Nber Working Paper Series Human Decisions And

NBER WORKING PAPER SERIES

HUMAN DECISIONS AND MACHINE PREDICTIONS

Jon Kleinberg Himabindu Lakkaraju Jure Leskovec Jens Ludwig Sendhil Mullainathan

Working Paper 23180 http://www.nber.org/papers/w23180

NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 February 2017

We are immensely grateful to Mike Riley for meticulously and tirelessly spearheading the data analytics, with effort well above and beyond the call of duty. Thanks to David Abrams, Matt Alsdorf, Molly Cohen, Alexander Crohn, Gretchen Ruth Cusick, Tim Dierks, John Donohue, Mark DuPont, Meg Egan, Elizabeth Glazer, Judge Joan Gottschall, Nathan Hess, Karen Kane, Leslie Kellam, Angela LaScala-Gruenewald, Charles Loeffler, Anne Milgram, Lauren Raphael, Chris Rohlfs, Dan Rosenbaum, Terry Salo, Andrei Shleifer, Aaron Sojourner, James Sowerby, Cass Sunstein, Michele Sviridoff, Emily Turner, and Judge John Wasilewski for valuable assistance and comments, to Binta Diop, Nathan Hess, and Robert Webberfor help with the data, to David Welgus and Rebecca Wei for outstanding work on the data analysis, to seminar participants at Berkeley, Carnegie Mellon, Harvard, Michigan, the National Bureau of Economic Research, New York University, Northwestern, Stanford and the University of Chicago for helpful comments, to the Simons Foundation for its support of Jon Kleinberg's research, to the Stanford Data Science Initiative for its support of Jure Leskovec’s research, to the Robert Bosch Stanford Graduate Fellowship for its support of Himabindu Lakkaraju and to Tom Dunn, Ira Handler, and the MacArthur, McCormick and Pritzker foundations for their support of the University of Chicago Crime Lab and Urban Labs. The main data we analyze are provided by the New York State Division of Criminal Justice Services (DCJS), and the Office of Court Administration. The opinions, findings, and conclusions expressed in this publication are those of the authors and not those of DCJS. Neither New York State nor DCJS assumes liability for its contents or use thereof. The paper also includes analysis of data obtained from the Inter-University Consortium for Political and Social Research at the University of Michigan. Any errors and all opinions are our own. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

© 2017 by Jon Kleinberg, Himabindu Lakkaraju, Jure Leskovec, Jens Ludwig, and Sendhil Mullainathan. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Human Decisions and Machine Predictions Jon Kleinberg, Himabindu Lakkaraju, Jure Leskovec, Jens Ludwig, and Sendhil Mullainathan NBER Working Paper No. 23180 February 2017 JEL No. C01,C54,C55,D8,H0,K0 ABSTRACT We examine how machine learning can be used to improve and understand human decision- making. In particular, we focus on a decision that has important policy consequences. Millions of times each year, judges must decide where defendants will await trial—at home or in jail. By law, this decision hinges on the judge’s prediction of what the defendant would do if released. This is a promising machine learning application because it is a concrete prediction task for which there is a large volume of data available. Yet comparing the algorithm to the judge proves complicated. First, the data are themselves generated by prior judge decisions. We only observe crime outcomes for released defendants, not for those judges detained. This makes it hard to evaluate counterfactual decision rules based on algorithmic predictions. Second, judges may have a broader set of preferences than the single variable that the algorithm focuses on; for instance, judges may care about racial inequities or about specific crimes (such as violent crimes) rather than just overall crime risk. We deal with these problems using different econometric strategies, such as quasi-random assignment of cases to judges. Even accounting for these concerns, our results suggest potentially large welfare gains: a policy simulation shows crime can be reduced by up to 24.8% with no change in jailing rates, or jail populations can be reduced by 42.0%with no increase in crime rates. Moreover, we see reductions in all categories of crime, including violent ones. Importantly, such gains can be had while also significantly reducing the percentage of African-Americans and Hispanics in jail. We find similar results in a national dataset as well. In addition, by focusing the algorithm on predicting judges’ decisions, rather than defendant behavior, we gain some insight into decision-making: a key problem appears to be that judges to respond to ‘noise’ as if it were signal. These results suggest that while machine learning can be valuable, realizing this value requires integrating these tools into an economic framework: being clear about the link between predictions and decisions; specifying the scope of payoff functions; and constructing unbiased decision counterfactuals.

Jon Kleinberg Jens Ludwig Department of Computer Science University of Chicago Department of Information Science 1155 East 60th Street Cornell University Chicago, IL 60637 Ithaca, NY 14853 and NBER [email protected] [email protected]

Himabindu Lakkaraju Sendhil Mullainathan Stanford University Department of Economics Littauer M-18 Gates Computer Science Building Harvard University 353 Serra Mall Cambridge, MA 02138 Stanford, CA 94305 and NBER [email protected] [email protected]

Jure Leskovec Stanford University Gates Computer Science Building 353 Serra Mall Stanford, CA 94305 [email protected] R AMi`Q/m+iBQM

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72im`2b i?i i?2 H;Q`Bi?K b22b- +Q``2bTQM/BM; iQ i?2 72im`2b xi i?i T`QpB/2 i?2 BMTmi

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T`2/B+iBQMb Q7 /272M/Mi `BbFc i?i Bb- Ri = f(h(xi,zi)) = 1(h(xi,zi)

9 Cm/;2 /2+BbBQMb M/ K+?BM2 T`2/B+iBQMb

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(6B;m`2 k #Qmi ?2`2X)

"mi r2 HbQ b22 i?i i?2 H;Q`Bi?K M/ i?2 Dm/;2b /Bb;`22- TìB+mH`Hv i i?2 ?B;? 2M/ Q7 i?2 `BbF /Bbi`B#miBQMX A7 i?2 T`2/B+iBQMb Q7 i?2 Dm/;2b M/ i?2 H;Q`Bi?K r2`2 B/2MiB+H- r2 rQmH/ 2tT2+i iQ b22 bi2T 7mM+iBQM BM 6B;m`2 k, h?2`2 rQmH/ #2 bQK2 T`2/B+i2/@`BbF i?`2b?QH/ r?2`2 i?2 `2H2b2 ì2 rQmH/ #2 y #Qp2 M/ R #2HQrX "mi i?i Bb MQi r?i r2 b22X h?2 +m`p2 `2HiBM; Dm/;2 `2H2b2 ì2b iQ i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbF ~ii2Mb Qmi b T`2/B+i2/ `BbF BM+`2b2bX KQM; i?2 `BbFB2bi RW Q7 `2H2b2/ /272M/Mib- r?Q ?p2 T`2/B+i2/ `BbF Q7 ekXeW- i?2 Dm/;2 `2H2b2b i?2K i ì2 Q7 7mHHv 93X8WX h?2 Dm/;2b `2 i`2iBM; KMv T2QTH2 rBi? ?B;? T`2/B+i2/ `BbF b B7 i?2v r2`2 HQr `BbFXjd P7 +Qm`b2 i?2 H;Q`Bi?KǶb T`2/B+iBQMb `2 Dmbi T`2/B+iBQMbX AM T`BM+BTH2 i?2b2 /272M/Mib +QmH/ +imHHv #2 HQr `BbF- M/ i?2 Dm/;2b KB;?i `2HBx2 i?Bb 2p2M B7 i?2 H;Q`Bi?K /Q2b MQiX h?i Bb- T2`?Tb i?2 Dm/;2b `2 #H2 iQ B/2MiB7v /272M/Mib r?Q HQQF HQr `BbF rBi?

`2bT2+i iQ i?2 +?`+i2`BbiB+b pBH#H2 iQ i?2 H;Q`Bi?K- xi- #mi `2 +imHHv ?B;? `BbF rBi?

`2bT2+i iQ 72im`2b i?i QMHv i?2 Dm/;2b b22- ziX "mi 6B;m`2 k HbQ b?Qrb i?i i?2 T2QTH2 i?2 H;Q`Bi?K T`2/B+ib `2 `BbFv `2 BM/22/ `BbFvX h?Bb Bb 2bB2bi iQ b22 BM i?2 T`QD2+iBQM Q7 i?2 +m`p2 QMiQ i?2 irQ@/BK2MbBQMH bT+2 i i?2 #QiiQK Q7 i?2 };m`2 `2HiBM; Q#b2`p2/ +`BK2 ì2b iQ T`2/B+i2/ `BbF- E[y m(x )]- i| i KQM; `2H2b2/ /272M/MibX h?Bb THQi HB2b HKQbi 2t+iHv HQM; i?2 98 /2;`22 HBM2 Qp2` i?2 7mHH `BbF /Bbi`B#miBQMX h?2 /272M/Mib i?2 Dm/;2b `2H2b2 /Q MQi b22K iQ ?p2 mMmbmH mMQ#b2`p#H2b i?i +mb2 i?2B` Q#b2`p2/ Qmi+QK2b iQ bvbi2KiB+HHv /Bp2`;2 7`QK r?i i?2 H;Q`Bi?K ?/ T`2/B+i2/X h?Bb T`QpB/2b KQ`2 i?M Dmbi 2pB/2M+2 i?i Qm` H;Q`Bi?KǶb T`2/B+iBQMb `2 r2HH +HB@ #ì2/c Bi b?Qrb i?i i?2 /272M/Mib Dm/;2b `2H2b2/ r?Q r2`2 T`2/B+i2/ iQ #2 ?B;? `BbF `2 BM 7+i ?B;? `BbFX q2 b22- 7Q` 2tKTH2- i?i mbBM; Dmbi BM7Q`KiBQM i?2 Dm/;2 ?/ i i?2 iBK2 Q7 i?2 #BH ?2`BM;b- i?2 /272M/Mib T`2/B+i2/ iQ #2 `BbFB2bi #v i?2 K+?BM2 H2`MBM; H;Q`Bi?Kěi?2 `BbFB2bi RWě;Q QM iQ ?p2 M Q#b2`p2/ +`BK2 ì2 Q7 y¯ =56.3WX

je A7 i?2 Dm/;2 `2H2b2 /2+BbBQMb `2 #b2/ QM i?2B` T`2/B+iBQM Q7 /272M/Mi `BbF i?2M Ri = f(h(xi,zi))X h?2 Dm/;2Ƕb `2H2b2 `i2 +QM/BiBQMH QM i?2 H;Q`Bi?KǶb T`2/B+i2/ `BbF Bb E[f(h(x ,z )) m(x )] = P [h(x ,z ) 0.X jdAM T`BM+BTH2 /Bz2`2Mi `2bQM r?v r2 KB;?i MQi b22 +H2M /BpBbBQM Q7 /272M/Mib `2H2b2/ p2`bmb /2iBM2/ `QmM/ bQK2 `BbF i?`2b?QH/ Bb B7 i?2 /Bz2`2Mi Dm/;2b ?2`BM; +b2b BM Qm` /ib2i 2+? mb2 /Bz2`2Mi i?`2b?QH/X AM i?i +b2 i Mv ;Bp2M T`2/B+i2/ `BbF H2p2H r2 rQmH/ b22 bQK2 /272M/Mib `2H2b2/ M/ bQK2 /2iBM2/ #2+mb2 i?i `BbF H2p2H rQmH/ #2 #Qp2 i?2 i?`2b?QH/ mb2/ #v bQK2 Dm/;2b #mi #2HQr i?i mb2/ #v Qi?2`bX "mi i?Bb +QmH/ QMHv 2tTHBM i?2 Tii2`M r2 b22 BM 6B;m`2 k B7 bQK2 Dm/;2b #bB+HHv `2H2b2/ HKQbi 2p2`vQM2 M/ Qi?2` Dm/;2b /2iBM2/ HKQbi 2p2`vQM2- bBM+2 r2 b22 Dm/;2b `2H2bBM; T2QTH2 7`QK i?`Qm;?Qmi i?2 2MiB`2 T`2/B+i2/ `BbF /Bbi`B#miBQMX AM T`+iB+2 r2 /Q MQi b22 i?Bb Km+? p`BiBQM +`Qbb Dm/;2b BM i?2B` `2H2b2 `i2bX

