1 D 5 > 5@K63 ]h</; K . � 3 ;=<�;=<�> 3 O�I 1 > G 5 > 3 O�O ? A - > 1 DJF�ObDaB�> 5

� 5 >C> H 3 ] ?�1 > O � = R � � � D�� > P > 1 ;=< 3Q5 5 A G K6K G - > 141 G ; 3 DJO 365 A D 5 ; KQ3 X > K . 1 > K GW;4>CB ;=D�;=] 1 > GW;4> 1 3QK6K � ICDhObB 3 ; 3 DhO 3 O�]fG 5@5 D9I 3 G ;=>CB � 3 ;=<�;4<�> K G 1 ]h> 1 8 1 D - K > A 5 GJO�B�B�D9> 5 ObDJ;(G 8�8 > G 1;=D 3 O�B 3 ICGW;=>(G�IZDhO P > 1 ]h>CObIC> 1 GW;=> ;4<UGW; 365 O�D9B�> 543�� >(B�> 8 >ZO�B�>CO/; D 1 GW; K > G 5 ; O�DJ;2;=Df;=B�>Z] 1 >Z>\;4D B 3QP > 1 ]h> 5@3 ]hO 3 T I GWO"; K . F 1 D A � � � � ICDJO P > 1 ]h>CO�IZ> �

RVO

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1 cycle error

�� ; :�\ � L <�> >�� >CIZ; DJF 8 1 D - K > A 543 � >+DhO�GJICI ?�1 GJI . � L +> 1@1 D 1^3 O�;4<�> 5 D K6? ; 3 DJO� . � G � 365 � 3Q5 8 K DW;4;=>ZB P > 1@54?�5 ;=<�>\O ? A - > 1 DJFXO�D9B�> 5 � � � G � 365 � F[D 1 ;=> 5 ; 5 >Z; 5 @ � R

: KQ5 D ;=<�> ;=> 5 ;RDJF P G 143 >CB A > G 54?�1 > A >CO/;RO�D 365 > 5 <bD�� >CB ;4<�> 5 D K6? ; 3 DJO^> 141 D 1 DJF A ?�K ; 3 ] 1@3 B3 ObI 1 >CG 5 >ZB KQ3 O�>CG 14K . 3 O 1 > K G ; 3 DJO ;=D�;=<�> GJB�B 3 ; 3 DhO2DJF�ObD 365 > ;4D�;4<�> 54?�1 FHGJIC> 3 O 3 ; 3 G K IZDhO�B 3 ; 3 DJO 5 �� O GWB�B 3 ; 3 DhO A ?bK ; 3 ] 143 B&B�> A DhO 5 ; 1 GW;=>ZB G ] 1 >CGW;=> 1 GJIZI ?�1 GJI . ;4<UGJO�IZDhO � ? ]hGW;=>f] 1 GJB 3 >ZO/;

��<�>ZO;4<�> GJB�B 3 ; 3 P > O�D 365 > K > P > K65 � > 1 > 3 O�I 1 > G 5 >CB � � 3 ;4< eJg � � _ ` > 141 D 1 GJB�B�>ZB�;4D

;=^;=D 145 D 3 O 3 ; 3 G K ICDhObB 3 ; 3 DhO 5 A ?�K ; 3 ] 1@3 BfICDhO P > 1 ]J>CB ;=D e P � > 1@1 D 1 GWF ;=> 1 T�P > I . I K > 5 GWO�BICDJO � ? ]/GW;4>\] 1 GJB 3 >CO/;�IZDhO P > 1 ]h>CB ;=D ihi � > 141 D 1 �

� � � � � ��

H ?�K6K . 3 A 8 K > A >CO/; 3 O�] A ?�K ; 3 ] 1@3 B�;=D�>�� >CI ; 3QP > K . 5 D KQP > ;4<�> 3 O P > 145 > - 3 D9> K >ZIZ; 143 I T > K B8 1 D - K > A 3Q5 G K G 1 ]J> GJO�B 3 O P D K P >CB 8 1 D � >ZIZ;2;=<�GW; � 36KQK A D 5 ; KQ3 X > K . 1 >ZY ?�361 >N;=<�> A D 5 ;\GJB �P GJO�IZ>CB A ?�K ; 3 ] 143 B(;4>CIS<�O 3 Y ? > 5 U8 G 1 G K6K > K63�� >ZB 3 A 8 K > A >CO/;=GW; 3 DhO GJO�B+GJB P GJO�IZ>CB�<UG 1 B � G 1 > �L < 3Q5�1 > 5 > G 1 IS< 365 ;4<�> TU145 ; 5 ;=> 8 ;4D GWIS< 3 > Pa3 O�]E;=< 3Q5 ]hD/G K �

HUD 1 ICDJO P > 1 ]h>CO�IZ> 3 ; 365 O�>ZIC> 545 G 1 . ;=D 3 A 8 K > A >CO/; G 1 D - ?b5 ; GJICI ?�1 GW;4> 5 A DaDJ;4<�> 1;=<�GW;EI GWO 1 >CB ? IC>�< 3 ]h< � F 1 >CY ? >ZO�I . > 1@1 D 1 DhO�GJO 3QK6K � ICDhObB 3 ; 3 DhO�>ZB 8 1 D - K > A � L <�> K GJI X DJF

R P54? IS<�G 5 A D9DJ;=<�> 1+3 O ;4< 365 5 ; ? B .� 1 > 5@?�K ;4>CB 3 O ;4<�> A ?�K ; 3 ] 143 B�B 3QP > 1 ] 3 O�]�G F ;=> 1 5 > P > 1 G K3 ;4> 1 GW; 3 DhO 5 F[D 1 ;4<�> K G 1 ]J> 1 ;=> 5 ; 5 >Z; 5 � e GJObB T � � � < 3QK > ;=<�> A ?�K ; 3 ] 1@3 B 54? ICIC> 545 F ?�K6K . 1 >CB ? IZ>CBK D�� F 1 >CY ? >ZO�I . > 1@1 D 1 3 O�;= - >Z] 3 ObO 3 O�]�I . I K > 5 � 3 ;= 1 . K63 ;4; K >(< 3 ]h< � F 1 >ZY ? >CO�I . > 141 D 11 >ZB ? I ; 3 DJO 5 ;=G - 36KQ3 ; . � G 5 B 3 � I ?�K ; ;=D 5@?�5 ;=G 3 O � ` A G K6K > 1 ;4> 5 ; 5 >Z; 5 <UGJB 1 > G 5 DhOUG - K > 54? ICIC> 545� 3 ;4< ;=<�> K G ?�5@5 � à> 3 B�> KX5 A DaDJ;4< 3 Ob] � 5 >C> H 3 ] ?�1 > 5 O �QP � O � = e F[D 1 G F ?�K6KX5 >CY ? >ZO�IC>dDJF ;=8 DJ;=>ZO"; 3 G K P G K6? > 5V3 O ;=> 5 ; 5 > ; = 8 1 Dh] 1 > 545@3 O�] ;4< 1 D ? ]h<fG A ?�K ; 3 ] 143 BdI . I K > � b- ? ; F[D 1 K G 1 ]h> 1 A D 1 > 3QK6K � ICDhObB 3 ; 3 DhO�>ZB 8 1 D - K > A 5 3 A 8 1 D P >ZB 5 A D9DJ;= 145 G 1 >\O�>CIZ> 5@5 G 1 . �

� O D 1 B�> 1 ;=D GJIS< 3 > P > ; 14? > 5 ICG K G - 36KQ3 ; .� GJO 3 Ad8 1 D P >CB A >Z;4<�D9BNDJFUB 1 D 8�8 3 O�]�ICDhObO�>CI ; 3 DJO 5B ?�1@3 O�]�] 143 B�IZD/G 145 >CO 3 O�] A ?�5 ; - >'G 8�8 KQ3 >CB � � 3 ;=<,;=<�> A G ; 143 ��B�>ZO 543 ; .�- >CIZD A 3 O�]�GJO3 Ad8 D 1 ;=GJO/; 3Q5454? > � 3 ;=< K G 1 ]h> 1 BUGW;SG 5 >Z; 5 3 ; � D ?bK B - > - >ZO�> T I 3 G K ;=D - >�G - K > ;4D 3 O/;=> K6KQ3 �]h>ZO"; K . > K63 A 3 O�GW;=> 5 A G K6K > 1 F[>�� > 1 3 Ad8 D 1 ;=GJO/;�>CO/; 1@3 > 5 GJO�B'GJB � ?�5 ; ;4<�> 1 > A G 3 O 3 O�]E>CO/; 143 > 5

;=D A G 3 O/;SG 3 O�GJIZI ?�1 GJI . � : 5 A >ZO"; 3 DhOb>CB> G 1@K63 > 1 � 3 ;=<�;=<�> 5 ;=GJO�BUG 1 B$G K ]hD 1@3 ;4< A� ;=< 3 ]h<�> 1 ;=D K > 1 GWO�IC> K > P > K65 F[D 1 I GW;4>C]hD 1@3 �Z3 O�] IZDhO�O�>ZIZ; 3 DhO 5E3 O/;=D � > G X IZDhO�O�>ZIZ; 3 DhO 5 ICG ?�5 > 5;=fGJICI ?�1 GJI . DJF�; 1 GJO 5 F[> 1 D 8 > 1 GW;4D 1 ;=D 5@? � > 1 ] 1 > GW; K . � L D G 8�8 K . ;4< 365 G 8�8 1 D/GJIS< � 3 ;4<K G 1 ]h>\BUGW;=G 5 > ; 5 � 3 ;4< 1 > G 5 DhOUG - K > A > A D 1 . ICDhO 5 ; 1 G 3 O/; 5 F ?b1 ;= 1 1 > 5 > G 1 IS< 365 O�>C>ZB�>CB'F[D 1G A >Z;=<bDaB&DJF�B�>ZI 3 B 3 O�] ��< 3 IS<�ICDhObO�>CI ; 3 DJO 5 � 36KQK <UG P >f;4<�> K > G 5 ;E>�� >CI ; DJO*;=<�> 5 . 5 ;=> A��<�>ZO�B 1 D 8b8 >ZB GJObB+<�D��GJB � GJIZ>CO/; IZDhO�O�>ZIZ; 3 DhO 5 I GJO - > G K ;=> 1 >ZB ;=DÎCD Ad8 >ZO 5 G ;=> F[D 1 ;=