R3 h?Bb HbQ T`QpB/2b M QTTQìmMBiv iQ 2tTHQ`2 i?2 pHm2@//2/ Q7 K+?BM2 H2`MBM; Qp2` mbBM; KQ`2 biM/`/ 2+QMQK2i`B+ K2i?Q/b 7Q` KFBM; i?2b2 T`2/B+iBQMbX h#H2 j +QKT`2b i?2 T`2/B+i2/ `BbF /Bbi`B#miBQM Q7 i?2 JG H;Q`Bi?K iQ i?i T`Q/m+2/ #v HQ;BbiB+ `2;`2bbBQMc bT2+B}+HHv- r2 +QKT`2 i?2 +b2b ~;;2/ b `BbFv #v 2Bi?2` T`Q+2/m`2X 1+? `Qr Q7 i?2 h#H2 mb2b /Bz2`2Mi i?`2b?QH/- 7`QK i?2 1st T2`+2MiBH2 Q7 `BbF U`Qr RV iQ i?2 25th T2`+2MiBH2 Q7 `BbF U`Qr 9VX i i?2 1st T2`+2MiBH2- r2 b22 bm#biMiBH /Bb;`22K2Mi BM r?Q Bb ~;;2/ b `BbFvěQMHv jyXeW Q7 +b2b `2 ~;;2/ b iQT T2`+2MiBH2 BM i?2 T`2/B+i2/ `BbF /Bbi`B#miBQM #v #Qi? Qm` JG H;Q`Bi?K M/ HQ;BbiB+ `2;`2bbBQM U+QHmKM RVX h?2b2 /272M/Mib B/2MiB}2/ b ?B;? `BbF #v #Qi? T`Q+2/m`2b HbQ ?p2 i?2 ?B;?2bi `2HBx2/ +`BK2 ì2b UeyX3W BM +QHmKM jVX h?Qb2 ~;;2/ QMHv #v i?2 JG H;Q`Bi?K `2 M2`Hv b `BbFv U89X9W BM +QHmKM kV- r?BH2 i?Qb2 ~;;2/ QMHv #v i?2 HQ;Bi `2 7` H2bb `BbFv U9yW BM +QHmKM jVX b `2bmHi- JG@~;;2/ /272M/Mib U+QHmKM 9V `2 `BbFB2` b r?QH2 i?M HQ;Bi@~;;2/ QM2b U+QHmKM 8VX h?Bb Tii2`M `2T2ib BM i?2 Qi?2` `Qrb #mi #2;BMb iQ ii2Mmi2 i?2 7mì?2` r2 KQp2 /QrM i?2 T`2/B+i2/ `BbF /Bbi`B#miBQM U`Qrb k i?`Qm;? 9VX "v i?2 iBK2 r2 `2+? i?2 25th T2`+2MiBH2 Q7 i?2 /Bbi`B#miBQM U`Qr 9V i?2 irQ T`Q+2/m`2b ;`22 QM djW Q7 i?2 +b2bX b r?QH2- i?2b2 `2bmHib bm;;2bi i?i 2p2M BM i?2b2 /i- r?B+? +QMiBM `2HiBp2Hv 72r p`B#H2b U+QKT`2/ iQ bKTH2 bBx2V- i?2 JG H;Q`Bi?K }M/b bB;MB}+Mi bB;MH BM +QK#BMiBQMb Q7 p`B#H2b i?i KB;?i Qi?2`rBb2 #2 KBbb2/X h?2b2 ;BMb `2 KQbi MQi#H2 i i?2 iBH Q7 i?2 /Bbi`B#miBQM M/ UbQK2r?i T`2/B+i#HvV ii2Mmi2 b r2 KQp2 iQr`/b i?2 +2Mi2`X h?Bb BMimBiBQM bm;;2bib i?i r2`2 r2 HQQF i Qmi+QK2b i?i ?p2 `2HiBp2Hv HQr2` T`2pH2M+2 Ubm+? b pBQH2Mi +`BK2b b r2 /Q BM a2+iBQM eXRXRV i?2 /Bz2`2M+2 BM `2bmHib #2ir22M i?2 irQ T`2/B+BiQM T`Q+2/m`2b rQmH/ ;`Qr 2p2M bi`F2`X

(h#H2 j #Qmi ?2`2X)

9Xk JBb@`MFBM; Q` ?B;? /2i2MiBQM i?`2b?QH/\

1bi#HBb?BM; i?i i?2 K`;BMH /272M/Mi b B/2MiB}2/ #v i?2 K+?BM2 H2`MBM; H;Q`Bi?Kě i?2 pBH#H2 /272M/Mi i?i i?2 H;Q`Bi?K rQmH/ `MF ?B;?2bi 7Q` /2i2MiBQMě?b bm+? ?B;? H2p2H Q7 T`2/B+i#H2 `BbF Bb +2`iBMHv bm;;2biBp2 Q7 KBb@T`2/B+iBQM #v i?2 Dm/;2X "mi b HQ;B+H Kii2` i?2`2 Bb M Hi2`MiBp2 2tTHMiBQM b r2HH, Cm/;2b Kv bBKTHv TH+2 ?B;? +Qbi QM DBHBM; /272M/Mib- r?B+? rQmH/ H2/ i?2K iQ /2iBM QMHv i?Qb2 rBi? 2p2M ?B;?2` `BbFX >Qr +M r2 i2HH r?2i?2` Dm/;2b `2 KBb@T`2/B+iBM; `BbF Q` bBKTHv b2iBM; p2`v ?B;? `BbF i?`2b?QH/ 7Q` /2i2MiBQM\ A7 r2 +QmH/ /B`2+iHv Q#b2`p2 Dm/;2 T`2/B+iBQMb Q7 2+? /272M/MiǶb

`BbF- h(xi,zi)- i?Bb rQmH/ #2 i`BpBH 2t2`+Bb2, q2 +QmH/ bBKTHv 2tKBM2 r?2i?2` Dm/;2b

RN 2tT2+i2/ 2p2`vQM2 i?2v /2iBM2/ iQ #2 Q7 2p2M ?B;?2` `BbF i?M i?2 K`;BMH /272M/Mi i?2v `2H2b2/X q2 +MMQi i2bi i?Bb rBi?BM Mv BM/BpB/mH Dm/;2Ƕb +b2HQ/ #2+mb2 r2 /Q

MQi /B`2+iHv Q#b2`p2 h(xi,zi)X GQQFBM; +`Qbb i?2 +b2HQ/b Q7 Dm/;2b rBi? /Bz2`2Mi H2p2Hb Q7 H2MB2M+v U`2H2b2 ì2bV /Q2b HHQr mb iQ mM+Qp2` i?2 BKTHB+Bi `MF@Q`/2`BM; Q7 /272M/MibX AM TìB+mH`- Bi HHQrb mb iQ [mMiB7v i?2 `BbF Q7 i?2 K`;BMH /272M/Mib /2iBM2/X amTTQb2 7Q` BMbiM+2 i?i r2 ?p2 irQ Dm/;2b r?Q /Bz2` BM i?2B` `2H2b2 ì2b- 2[mH iQ bv NyW M/ 3yW- M/ i?i /272M/Mib `2 `M/QKHv bbB;M2/ iQ Dm/;2bX "2+mb2 r2 +M +H+mHi2 i?2 H;Q`Bi?KǶb T`2@ /B+i2/ `BbF 7Q` 2+? /272M/Mi BM 2+? Dm/;2Ƕb +b2HQ/- r2 +M +QKT`2 i?2 /Bbi`B#miBQMb Q7 T`2/B+i2/ `BbF KQM; i?2 irQ Dm/;2Ƕb +b2HQ/b iQ /2i2`KBM2 r?2`2 BM i?2 /Bbi`B#miBQM i?2 //BiBQMH /272M/Mib DBH2/ #v i?2 bi`B+i2` Dm/;2 +QK2 7`QKXj3 hrQ i?BM;b `2 rQì? MQiBM;X 6B`bi- i?Bb T`Q+2/m`2 /Q2b MQi `2Hv QM Dm/;2b ?pBM; bBKBH` `MF Q`/2`BM;bX 6Q` 2tKTH2- r2 HHQr 7Q` i?2 TQbbB#BHBiv i?i i?2 KQbi H2MB2Mi Dm/;2ěi?2 QM2 rBi? i?2 ?B;?2` Qp2`HH `2H2b2 ì2ě+imHHv DBHb KQ`2 T2QTH2 BM bQK2

T`2/B+i2/@`BbF #BMb m(xi)X a2+QM/- i?Bb T`Q+2/m`2 /Q2b KF2 bT2+B}+ bbmKTiBQM #Qmi i?2 /Bbi`B#miBQM Q7 mMQ#b2`p#H2bX Ai `2[mB`2b i?i- rBi?BM 2+? T`2/B+i2/ `BbF #BM- i?2 /Bz2`2Mi Dm/;2b ?p2 bBKBH` /Bbi`B#miBQMb Q7 mMQ#b2`p#H2b KQM;bi i?2 `2H2b2/, bT2+B7@ B+HHv i?i i?2B` p2`;2 `BbF Bb i?2 bK2 7Q` KQ`2 M/ H2bb H2MB2Mi Dm/;2bX 6Q` 2tKTH2- i?Bb T`Q+2/m`2 rBHH #2 #Bb2/ B7 i?2 KQbi H2MB2Mi Dm/;2b `2 #2ii2` i mbBM; mMQ#b2`p#H2b BM /2+B/BM; r?QK iQ `2H2b2X q2 2tKBM2 i?Bb bbmKTiBQM BM ;`2i2` /2iBH #2HQrX Pm` 2KTB`B+H TTHB+iBQM Q7 i?Bb TT`Q+? BM i?2 Lu* /i iF2b /pMi;2 Q7 i?2 7+i i?i r2 ?p2 UMQMvKQmbV Dm/;2 B/2MiB}2`b- iQ;2i?2` rBi? i?2 7+i i?i +QM/BiBQMH QM #Q`Qm;?- +Qmì ?Qmb2- v2`- KQMi?- M/ /v Q7 r22F- p2`;2 /272M/Mi +?`+i2`BbiB+b /Q MQi TT2` iQ #2 bvbi2KiB+HHv `2Hi2/ iQ Dm/;2 H2MB2M+v ì2b rBi?BM i?2b2 +2HHb Ub22 TT2M/Bt VXjN h?2 Qi?2` i?BM; r2 M22/ 7Q` i?Bb /2bB;M iQ rQ`F `2 /Bz2`2M+2b BM Dm/;2 H2MB2M+v rBi?BM +2HHbX *QMbBbi2Mi rBi? Tbi `2b2`+?- i?i Bb r?i r2 b22 BM Qm` /i b r2HHX h?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2b `2H2b2 3kXNW Q7 /272M/MibX _2HiBp2 iQ i?2 KQbi H2MB2Mi Dm/;2 [mBMiBH2- i?2 H2bb H2MB2Mi [mBMiBH2b ?p2 p2`;2 `2H2b2 ì2b i?i `2 6.6- 9.6- 13.5 M/ 22.3 T2`+2Mi;2 TQBMib HQr2`- `2bT2+iBp2HvX

(6B;m`2 j #Qmi ?2`2X)

h?2 `2H2b2 /2+BbBQMb Q7 i?2 KQbi H2MB2Mi [mBMiBH2 Q7 Dm/;2b `2 b?QrM BM i?2 KB//H2 TM2H

j3h?i Bb- B7 E[RL]=0.9 M/ E[RS ]=0.8 `2 i?2 `2H2b2 `i2b 7Q` i?2 H2MB2Mi M/ bi`B+i Dm/;2b- `2bT2+iBp2Hv- i?2M i 2+? pHm2 Q7 i?2 H;Q`Bi?KǶb T`2/B+i2/ `BbF r2 +M Q#b2`p2 E[RL m(x)] M/ E[RS m(x)] M/ +H+mHi2 E[RL m(x)] | | | − E[RS m(x)] = P [hL(x ,z )

ky Q7 6B;m`2 jc i?2 iQT #Qt b?Qrb i?2 RdXRW Q7 /272M/Mib i?2v DBH2/- i?2 #QiiQK b?Qrb i?2

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(6B;m`2 9 #Qmi ?2`2X)

6B;m`2 9 b?Qrb bBKBH` Tii2`M ?QH/b 7Q` HH Q7 i?2 Dm/;2@H2MB2M+v [mBMiBH2b b r2HHX q2 bQì /272M/Mib #v T`2/B+i2/ `BbF M/ #BM i?2K BMiQ ky 2[mH@bBx2/ ;`QmTbX h?2 #H+F b2;K2Mi i i?2 iQT Q7 2+? #BM b?Qrb r?i b?`2 Q7 /272M/Mib BM i?i #BM Bb /2iBM2/ #v i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2bX h?2 #Hm2 b2;K2Mib QM i?2 H27i b?Qrb i?i i?2 H;Q`Bi?K rQmH/ T`BQ`BiBx2 7Q` /2i2MiBQM T2QTH2 BM i?2 ?B;?2bi T`2/B+i2/ `BbF #BMb B7 i?2 ;QH r2`2 iQ HQr2` i?2 `2H2b2 ì2 7`QK i?2 KQbi H2MB2Mi [mBMiBH2Ƕb ì2 /QrM iQ i?2 b2+QM/@KQbi@H2MB2Mi [mBMiBH2Ƕb ì2 UiQT TM2HV- Q` i?B`/@KQbi@H2MB2Mi [mBMiBH2Ƕb ì2 Ub2+QM/ TM2HV- 2i+X h?2 #Hm2 b?/BM; QM i?2 `B;?i b?Qrb 7`QK r?B+? `BbF #BMb i?2 Dm/;2b +imHHv b2H2+i K`;BMH /272M/Mib iQ /2iBM @ 2bb2MiBHHv 7`QK i?`Qm;?Qmi i?2 T`2/B+i2/@ `BbF /Bbi`B#miBQMX Ai Bb rQì? MQiBM; i?i i?2`2 `2 MQ T`2/B+i2/@`BbF #BMb r?2`2 i?2`2 `2 KQ`2 /272M/Mib `2H2b2/ #v bi`B+i2` Dm/;2 i?M #v KQ`2 H2MB2Mi Dm/;2X h?2 Dm/;2b /Q MQi b22K iQ /Bb;`22 Km+? rBi? 2+? Qi?2` #Qmi ?Qr iQ `MF@Q`/2` /272M/Mib #b2/ QM i?2B` Q#b2`p#H2 +?`+i2`BbiB+bX h?Bb 6B;m`2 +H2`Hv BHHmbiì2b i?i HH H2MB2M+v [mBMiBH2b Q7 Dm/;2b #2?p2 b i?2 b2+QM/ [mBMiBH2 /Q2b, DBHBM; T`2/B+i#Hv HQr@`BbF BM/BpB/mHb r?BH2 ?B;?@`BbF QM2b `2 pBH#H2X

9y#Qp2 r2 b?Qr2/ i?i i?2 /Bz2`2M+2 BM `2H2b2 `i2b #2ir22M i?2 KQbi M/ b2+QM/@KQbi H2MB2Mi [mBMiBH2Ƕb +b2HQ/b Bb 6.6 T2`+2Mi;2 TQBMibX h?2 b2+QM/@KQbi H2MB2Mi [mBMiBH2 DBHb QMHv M 2ti` kXRN T2`+2Mi;2 TQBMib 7`QK i?2 iQT 12.0W Q7 i?2 `BbF /Bbi`B#miBQMX

kR h?2 2ti2Mi Q7 i?Bb 2``Q` Bb [mMiB}2/ BM i?2 }`bi irQ +QHmKMb Q7 h#H2 9X h?2 }`bi +QHmKM b?Qrb ?Qr 7` BMiQ i?2 `BbF /Bbi`B#miBQM Dm/;2b rQmH/ M22/ iQ ;Q r2`2 i?2v iQ DBH #v T`2/B+i2/ `BbFX h?2 b2+QM/ +QHmKM b?Qrb i?2 7`+iBQM i?i +imHHv +QK2b 7`QK i?Bb Tì Q7 i?2 /Bbi`B#miBQMX 6Q` 2tKTH2- HH i?2 //BiBQMH DBHBM; Q7 i?2 b2+QM/ [mBMiBH2 +QmH/ #2 ?/ #v DBHBM; 2p2`vQM2 BM i?2 iQT 12.0W ?B;?2bi `BbF- r?2`2b QMHv 33.2W +QK2 7`QK i?Bb Tì Q7 i?2 /Bbi`B#miBQMX h?Bb Hi2` T2`+2Mi;2 Bb `2HiBp2Hv +QKKQM i?`Qm;? HH i?2 [mBMiBH2bX b r?QH2 i?2b2 `2bmHib b?Qr i?i HH [mBMiBH2b Q7 H2MB2M+v i #2bi DBH QMHv TìHv ++Q`/BM; iQ T`2/B+i2/ `BbFX

(6B;m`2 8 #Qmi ?2`2X)

:Bp2M i?i i?2 Dm/;2b M/ i?2 H;Q`Bi?K /Bb;`22 #Qmi r?QK iQ /2iBM QM i?2 K`;BM-

Mim`H [m2biBQM Bb, q?QǶb `B;?i\ `2 i?2 Dm/;2b mbBM; T`Bpi2 BM7Q`KiBQM- zi- iQ B/2MiB7v K`;BMH /272M/Mib r?Q ?p2 2p2M ?B;?2` `BbF i?M i?Qb2 i?2 H;Q`Bi?K +M B/2MiB7v mbBM; Dmbi Q#b2`p#H2b\ h?Bb +M #2 i2bi2/ /B`2+iHvX aiìBM; rBi? i?2 `2H2b2 b2i Q7 i?2 KQbi H2MB2Mi Dm/;2b- r2 +M +?QQb2 //BiBQMH BM+`+2ìBQMb ++Q`/BM; iQ T`2/B+i2/ `BbFX 6Q` 2+? KQmMi Q7 //BiBQMH BM+`+2ìBQM- i?Bb HHQrb mb iQ +H+mHi2 i?2 +`BK2 ì2 i?i r2 Q#b2`p2 7Q` 2+? Q7 i?2b2 UbKHH2`V `2H2b2 b2ibX AKTQìMiHv- #2+mb2 +b2 HQ/b `2 QM p2`;2 bBKBH` +`Qbb Dm/;2b- i?2b2 MmK#2`b +M #2 +QKT`2/ iQ i?2 Qmi+QK2b T`Q/m+2/ #v i?2 bi`B+i2` Dm/;2bX h?2b2 `2bmHib `2 T`2b2Mi2/ ;`T?B+HHv BM 6B;m`2 8 b r2HHX h?2 bQHB/ U`2/V +m`p2 +H+mHi2b i?2 +`BK2 i?i rQmH/ ?p2 `2bmHi2/ B7 //BiBQMH /272M/Mib ?/ #22M /2iBM2/ BM Q`/2` Q7 i?2 H;Q`Bi?KǶb T`2/B+i2/ `BbFX 1+? Q7 i?2 TQBMib /2MQi2b i?2 Dm/;2b Q7 /Bz2`2Mi [mìBH2bX aBM+2 Mv //BiBQMH /2i2MiBQM `2/m+2b +`BK2 7Q` Tm`2Hv K2+?MB+H `2bQMb U/272M/Mib BM+T+Bii2/ BM DBH +MMQi +QKKBi +`BK2V- 2p2M `M/QKHv b2H2+iBM; //BiBQMH /272M/Mib iQ DBH 7`QK i?2 KQbi H2MB2Mi [mBMiBH2Ƕb +b2HQ/ rQmH/ HbQ `2/m+2 +`BK2- b b?QrM #v i?2 /b?2/ HBM2 BM i?2 };m`2X9R

(h#H2 9 #Qmi ?2`2X)

q?2M +QKT`BM; 2+? Q7 i?2 bi`B+i2` [mBMiBH2 Dm/;2b iQ r?i i?2 H;Q`Bi?K +QmH/ +?B2p2- irQ TQBMib `2 TìB+mH`Hv bHB2Mi, UBV ?Qr Km+? /Q2b +`BK2 7HH r?2M i?2 H@ ;Q`Bi?K BM+`2b2b DBHBM; ì2b #v i?2 bK2 KQmMic M/ UBBV r?i DBHBM; BM+`2b2 /Q2b i?2 H;Q`Bi?K M22/ iQ +?B2p2 i?2 bK2 +`BK2 `2/m+iBQM b i?2 Dm/;2X h?2b2 MmK#2`b `2 T`2b2Mi2/ BM h#H2 9X q2 b22 bB;MB}+Mi ;BMb Qp2` r?i Dm/;2b KM;2X h?2 b2+QM/ [mBMiBH2 Q7 Dm/;2b `2/m+2 +`BK2 #v 9.9W #v BM+`2bBM; i?2 /2i2MiBQM ì2 #v 6.6 T2`+2Mi;2 TQBMibX h?2 bK2 +`BK2

9Rh?2 Dm/;2 /2i2MiBQM /2+BbBQMb `2 #2ii2` i?M `M/QK- i?Qm;? QM2 +MMQi i2HH r?2i?2` i?2v `2 /QBM; Km+? Q` QMHv KQ/2biHv #2ii2` rBi?Qmi +QmMi2`@7+imHX

kk `2/m+iBQM +QmH/ ?p2 #22M ++QKTHBb?2/ #v BM+`2bBM; i?2 /2i2MiBQM ì2 #v QMHv 2.8 T2`+2Mi;2 TQBMib- Q` 2[mBpH2MiHv #v BM+`2bBM; i?2 /2i2MiBQM ì2 #v 6.6 T2`+2Mi;2 TQBMib r2 +QmH/ ?p2 `2/m+2/ +`BK2 #v 20.1WX Smi /Bz2`2MiHv- `2HiBp2 iQ i?2 Q#b2`p2/ Dm/;2 Qmi+QK2b r2 +QmH/ ?p2 `2/m+2/ i?2 BM+`2b2 BM DBH TQTmHiBQM #v QMHv 9kXRW b Km+?- Q` BM+`2b2/ i?2 bBx2 Q7 i?2 +`BK2 /`QT #v 103.0WX h?2 K;MBim/2b Q7 i?2b2 2z2+ib /BKBMBb? bQK2r?i b r2 KQp2 iQ i?2 Qi?2` H2MB2M+v [mBMiBH2bX "v i?2 }7i? UH2biV H2MB2Mi [mBMiBH2 Q7 Dm/;2b- r2 +QmH/ BM+`2b2 i?2 DBH TQTmHiBQM #v QMHv 8yXjW iQ ;2i i?2 bK2 +`BK2 /`QT Q` BM+`2b2 i?2 +`BK2 /`QT #v ekXjWX q2`2 r2 iQ p2`;2 +`Qbb HH 7Qm` Q7 i?2b2 [mBMiBH2b r2 +QmH/ DBH QMHv 93XkW b KMv T2QTH2- Q` r2 +QmH/ ;2i +`BK2 `2/m+iBQMb i?i `2 d8X3W H`;2`X q2 ?p2 2bi#HBb?2/ i?i /2iBMBM; /272M/Mib mbBM; +QK#BMiBQM Q7 i?2 H2MB2Mi Dm/;2 /2+BbBQMb M/ i?2 H;Q`Bi?K +M vB2H/ HQr2` +`BK2 i ;Bp2M `2H2b2 ì2 i?M r?i `2bmHib 7`QK i?2 +imH /2+BbBQMb Q7 i?2 bi`B+i2` Dm/;2bX "mi T2`?Tb i?Bb Bb MQi bQ Km+? i2biK2Mi iQ i?2 H;Q`Bi?K b Bi Bb iQ i?2 bFBHH Q7 i?2 KQbi H2MB2Mi Dm/;2b- M/ BM TìB+mH` rBi? `2bT2+i iQ i?2B` TQi2MiBH bFBHH mbBM; mMQ#b2`p#H2b BM b2H2+iBM; /272M/Mib iQ /2iBMX h?i Bb- i?2 +QK#BM2/ DBHBM; /2+BbBQMb Q7 i?2 H;Q`Bi?K M/ KQbi@H2MB2Mi [mBMiBH2 Dm/;2b +QmH/ /QKBMi2 i?Qb2 Q7 i?2 H2bb@H2MB2Mi [mBMiBH2 Dm/;2b #2+mb2 i?2 KQbi@H2MB2Mi [mBMiBH2 mb2b mMQ#b2`p#H2b KQ`2 2z2+iBp2Hv i?M /Q i?2 Qi?2` Dm/;2b @ r?B+? i?2 H;Q`Bi?K Bib2H7 +QmH/ MQi `2THB+i2X9k LQi2 i?i i?Bb +QmMi2`@2tTHMiBQM iQ Qm` }M/BM;b bm;;2bib i2bi#H2 ?vTQi?2bBb, A7 i?2 KQbi@H2MB2Mi [mBMiBH2 Dm/;2b r2`2 mMmbmHHv 2z2+iBp2 BM mbBM; mMQ#b2`p#H2b iQ b2H2+i T2QTH2 iQ DBH- i?2M i?2 T2QTH2 i?i i?2 KQbi@H2MB2Mi [mBMiBH2 `2H2b2/ rQmH/ #2 H2bb +`BK2@ T`QM2 +QKT`2/ iQ T2QTH2 rBi? bBKBH` Q#b2`p#H2 +?`+i2`BbiB+b r?Q r2`2 `2H2b2/ #v H2bb@H2MB2Mi Dm/;2bX h?Bb K2Mb i?i B7 r2 i`BM M H;Q`Bi?K QM i?2 `2H2b2/ b2i Q7 i?2 KQbi@H2MB2Mi [mBMiBH2 M/ i?2M mb2/ i?i iQ BKTmi2 +`BK2 ì2b iQ /272M/Mib `2H2b2/ #v i?2 H2bb@H2MB2Mi [mBMiBH2 Dm/;2b- i?2 BKTmi2/ pHm2b rQmH/ #2 #2HQr i?2 +imH +`BK2 Qmi+QK2b rBi?BM i?2 +b2HQ/b Q7 i?2 H2bb@H2MB2Mi Dm/;2bX9j u2i r?i r2 b22 Bb i?i i?2 BKTmi2/ M/ +imH pHm2b `2 [mBi2 bBKBH` QM p2`;2 7Q` 2+? Q7 i?2 bi`B+i2` Dm/;2 [mBMiBH2b- b b?QrM BM i?2 #QiiQK 7Qm` TM2Hb Q7 6B;m`2 eX qBi?BM 2+? Q7 i?2 bi`B+i2` [mBMiBH2b i?2 BKTmi2/ M/ +imH pHm2b `2 r2HH +HB#ì2/ +`Qbb i?2 7mHH `M;2 Q7 i?2