B 1 D 8�8 >CB ICDhO�Ob>CIZ; 3 DhO 5 �_'?�K ; 3 ] 143 B � 5 A G 3 O GWB P GJO/;SGJ]h> 365\3 ; 525 ICG K G - 36KQ3 ; . GJO�B ;=<�> 1 > F[D 1 > 3Q5 A D 5 ;Ôb>C>CBb>CB 3 O

8 1 D - K > A 5 � 3 ;4< G K G 1 ]h>NO ? A - > 1 DWF ObDaB�> 5 � � O D 1 B�> 1 F[D 1 A ?�K ; 3 ] 1@3 Bf;=D+; 1@?�K . - >(G+< 3 ]J<8 > 1 F[D 1 A GJO�IC>�G K ]hD 1@3 ;4< A� 3 ; A ?�5 ; - > 8 1 DJ] 1 G AdA >CB ;=D 1@? O(DhO A ?�K ; 3 8 K > 8 1 DaIZ> 5@5 D 1@5 � HUD 1 �; ? OUGW;=> K . G K6K G 5 8 >ZIZ; 5 DJF A ?�K ; 3 ] 1@3 B � D 1YX(3 O G K D9I G K A GJO�O�> 1 GJO�B ;4<�> 1 >ZF[D 1 > 3 ; 3 O�<�> 1 >ZO"; K .� D 1YX"5 > � I 3 >ZO/; K . 3 O�G 8 G 1 G KQK > K 5 ; 1@? IZ; ?�1 > � L <�> ] 143 B�ICGJO - > - 1 D X >CO ? 8 3 O/;=D - K D9I X"5F[D 1 > P > 1 . 5 ;4> 8 DJF A ?�K ; 3 ] 1@3 B 3 O�I KQ? B 3 Ob]&ICD/G 1@5 >ZO 3 O�] 3 O/;4> 1 8 D K GW; 3 DhO 1 > 5 ; 1@3 I ; 3 DJO GWO�B5 A D9DJ;=< 3 O�] � L <�> DJO�> > �aIC> 8 ; 3 DJO 365 ;= IZD/G 145 > 5 ; K > P > K 5 D KQP > � L < 3Q5 Bb> 8 >CO�B 5 DhO ��<UG ;A >Z;=<bDaBdDhO�> ?�5 > 5 ;4D 8 > 1 F[D 1 A ;=< 3Q5 5 D K P > � � F . D ? ?�5 > G 5 > 1@3 G KU5 D KQP > 1 � 3 ;=< G 8 G 1 G KQK > K63 � >CB3 Ad8 K > A >CO/;SGW; 3 DhO ?�5@3 O�] A GJO . K > P > K65 DJF ICD/G 1@5 >ZO 3 O�]\;=D^GJIS< 3 > P > G P > 1 . IZD/G 1@5 >�B�>C> 8 K > P > K� D ?�K B K > GJB ;4D�G*Y ?�3 I X > 1 ICDhG 145 > K > P > K 5 D KQP > ��B FÎZD ?�1@5 > �8 1 Dh] 1 G A A 3 O�]�G�ICD A 8 K >��G K ]hD 143 ;=< A 3 O 8 G 1 G K6K > K 365 A D 1 > B 3�� I ?bK ; GJO�B Bb> G KQ3 O�] � 3 ;4< - D ? O�BUG 143 > 5 - >Z; � >C>ZO - K D9I X"5GJB�B 5 ;4DE;=<�> 8 1 Dh] 1 G A A 3 O�]NB 3�� I ?bK ; . �

RVRL <�> 1 >'G 1 >fG O ? A - > 1 DJF D 8 ; 3 A 3 � G ; 3 DJO 5 ;4<UGW;(ICGJO - > ? ; 36KQ3 � >ZB*;=D >ZO�<UGJO�IZ> 8 > 1 F[D 1 �

A GJO�IC> � � > 5 >CG 1 IS< 5 <�D ?�K B - > 8 > 1 F[D 1 A >ZB�DhO�D 8 ; 3 A 3 �Z3 O�] ;=<�> 8 G 1 G A >Z;4> 145 F[D 1 A ?�K ; 3 ] 143 B �L <�> 1 > G 1 >EB 3 � > 1 >ZO";\;4D K > 1 GJO�IZ> K > P > KQ5 � 5 ; 1 DhOb] P > 1@54?�5 � >CG X ICDhObO�>CI ; 3 DJO 5 GJO�B 5 ; 3 � O�> 5@5A GW; 1@3 ��>ZO"; 1 . �+;4<UGW;�I GJO - >�GJB � ?�5 ;=>ZB � ;=<�> 1 >Z] ?�K G 143 � GW; 3 DhO 8 G 1 G A > ;=> 145 I GJO�G K65 D - >GJB � ?b5 ;=>ZB � : K65 D B 3 � > 1 >ZO/;+O ? A - > 1@5 DJF 5 > A 3 IZD/G 145 >CO�>ZB 54? - K > P > KQ5 F[D 1 > GWIS< A ?�K ; 365 ;=> 8K > P > K ICD ?�K B - >�;=> 5 ;=>ZB � � O�GJB�B 3 ; 3 DhO ;=<�> 1 >2G 1 > B 3 � > 1 >ZO/;VICDhG 145 > ] 1@3 B 5 > K >CIZ; 3 DhO 5 5 IS A > 5;=<�GW;�ICD ?�K B - > 1 > 5 > G 1 IS<�>ZB � F[D 1 ;4<�>\I 1 >CGW; 3 DhO DJFX;4<�> ICD/G 1@5 > ] 143 Bf]hD/G K F[D 1 ;4<�> A ?�K ; 365 ;=> 8G 8�8 1 D/GJIS< � � : O�DW;=<�> 1 3 Ad8 D 1 ;SGJO/; ICDhO/; 1@3 - ? ; 3 DJO � D ?bK B - > ;4D(B�>Z;4> 1 A 3 Ob>\GJO G 8�8 1 D 8 143 GW;=>5 ;4D 8�8 3 O�](I 1@3 ;=> 143 GNF[D 1 ;=<�> A ?bK ; 3 ] 143 B+I . I K > 5 �

� � � ) �� _ . 1 > 5 > G 1 IS< 3 O"; 1 D9B ? IZ> 5 GJO(G 8�8 1 DhGJIS<E;=D 3 Ad8 K > A >CO/; 3 O�] G K ]h> - 1 G 3 I A ?�K ; 3 ] 1@3 B\F[D 1 ;=

3 O P > 145 > - 3 D9> K >CI ; 143 I T > K B 8 1 D - K > A � L < 3Q5 3 O P D KQP > 5 G 5 8 >ZI 3 T I F[D 1 A ?�K G ; 3 DJO DJF ;4<�> 5@?�1 FHGJIZ>;=D 5@?�1 FHGWIC> >CY ? G ; 3 DJO � 3 ;=< 1 >C] ?�K G 1@3 � GW; 3 DhO GJObB�G*ICD 1@1 > 5 8 DJO�B 3 Ob]�G K ]h> - 1 G 3 I A ?�K ; 3 ] 1@3 B3 Ad8 K > A >CO/;SGW; 3 DhO B�> 543 ]hO�>CB�;=D � D 1YX � 3 ;4<�;4< 365 8 1 D - K > A ?b543 Ob] 5 > 8 G 1 GW;=> 5 ; 3 � O�> 545 GWO�B]h>ZD A > ; 1 .fA GW; 143 IC> 5 � L < 365 � D 1YXf5 <�D�� 5 <bD��;4< 365 G 8�8 1 D/GJIS<'I GJO - >NG 8�8 KQ3 >CBf;=D 5 A G K6K > 18 1 D - K > A 5 GJObB GJIS< 3 > P > 8 1 D A 3Q543 O�] 1 > 54?�K ; 5 � _ . 3 O 3 ; 3 G K � D 1YX DJO^;=< 365 3 Ad8 K > A >ZO/;SGW; 3 DhO2<UG 5- >C>CO 8 ? - K63Q5 <�>ZB 3 OEG � D 3 O/; � D 1YX � 3 ;=< c < 14365 � Dh<�O 5 DhO _ G 1 I ?�5 _ DJ< 1 M K6143 IS< ��? B�> GWO�B: K >��a> . `bG A 5 DhO�D P F[D 1 ;=<�>�� 3 O eJgJg = � P O � �

� O GJB�B 3 ; 3 DhO;4D�B�> ;SG 3QK63 O�]�GWO$G K ]h> - 1 G 3 I A ?�K ; 3 ] 143 B 3 Ad8 K > A >ZO";=GW; 3 DhO G A ?�K ; 365 ;=> 8G 8�8 1 D/GJIS< <UG 5 G KQ5 D - >C>ZO�B�> 5 I 143 - >CB ;=D(<UGJObB K > ;4<�>\ICD/G 1@5 >\] 1@3 B�ICD 141 >ZIZ; 3 DhO 3 O�GJICI ?�1 GJI 3 > 5