9khQ b22 i?2 TQi2MiBH T`Q#H2K- bmTTQb2 H2MB2Mi M/ bi`B+i Dm/;2 `2 T`2/B+iBM; `BbF mbBM; Dmbi irQ #BM`v 7+iQ`b, QM2 Q#b2`p#H2 iQ i?2 H;Q`Bi?K UxiVc i?2 Qi?2` mMQ#b2`p#H2 UziVX q2 bbmK2 `M/QK bbB;MK2Mi Q7 +b2b iQ Dm/;2bX G2i yi = αxi + βzi M/ α>0 M/ β>0X amTTQb2 i?i KQM; i?2 xi =1T2QTH2- i?2 H2MB2Mi Dm/;2 `2H2b2b HH i?Qb2 r?Q ?p2 zi =0M/ /2iBMb HH i?Qb2 rBi? zi =1X AM i?Bb 2tKTH2- i?2 +`BK2 `i2 KQM; vQmM; T2QTH2 `2H2b2/ #v i?2 H2MB2Mi Dm/;2 rBHH #2 α- HQr2` i?M r?i r2 b22 KQM; i?Qb2 `2H2b2/ #v i?2 bi`B+i Dm/;2- Uα + βE[zi xi =1]Vc BX2X- L S | E[yi Ri =1,m(xi)]

kj `BbF /Bbi`B#miBQM @ BM/22/ MQi p2`v /Bz2`2Mi 7`QK THQiiBM; i?2 T`2/B+i2/ pHm2b +H+mHi2/ mbBM; i?2 7mHH i`BMBM; b2i ;BMbi Q#b2`p2/ Qmi+QK2b rBi?BM i?2 7mHH i`BMBM; b2i Ub?QrM BM i?2 iQT TM2H Q7 6B;m`2 eVX h?2b2 }M/BM;b `2 MQi +QMbBbi2Mi rBi? i?2 B/2 i?i i?2 KQbi H2MB2Mi Dm/;2b `2 mMmbmHHv 2z2+iBp2 BM mbBM; mMQ#b2`p#H2b- M/ bm;;2bi BMbi2/ i?i Bi Bb i?2 H;Q`Bi?K Bib2H7 i?i Bb /QKBMiBM; i?2 +?QB+2b Q7 i?2 bi`B+i2` Dm/;2bX

(6B;m`2 e #Qmi ?2`2X)

/Bz2`2Mi i2bi r2 +M +QMbi`m+i iF2b /pMi;2 Q7 i?2 7+i i?i i?2`2 Bb BMi`@Dm/;2 b r2HH b BMi2`@Dm/;2 p`BiBQM BM H2MB2M+vX h?i Bb- Dm/;2b r?Q ?2` +b2b +`Qbb /B7@ 72`2Mi #Q`Qm;?- +Qmì ?Qmb2- v2`- KQMi?- /v Q7 r22F ǵ+2HHbǶ Q7i2M ?p2 /Bz2`2Mi `2H2b2 ì2b +`Qbb +2HHbX A7 Dm/;2b `2 mbBM; mMQ#b2`p#H2b iQ ?2HT KF2 `2H2b2 /2+BbBQMb i?2M U+QM/BiBQMH QM Q#b2`p#H2bV r2 b?QmH/ b22 i?i +`BK2 ì2b `2 `2HiBp2Hv HQr2` BM +2HHb r?2`2 i?2 Dm/;2 ?b `2HiBp2Hv ?B;?2` `2H2b2 ì2b @ i?i Bb- Q#b2`p2/ +`BK2 ì2b BM i?2b2 ?B;?@`2H2b2 +2HHb b?QmH/ #2 HQr2` i?M r2 rQmH/ ?p2 T`2/B+i2/ #b2/ QM i?2B` Q#b2`p#H2 +?`+i2`BbiB+b HQM2X "mi i?Bb Bb MQi r?i r2 b22X99 Cm/;2b /Q MQi b22K iQ #2 bBKTHv b2iiBM; ?B;? #` 7Q` /2i2MiBQMX h?2v BMbi2/ b22K iQ #2 KBb@`MFBM; /272M/Mib r?2M /2+B/BM; r?QK iQ /2iBMX

8 h`MbHiBM; T`2/B+iBQMb BMiQ TQHB+B2b hQ b+QT2 i?2 K;MBim/2b Q7 i?2 TQi2MiBH ;BMb iQ #2 ?/ 7`QK mbBM; H;Q`Bi?KB+ T`2/B+@ iBQMb iQ BM7Q`K `2H2b2 /2+BbBQMb- r2 bBKmHi2 i?2 `2bmHib Q7 bT2+B}+ TQHB+v +?M;2bX 6Q` 2tKTH2 ;Bp2M Qm` }M/BM; i?i Dm/;2b KBbiF2MHv `2H2b2 T`2/B+i#Hv@`BbFv /272M/Mib- QM2 Mim`H TQHB+v `2bTQMb2 +QmH/ #2 r`MBM; r?2M bm+? M 2``Q` Bb #Qmi iQ ?TT2MX h?2 `2bmHiBM; iQQH rQmH/ #2 MHQ;Qmb iQ ǵ/`Bp2` bbBbiǶ bvbi2K i?i T`QpB/2b r`MBM; r?2M2p2` i?2 +` #2;BMb iQ /Q bQK2i?BM; i?2 /`Bp2` KB;?i MQi `2HHv rBb? iQ /Q- HBF2 /`B7i BMiQ MQi?2` HM2X AM i?2 #BH +QMi2ti- i?2 r`MBM; KB;?i i`B;;2` r?2M2p2` i?2 Dm/;2 Bb #Qmi iQ `2H2b2 ?B;?@`BbF /272M/Mi- r?B+? rQmH/ BM 2z2+i +QMi`+i i?2 `2H2b2/ b2iX PM2 /`r#+F Q7 /`Bp2` bbBbi bvbi2Kb Bb i?2v `2 HBKBi2/ iQ r`MBM; Q7 TQi2MiBH /`Bp2` KBbiF2bX h?2v /Q MQi iF2 /pMi;2 Q7 i?2 #BHBiv Q7 i?2 bK2 i2+?MQHQ;v iQ bmTTQ`i M ǵmiQ@TBHQiǶ i?i T`Q@+iBp2Hv BMBiBi2b +M/B/i2 KM2mp2`b iQ pQB/ ++B/2MibX AM i?2

99q2 BKTH2K2Mi i?Bb i2bi rBi? bBKTH2 `2;`2bbBQMX G2i RJ #2 Dm/;2 JǶb Qp2`HH `2H2b2 ì2 KQM; HH i?2 +b2b i?2v ?2`- J M/ H2i Rc #2 i?2 Dm/;2Ƕb `2H2b2 ì2 rBi?BM ;Bp2M +2HH U+VX G2i yicJ #2 i?2 Q#b2`p2/ +`BK2 Qmi+QK2 7Q` /272M/Mi UBV ?2`/ #v Dm/;2 UDV BM +2HH U+V- M/ H2i m(xicJ ) #2 i?2 /272M/MiǶb T`2/B+i2/ +`BK2 ì2 b 7mM+iBQM Q7 Q#b2`p#H2bX A7 Dm/;2b `2 mbBM; mMQ#b2`p#H2b 2z2+iBp2Hv iQ KF2 /2i2MiBQM /2+BbBQMb i?2M r?2M r2 `mM i?2 `2;`2bbBQM yicJ = γ0 + γ1m(xicJ )+ J J γ2[R R ]+ϵ U+Hmbi2`BM; biM/`/ 2``Q`b i i?2 H2p2H Q7 i?2 Dm/;2@+2HHV r2 rQmH/ 2tT2+i iQ b22 γ2 < 0X u2i Qm` c − icJ +imH 2biBKi2 7Q` γ2 rBi?BM i?2 i2bi b2i Bb MQi /BbiBM;mBb?#H2 7`QK x2`Q UyXyRk rBi? biM/`/ 2``Q` Q7 yXyRkVX "v rv Q7 +QKT`BbQM- i?2 2biBKi2 7Q` γ1 2[mHb yXNdy UbiM/`/ 2``Q` Q7 yXyRkV BM i?2 i2bi b2iX

k9 Dm/B+BH TTHB+iBQM- +QMi`+iBQM HBKBib mb iQ DBHBM; KQ`2 T2QTH2c r2 /Q MQi KF2 mb2 Q7 i?2 H;Q`Bi?KǶb #BHBiv iQ b2H2+i T2QTH2 7Q` `2H2b2X KQ`2 /`KiB+ TQHB+v +?M;2- i?2M- rQmH/ #2 7mHH `2@`MFBM; TQHB+v i?i rQmH/ H2i i?2 `BbF iQQH `MF@Q`/2` HH /272M/Mib #v T`2/B+i2/ `BbF M/ KF2 `2+QKK2M/iBQMb 7Q` HH Q7 i?2 DBH M/ `2H2b2 /2+BbBQMbX am+? `2@`MFBM; iQQH rQmH/ #2 2[mBpH2Mi iQ M ǵmiQ TBHQiǶ 7Q` #BH /2+BbBQMb- r?B+? i?2 Dm/;2 +QmH/ Qp2`@`B/2 Mv iBK2 #v ;`##BM; i?2 bi22`BM; r?22HX 1pHmiBM; i?2b2 TQHB+v +?M;2b `2[mB`2b T`Q/m+BM; +QmMi2`@7+imHb- r?B+? `Bb2b irQ Bbbm2bX 6B`bi- r2 Kmbi FMQr +QKTHBM+2 ì2b, rBHH i?2 Dm/;2 Tv ii2MiBQM iQ i?2 r`MBM; bvbi2K M/ +QKTHv rBi? i?2 `BbF b+Q`2\ h?Bb +MMQi #2 FMQrM 7`QK i?2 /i r2 ?p2X aQ r2 7Q+mb QM i?2 +b2 Q7 7mHH +QKTHBM+2 M/ b+QT2 i?2 TQi2MiBH TQHB+v ;BMbX h?2 +imH TQHB+v BKT+ib +MMQi #2 FMQrM rBi?Qmi 2tT2`BK2MiH TBHQibX h?2 BKT+ib +QmH/ #2 bKHH2` B7 Dm/;2b Qp2``mH2 2Bi?2` Q7 i?2 M2r H;Q`Bi?KB+ bvbi2Kb #/HvX h?2 ;BMb +QmH/ #2 ?B;?2` B7 i?2 Qp2`@`B/2 /2+BbBQMb Q7 Dm/;2b H2/ iQ 2p2M #2ii2` Qmi+QK2bX Pm` TQHB+v b+QTBM; K2`2Hv T`QpB/2b #b2 +b2X h?2 b2+QM/ T`Q#H2K `Bb2b BM +H+mHiBM; +`BK2 ì2bX PM+2 r2 KF2 M bbmKTiBQM #Qmi Dm/;2 +QKTHBM+2- i?Bb Bb i`BpBH 2t2`+Bb2 7Q` i?2 /`Bp2`@bbBbi@HBF2 +QMi`+iBQM 2t2`+Bb2 bBM+2 i?Bb TQHB+v rQmH/ H2/ QMHv iQ DBHBM; bQK2 //BiBQMH /272M/Mib- #mi MQi `2H2bBM; Mv M2r QM2bX AM i?Bb +b2 r2 +QmH/ 2pHmi2 BKT+ib #v +H+mHiBM; rBi?BM i?2 ?QH/@Qmi b2i i?2 +`BK2b +QKKBii2/ #v i?2 M2r- +QMi`+i2/ `2H2b2/ b2iX "mi 2pHmiBM; i?2 `2@`MFBM; TQHB+v Bb KQ`2 +QKTHB+i2/- bBM+2 Bi rBHH `2H2b2 bQK2 /272M/Mib i?2 Dm/;2b DBH2/ @ `2bmHiBM; BM b2H2+iBp2 H#2Hb T`Q#H2KX98 h?2 +QMi`bi BM i?2 bbmKTiBQMb `2[mB`2/ 7Q` i?2b2 irQ TQHB+v b+QTBM; 2t2`+Bb2b BHHmbiì2b M BKTQìMi TQBMi, i?2 /2;`22 iQ r?B+? i?2 b2H2+iBp2 H#2Hb T`Q#H2K +QKTHB+i2b Qm` #BHBiv iQ 2pHmi2 TQHB+v +QmMi2`@7+imHb /2T2M/b QM i?2 bT2+B}+ TQHB+v #2BM; 2pHmi2/X

8XR *QMi`+iBQM

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98h?2 H+F Q7 H#2Hb 7Q` /272M/Mib r?Q `2 /2iBM2/ #v i?2 Dm/;2b +M- B7 i?2 Dm/;2b ?p2 T`Bpi2 BM7Q`KiBQM M/ mb2 Bi 2z2+iBp2Hv r?2M KFBM; `2H2b2 /2+BbBQMb- #Bb Qm` K+?BM2 H2`MBM; T`2/B+iBQMb @ M/ bQ `2/m+2 T`2/B+iBQM ++m`+vX "mi Mvi?BM; i?i `2/m+2b T`2/B+iBQM ++m`+v 7Q` i?2 K+?BM2 H2`MBM; H;Q`Bi?K bBKTHv ?b i?2 2z2+i Q7 mM/2`biiBM; i?2 ;BMb 7`QK `2HvBM; QM K+?BM2 `i?2` i?M ?mKM T`2/B+iBQMbX AM i?2 bK2 bTB`Bi MQi?2` KBMQ` T`Q#H2K `Bb2b #2+mb2 K+?BM2 H2`MBM; H;Q`Bi?Kb `2 /i ?mM;`v @ T`2/B+iBQM ++m`+v BM+`2b2b BM i?2 MmK#2` Q7 Q#b2`piBQMb K/2 pBH#H2 iQ i?2 K+?BM2 H2`M2` @ bQ i?i Mvi?BM; i?i `2/m+2b i?2 KQmMi Q7 Q#b2`piBQMb pBH#H2 BM i?2 i`BMBM; /ib2i rBHH `2/m+2 T`2/B+iBQM ++m`+vX

k8 T2QTH2 r?Q rQmH/ MQi ?p2 +QKKBii2/ +`BK2 ?/ i?2v #22M `2H2b2/X q?BH2 i?2 T`B+2 bQ+B2iv rQmH/ #2 rBHHBM; iQ Tv Bb mHiBKi2Hv MQ`KiBp2 +?QB+2- r2 +M bBKmHi2 i?2 2z2+ib Q7 Mv TQbbB#H2 rBHHBM;M2bb iQ TvX AM 6B;m`2 d r2 b?Qr i 2+? TQbbB#H2 `BbF i?`2b?QH/ i?2 T2`7Q`KM+2 i?i bm+? bvbi2K +QmH/ +?B2p2 BM i2`Kb Q7 iQiH +`BK2 `2/m+2/ M/ 2ti` T2QTH2 /2iBM2/ mM/2` i?2 bbmKTiBQM i?i Dm/;2b +QKTHv T2`72+iHv rBi? HH r`MBM;bX

(6B;m`2 d #Qmi ?2`2X)

*QMbBbi2Mi rBi? i?2 T`2pBQmb }M/BM; i?i Dm/;2b `2H2b2 p2`v ?B;? `BbF BM/BpB/mHb- r2 b22 bi22T `2/m+iBQM BM +`BK2 7Q` bKHH BM+`2b2b BM DBHBM;, 7Q` 2tKTH2- R T2`+2Mi;2 TQBMi BM+`2b2 BM /2i2MiBQM `2/m+2b +`BK2 `i2b #v M2`Hv 8WX h?2 +?QB+2 Q7 i?`2b?QH/b Bb- ;BM- MQ`KiBp2 Kii2`X "mi r2 +M ;2i TQi2MiBH +Hm2 7`QK i?2 BKTHB+Bi i?`2b?QH/b Dm/;2b b2i b i?2v BM+`2b2 H2MB2M+v- b r2 br BM 6B;m`2 8X q2 FMQr i?2 T`2/B+i2/ `BbF Q7 i?2 K`;BMH /272M/Mib 7Q` 2+? [mBMiBH2X P7 +Qm`b2 i?2b2 `2 i?2 H;Q`Bi?KǶb T`2/B+iBQMbc r2 /Q MQi FMQr r?i `BbF i?2 Dm/;2 ǳi?Qm;?iǴ i?2v r2`2 `2H2bBM;X A7 Dm/;2b r2`2 mM#Bb2/ BM i?2B` T`2/B+iBQMb- i?2 p2`;2 T`2/B+i2/ `BbF ?2`2 rQmH/ #2 `2bQM#H2 2biBKi2X KQ`2 +QMb2`piBp2 2biBKi2 rQmH/ bbmK2 bQK2 KQmMi Q7 KBb@T`2/B+iBQM QM i?2 T`i Q7 i?2 Dm/;2X aQK2r?i `#Bi``BHv- r2 +H+mHi2 i?2 ir2Miv@}7i? T2`+2MiBH2 Q7 T`2/B+i2/ `BbF Q7 i?2 K`;BMH /272M/Mib 7Q` 2+? [mBMiBH2X h?Bb Bb HBF2Hv HQr2` #QmM/ QM i?2 `BbF i?`2b?QH/ 2+? [mBMiBH2 Q7 Dm/;2b ?/ BM KBM/X h?2b2 H2/ iQ K`;BMH `BbFb Q7 .397- .351- .338 M/ .307 7Q` 2+? Q7 i?2 H2MB2M+v [mBMiBH2běb?QrM b /b?2/ HBM2b BM 6B;m`2 dX q2 +M mb2 i?2b2 /b?2/ HBM2b iQ bBKmHi2 r?i rQmH/ ?TT2M r2`2 i?Bb b72;m`/ iQ #2 BKTH2K2Mi2/ i i?2b2 i?`2b?QH/bX i i?2 b2+QM/ [mBMiBH2 bi`BM;2M+v i?`2b?QH/- r2 rQmH/ BM+`2b2 DBHBM; 2.9 T2`+2Mi;2 TQBMib KQ`2 M/ `2/m+2 +`BK2 #v 11.8 T2`+2MiX 6Q` i?2 Qi?2` [mBMiBH2 i?`2b?QH/b i?2b2 MmK#2`b BMpQHp2 DBHBM; BM+`2b2 Q7 4.4 T2`+2Mi;2 TQBMib M/ +`BK2 /2+`2b2 Q7 16.9Wc DBHBM; BM+`2b2 Q7 5.0 T2`+2Mi;2 TQBMib M/ +`BK2 − /2+`2b2 Q7 18.7Wc M/ DBHBM; BM+`2b2 Q7 6.7 T2`+2Mi;2 TQBMib M/ +`BK2 /2+`2b2 Q7 − 23.4WX h?2b2 `2bmHib HH `2BM7Q`+2 i?i i?Bb TQHB+v +QmH/ +`2i2 bi22T +`BK2 `2/m+iBQMb − 7Q` KQ/2bi DBHBM; BM+`2b2bX

8Xk _2@`MFBM;

P7 +Qm`b2- TQHB+v KF2`b rQmH/ `B;?iHv #2 BMi2`2bi2/ BM iQQHb i?i /Q MQi bBKTHv BM+`2b2 DBHBM;X AM `2@`MFBM;- r2 +M b2i Mv DBH `i2X "mi 2pHmiBM; i?Bb `2@`MFBM; `2[mB`2b KQ`2 K#BiBQmb TQHB+v bBKmHiBQMX q?BH2 i?2`2 Bb MQ T2`72+i bQHmiBQM iQ i?2 b2H2+iBp2 H#2Hb T`Q#H2K- QM2 Q#pBQmb BMBiBH TQbbB#BHBiv Bb iQ BKTmi2, bbB;M i?2 bK2 +`BK2 Qmi+QK2b iQ /272M/Mib i?2 Dm/;2b /2iBM2/ b i?Qb2 Q7 Q#b2`piBQMHHv 2[mBpH2Mi /272M/Mib r?QK

ke i?2 Dm/;2b +imHHv `2H2b2/X h?Bb TT`Q+? ;2M2ì2b bQK2 Q#pBQmb +QM+2`Mb- iQ r?B+? r2 `2im`M #2HQrX hQ 2biBKi2 i?2 H;Q`Bi?KǶb `2H2b2 `mH2 7Q` i?Bb TQHB+v bBKmHiBQM- r2 /BpB/2 Qm` rQ`FBM; bKTH2 BMiQ i`BMBM; U9yWV- BKTmiiBQM U9yWV- M/ i2bi UkyWV b2ibX q2 i`BM QM2 b2i Q7 ;`/B2Mi@#QQbi2/ i`22b QM i?2 i`BMBM; b2i- r?B+? vB2H/b T`2/B+iBQMb Q7 2+? /272M/MiǶb +`BK2 ì2X q2 i?2M `MF@Q`/2` HH /272M/Mib BM i?2 i2bi b2i #v i?Bb T`2/B+i2/ +`BK2 ì2X 6Q` Mv `2H2b2 ì2 x- i?2M- i?2 H;Q`Bi?K bBKTHv `2H2b2b i?2 T`2/B+i#Hv `BbFB2bi 7`+iBQM x Q7 /272M/MibX h?2 +imH +`BK2 ì2b Q7 i?2b2 /272M/Mib Bb i?2M +H+mHi2/X

(6B;m`2 3 #Qmi ?2`2X)

6B;m`2 3 ;`T?b i?2 +`BK2 ì2 Uv@tBbV i?i `2bmHib i 2p2`v TQbbB#H2 i`;2i `2H2b2 ì2 Ut@tBbVX "2+mb2 r2 rQmH/ HBF2 +`BK2 ì2 i?i +M #2 K2MBM;7mHHv +QKT`2/ +`Qbb `2H2b2 ì2b- 7Q` Tm`TQb2b Q7 6B;m`2 3 r2 mb2 i?2 ìBQ Q7 +`BK2b +QKKBii2/ #v `2H2b2/ /272M/Mib iQ i?2 iQiH MmK#2` Q7 /272M/Mib ?2`/ #v i?2 Dm/;2 UMQi Dmbi i?2 MmK#2` `2H2b2/VX A7 i?2 H;Q`Bi?K +?QQb2b iQ `2H2b2 bQK2QM2 i?2 Dm/;2b `2H2b2/- r2 mb2 i?2 +imH Q#b2`p2/ #2?pBQ` Q7 i?2 /272M/MiX A7 i?2 H;Q`Bi?K +?QQb2b iQ `2H2b2 bQK2QM2 i?2 Dm/;2 /2iBM2/- r2 mb2 i?2 BKTmi2/ +`BK2 pHm2X 6B;m`2 3 bm;;2bib i?2`2 +QmH/ #2 bBx#H2 ;BMb BM Qmi+QK2b mM/2` i?2 H;Q`Bi?KǶb `2H2b2 `mH2 `2HiBp2 iQ i?2 Dm/;2bX lM/2` i?2 +m``2Mi Dm/;2 /2+BbBQMb- i?2 Dm/;2b `2H2b2 djXeW Q7 /272M/Mib M/ i?2 +`BK2 ì2 U/2}M2/ ?2`2 b i?2 ìBQ Q7 +`BK2b iQ HH /272M/MibV 2[mHb RRXjWX h?2 +m`p2 b?QrBM; i?2 +`BK2 ì2 pbX `2H2b2 ì2 +QK#BMiBQMb +?B2p2/ #v i?2 H;Q`Bi?KǶb `2H2b2 `mH2 HB2b #2HQr i?Bb TQBMiX "2+mb2 r2 /Q MQi FMQr i?2 miBHBiv 7mM+iBQM Q7 i?2 Dm/;2b Q` bQ+B2iv b r?QH2 BM r2B;?BM; i?2 ;BMb 7`QK +`BK2 `2/m+iBQM p2`bmb `2/m+BM; i?2 DBH TQTmHiBQM- r2 KF2 /QKBMM+2 `;mK2MiX A7 r2 mb2/ i?2 H;Q`Bi?KǶb `2H2b2 `mH2 iQ Ki+? i?2 +m``2Mi `2H2b2 ì2 Q7 i?2 Dm/;2b- r2 rQmH/ #2 #H2 iQ `2/m+2 i?2 +`BK2 ì2 #v k9XdWX Hi2`MiBp2Hv- r2 +QmH/ ?QH/ i?2 +`BK2 ì2 +QMbiMi M/ `2/m+2 i?2 DBH /2i2MiBQM ì2 7`QK keX9W iQ R8X9W- /2+HBM2 Q7 9kXyWX h?Bb TQHB+v bBKmHiBQM bm;;2bib i?2 TQi2MiBH 7Q` H`;2 bQ+BH BKT+i- ;Bp2M i?i i?2 la ?b r2HH Qp2` dyy-yyy T2QTH2 BM DBH i Mv TQBMi BM iBK2X am+? H`;2 ;BMb `2 TQbbB#H2 #2+mb2 i +m``2Mi `2H2b2 ì2b i?2 `BbF Q7 i?2 K`;BMH /272M/Mi Bb biBHH `2HiBp2Hv HQr- b b?QrM BM i?2 #QiiQK TM2H Q7 6B;m`2 3X qBi? Km+? H`;2` `2/m+iBQMb BM i?2 /2i2MiBQM ì2 i?2 `BbF Q7 i?2 K`;BMH /272M/Mi #2;BMb iQ BM+`2b2 `TB/HvX h?2b2 TQi2MiBH ;BMb `2 MQi Dmbi Kii2` Q7 i?2 H;Q`Bi?K #2iBM; bBM;H2 Dm/;2 r?Q b2`p2b M Qmi@bBx2/ +b2HQ/X 6B;m`2 N b?Qrb i?2 `2HiBp2 ;BMb Q7 i?2 H;Q`Bi?K rBi? `2bT2+i iQ `2/m+BM; +`BK2 U?QH/BM; `2H2b2 ì2 +QMbiMiV Q` `2/m+BM; i?2 DBH TQTmHiBQM