3 O/; 1 D9B ? IZ; 3 DhO � 3 ;=<�;4<�> 36KQK � IZDhO�B 3 ; 3 DhO�>CB A GW; 1@3 IC> 5 � � < 36K >�;=&IS<�D 3 IZ>&DJF G ; 1 GWO 5 F[> 1D 8 > 1 GW;=D 1 3Q5 G\; 1 GJB�>ZD � - >Z; � >C>CO+GJICI ?�1 GJI . GJO�B ICD Ad8 ? ;=GW; 3 DhOUG K > � I 3 >CO�I .� ;4<�> A ?�K ; 365 ;=> 8G 8�8 1 D/GJIS< � <UG P > B�> 5 I 1@3 - >CB 5 <�D�� 5 G 543 ]hO 3QT I GJO/; 3 Ad8 1 D P > A >CO/; 3 O�GJICI ?�1 GWI .�X- ? ;NGW;^GK G 1 ]h> 8 > 1 F[D 1 A GWO�IC> ICD 5 ; � � 3 ;=< 5 >CO 543 ; 3QP > 36KQK � IZDhO�B 3 ; 3 DhO�>CB 8 1 D - K > A 5 KQ3 X > ;4<�> 3 O P > 145 >- 3 Da> K >CI ; 1@3 I T > K B 8 1 D - K > A� ;4< 365 ; 1 GJB�>ZD ��O�>Z>CB 5 ;=D 5 ; 1 > 545 GWICI ?b1 GJI .(A D 1 >V;=<UGWO 3 O(; .98 3 I G KG 8�8 K63 ICGW; 3 DhO 5 DJF A ?�K ; 3 ] 143 B � _ D 5 ; G 8�8 KQ3 I G ; 3 DJO 5 DJF A ?bK ; 3 ] 143 B�BbD�O�DJ; 1 >CY ?�361 > ;=< 3Q5 K > P > KDJF GWICI ?b1 GJI . GWO�B�;4<�> A ?bK ; 3Q5 ;4> 8 G K ]JD 143 ;=< A � 36K6K DJO K . 5@K D��$;= 8 1 DaIZ> 5@5 B�D��O - ? ;�;=< 3Q5G K ]hD 143 ;=< A >�� >ZIZ; 3 P > K . Bb> G KQ5 � 3 ;=<&;4<�> 5 >ZO 543 ; 3QP93 ; . DJF�;= 3 O P > 1@5 > - 3 Da> K >CI ; 1@3 I 8 1 D - K > AGJO�B A G X > 5�3 ; 8 D 545@3 - K > ;=D 5 D K P > ?�543 O�] A ?�K ; 3 ] 143 B �

R T_'?�K ; 3 ] 143 B 8 1 D P > 5N?�5 > F ?�K 3 O�G K G 1 ]h> O ? AN- > 1 DJF 5 I 3 >CO/; 3 T I IZD Ad8 ? ; 3 O�]�G 1 >ZOUG 5 54? IS<

;= 1 A D9B . OUG A 3 I 5 � ?b3 B B . OUG A 3 I 5 GJObB 1 GJB 3 GW; 3 DhO 5@3 A ?bK GW; 3 DhO � � O ;4<�> - 3 Da>ZO�] 3 Ob>C> 1@3 O�]G 1 >COUG ;=<�> ; 1 > GW; A >ZO/; DJFUG O ? A - > 1 DJF A G � D 1 A >CB 3 I G K/3Q5454? > 5 � D ?�K B - >CO�> T ;R] 1 > G ; K . F 1 D A3 OaF[D 1 A GW; 3 P > B 3 GW]hO�D 5@365 G 54543Q5 ;=GJO�IC>EF 1 D A GWICI ?b1 GW;4> 3 O/;=> 1 OUG K BUGW;=G ;=< 1 D ? ]h< O�DJO � 3 O P G 5@3QP >> K >CI ; 1 D9I G 1 B 3 Dh] 1 G 8 < . GWO�B�> K >CIZ; 1 D9>CO�IZ> 8 <�G K Dh] 1 G 8 < . ;=> 5 ; 5 � � 3 ;=< A ?�K ; 3 ] 1@3 B 54? IZIC> 545 F ?bK6K .G 8�8 K63 >ZB 3 O�;=< 3Q5+T > K B ;= 3 O�I 1 > G 5 > 3 O 5 8 >Z>CB�GWO�B�GWICI ?b1 GJI . ICD ?�K B - >�G 5@3 ]hO 3 T I GWO";ICDJO"; 143 - ? ; 3 DhO ;=D�;4<�>E; 1 >CGW; A >CO/;\DJF G�O ? A - > 1 DJF A >ZB 3 ICG K 8 1 D - K > A 5 � � D 8 >ZF ?�KQK .� ;4<�> 5 >T O�B 3 O�] 5 � 36K6K G KQK D�� 1 > 5 >CG 1 IS 145 ;4D � 365 > K . IS<�D9D 5 > ; 1 GWO 5 F[> 1 D 8 > 1 G ;=D 1@5 5 D ;4<UGW; A ?�K ; 3 ] 1@3 BA G . - > ?�5 >CB ;=D(> � I 3 >CO/; K . 5 D KQP >2;4<�> 3 O P > 145 > - 3 Da> K >CI ; 1@3 I T > K B 8 1 D - K > A �

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� = e � ��!��%��V@@�G *Y+[ �'��iP #�>>]� *@��%��(0 � c�-�@�� : K ]h> - 1 G 3 I A ?bK ; 3 ] 143 B � G A ]��F[D 1 G ? ;=D A GW; 3 I A ?�K ; 3 ] 143 B 5 D KQ? ; 3 DhO 5 � 3 ;=<(G 8�8 K63 I GW; 3 DhO 5 ;4D2]h>CD9B�>Z; 3 IVIZD Ad8 ? ;SG ; 3 DJO 5 =�� T e � � O 5 ; 3 ; ? ;=> F[D 1 c D Ad8 ? ;SG ; 3 DJOUG K `9; ? B 3 > 5 N B F = T O e HUD 1 ; c D K6KQ3 O 5 c D K D 1 GJB�D �

� = i � ��!��%��V@�� +� �'��P #�>@]� ��C ��%��0 � c�-�� : K ]h> - 1 G 3 I A ?�K ; 3 ] 1@3 B� : _ K ��F[D 1 5 8 G 145 > A GW; 143 �'>ZY ? GW; 3 DhO 5 � � O�� \ � ��eX � � H �� W � � �J P GJO 5 J B � c G A - 143 B�]h>\M�O 3QP > 145@3 ; . N 1 > 545 c G A - 1@3 B�]h> =�� T @ �

� = @�� !P cEcE�D�� *;F�-O%��$-O%&�R� *;��%�� +[ �';��P #�)]� H � � � � � � b � � � � � e ObB�>ZB � ` � : _ N < 3QK GJBb> K 8 < 3 G beJghgJg �

� = O � ��E�D �� . �� %�� +��! #,.-/��j02 _'?�K ; 3 8 K . ICDhO 5 ; 1 G 3 O�>ZB3 O P > 1@5 > > K >ZIZ; 1 DaICG 1 B 3 D K Dh] . � c D AN- 3 O 3 O�] ;=> A 8 D 1 G K A ?�K ; 3 8 K > 5 8 GW; 3 G K GJO�B 3 ;=> 1 GW; 3QP >1 >C] ?�K G 143�� GW; 3 DhO � � O 3 � � � � � � �� 54 � � � X <&<Y<(<�� ? �� \ � � �� \ 7�L � � H � � � �OX � � � � � �� A � �B4 � � � � � � � =�� @ � � J�J.J c D A 8 ? ;=> 1`aD9I 3 >Z; . U8�8 � = i R � = i T �

� = P � ��E�D�� M��#�� +��! #,.-/��M02 �M��%��j+��!�MV!��#�� O P > 145 > > K >CI �; 1 D9I G 1 B 3 Dh] 1 G 8 < .�-/. 543 A ?�K ;=GJO�>ZD ?�5 3 A 8 D 543 ; 3 DhO�DJF A ?�K ; 3 8 K >dICDhO 5 ; 1 G 3 O/; 5 � X <&<Y G 1 ; � P >CI ;=D 1 GWO�B K > GWB 5 � N G 1 ; � � ? � :� � � � � �8:�� =�� @VP � = OVR � P = �� = T � � � ��c�-O�Y F� �i��%�� % +�PQND��%&i�� > G 1 ; � P >ZIZ;=D 1 GJO�B K >CGJB 5 � N G 1 ; � � � ? � :� � � � � �8: n � =�� @ R � = O @ � P g �� =�� c�-O�Y FG � ��%��8��% +�PQND��%&j�� >CG 1 ; � P >ZIZ;4D 1 GJO�B K > GJB 5 � N G 1 ; � � � �K >CD A >Z; 143 I G K 1 > 8 1 > 5 >CO/;SG ; 3 DJO � ? � : � � � � �� : 7Kq � =�� @ T � ehe � �aihi �� eJg � � � �!%�-h�Dh�� U��%�-h�gO02 *��[��ND��./�G �h��%�� 0 � �� A GW] 3 O�] B 365 8 > 1@543 DhODJF A^. D9I G 1 B 3 G K�1 > 8 D K G 1@3 � G ; 3 DJO 3 � IZD Ad8 G 143Q5 DhO�DJF � A � �B: 7Kq � =V= � `9> 8eJghg = �

= e � � � = O g O �� e = � � � �!%�-h�D �� *�� #��!��P �U * ��%�� 0 � �� : O�DhO 3 O P G 543 P > 3 A GJ] 3 O�]A DaB�G K63 ; . F[D 1 I G 1 B 3 GJI G 1@1 < . ;=< A 3 G 5 � A � �B: 7Kq 6 � eWghghg � e = O e �be = O T �

� ehe � � � �!%��D �� #��!��P ;�U ��+��! /,-h��.i02 �i��%�� 0 � ��>�� DhO 3 O P G 5@3QP >> K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < 3 I 3 A GJ] 3 Ob]2DJF > K >CI ; 1 D 8 < . 543 D K Dh] 3 I G KQK . G - O�D 1 A G K�54? - 5 ; 1 GW;4> 5V3 O3 ObFHG 1 I ;=>ZB G 1 ; 5�� : A DaB�> K 5 ; ? B . � A � �B: 7KqK7 � eWghghg � O ihi�� O @ g �

� eJi � ' � _O_O-O%&@�� c G K I ?�K G ; 3 Ob] ;=<�> 365 DaIS< 1 DhO�> 5 DWF P >ZO/; 143 I ?�K G 1 B�> 8 D K G 143�� GW; 3 DhO � � X H ��8: � ��*: � � �� p: A � � �#:�� = � T @ � = g O � = eJg �

� e @�� ' � _O_O-O%&C�� C��%��8��% WU��BV�-O��g�� _ D9B�> K 5 ; ? B 3 > 5 � 3 ;=<&;4<�> 3 O P > 145 > K .ICG K I ?�K GW;4>CB 365 DaIS< 1 DhO�> 5 DWF P >CO/; 1@3 I ?bK G 1 B�> 8 D K G 143�� GW; 3 DhO � X <Y<Y< b � � � � ? � � � �D:D<��K:� 7 � = � T @ � P O e�� P O � �

T =

� e O � � -/�i�� P �� , �iW��-O%& �� * 0)�! #�� P �� * ��%��aF��!��WG L D��VG 1 BG ? O 3QP > 145 G K < � 8 GJBUG 8 ; 3QP > T O 3 ;4> > K > A >CO/; 5 ; 1 G ;=>C] .� N G 1 ; = � c DJO 5 ; 1 G 3 O�>CB G 8�8 1 D � �3 A GW; 3 DhO GJO�B�BUGW;SG 5 ; 14? IZ; ?b1 > � A � � � � �� H �� <�� =�� T � � R � �

� e P � � � � c�ND�� '� ') *&��%��e� � c�N��D>+a &�U _ ]hO�> ; - 3 - K63 Dh] 1 G 8 < . � L >ZIS< � 1 > 8 � � G K >(M O 3 P > 14543 ; .� W > 8 G 1 ; A >CO/;\DJF c D Ad8 ? ;=> 1 `aI 3 >CO�IZ> � >�� G P >ZO c L � M `9: � =�� = � = � � � �

� e R � � �!P � #��NDNh�� %��[0 � �$�&@]E J�J K > K >CI ; 1 DaB�> 5 >CO 543 ; 3QP93 ; . � GJO G 8b8 K63 I GW; 3 DhOdDJF1 >CI 3 8 1 D9I 3 ; . � X <&<Y K G��G ; 3 DJO A > ;=<�D9B$F[D 1 5 D KQP93 Ob] > K6KQ3 8 ; 3 I�B 3 � > 1 >CO�IZ>>ZY ? GW; 3 DhO 5 �� :��\ �� =: � ��m: *: � ��m:Ek � B: 7 � = � P = � � eJe�� e R � : K65 D 3 O M � ` � ` � � �c D Ad8 ? ; � _ GW;4< � GJO�B _ GW;4< � N < . 5 � = � =�� P e � b8�8 � = g � e�� = g � P �� e � � � �!��%��K��%�-��) )') *��U��$�B��%�P c��&U�� *�� -O�!�!P g,� * �.�! � #��!��P )� �g��%��RUP c��%��V�V#P ') �: ICI ?�1 GJI . > P G K6? G ; 3 DJO 3 O�B 3Q1 >CI ;�GJObB 3 O P > 145 > > K >CIZ; 1 D9I G 1 B 3 D K �Dh] . � � O 3 � � � � � � � �Z< � � � � � � � � � � � � � �� K\ � =�� R � � N � _ GJIZFHG 1@K GJOb> J B � N 3 ; A GWO_ >ZB 3 ICG K b8�8 �<T i � T R �

� ihg � � �!��%��K��%�-��) �') *�� -O�!�!P �, ��! � #��!��P ��U ��%�� RUP c��%��V�V�P �'� L <�>B 3Q1 >ZIZ; GJO�B 3 O P > 1@5 > 8 1 D - K > A 5 3 O > K >CI ; 1 D9I G 1 B 3 D K Dh] . � � ? A > 1@3 ICG K G 5 8 >ZIZ; 5 DWF 5 D A >1 >C] ?�K G 143�� GW; 3 DhO A > ;=<�D9B 5 GJO�B G 8b8 K63 I GW; 3 DhO 5 ;=D�BUGW;=G ICD KQK >CI ;=>ZB 3 O 365 D K GW;4>CB2B�DJ]� G 1 ;> � 8 > 1@3 A >CO/; 5 � l ��B: H � � �=:!9 �� jAY:=9�:�� : 3 ��B:�9 � =�� R � � eheJe �

� i = � � �!��%��K��%�-��g '� �� -O�!�!P ,� * �� #��!��P 2�U *e��%�� RUP c��%��V�V�P '� H 3 O 3 ;4>2> K > A >CO/;�G 8�8 1 D � 3 A G ; 3 DJO�DJF 1 >C] ?�K G 143�� >ZB 5 D K6? ; 3 DJO�DJF ;4<�> 3 O P > 145 > 8 DW;=>CO/; 3 G K8 1 D - K > A DJFb> K >ZIZ; 1 D9I G 1 B 3 Dh] 1 G 8 < . GJObB G 8�8 K63 ICGW; 3 DhO ;=D�>�� 8 > 1@3 A >CO/;SG K BUG ;SG � A � � � � � �6K6 � = � T O � ��= �

� i/e � � �!��%��K��%�-��g '� � ��! � /��!��P �U *>��%��aRUP c��%��V�V�P i') d: O�G 8b8 1 D/GWIS< ;4D3 O P > 1@5 > I G K I ?�K GW; 3 DhO,DJF > 8 3 I G 1 B 3 G K 8 DJ;=>ZO"; 3 G KQ5 F 1 D A - D9B . 5@?�1 FHGWIC> A G 8 5 � H � � :A � � � � �=: 687 � = � R T � O g � O @ �

� ihi � �U� �PQV@/,� *h�C��PQNDND-OV@!]� �/+��%�c�PQ%&h�� *�� -h� /�MV!��!-�O�� *h��%��Z�U��!%�-O��O, : A ?�K ; 361 > 5 D K6? ; 3 DhO^F 1 G A >�� D 1YX ;4D A >C] M >C>Z] 5 D ?�1 IZ> 3 A GJ] 3 O�] � X <&<Y A G ; 3 ICG K � 8 < . 543 ICG K A D9B�> K DWF ;=]h>ZO�> 5@365 DJF ;=<�>\> K >CI ; 1 D9I G 1 B 3 Dh] 1 G A � ? � � �K\ � : �8:� � =�� P @ � e TVO �aihg = �

� i O � �U-h��#c�-��) H � � �� 3QK > . � >�� D 1 X =�� = �� i P � �UP ��c�P U') ;��-O� � o02 ��!P ��-O� � o02 *)';��_`�&g+I *)';��!��PQ%��N��D02 � ]/��-O%��B�&S+a �T��%��@��c �-�!�) c D A 8 G 1 GW; 3QP >,GJIZI ?�1 GJI . DJF ;=<�> P >CI �;4D 1 ICG 1 B 3 Dh] 1 G A GJO�B > K >CIZ; 1 D9I G 1 B 3 DJ] 1 G A 3 O ;=<�> K D9I G K63 � GW; 3 DhO$DJF ;=<�>�GJICIZ> 5@5 D 1 .8 G ;=< �VG . 3 O 8 G ; 3 >ZO/; � 3 ;4< � D K � � N G 1YX"3 O 5 DhO � � < 3 ;4> 5 . O�B 1 D A > � > G K63 B�GW; 3 DhO DJF�GO�>�� P >CI ;=D 1 I G 1 B 3 DJ] 1 G 8 < 3 I G K ]JD 143 ;=< A -". 3 O/; 1 G 8 Da> 1 GW; 3QP >�> 8 3 ICG 1 B 3 G K A G 8�8 3 O�]NGWO�B> K >CI ; 1 D 8 < . 543 D K Dh] 3 I G K 5 ; ? B 3 > 5 �.H � : � � � � ��8: 7K7Kn � =�� g � O � e�� O � T �

T e

� i R � � ��N8c��ND��"�.�G _ G KQ36K6K > ?�1 ; 143 B 3 A >CO 543 DJO�O�> K G ? ;=D A GW; 3 Y ? > 8 D ?b1 B�> 5 ]h>ZD A > ; 1@3 > 5IZD A 8 K >��a> 5 � L >ZIS< � 1 > 8 � � G 8�8 D 1 ;�B�> � >ZIS<�> 1 IS<�>NO�D � = ghg @ � � � � : =�� T � �� i T � � ��N � "�.�� *EF�-O�MV��&@+a ��%�� "h�&.�� K >COb> 1 G K63 � >CBfI 1 D 545 � P G KQ3 BUGW; 3 DhOfG 5G A > ;=<�D9B&F[D 1 IS<�D9D 543 O�]�G ]hDaD9B 143 B�]h> 8 G 1 G A >Z;4> 1 � b � � �� 687 � =�� R � � e = O �beheJi �

� i � � � ��N � "�� *U��%�� ,>�!��%&�'� oR� � �� A � � � � �� DJ<�O 5 � D 8 X93 O 5 F G K ; 3 A D 1 > =�� T � �� @ g � �U�!-O-O%& ,� *^, �� 02 *^F�� D ') * � PQNDNDPQ�� D�02 � F � %�V@I]� * ��%�� c�-h�$�D +a J � >CI ; 5 DJF^GJ]h> 5 > � GJO�B - D9B . <UG - 3 ; ?�5 DhO � � `�GWO�B�` L � L8 DJ;=>ZO/; 3 G K A G 8 5 DJF = = ghg O�D 1 A G K 54? - � >CIZ; 5 � A � �B: � 7 � =�� TVO � e @V@ �be O i �

� @ = � �U�!-O-O%��$PQV#-� � �@F � P �B��i_�� E��%�� 8��%IWU��BV�-O��g@�G � >�� Y ? GJO/; 3 ;SG �; 3QP >dGJObB�Y ? G KQ3 ;=GW; 3 P >EG 8b8 1 D/GWIS<�> 5 ;=D�;= 3 O P > 1@5 > 8 1 D - K > A DJF > K >ZIZ; 1 D9I G 1 B 3 D K Dh] . �;4<�> 3Q1 ;=CD 1 >Z; 3 I G K 1 > K GW; 3 DhO 5 < 3 8 GJO�B'>�� 8 > 143 A >ZO";=G K ICDhO 5@365 ;=>CObI . � � � � �� 3 �K\ � �� 7 �� i � = � � g � �i P � �ai R � �

� @ e � � � ND�!�� %�P E02 *�0o��"/-O��c�-��C *��%��[+��PQN�N�� &�� L <�>2F[D 1 � G 1 B 8 1 D - K > ADJF\> K >ZIZ; 1 DaICG 1 B 3 Dh] 1 G 8 < . � � O A � � � � � � � � � � � < � � � � � � � � � � � � � � \ N � _ GWIZFHG 1@K GJO�>GJObB L � > � � G � 143 > J B 5 � N > 1 ]/G A DhO5N 1 > 545 B �9F[D 1 B J Ob] K GJObB =�� T � h8�8 � =�� R �aeJi P �� @ i � � � ND�!�� %�P 02 *0 ��"h-O��c�-� �C ��%�� ]#� 8��!�. �) L <�> 3 O P > 145 > 8 1 D - K > A DJF> K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < . � � O A � � � � � � � � � � � < � � � � � � � � � � � � � � \ N � _ GJI FHG 14K GJO�> GWO�BL � > � � G � 1@3 > �J B 5 � N > 1 ]/G A DhO9N 1 > 5@5 B �9F[D 1 B �J Ob] K GJObB =�� T � b8�8 � eWi R �be T T �

� @V@�� ND�!�� %�P 02 � ]#� 8��!�. �g *)��%�� 0o��"/-O��c�-� �C L <�> 3 O P > 145 > 8 1 D - K > A3 O�> K >ZIZ; 1 DaICG 1 B 3 Dh] 1 G 8 < . � `aD KQ? ; 3 DhO 523 O ;=> 1 A 5 DJF >ZY ?b3QP G K >ZO/; 5 D ?�1 IC> 5 � A � �p: � � � :? � � � �D:!< ��K: 7�L � =�� TVT � = R = �be = @ �

� @ O � F��! #��" � �$ #�& � _�?�K ; 3 � ] 143 B A >Z;=<bDaB 5 GWO�B(G 8�8 KQ3 ICGW; 3 DhO 5 � L >CIS< � 1 > 8 � ` 8 1@3 O�]J> 1 F > 14KQ3 O = � T O �� @ P � F��! #��" � �$ #�& � � ;=> 1 GW; 3 P > 5 D K6? ; 3 DhO�DJF K G 1 ]h> 5 8 G 145 > 5 . 5 ;=> A 5 � L >CIS< � 1 > 8 � ` 8 143 Ob]h> 1 � >�� D 1YX =�� @ �� @ R � F��! #��" � �B�& � J 3 O 3 ;=> 1 GW; 3 P > 5 P > 1 FHGJ< 1 >CO �C?�1 5 IS<�O�> K6K >ZOdG ? �UD 5@? O�]\> KQK63 8 ; 3 I G 5 <�> 11 GJO�B � > 1 ; 8 1 D - K > A > � L >ZIS< � 1 > 8 � M�O 3QP > 145@3 ;=GW; 0 D K O =�� R P �

� @ T � F��!��!�Y�� ` ?�1�K > 5 8 1 D - K > A > 5 G ? �fB�> 1@3QP >C> 5 8 G 1@3 > KQ3 > 5 >Z; K > ?�1 543 ]hO 3 T I GW; 3 DhO8 < . 543 Y ? > � ? �� =:�� : �54 3 � � � � � � � � =�� ghe � @ � � O e �� @ � � F��N�c��!-O%.2f) �2�C� � ��-O%��& �) �j' ND��!��-�� GF�PQV�-� �� * ,.PQ-/c�-/��P �D�') *]/�� -hNh �g * ��%�� + � �$��NDPQ%�� G � O/; 1 GJIC> 1 > - 1 G K 8 DJ;=>ZO/; 3 G K65 ;4D 1 G 1 > ;=G 1 �]h> ;�GJObB B 365 ; 1 GJIZ;4D 1 G ? B 3 ;4D 1 . GWO�B P9365@? G K�5 ; 3 A ?�KQ3 � � � ` ? 8 > 1@3 D 1 ;=> A 8 D 1 G K�K D - > �< � � � � � � � � � � � �� K\�� O9 � � � � �K\ � � � � � \ n � � =�� O � =��= �beJeJg �� O g � F��%��-�g+a c DhO � ? ]/GW;=>f] 1 GJB 3 >CO/;E; .98 > A > ;=<�D9B 5 F[D 1(36KQK 8 D 5 >ZB 8 1 D - K > A 5 � � O3 � �� 9 � � � � �� DJO�] A GJO =�� O �

T i

� O = � F��%��$-O%&��) : OUG K . 54365 DWF B 3Q5 I 1 >Z;4> 3QK6K � 8 D 5 >ZB 8 1 D - K > A 5 -/.EA > GJO 5 DWF ;4<�> � � I ?�1 P > �� X H � � � � � � � � @ � =�� e � O P = � O T g �

� O e � F � P �B��_�� *��%�� 8��% WU��BV�-O�#��g>�G L EB�> 8 D K G 143 � GW; 3 DhO 5 >CY ? >ZO�IC>dDJF;4<�> < ? A GJO�<�> G 1 ; 54?�1 FHGJIC>dICD Ad8 ? ;4>CB�F 1 D A A > G 54?�1 >CB - D9B . 54?�1 FHGJIC> 8 DJ;=>ZO"; 3 G KQ5 �X <&<YCB P > 145@?�5�5 ;=GJO�BUG 1 Bf]h>CD A > �; 1 . 3 O ;4<�> 3 O P > 1@5 > 8 1 D - K > A DJF > K >CIZ; 1 D9I G 1 B 3 DJ] 1 G 8 < . � X <Y<YCB IZDhO 5 ; 1 G 3 O/; 5 3 O�;4<�> 3 O P > 1@5 > 8 1 D - K > A DJF > K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < . � � O 3 � � � � � �� 54 � � � X <Y<Y< <�� ? � � � � \ � � �� \ 7 � � � H � � � �X � � � � � �� @A � �B4 � � � � � � � = � � O � � J�J.J N 1 > 545 8�8 � eJg R �beJg T �

� OVO � �� C��D � G� P �B��PQ%&S�G �U L >��9; - DaD X A ?bK ; 3 ] 143 B�> � I 3 >CO�I . F[D 1 ;=3 O�ICD Ad8 1 > 545@3 - K >�O�G P93 > 1 � 5 ;4D X > 5 >CY ? GW; 3 DhO 5�� 3 ]h< 1 > . O�D K B 5 O ? A - > 1 �VG X > 5 GWO�B- D ? O�B�G 1 . K G . > 1@5 � � O A � �� A � �B4 � � � � � � � � �� eJghg = � �

� O P � �� >R ��%aND-O%�VE ]� R� _'?�K ; 3 ] 143 B �VG P >ZF[D 1 A 1 > K G �bGW; 3 DhO F[D 1 GJO 365 DW; 1 D 8 3 I 8 G 1 ; 3 G KB 3 � > 1 >ZO"; 3 G K >ZY ? GW; 3 DhO 5 � � O A � �� SA � �B4 � � � � � � � � �� eJghg = � �

� OVR � ��PQ%&�� b � � k � � � < � � � � � � � � � � � � � < � � � � � � �� Dh<�O � 3QK > . GWO�B`aDJO 5 =�� i �� O T � �O��%��$��%& ') b � � � � � � � � � � � � X � � � � ��3 � �� < � � � � � � � � � � � � � �� K\��b � � � � � � �� YA � � � � �� ;< � � � � � � � � � � � � � �� N < W ;=<�> 543Q5 M�O 3QP > 1@543 ; .DJF M�;=GJ< `bG K ; � G X > c 3 ; .� M�;=GJ< = � T � �� O � � �O��%��$��%&e'� c D A 8 ? ;SGW; 3 DhO�G K GJO�B O ? A > 1@3 I G K A >Z;4<�D9B 5 F[D 1 - 3 Da> K >CI ; 1@3 I T > K B8 1 D - K > A 5 � A � � �� ? � � � � �� h< �� 6 �� = � =�� R � = � T = �� P g � �O��%��$��%&S'� : BUG 8 ; 3QP > T O 3 ;=>*> K > A >CO/;�GJObB K DaICG K 1 >C] ?�K G 1@3 � GW; 3 DhO A >Z;4<�DaB 5F[D 1 ;4<�> 3 O P > 145 > J cLK 8 1 D - K > A � � O X � � � � �� 3 � �� < � � � � � � � � � � � � � � \ N � � Dh<�O 5 ;=DhO J B � : B P GJO�IC> 5 3 O c D Ad8 ? ;=GW; 3 DhOUG K F 3 D A >ZB 3 I 3 O�> �� L N 1 > 545 beWghghg �� P = � �O��%��$��%&�'� ��%�� +��! #,-h��102 � O P > 1@5 > 5 D K6? ; 3 DhO 5 F[D 1 > K >CIZ; 143 I�GWO�B8 DJ;=>ZO/; 3 G KVT > K B 3 A GJ] 3 O�] � � O 3 �K\ � � � � � �� YX �� O\�� T< � � � \

� � � � � � � � � � � � � � � �� F G 1 - D ?�1 GJObB _ � c G 1@P9KQ3 O �J B 5 � P D K � = TVT R �` N � J =�� i �8�8 � = iJg � = i � �� P e � �O��%��$��%&E'� ��%�� +��! /,-h��.!02 � DJO ? O 3 F[D 1 A 5 8 GW; 3 G K A > 5 < GJBUG 8 ;SGW; 3 DhO ?�5 �3 O�]2G 8 D 5 ;=> 1@3 D 1@3 > 141 D 1 > 5 ; 3 A G ;=> 5�� G 8�8 KQ3 I G ; 3 DJO 5 ;4D F[D 1 �VG 1 B(GJO�B 3 O P > 145 > 8 1 D - K > A 5 �

H �� 9 �� o7 � � =�� @ � bi =V= �aihe P �� P i � �O��%��$��%&�'� � ��%�� +��! #,-h��Z02 � D9I G K 1 >C] ?�K G 143�� GW; 3 DhO GJObB GJBUG 8 ; 3QP >A >Z;4<�DaB 5 F[D 1 ;4<�> 3 O P > 145 > � G 8 K GWIC> 8 1 D - K > A � � O ? � � � � �� l 4 � 3 �K\ � �� W � K < 3Q5 ;SG �J B � > 3 >�� >C] � > > 14K GJ] F 1 G ? O 5 IS< � > 3 ] =�� P �8�8 � ehe @ �beWi @ �

T @� P @�� O��%��$��%& '� ��%�� +��! #ND-h��.i02 ': B�G 8 ; 3 P > K D9I G K 1 >C] ?�K G 143�� GW; 3 DhO A >Z;4<�DaB 5F[D 1 ;=<�> 3 O P > 145 > J cLK 8 1 D - K > A � 3 � � � � � � � � ? � � �K\ � �� ? � � � � � � � � \ L n� =�� T � @ g O � @ eJi �

� P O � �O��%��$��%&�'� �h+��YO+a *M0 � -O��-� � */]/�� $��%��.h�G �M��%�� _��dj _'?�K �; 36K > P > K A >Z;4<�DaB 5 F[D 1 3 O P > 145 > - 3 D9> K > K >CIZ; 143 I T > K B 8 1 D - K > A 5 � � O � � �� >CI ; ?�1 > `a> 143 > 5�3 O c D Ad8 ? ;=> 1 `9I 3 >ZO�IC> � ` 8 143 O�]h> 1 � > > 14K GJ] eJgJg = �8 � � 3 O 8 1 > 545 � �

� PVP � �O��%��$��%&J') *&��%�� ;��NDND��!��G J K >CI ; 143 I G K GJI ; 3QP GW; 3 DhO DJFR;4<�> <�>CG 1 ; � c D A �8 ? ;SGW; 3 DhOUG K95 ; ? B 3 > 5 DJFb;4<�> F[D 1 � G 1 BNGJO�B 3 O P > 1@5 > 8 1 D - K > A 5 3 ON> K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < . �� O A � � � � � � H � � � � � � � � � � � �� X ? � � qKnKq 0 � F 3QK6K63 O�] 5@K > . � � F �� GWO�BJ � W ?�1 Dh<UGJO�> 5 J B 5 � F G K B � 3 O[N 1 > 5@5 M O 3 P > 14543 ; . DJF K >ZD 1 ] 3 G :V;4<�>CO 5 K >ZD 1 ] 3 G =�� e �8�8 � O T i � P e T �

� P R � de-OV�V#N�-O�Y 02 : O�G K . 543Q5 GWO�B�IZD A 8 G 143Q5 DhODJF 1 > K G��G ; 3 DJO 5 IS<�> A > 5 3 O 1 D - ?�5 ;A ?bK ; 3 ] 143 B GJObB 8 1 >ZICDhO�B 3 ; 3 DhO�>ZB ICDhO � ? ]/GW;=> ] 1 GJB 3 >CO/; A >Z;4<�DaB 5 � � O �� F > 1@K63 O = � T e � � � � GJI X - ?�5 IS< GJO�B�M � L 1 DW;4;=>ZO - > 1 ] .J B 5 � P D K � � P gDJFYl � � � � � 9 � � � � �� ` 8 1@3 O�]h> 1 � > > 14K GJ] b8b8 � O g/e�� O i @ �

� PVT � deP /��PQ%�c�-O�Y�� d: K ]J> - 1 G 3 I A ?�K ; 3 ] 1@3 B�F[D 1 B 365 I 1 >Z;=>(> K6K63 8 ; 3 I 5 >CICDJO�B�D 1 B�> 1 8 1 D - �K > A 5 � L >CIS< � 1 > 8 � _ K � >Z; � D P > A - > 1 = � � R �� P � � deP �oi'� N:�; � D � K > P > K 8 1 >CIZDhO�B 3 ; 3 DJO�> 1 F[D 1 GJO GJO 365 DW; 1 D 8 3 I A 3 �a>CB T O 3 ;=>N> K > A >ZO/;8 1 D - K > A � � O A � �� 1A � �B4 � � � � � � � �� eWghg = � �� R g � de% � _O_� �) �.��%�� ]/V�-OPQ%�"h-O��c> ]E k �� 54 � � �!� � � � � �� c � cN 1 > 545 F D9I G � GW;=DJO =�� i �� R = � d � %�� G *!��%�� +�PQV��!�&�]� �dj :�O�>��G K ]hD 1@3 ;4< A F[D 1 3 A GW]h> >CB�]J> > �a; 1 GJI ; 3 DhO?�5@3 O�] G 5 ;SGW; 365 ; 3 ICG K I K G 5@543QT > 1 G 8�8 1 D/GJIS< � X <Y<Y< b � � � � : � � 3 �� H � � � \ � � � �� X � � � � � � � � � �gn @ � =�� T R � O P � � OVRVR �� R e � +�� #,-h��.#02 3 � � � � � � � � � b � � � � � �� /A � � � � � � \ H �� \ � � � � � � � �

�54 A � � � � ��X � � � � � � �)A � � �� N < W ;=<�> 54365 W G K <�D ?�5@3 >M�O 3QP > 145@3 ; . � G K63 FHG � � � ` � c GJO�GJBUG =�� g �� R i � +�� #,-h��.)02 *)�� W�%&)FG *)de�!P �g�FG *), �� )02 ��%�� dU��

�!%��!-OP #�&��C : OUG K . 5@365 DJF N L c : � 3 O�B ? IC>ZB 365 IS A 3 G ?�543 O�] - DJ;=<'GJO'> K >ZIZ; 1 DaICG 1 �B 3 Dh] 1 G 8 < 3 I 3 O P > 1@5 > 5 D K6? ; 3 DhO�GJO�B�;=<�> � G P > K >Z; ; 1 GWO 5 F[D 1 A � �8:�< � � � � � � � � � � � �=: 6 ��` ? 8�8 K � =�� @ � � g � � P �

� R @�� +�� #,-h��.!02 *��O��%��$��%&E'� ��%�� f ��B��ND-O�Y��) c DJO 5 ; 14? I ; 3 DJO DJF G^< ? A GJO;4D 145 D A D9B�> K F 1 D A A GW]hO�>Z; 3 I 1 > 5 DhO�GJO�IC> 3 A GW]h> 5 F[D 1 8 1 D - K > A 5 3 O'IZD Ad8 ? ;SG ; 3 DJOUG K> K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < . � L >CIS< � � > 8 � M M c ` � � @ � g = R M O 3QP > 145@3 ; . DJFVM�;=GJ< W > 8 G 1 ; �A >CO/;�DJF c D A 8 ? ;=> 1 `9I 3 >ZO�IC> =�� @ �

� RVO � +�� #,-h��.@02 *Y�O��%��$��%&>'� � �U��!��%�-O�YY+a �@��%�� FU�� #-O�>&�U � DaICG K �3�� GW; 3 DhO�DJF 365 IS<�> A 3 G B ?�143 O�](ICD 1 DhOUG 1 . GJO�] 3 D 8 K G 5 ; . ?�543 O�] - D9B . 54?�1 FHGJIC> 8 DW;=>CO/; 3 G K

T OA G 8�8 3 O�] GJO�B�GJO�> K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < 3 I 3 O P > 145 > 5 D KQ? ; 3 DhO � � O X <&<Y< A � � � � � � � �1A � � � � � � � \ � =�� e � � J�J�J N 1 > 545 8�8 � e O = �be O @ �

� R P � +�� #,-h��.�02 *��O��%��$��%&&'� ��%��+��MV��-h�$��%&�+a > 3654? G K63�� GW; 3 DhOE;=D9D KQ5 F[D 1IZD A 8 ? ;SGW; 3 DhO�G K > K >ZIZ; 1 D9I G 1 B 3 Dh] 1 G 8 < . � � O � � � � � �� ? � � � � �� YA � � � � � �� F > K6KQ3 O�]J<UG A � G 5 < � =�� e � N 1 DaIZ>C>CB 3 O�] 5 DJF ;= ` N � J�� = T g T /8�8 �V@ ihi � @V@V@ �

� RVR � +��8V�PQ% F��%��-�Cdj �C��%�� -O� ';��!P �BV�PQ��% F��%��B-O%&C,� � >Z] ?�K G 143�� GW; 3 DhOA >Z;4<�DaB 5 F[D 1XK G 1 ]h> � 5 I G K > 8 1 D - K > A 5 � � � � � \ � � � �� X �� \ � =�� i � �

� R T � +[ �';��!ND-�� 02 �G]/��-O%�V��%&e+a �2W�� e��%�%�-ONDNhe�U * �#� � � 2]E � dePQ��PQ%�P ��02 � �U-h�BV!��Y �) * ��%�� O��ND-h� �� : ? B 3 ;=D 1 . N ihghg G - O�D 1 A G KQ3 ; 3 > 5 GJObB K >ZF ;8 D 5 ;4> 1@3 D 1 5@? 8 > 143 D 1 ;4> Ad8 D 1 G K ] . 1@?�5 P D K6? A > 1 >ZB ? I ; 3 DJO 3 O 5 IS< 3 � D 8 < 1 >ZO 3 G �gH � � �8:� � �/: 3 � \ � � �� \ � � � =�� i � = R O � = T @ �

� R � � +�-h�$�BPQ%�c�-O� � 0)��_O_/�� V@�� C��%�� 0 � �� >Z] ?�K G 143�� GW; 3 DhO�DJF�;=<�> 3 O P > 145 >8 1 D - K > A 3 O&> K >CIZ; 1 D9I G 1 B 3 DJ] 1 G 8 < . � : A D9B�> K 5 ; ? B . � � �� 8: ? � � ��*: � n � =�� T T � R � � =V= T �

� T g � +[��Y�+a �J��%�� 0�� -� � _'?�K ; 36K > P > K L >CIS<�O 3 Y ? > 5 F[D 1 ;=<�> `aD KQ? ; 3 DhO DJFV;=� O P > 145 >�N 1 D - K > A DJF J K >CIZ; 1 D9I G 1 B 3 DJ] 1 G 8 < . �

� T = � +[��%�V8�!c � -�� Y]#��PQV��&�f) �@' ��i-h�#��%&�� *�0)� � V�� ) ��deND��$�B-h%&�� ND-h��PQ%�c�V!��%&@'� ��%��FU�� #-O�>�� 5 D 3 O";4>C] 1 G K GWOUG K . 5@365 DWF - D9B . 54?�1 �FHGJIZ> A G 8 5�� ` ?�1 FHGJIZ>^B 365 ; 143 - ? ; 3 DhO GJO�B ;=> Ad8 D 1 G K P G 143 G - 36KQ3 ; . 3 O O�D 1 A G K 5@? - � >ZIZ; 5 �A � �B: L � � = � T = � =V= P R � =V= R e �� T e � +[��B��-O�Y@�� &��%�� ,-O�� @02 `aD ?�1 IZ> K DaICG K63�� GW; 3 DhO ?b543 Ob] 1 >CI ?b14543 P > K . G 8�8 KQ3 >ZBGJObB 8 1 D � >ZIZ;=>ZB � 1 G 8 � A ?�543 I � X <Y<& 3 O P > 145 > 5�3 OG K ]J> - 1 G 3 I A ?bK ; 3QK > P > K A > ;=<�D9B 5 �9 �� q i � = � � T � Ui � R � @ = R �� T @�� WG �;�� V�%�PQ�!c � PQ%�-�.� � �&��%��a�O��%��$��%& '� H D9I ?b543 Ob] 3 O P > 145@3 DhO'DJF > K >CI �; 1 D9>CO�IZ> 8 <UG K Dh] 1 G 8 < . GJO�B A GJ]hOb>Z;=D9>CObIC> 8 <UG K DJ] 1 G 8 < . B�GW;SG � � O � � �oX � � � � � �� \�� 9 � � � � � � � � k�� X �� eJghg = � �

� T O � W��-O%&J�� -h�� P ��>,� * 0)�! #�� P �� * ��%��aF��!��WG L D��VG 1 BG ? O 3 P > 1@5 G K < � 8 GJBUG 8 ; 3QP > T O 3 ;4>�> K > A >CO/; 5 ; 1 GW;4>C] . N G 1 ; e � : 8 D 5 ;=> 143 D 143 > 141 D 1> 5 ; 3 A G ; 3 DJO � A � � � � �� H �� Y<�� =�� T � � =V= i �

� TVP � WU��BV�-O%��!_� � � ��%�� 8��% WU��BV�-O��g�� `9D ?�1 IZ> 8 G 1 G A > ;=> 1 > 5 ; 3 A G �; 3 DhO 3 O 3 Ob<�D A Dh]h>COb>CD ?�5 P D KQ? A > ICDJO�B ? I ;=D 1@5 DJF G 1 - 3 ; 1 G 1 . 5 <UG 8 > � X <&<Y 8 DJ;4>CO/; 3 G K B 365 ; 1@3 - ? ; 3 DhO]h>ZO�> 1 GW;=>ZB -/. 5@?�1 FHGJIZ>�> K >ZIZ; 1 D9B�> 5�3 O 3 O�<�D A Dh]h>ZO�>CD ?b5*P D KQ? A > IZDhO�B ? IZ;=D 145 DJFG 1 - 3 ; 1 G 1 . 5 <UG 8 > � X <Y<Y< b � � � � ? � � � �D:!< ��K: � � � =�� = � @ g � � @ = R �

TVP� TVT � WU�BV�-O�YZFG �Z��%�� 0 � ��> � L <�> ?�5 > DJF�;4> Ad8 D 1 G Kd3 ObF[D 1 A GW; 3 DhO 3 O�;=1 >C] ?�K G 143�� GW; 3 DhO�DJF\;=<�> 3 O P > 1@5 > 8 1 D - K > A DWF^> K >ZIZ; 1 DaICG 1 B 3 Dh] 1 G 8 < . � X <&<YZ] ?�K G 143 � GW; 3 DhO A >Z;4<�DaB 5 F[D 1fK G 1 ]h> � 5 I G K > 8 1 D - K > A 5 �� : � �� 8:!X ��D: Ui � =�� i � e O i��ai = O �� g � � -O%�%�- �>!'� ��' N�-h��-O%�V!�D#�� U��!��%�-O�Y#+I *!]#V#-h�!%��DO, �/��%��SFU�� #-O�>�U L <�> 3 O P > 145 > 8 1 D - K > A DJF > K >CI ; 1 D9I G 1 B 3 Dh] 1 G 8 < . � : 8�8 KQ3 ICGW; 3 DhO ;=D K D9I G K63 � GW; 3 DhODJF � D K � � N G 1YX"3 O 5 DhO � � < 3 ;4> 8 1 > � > �bI 3 ;=GW; 3 DhO 543 ;4> 5 � � O 3 � � � � � � �� 54 � � � X <&<Y<<�� ? � � � � \ � � �� \ 7 � � � H � � � ��X � � � � � �� !A � � �4 � � � � � � � =�� O � � J�J�J N 1 > 5@5 8�8 � e = O �be = P �

� ��= � � N��%��B- �@02 � >CI 3 8 1 D9I 3 ; . G 8�8 K63 >ZB ;4D P D K6? A >\ICDJO�B ? I ;=D 1@5 GJO�B ;=<�> >CIZ] � X <&<Y)�� ? � � � � � � � �� 3 � � � � � � � � � _ I K 1 G � � � 3QK6KF D9D X c D A 8 GWO . � >�� D 1 X = � P � �� i � �;��V�V!�D>�� *�� -OPQ%��$V#-hPQ%&@�� W�� e��%�%�-ONDN/&�U *]/��-h%�V!��%&.+a �Y�O��%�� %&

') *��%��1+[ �';��!ND-��02 F 3 Da> K >ZIZ; 1@3 I A DaBb> K63 O�]\DJF ;4<�> N ihgJg 3 O 5 IS< 3�� D 8 < 1 >ZO 3 G �? � � � � �� 3 � \ � � �� \ � � � �=:�� =�� T � Ui � P �� @�� ;��V�V!�D�� * � P "/ND-��'� �j]/��-O%�V��%&2+a * � -OPQ%��$V#-hPQ%& �� P �$��-O�Y��$ *

,.- �-O%�V�P ��%& +a �� c�PQ%��Z, � ��%�� +� �';��!ND- �>Z02 � D9I G K63 � GW; 3 DhO DJFP9365@? G K ICD 1 ;=> � � 3 ;=< ICD 1 >C] 365 ;4> 1 >CB�F ? O�IZ; 3 DhOUG K A GJ]hOb>Z; 3 I 1 > 145 DJOUGJO�IZ> 3 A GJ] 3 O�] a- 3 D �> K >CI ; 1@3 I G K6K . A D9B�> K >CB�ICD 1 ; 3 ICG K P93654? G K > P D X >CB 8 DJ;=>ZO"; 3 G K GJO�B�; 1 GJO 5 I 1 GJO 3 G K A GJ] �O�> ; 3 I 5 ; 3 A ?�K GW; 3 DhO 3 O�B ? IZ>CB Pa3Q54? G K 5@? 8�8 1 > 5@543 DJO � A � � � � � � 9 � � � � �� =:�� =�� T � @ e �

� � O � 0)�! /�� P �� EW��-O%&�� *��%��1� -h�� P ��,� L D�� G 1 B+G ? O 3 P > 145 G K < � 8GJB�G 8 ; 3 P > T O 3 ;4> > K > A >CO/; 5 ; 1 GW;4>C] . N G 1 ; i � W > 543 ]hONDJF�< � 8 A > 5 <�> 5 � A � � � � � � � � � �� H �� /<�� =�� T � � = T = �

� � P � 0 ��"h-h�8V �C�!PQ��$��%&�� g � _'?�K ; 3Q1 > 5 D K6? ; 3 DJO'G 8b8 1 D � 3 A GW;=> 3 O P > 145 > 8 1 >ZICDhO �B 3 ; 3 DhO�> 1 � � X H � � � � � � � � � � �� A � � � � �� 6 � e � eWghg = � @ P i � @ R � �

� � R � 0 �� `-h%&�FG *��%��8��%^W��BV�-O��g��G c D A 8 ? ; 3 Ob] ;4<�> GJI ; 3 P G ; 3 DJO 5 >CY ? >ZO�IC>GW;�;= P >ZO/; 143 I ?�K G 1 G 1 ; 54?b1 FHGJIZ>�F 1 D A - D9B . 8 DW;=>CO/; 3 G KQ5 � � � �D:U? � �=:�<��K:A � � � �m: 6 � � =�� T R � Ue O g �be P g �

� � T � 0 � ��> � �E��%��(+�-h�$�BPQ%�c�-O� � 0)��_O_/�� V@��U L 3 O P > 1@5 > 5 D KQ? ; 3 DhO 3 O > K >CIZ; 1 D �ICG 1 B 3 Dh] 1 G 8 < . � `aD KQ? ; 3 DhO 5 3 O ;4> 1 A 5 DJF > 8 3 I G 1 B 3 G K 8 DJ;4>CO/; 3 G K65 � A � �p:�� :#? � � � �D:<��K: 7�L � = � TVT � e = O �ae PVT �

� � � � 0 � ��> � ��%��W��$V#-h�Y/F� L <�>�> K >ZIZ; 1 D9I G 1 B 3 Dh] 1 G 8 < 3 I 3 O P > 1@5 > 8 1 D - K > A � A � �p:� � � :�? � � � �D:�< ��K: 68q � =�� e � ehe � @ O �

T R� = ghg � 0 � ��>�� *J��%�� WU�BV�-O�Y F� L <�> > K >CI ; 1 DaICG 1 B 3 Dh] 1 G 8 < 3 I 3 O P > 145 > 5 D K6? ; 3 DhO � � O� � �� 3 � � 4 � � �� A � � � � �� ? � � � � �� L � N 36K X93 O�]J;4DhO � � F �

� � L <�D Ad8 5 DhO ` � � DaD L � c � NRG K A > 1 GWO�B L � F ? B 3 O�]J> 1 J B 5 � c � c N 1 > 545 = � � i IS< � P b8�8 � = i O � = OVO �

� = g = � ]# #�� -h�Y.]� V: 5 > A 3 ICD/G 1@5 >ZO 3 O�] A ?bK ; 3 ] 143 B A >Z;4<�DaB�F[D 1 > K6K63 8 ; 3 I 8 G 1 ; 3 G K B 3 � > 1 �>ZO"; 3 G K >CY ? GW; 3 DhO 5 � 3 ;=<f< 3 ]h< K . B 3Q5 IZDhO/; 3 O ? D ?�5 GJO�B GJO 3Q5 DJ; 1 D 8 3 I IZDa> � I 3 >ZO"; 5 � � � �� A � � � � �� 68q = � =�� eJe T �be @ e �

� = g/e � ]# #��-O�Y �� 2��%�� '��"/PQ%&�,� ?N 1 > 5 >CO/; 5 ;SGW;4>�DJFN;=<�>�> K >CIZ; 1 D9I G 1 B 3 DJ] 1 G 8 < 3 IF[D 1 �VG 1 B 8 1 D - K > A �YH � � :>A � � � � �=: 687 � =�� R T � �e�� R �

� = ghi � ]# #��PQ��V@�� *��O��%��$��%& ') *)f ��$��%&)�� %�� +��! #,-h��g02 $: 8b8 K63 I G �; 3 DhO 5 DJF G ? ;=D A GW; 3 I A > 5 < ]J>CO�> 1 GW; 3 DhO'GJO�B GJB�G 8 ; 3 P > A > ;=<�D9B 5 3 O'IZD Ad8 ? ;SG ; 3 DJOUG KA >CB 3 I 3 O�> � � O � � � � � �� H �� 4 � � 3 � � � � �� <�� F G - ?b5YX G � � H K GW<�> 1 ; .� � � � >ZO 5 <UG � � � � D 8 I 1 DJF ; � � B K63 ]h> 1 GJObB L � L > � B ? . G 1 <J B 5 � ` 8 1@3 O�]J> 1 � > > 1@K GJ] =�� O �8�8 � i P R �ai � g �

� = g @�� ]# #��PQ��V@;02 H � � � � � � �� N < W ;4<�> 5@365 `9;SGJOaF[D 1 B M O 3QP > 145@3 ; .� =�� T = �

� = g O � ]# #��PQ��V@)02 _'?�K ; 3 8 K >f> A 3 ;@;=> 1dK DaICGW; 3 DhO�GJO�B 543 ]JOUG K 8 G 1 G A >Z;=> 1 > 5 ; 3 A GW; 3 DhO �X <&<Y 1@5 > 8 1 D - K > A 5

DJF > K >ZIZ; 1 D9I G 1 B 3 Dh] 1 G 8 < . � _ D9B�> K63 Ob]�GJObB 1 >ZICD P > 1 . DJFE> 8 3 I G 1 B 3 G K 8 DW;=>CO/; 3 G KQ5�3 O< ? A GJO 5 � X <Y<&ZB�FHG 5 ; A ?bK ; 3Q5 ICG K >3 A GJ]J> 5 >C] A >CO/;SG ; 3 DJO � � O A � �� [A � �B4 � � � � � � � � �� =��

� = g T � ]/��-O%.�FG � ��%�� O��%��$��%&T') `a> A 3 � G ? ;=D A GW; 3 I 3 A GJ]h> 5 >C] A >ZO";=GW; 3 DhO � :- 3 A D9B�> K ;=< 1 > 5 <bD K B 3 O�] G 8�8 1 DhGJIS< � L >ZIS< � 1 > 8 � M M c ` � � @ � g = � W > 8 ; � DJF c D A 8 ? ;=> 1`aI 3 >ZO�IC> M�O 3QP � DWFRM�;SGJ< = � � @ �

� = g � � ]/��-O_h��!�.�+a �[� � -O�!PQ%��%�P � ��JND��-O� V �1�� , � � � P c>102 * ��%��-h��%�%& �) : BUG 8 ; 3QP > 5 D K6? ; 3 DhO 5 DJF ;=<�> J ?�K > 1 >CY ? GW; 3 DhO 5*?�543 O�] T O 3 ;4>Y ? GJBa; 1 >Z>NGWO�B�D9IZ; 1 >Z> ] 143 B 5 � A � � � � � � � � �� q � = � TVT � �i/e R �aihi P �

� =V= g � ]/��-O_h��!�..+a �@��%�� -O�!�!P .+a : O G 8�8 1 D/GJIS<�;=D+G ? ;=D A GW; 3 I T O 3 ;=> > K > A >ZO/;A > 5 <�]h>ZO�> 1 GW; 3 DhO � A � � �#: ��< ��K: � � =�� T e � Ue = �be T �

� =V=V= � ]#��%��.�+a ��F�ND� 8�! E�R� *��%�� ND-��02 X �� 3 � � � � � � �� H � � � \ � � � �� c <UG 8�A GJO�GJO�B � G KQK =�� i �� =V= e � ]/V ��V ��J+a � � �!PQ-O��-h�Y�� %�� !PQ-O��-O�Y�WG L < 1 >Z> � B 3 A >CO 5@3 DhO�G K A >CB 3 I G K

3 A GJ] 3 O�] � : K ]JD 143 ;=< A 5 GJO�B&ICD A 8 ? ;=> 1^5 . 5 ;4> A 5 �TH A � b � � � � :;A � � �#: � � � � \ � :6 � @ � = � ��= � @ e = � @ � � �

TVT� =V= i � ] � PQ�� VE �� ? A > 143 ICG K A > ;=<�D9B 5 F[D 1^5 D K P93 O�]';4<�> F[D 1 �VG 1 B 8 1 D - K > A 3 O*> K >CI �

; 1 D9I G 1 B 3 D K Dh] . � � O b � � b � � � � � � �� ? � � � �54g< � � � � � � � � � � � � � � \ c � � > K65 DhO*GWO�BW � K > 5 > K D�� 3 ; � �J B 5 � c K G 1 >CBbDhO*N 1 > 545 B �9F[D 1 B =�� R P b8�8 � e OVR �be � i �

� =V= @�� !��& �$ �o]#V��P �C� *��BPQND-� , �;��%�� @��_`��%�P �� ND�!� � ��G J K >CI �; 143 I 5 D ?�1 IC> K D9I G KQ3 � G ; 3 DJO�DJF ;=�G ? B 3 ;4D 1 . N ihghg GJ] 1 >C> 5 � 3 ;=< A GJ]JO�>Z; 3 I 5 D ?�1 IZ>K DaICG K63�� GW; 3 DhO � < � � � � � � � � � � � �� K\ � �� 9 � � � � �K\ � � � � � \ n�L � =�� O � O i T � O @ O �

� =V= O � �� V�-h"/-�CWG L <�> A ?�K ; 3 ] 1@3 B 8 1 >ZICDhObB 3 ; 3 DhO�>ZB�IZDhO � ? ]/G ;=> ] 1 GJB 3 >CO/; A > ;=<�D9B � � O� � � � A � �� A � �B4 � � � � � � � � �� G Ad8 ;4DhO > : =�� i � � �]W � _ > K65 DhO L � : � _ GJO/;=> ? � > K GJO�B ` � H � _ I c D 1 A 3 I X J B 5 � P D K � c Ni/eJe @ � :2`a: U8�8 �CB GWO�B ? O 5 ; 14? IZ;=>ZB ] 143 B]h>ZO�> 1 GW; 3 DhO � � O � � �� 3 � � 4 � � �� A � � � � �� ? � � � � �� L � N 36K X �3 O�]J;=DJO F � � DJF ; 365 � � L <�D A 8 5 DhO ` � � � � � DaD L � NRG K A > 1 GWO�B L � F ? B 3 O�]h> 1 J B 5 �c � c N 1 > 5@5 F D9I G � G ;=DhO =�� i b8�8 �<P i � =V= e �

� =V= R � �CPQ��%��.��G ��%��T��$-O%�PQ%&/R� � � � � � � �54YX � � � � � �� 3 � �� 3 O 5 ;=DhO � G 5 < 3 O�]J;4DhO W c = � RVR �

� =V= T � R ��%��-O�^]#N � P �D��G ��%��R ��%��-h� Rg��BV@�FG L <�> 1 GW;=> DWFXIZDhO P > 1 ]h>ZO�IC> DJFIZDhO � ? ]/G ;=>\] 1 GWB 3 >ZO"; 5 � 9 �� : � �� 8: � =�� TVP � �� =V=�� 8��% WU��BV�-O��oe�� %�� F � P �$��_�� L <�>�>�� >CIZ;'DJFN;4D 145 D 3 O�<�D A D �

]h>ZO�> 3 ; 3 > 5 DhO - D9B . 5@?�1 FHGWIC> 8 DJ;4>CO/; 3 G K65 Y ? GJO/; 3QT >CB ?b543 Ob] � ;SG 3QK D 1 >CB � ]J>CD A >Z; 1 . � �8:< � � � � � � � � � � � �=: 6K6 � =�� T � � O i � R e �� = eJg � � ��%�c � � ` 8 G 1@5 >�G 8�8 1 D � 3 A GW;=> 3 O P > 145 > 5 A D9DJ;4<�> 1 F[D 1 A ?�K ; 3 ] 143 B � � � �

� � � � � � � � � �� A � � � � �� 687 @ � eJghgJg � = eJi P � = e O e �� = e = � ��ND��-h�Y�]� *e��%�� d PQN�_ �MV��!P #�2� ?HUD 1 �VG 1 B�GWO�B 3 O P > 1@5 >�> K >ZIZ; 1 DaICG 1 B 3 D �

] 1 G 8 < 3 I I G K I ?bK GW; 3 DhO 5 ?�543 O�] 1 > 543Q5 ;=D 1 O�>Z; � D 1YX A D9B�> KQ5 DJF ;4<�>2< ? A GWOf;4D 145 D � A � �B:� � � : L 7 � =�� T R � O g @ � O = i �� = ehe � � -OPQ%��BV�-OPQ%.!� * �� .!, ��%�� O��%�� %&@') � > GJB � T > K B - G 5 > 5 F[D 1 J�J K

5 D ?�1 IZ> 3 A GW] 3 O�] �EH � � � � � �54 ? � � � � �� h<�� 6 � � eJgJghg � = � R �� = eJi � � -h�$�B-hNDPQ%�c>��) H �GX � � � � � � � � � � � � � � � � � � � � � � � � � � Dh<�O � 3QK > . � `aDhO 5

c < 3 IS<�> 5 ;=> 1 =�� e � � > 8 143 O";4>CB -/. � � � � _ K � >Z; � D 1 ] �� = e @�� $��PQV��& � L <�>ZD 1 > ; 3 ICG K 5 ; ? B 3 > 5 DhO�;=<�> 3 O P > 1@5 > 8 1 D - K > A 3 O&> K >ZIZ; 1 DaICG 1 �B 3 Dh] 1 G 8 < . GJO�B ;=<�> ? O 3 Y ? >COb> 545 DJF ;4<�> 5 D KQ? ; 3 DhO � X <Y<Y 1 >C] 3 DhO2] 1 D�� 3 O�]�D 8 > 1 G ;=D 1@5 F[D 1 3 A GJ]h> 5 >C] A >CO �;=GW; 3 DhO � � O H � � � � � � � �ZX �� 3 �� > � c G 8 �8 > KQ3 O 3 GWO�B � � _ G 1 ICDJO 3 �J B 5 � � D 1 ;=< � D KQK GJObB : A 5 ;=> 1 BUG A =�� T P �8�8 � eWg @ �beJg T �

The Transfer Operator for Multigrid on Inverse Bioelectric Field … · 2009-04-02 · 1 The...

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Transcript of The Transfer Operator for Multigrid on Inverse Bioelectric Field … · 2009-04-02 · 1 The...