kd U?QH/BM; +`BK2 +QMbiMiV 7Q` i?2 k8 Dm/;2b rBi? i?2 H`;2bi +b2HQ/b- `MF@Q`/2`2/ #v +b2HQ/ bBx2X q2 7Q+mb QM i?Bb ;`QmT bQ r2 ?p2 2MQm;? +b2b T2` Dm/;2 iQ 2pHmi2 i?2B` BM/BpB/mH T2`7Q`KM+2c iQ;2i?2` i?2v ++QmMi 7Q` 9dXkW Q7 HH +b2b BM i?2 i2bi b2iX q?BH2 i?2`2 Bb bQK2 p`BiBQM +`Qbb Dm/;2b- i?2 H;Q`Bi?K /QKBMi2b 2+? Dm/;2X

(6B;m`2 N #Qmi ?2`2X)

h?2 KQbi BKTQìMi TQi2MiBH +QM+2`M rBi? i?Bb bBKmHiBQM Bb r?2i?2` i?2 ;BMb `2 bBKTHv ìB7+ib Q7 BKTmiiBQM #BbX aT2+B}+HHv- Dm/;2b b22 7+iQ`b r2 /Q MQiX A7 Dm/;2b mb2 i?Bb T`Bpi2 BM7Q`KiBQM r2HH- i?2M i?Qb2 i?2v `2H2b2 Kv MQi #2 +QKT`#H2 iQ i?Qb2 i?2v /Q MQi- 2p2M +QM/BiBQMH QM Q#b2`p2/ xX *QMbB/2` p2`v bivHBx2/ 2tKTH2X amTTQb2 i?i 7Q` vQmM; /272M/Mib- Dm/;2b b22 ;M; iiiQQb M/ r2 /Q MQi- i?i Dm/;2b FMQr i?Bb ivT2 Q7 iiiQQ Bb ?B;?Hv T`2/B+iBp2 Q7 +`BK2 `BbF- M/ bQ i?2v M2p2` `2H2b2 MvQM2 rBi? iiiQQX h?2 BKTmi2` rQmH/ ii`B#mi2 iQ HH vQmM; T2QTH2 i?2 +`BK2 ì2 Q7 i?Qb2 rBi?Qmi ;M; iiiQQbX h?Bb +QmH/ b2`BQmbHv mM/2`bii2 i?2 BM+`2b2 BM +`BK2 i?i rQmH/ `2bmHi 7`QK `BbF iQQH i?i- 7Q` 2tKTH2- `2H2b2/ HH vQmM; T2QTH2X >Qr2p2`- irQ bBKTH2 #QmM/BM; 2t2`+Bb2b bm;;2bi i?Bb Kv MQi #2 KDQ` T`Q#H2K BM T`+iB+2X 6B`bi- r2 }M/ i?i i?2 `2@`MFBM; ;2ib Km+? Q7 Bib ;BM 7`QK i?2`2 #2BM; KMv ?B;?@`BbF T2QTH2 iQ DBH U ;BM r2 +M K2bm`2 /B`2+iHvV- MQi 7`QK K#BiBQmb bbmKTiBQMb #Qmi i?2`2 #2BM; KMv HQr `BbF T2QTH2 iQ `2H2b2X q2 BHHmbiì2 i?Bb TQBMi BM 6B;m`2 RyX

(6B;m`2 Ry #Qmi ?2`2X)

AM TìB+mH`- MQiB+2 `2@`MFBM;ěr?2M r2 `2 ?QH/BM; i?2 `2H2b2 ì2 +QMbiMiě+M #2 mM/2`biQQ/ b b2i Q7 brTbX q2 +M #2;BM rBi? i?2 `2H2b2/ b2i Q7 i?2 Dm/;2 M/ i?2M iF2 i?2 `BbFB2bi `2H2b2/ T2`bQM M/ brT i?2K 7Q` i?2 H2bi `BbFv DBH2/ T2`bQMX b HQM; b i?2b2 irQ ?p2 /Bz2`2Mi ì2b- r2 +M F22T brTTBM; M/ BKT`Qp2 T2`7Q`KM+2X h?2b2 brTb +M #2 #`QF2M BMiQ irQ /BbiBM+i bi2Tb, UBV DBH ?B;? `BbF /272M/Mi M/ `2H2b2 M p2`;2 +`BK2 `BbF /272M/Mic UBBV `2H2b2 HQr `BbF /272M/Mi M/ DBH M p2`;2 +`BK2 `BbF /272M/MiX q?2M i?2b2 bi2Tb `2 T2`7Q`K2/ #+F@iQ@#+F i?2v `2 i?2 bK2 b brT #mi #v /2+QKTQbBM; i?2K BM i?Bb rv r2 +M /2+QKTQb2 i?2 ;BMb 7`QK i?2 irQ /Bz2`2Mi +iBpBiB2bX h?2 iQT TM2H b?Qrb ?Qr 2+? Q7 i?2b2 bi2Tb bHQrHv KQp2b mb 7`QK i?2 Dm/;2Ƕb +`BK2 ì2 iQ i?2 H;Q`Bi?KǶb +`BK2 ì2X AM i?2 #QiiQK TM2H- i?2 ?2B;?i Q7 2+? #` BM 6B;m`2 Ry /BbTHvb i?2 ;BM 7`QK 2+? bi2TX h?2 `2/ #`b `2 i?2 DBHBM; bi2Tb Ur?B+? /Q MQi `2[mB`2 BKTmiiBQMV M/ i?2 #Hm2 #`b `2 i?2 `2H2b2 bi2Tb Ur?B+? `2[mB`2 BKTmiiBQMVX Ai Bb +H2` 7`QK i?2 #QiiQK TM2H i?i KQbi Q7 i?2 ;BMb +QK2 7`QK i?2 DBHBM; bi2TX AM 7+i- Tìrv i?`Qm;?- i?2 H;Q`Bi?K biìb `2H2bBM; BM/BpB/mHb i?i `2

k3 +QbiHv U?B;?2` i?M p2`;2 `BbFV bBKTHv #2+mb2 i?2`2 `2 biBHH p2`v H`;2 ;BMb iQ #2 ?/ BM DBHBM; ?B;? `BbF BM/BpB/mHbX

(h#H2 8 #Qmi ?2`2X)

h#H2 8 T`2b2Mib [mMiBiiBp2 #QmM/BM; 2t2`+Bb2 i?i 2tKBM2b ?Qr b2MbBiBp2 Qm` TQHB+v b+QTBM; 2t2`+Bb2 Bb iQ Qm` bbmKTiBQMb #Qmi i?2 /Bbi`B#miBQM Q7 +`BK2 `BbF KQM;bi i?2 DBH2/X PM2 i?BM; iQ Q#b2`p2 Bb i?i r2 `2 r2HH +HB#ì2/ rBi?BM i?2 H2MB2Mi Dm/;2Ƕb /iX aQ B7 i TìB+mH` `BbF H2p2H yˆ r2 b22 i?2 KQbi H2MB2Mi Dm/;2 `2H2bBM; i ì2

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PM2 TQi2MiBH +QM+2`M Bb i?i r?2M KFBM; `2H2b2 /2+BbBQMb- Dm/;2b KB;?i ?p2 //BiBQMH Q#D2+iBp2b #2vQM/ i?2 Qmi+QK2 i?2 H;Q`Bi?K Bb T`2/B+iBM;X AM i?Bb +b2 Bi Bb TQbbB#H2 i?2 H;Q`Bi?KǶb `2H2b2 `mH2 /QKBMi2b i?2 Dm/;2b QM T`i Q7 r?i Dm/;2b +`2 #Qmi- #mi T2`?Tb i?2 Dm/;2b /QKBMi2 i?2 H;Q`Bi?K QM Qi?2` BMTmib iQ i?2B` Q#D2+iBp2 7mM+iBQMbX q2 +HH i?Bb +QM+2`M QKBii2/ TvQz #BbX

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MQi?2` //BiBQMH Q#D2+iBp2 Dm/;2b KB;?i ?p2 #2vQM/ ~B;?i `BbF Bb `+BH 2[mBivX 1p2M i?Qm;? r2 /Q MQi KF2 `+2 Q` 2i?MB+Biv pBH#H2 iQ i?2 K+?BM2 H2`MBM; H;Q`Bi?K- Bi 9ePM2 TQi2MiBH +QKTHB+iBQM rBi? HQQFBM; i TQi2MiBH 2z2+ib QM `2@``2bib Bb i?2 TQbbB#BHBiv Q7 ǳ`2TH+2K2MiǴ @ i?i Bb- B7 +`BK2 Bb +QKKBii2/ BM ;`QmTb Q` B7 bQK2QM2 2Hb2 rQmH/ bi2T BM iQ }HH M QTTQìmMBiv iQ +QKKBi +`BK2 DBH2/ /272M/Mi rQmH/ ?p2 +QKKBii2/c b22 7Q` 2tKTH2 i?2 /Bb+mbbBQM BM .QMQ?m2 UkyyNVX hQ i?2 2ti2Mi iQ r?B+? `2TH+2K2Mi Q++m`b- Qm` `2bmHib rBHH Qp2`bii2 i?2 TQi2MiBH ;BMb 7`QK `2/m+iBQMb BM Qi?2` +`BK2b- Hi?Qm;? i?Bb T`Q#H2K b?QmH/ MQi #2 `2H2pMi 7Q` Qm` KBM `2bmHib i?i 7Q+mb QM 6hX M/ iQ i?2 2ti2Mi iQ r?B+? `2TH+2K2Mi Bb M Bbbm2 7Q` Qi?2` BMi2`p2MiBQMb i?i b22F iQ `2/m+2 +`BK2 ì2b- r2 +M biBHH KF2 K2MBM;7mH +QKT`BbQMb #2ir22M i?2 ;BMb 7`QK Qm` #BH iQQH p2`bmb Qi?2` biì2;B2bX

jy Bb TQbbB#H2 i?2 H;Q`Bi?K rBM/b mT mbBM; i?2b2 7+iQ`b BM/p2ì2MiHv @ B7 Qi?2` T`2/B+iQ`b `2 +Q``2Hi2/ rBi? `+2 Q` 2i?MB+BivX h?Bb Bb T2`?Tb i?2 KQbi BKTQìMi +QM+2`M i?i ?b #22M `Bb2/ #v i?2 TQbbB#BHBiv Q7 mbBM; /i@/`Bp2M T`2/B+iBQMb iQ BM7Q`K +`BKBMH DmbiB+2 /2+BbBQMbX b i?2M@iiQ`M2v :2M2`H 1`B+ >QH/2` MQi2/ BM kyR9 bT22+?- ǳr2 M22/ iQ #2 bm`2 i?2 mb2 Q7 ;;`2;i2 /i MHvbBb rQMǶi ?p2 mMBMi2M/2/ +QMb2[m2M+2b-Ǵ +miBQMBM; i?i i?2b2 iQQHb ?p2 i?2 TQi2MiBH iQ ǳ2t+2`#i2 mMr``Mi2/ M/ mMDmbi /BbT`BiB2b i?i `2 H`2/v 7` iQQ +QKKQM BM Qm` +`BKBMH DmbiB+2 bvbi2K M/ BM Qm` bQ+B2ivXǴ9d hQ bQK2 i?Bb Qmi+QK2 Bb 7Q`2;QM2 +QM+HmbBQMc 7Q` 2tKTH2 Hr T`Q72bbQ` "2`M`/ >`+Qmì ?b `;m2/ i?i ǳmbBM; `BbF@bb2bbK2Mi iQQHb Bb ;QBM; iQ bB;MB}+MiHv ;;`pi2 i?2 mM++2Ti#H2 `+BH /BbT`BiB2b BM Qm` +`BKBMH DmbiB+2 bvbi2KǴ U>`+Qmì- kyRy- TX kc b22 HbQ ai`` kyR9VX

(h#H2 d #Qmi ?2`2X) h#H2 d +QKT`2b i?2 T2`7Q`KM+2 Q7 +m``2Mi Dm/;2 /2+BbBQMb iQ /Bz2`2Mi p2`bBQMb Q7 Qm` H;Q`Bi?KX h?2 }`bi `Qr b?Qrb i?2 `+BH +QKTQbBiBQM Q7 i?2 /272M/Mi TQQH b r?QH2X h?2 b2+QM/ `Qr b?Qrb i?2 Qmi+QK2 Q7 +m``2Mi Dm/;2 /2+BbBQMbX i i?2 +m``2Mi `2H2b2 ì2- i?2 +`BK2 ì2 Ui?2 ìBQ Q7 +`BK2b iQ iQiH /272M/MibV2[mHb RRXjW- M/ 33XNW Q7 BMKi2b BM DBH `2 K2K#2`b Q7 KBMQ`Biv `+2 Q` 2i?MB+ ;`QmTbX h?2 b2+QM/ `Qr `2T`Q/m+2b i?2 `2bmHib Q7 Qm` KBM H;Q`Bi?K- r?B+? /Q2b MQi ?p2 ++2bb iQ BM7Q`KiBQM #Qmi /272M/Mi `+2 Q` 2i?MB+BivX b MQi2/ #Qp2- i?2 `2bmHiBM; `2H2b2 `mH2 H2ib mb `2/m+2 +`BK2 #v k9XdW i ;Bp2M `2H2b2 ì2- rBi? DBH TQTmHiBQM i?i rQmH/ im`M Qmi iQ ?p2 #Qmi i?2 bK2 b?`2 KBMQ`Biv b r2 b22 mM/2` +m``2Mi Dm/;2 /2+BbBQMb- 2[mH iQ NyXRWX h?2`2 Bb bHB;?i BM+`2b2 #v 72r T2`+2Mi;2 TQBMib BM i?2 b?`2 Q7 i?2 DBH TQTmHiBQM i?i Bb #H+F- r?B+? Bb KQbiHv Qzb2i #v bKHH /2+HBM2 BM i?2 b?`2 >BbTMB+X "mi i?2b2 `2 p2`v bKHH /Bz2`2M+2b ;Bp2M i?2 bKTHBM; p`B#BHBiv BM Qm` i2bi b2iX h?2 `2KBMBM; `Qrb Q7 h#H2 d b?Qr i?i Bi Bb TQbbB#H2 iQ 2tTHB+BiHv +QMbi`BM i?2 H;Q`Bi?K iQ 2Mbm`2 MQ BM+`2b2 BM `+BH /BbT`BiB2b BM i?2 DBH rBi? p2`v HBiiH2 BKT+i QM i?2 H;Q`Bi?KǶb T2`7Q`KM+2 BM `2/m+BM; +`BK2X 6Q` 2tKTH2 i?2 i?B`/ `Qr b?Qrb r?i ?TT2Mb B7 r2 mb2 Qm` KBM H;Q`Bi?KǶb T`2/B+i2/ `BbF iQ `MF Q`/2` /272M/Mib b2Tì2Hv #v i?2B` `+2 M/ 2i?MB+ ;`QmT Ur?Bi2- #H+F M/ >BbTMB+VX q2 i?2M /2iBM /272M/Mib BM /2b+2M/BM; Q`/2` Q7 `BbF #mi biQT /2iBMBM; #H+F M/ >BbTMB+ /272M/Mib QM+2 r2 ?p2 ?Bi i?2 2t+i MmK#2` Q7 2+? ;`QmT /2iBM2/ #v i?2 Dm/;2b- iQ 2Mbm`2 i?i i?2 KBMQ`Biv +QKTQbBiBQM Q7 i?2 DBH TQTmHiBQM Bb MQ ?B;?2` mM/2` i?2 H;Q`Bi?KǶb `2H2b2 `mH2 +QKT`2/ iQ i?2 Dm/;2bX *QKT`2/ iQ i?2 +`BK2 ;BMb r2 +?B2p2/ mbBM; i?2 H;Q`Bi?KǶb

9d?iiT,ffrrrXDmbiB+2X;QpfQTfbT22+?fiiQ`M2v@;2M2`H@2`B+@?QH/2`@bT2Fb@MiBQMH@bbQ+BiBQM@+`BKBMH@/272Mb2@Hrv2`b@ 8di?

jR mbmH `MFBM;@M/@`2H2b2 `mH2- 2Mbm`BM; i?i r2 /Q MQ rQ`b2 i?M Ki+?BM; i?2 Dm/;2b QM `+BH /BbT`BiB2b BM i?2 DBH TQTmHiBQM H2/b iQ HKQbi MQ HQbb BM i2`Kb Q7 i?2 TQi2MiBH ;BM BM `2/m+2/ +`BK2X h?2 b2+QM/@iQ@Hbi `Qr b?Qrb r?i ?TT2Mb B7 r2 +QMbi`BM i?2 H;Q`Bi?K iQ #2 `+2 M2mi`H Ui?i Bb- iQ 2Mbm`2 i?2 b?`2 Q7 2+? KBMQ`Biv ;`QmT BM i?2 DBH TQTmHiBQM Bb MQ ?B;?2` i?M i?2B` b?`2 rBi?BM i?2 ;2M2`H TQQH Q7 /272M/MibVX h?2 }MH `Qr ;Q2b QM2 bi2T 7m`i?2` M/ +QMbi`BMb i?2 H;Q`Bi?K iQ 2Mbm`2 i?i i?2 b?`2 Q7 i?2 DBH TQTmHiBQM i?i Bb 2Bi?2` #H+F Q` >BbTMB+ Bb MQ ?B;?2` i?M 2Bi?2` i?2 b?`2 i?2 Dm/;2 DBHb Q` i?2 b?`2 rBi?BM i?2 ;2M2`H /272M/Mi TQQHX AM #Qi? +b2b r2 b22 i?i Bi Bb TQbbB#H2 iQ `2/m+2 i?2 b?`2 Q7 i?2 DBH TQTmHiBQM i?i Bb KBMQ`Biv @ i?i Bb- `2/m+2 `+BH /BbT`BiB2b rBi?BM i?2 +m``2Mi +`BKBMH DmbiB+2 bvbi2K @ r?BH2 bBKmHiM2QmbHv `2/m+BM; +`BK2 `i2b `2HiBp2 iQ i?2 Dm/;2X eXRXj PKBii2/ SvQz "Bb, am;;2biBp2 1pB/2M+2 7`QK S?BH/2HT?B

P7 +Qm`b2 BM T`BM+BTH2 i?2`2 +QmH/ #2 Qi?2` Qmi+QK2b Dm/;2b +`2 #Qmi b r2HH #2vQM/ i?Qb2 r2 ?p2 +QMbB/2`2/ ?2`2X 6Q` 2tKTH2- r?BH2 i?2 Hr bFb Dm/;2b iQ 7Q+mb QM +`BK2 `BbF- M/ iQ QMHv +QMbB/2` 7+iQ`b bm+? b 2KTHQvK2Mi Q` 7KBHv +B`+mKbiM+2b b i?2v Kv `2Hi2 iQ i?2 T`2/B+iBQM Q7 i?i `BbF- Bi Bb TQbbB#H2 i?i bQK2 Dm/;2b MQM2i?2H2bb iF2 bQK2 +QMbB/2`iBQM Q7 i?2b2 7+iQ`b BM KFBM; `2H2b2 /2+BbBQMb #Qp2 M/ #2vQM/ i?2B` BKT+i QM `BbFX q2 +MMQi /B`2+iHv 2tKBM2 i?Bb BM Qm` QrM MHvbBb #2+mb2 i?2 /i r2 ?p2 pBH#H2 iQ mb /Q2b MQi K2bm`2 2KTHQvK2Mi Q` 7KBHv biimbX LQM2i?2H2bb r2 +M +QMbi`m+i M BM/B`2+i i2bi 7Q` i?2 TQbbB#BHBiv Q7 Qi?2` mMK2bm`2/ Dm/;2 Q#D2+iBp2bX A7 H;Q`Bi?KB+ T`2/B+iBQM `mH2b r2`2 7BHBM; QM i?2b2 Qi?2` /BK2MbBQMb HBF2 DQ# Q` 7KBHv biimb- i?2M QM2 rQmH/ 2tT2+i i?i r?2M T`2b2Mi2/ rBi? `mH2b bm+? b i?2b2- Dm/;2b r?Q r2`2 H`2/v QTiBKBxBM; rQmH/ MQi KF2 mb2 Q7 i?2KX h?2 T2`72+i i2bi Q7 i?Bb ?vTQi?2bBb +QK2b 7`QK i?2 RN3R S?BH/2HT?B #BH 2tT2`BK2Mi U:QH/FKT M/ :Qii7`2/bQM- RN39- RN38-#V- r?B+? 2M`QHH2/ Re Dm/;2b M/ `M/QKHv bbB;M2/ ?H7 iQ `2+2Bp2 #BH ;mB/2HBM2b #b2/ QM H;Q`Bi?KB+ T`2/B+iBQMb #Qmi HBF2HB?QQ/ Q7 7BHm`2 UHBF2 `2@``2biVX iQiH Q7 R-Nky +b2b r2`2 ?M/H2/ #v i?2b2 Dm/;2bX h?2 H;Q`Bi?K rb MQi /2`Bp2/ 7`QK K+?BM2 H2`MBM; i2+?MB[m2b- #mi MQM2i?2H2bb H2ib mb i2bi r?2i?2` Dm/;2b `2bTQM/ iQ i?2b2 M2r `BbF T`2/B+iBQMbX

(6B;m`2 RR #Qmi ?2`2X)

6B;m`2 RR b?Qrb i?i `2+2BTi Q7 i?2 H;Q`Bi?KB+ T`2/B+iBQMb /Q2b BM/22/ +?M;2 Dm/;2 #2?pBQ`X h?2 b?`2 Q7 Dm/;2 /2+BbBQMb i?i +QKTHv rBi? i?2 `BbF iQQHǶb `2+QKK2M/iBQMb

jk Bb Km+? ?B;?2` 7Q` i?2 i`2iK2Mi i?M +QMi`QH ;`QmTX h?Bb Bb BM+QMbBbi2Mi rBi? i?2 Dm/;2b BMBiBHHv QTiBKBxBM;X93 eXk CBH M/ +b2HQ/ +QMbi`BMib h?2 T`2pBQmb bm#@b2+iBQM 2tKBM2/ i?2 TQbbB#BHBiv i?i Dm/;2b ?p2 /Bz2`2Mi T`272`2M+2b 7`QK i?2 Qmi+QK2 i?2 H;Q`Bi?K Bb T`2/B+iBM;X M Hi2`MiBp2 TQbbB#BHBiv Bb i?2 H;Q`Bi?K QMHv b22Kb iQ vB2H/ BKT`Qp2/ Qmi+QK2b `2HiBp2 iQ Dm/;2b #2+mb2 i?2 H;Q`Bi?K B;MQ`2b bQK2 +QMbi`BMib i?i #BM/ i?2 Dm/;2Ƕb /2+BbBQMbX 6Q` 2tKTH2- QM2 TìB+mH`Hv BKTQìMi +QMbi`BMi i?2 Dm/;2 Kv 7+2 Bb rBi? `2bT2+i iQ DBH +T+BivX h?Bb +QmH/ T`2p2Mi i?2 Dm/;2 U#mi MQi i?2 K+?BM2 H2`M2`V 7`QK TmiiBM; ?B;?@`BbF T2QTH2 BM DBH /m`BM; iBK2b r?2M i?2 HQ+H DBH Bb }HH2/ mTX9NX h#H2 3 b?Qrb i?i 2p2M 7i2` ++QmMiBM; 7Q` i?Bb +QM+2`M- r2 +QMiBMm2 iQ b22 H`;2 TQi2MiBH bQ+BH@r2H7`2 ;BMb 7`QK `2H2bBM; /272M/Mib mbBM; K+?BM2 ì?2` i?M Dm/;2 T`2/B+iBQMbX q2 `2@i`BM Qm` H;Q`Bi?K BM i?2 Lu* /i- #mi MQr +QMbi`BMBM; i?2 H;Q@ `Bi?K iQ ?p2 i?2 bK2 `2H2b2 ì2 b r?i r2 b22 Qp2` 2+? i?`22 KQMi? rBM/Qr BM L2r uQ`F *Biv b r?QH2X h?2 `2bmHib `2 p2`v bBKBH` iQ r?i r2 b22 BM Qm` KBM MHvbBb BM i2`Kb Q7 2Bi?2` i?2 p2`;2 +`BK2 ì2 Q7 i?2 T`2/B+i#Hv@`BbFB2bi RW i?i i?2 H;Q`Bi?K +M B/2MiB7v KQM; i?2 Dm/;2Ƕb `2H2b2/ b2i- Q` BM i2`Kb Q7 i?2 TQi2MiBH ;BMb 7`QK i?2 `2@`MFBM; TQHB+v bBKmHiBQMX h?2 bK2 }M/BM; ?QH/b B7 r2 +QMbi`BM i?2 H;Q`Bi?K iQ MQi 2t+22/ i?2 `2H2b2 ì2 Q#b2`p2/ rBi?BM 2+? [mì2`@v2`- bT2+B}+ iQ i?2 L2r uQ`F *Biv #Q`Qm;? BM r?B+? 2+? +b2 Bb #2BM; ?2`/X

(h#H2 3 #Qmi ?2`2X) eXj H;Q`Bi?K UBMVbi#BHBiv\

/Bz2`2Mi TQi2MiBH +QM+2`M Bb i?i Qm` MHvbBb Qp2`bii2b i?2 TQi2MiBH ;BMb Q7 i?2 H;Q`Bi?K `2HiBp2 iQ i?2 Dm/;2b #2+mb2 i?2 H;Q`Bi?K Bb mMbi#H2 @ i?i Bb- +?M;BM; Qp2` iBK2 BM rvb i?i ii2Mmi2 i?2 TQi2MiBH ;BMb Q7 i?2 H;Q`Bi?K `2HiBp2 iQ i?2 Dm/;2

93JQ`2 bT2+B}+HHv- 2tTQbm`2 iQ i?2 H;Q`Bi?K +mb2b Dm/;2b iQ BM+`2b2 T`2@i`BH `2H2b2 ì2b KQM; i?2 HQr2bi@`BbF Qz2M/2`b Ui?Qb2 ``2bi2/ 7Q` i?2 H2bi b2`BQmb Qz2Mb2bV M/ `2/m+2 `2H2b2 ì2b KQM; i?2 ?B;?2bi@`BbF /272M/Mib @ 2t+iHv b r2 rQmH/ T`2/B+i B7 Dm/;2b ?/ BMBiBHHv KBb@T`2/B+i2/ 7BHm`2 `BbF KQM; /272M/Mib Ub22- 7Q` 2tKTH2- :QH/FKT M/ :Qii7`2/bQM- RN39- h#H2 9X9c b22 HbQ #`Kb M/ _Q?H7b- kyRRVX 9N bBKTH2 bivHBx2/ 2tKTH2 ?2HTb BHHmbiì2 i?2 TQBMiX amTTQb2 i?i QM /v R i?2 HQ+H DBH Bb i RyyW +T+Biv r?BH2 QM /v k i?2 DBH Bb i 8yW +T+BivX amTTQb2 i?2 HQ+H Dm/;2 rBb?2b iQ `2H2b2 8yW Q7 /272M/Mib 2+? /vX AM T`+iB+2 i?Bb Dm/;2 rQmH/ `2H2b2 RyyW Q7 /272M/Mib i i?2B` /v R #QM/ +Qmì #2+mb2 Q7 i?2 DBH +T+Biv +QMbi`BMib- BM+Hm/BM; KMv ?B;?@`BbF /272M/Mib i?2 Dm/;2 rBb?2b i?2v +QmH/ ?p2 /2iBM2/ B7 i?2 DBH ?/ `QQKX A7 i?2 MmK#2` Q7 +b2b Bb i?2 bK2 /v #v /v r2 rQmH/ ii`B#mi2 iQ i?2 Dm/;2 M Qp2`HH `2H2b2 ì2 Q7 d8W- M/ bQ ?p2 i?2 K+?BM2 H2`M2` B/2MiB7v i?2 HQr2bi@`BbF d8W Q7 +b2b 2+? /v M/ ǳ`2H2b2Ǵ i?2K @ 2p2M i?Qm;? BM T`+iB+2 i?Bb rQmH/ MQi ?p2 #22M TQbbB#H2 QM /v R BM Qm` 2tKTH2

jj /2+BbBQMbX h?Bb +QmH/ H2/ mb iQ Qp2`@bii2 i?2 TQi2MiBH ;BMb BM i?2 7mim`2 7`QK /QTiBM; M H;Q`Bi?KB+ `2H2b2 `mH2- bBM+2 bQ 7` r2 ?p2 #22M +QKT`BM; i?2 `2HiBp2 T2`7Q`KM+2 Q7 i?2 H;Q`Bi?K iQ i?2 Dm/;2b p2`;2/ Qp2` Qm` 2MiB`2 bKTH2 T2`BQ/X u2i b b?QrM BM h#H2 3 i?2`2 `2 MQ bB;Mb i?i Qm` H;Q`Bi?K Bb T`iB+mH`Hv mMbi#H2X hQ +?2+F i?Bb- r2 `2@i`BM i?2 H;Q`Bi?K mbBM; Dmbi /i 7`QK i?2 }`bi 72r v2`b Q7 Qm` bKTH2 T2`BQ/ Ukyy3 i?`Qm;? kyRkVX AMbi2/ Q7 2pHmiBM; i?2 H;Q`Bi?KǶb T2`7Q`KM+2 QM `M/QKHv@b2H2+i2/ b2i Q7 +b2b /`rM 7`QK i?2 bK2 iBK2 T2`BQ/ Qp2` r?B+? i?2 H;Q`Bi?K rb i`BM2/- r2 MQr 2pHmi2 i?2 H;Q`Bi?K mbBM; /i 7`QK i?2 }`bi }p2 KQMi?b Q7 /i BM kyRjX8y h?2 ;BMb 7`QK `2HvBM; QM i?2 H;Q`Bi?KǶb T`2/B+iBQMb `i?2` i?M +m``2Mi Dm/;2 /2+BbBQMb `2- B7 Mvi?BM;- 2p2M bi`QM;2` r?2M r2 T`2/B+i Qmi Qp2` iBK2 +QKT`2/ iQ r?i r2 b22 BM Qm` KBM MHvb2bX eX9 lM/2`biM/BM; Dm/;2 KBb@T`2/B+iBQM h?2 T`2pBQmb `2bmHib bm;;2bib i?i Dm/;2b `2 KBb@T`2/B+iBM;X q2 MQr ii2KTi iQ mM/2`@ biM/ r?v i?2v `2 KBb@T`2/B+iBM;X h?Bb 2t2`+Bb2 +M ?2HT b?2/ HB;?i BMiQ r?i Dm/;2b `2 ;2iiBM; r`QM;- M/ KQ`2 ;2M2`HHv ?B;?HB;?ib i?2 TQi2MiBH Q7 K+?BM2 H2`MBM; iQQHb iQ ?2HT i2bi i?2Q`B2b Q7 ?mKM /2+BbBQM@KFBM; M/ #2?pBQ`- MQi Dmbi bQHp2 TQHB+v T`Q#H2KbX eX9XR q?B+? +b2b `2 ?`/\

6Q` bi`i2`b r2 +M `2pBbBi r?2`2 BM i?2 `BbF /Bbi`B#miBQM Dm/;2b `2 ?pBM; i?2 KQbi i`Qm#H2X q?BH2 2t Mi2 i?2 Mbr2` Bb MQi Q#pBQmb- HQQFBM; i Qi?2` /QKBMb +M T`QpB/2 mb rBi? bQK2 BMBiBH BMimBiBQM #Qmi r?i r2 KB;?i ?p2 2tT2+i2/X 6Q` 2tKTH2 BM 2/m+iBQM- bim/B2b }M/ i?i T`BM+BTHb /Q ;QQ/ DQ# B/2MiB7vBM; r?B+? i2+?2`b `2 BM i?2 iBHb Q7 i?2 T2`7Q`KM+2 /Bbi`B#miBQM @ i?2 p2`v ?B;? T2`7Q`K2`b M/ i?2 p2`v HQr T2`7Q`K2`b@ #mi ?p2 ?`/ iBK2 /BbiBM;mBb?BM; KQM; i2+?2`b BM i?2 KB//H2 Q7 i?2 /Bbi`B#miBQM UC+Q# M/ G27;`2M- kyy3VX b r2 rBHH b22- i?2 `2bmHib 7Q` Dm/B+BH /2+BbBQMb BM Qm` /i ;Q ;BMbi i?Bb BMimBiBQMX q2 +M 2tKBM2 i?Bb [m2biBQM BM Qm` /i #v BMp2biB;iBM; r?2`2 BM i?2 T`2/B+i2/@`BbF /Bbi`B#miBQM Dm/;2b ?p2 i?2 KQbi mM+2`iBMivX q?i r2 Q#b2`p2 Bb Dmbi #BM`v BM/B+iQ`

Q7 r?2i?2` i?2 Dm/;2b `2H2b2/ ;Bp2M /272M/Mi i- Q` R(h(xi,zi)) = Ri- r?B+? +MMQi +QMp2v Km+? #Qmi r?2M Dm/;2b `2 KQbi mM+2`iBMX >Qr2p2` r2 +M H2`M KQ`2 #Qmi i?Bb #v T`2/B+iBM; i?2 #2?pBQ` Q7 i?2 Dm/;2bX h?i Bb- r2 +M i`BM M2r H;Q`Bi?K iQ

8yb `2KBM/2`- r2 ?p2 iF2M Qmi i?2 /i 7`QK Jv i?`Qm;? LQp2K#2` kyRj 7Q` Qm` }MH ?QH/@Qmi b2i bQ i?2 }`bi T`i Q7 kyRj `2 i?2 Hi2bi Q#b2`piBQMb pBH#H2 BM Qm` rQ`FBM; /ib2iX

j9 T`2/B+i MQi i?2 #2?pBQ` Q7 i?2 /272M/Mib- #mi i?2 #2?pBQ` Q7 i?2 Dm/;2b- iQ +`2i2

T`2/B+i2/ p2`bBQM Q7 i?2 Dm/;2 Jˆ(xi)X

(6B;m`2 Rk #Qmi ?2`2X)

AM 6B;m`2 Rk r2 bQ`i HH /272M/Mib BM Qm` i2bi b2i BMiQ [mBMiBH2b #b2/ QM i?2 H;Q`Bi?KǶb

T`2/B+i2/ `BbF Q7 +`BK2- m(xi)- b b?QrM HQM; i?2 t@tBbX h?2M 7Q` 2+? [mBMiBH2 Q7 T`2@ /B+i2/ /272M/Mi `BbF- r2 b?Qr i?2 /Bbi`B#miBQM Q7 i?2 T`2/B+i2/ Dm/;2 DBHBM; T`Q##BHBiB2b-

Jˆ(xi)X //BiBQMHHv- r2 +QHQ` 2+? bHB+2 Q7 i?2 /Bbi`B#miBQM #v i?2 +imH DBHBM; ì2 BM i?i bHB+2X q2 b22 7`QK i?Bb i?i BM 2+? [mBMiBH2 Q7 `BbF- i?Qb2 rBi? ?B;?2bi T`2/B+i2/ DBHBM; ì2b `2 BM 7+i DBH2/ KQ`2, Qm` T`2/B+iBQMb Q7 i?2 Dm/;2 ?p2 bQK2 T`2/B+iBp2 TQr2`X JQ`2 BKTQìMiHv- r2 +M HbQ b22 BM 6B;m`2 Rk i?i +b2b BM i?2 HQr2bi@`BbF [mBMiBH2b ?p2 MQi QMHv HQr T`2/B+i2/ DBHBM; T`Q##BHBiv- #mi HbQ ?p2 [mBi2 +QKT+i /Bbi`B#miBQM Q7 T`2/B+i2/ T`Q##BHBivX h?2b2 +b2b TT2` `2HiBp2Hv 2bv @ Q` i H2bi Dm/;2b #2?p2 +QMbBbi2MiHvX AM +QMi`bi- i?2`2 Bb bm#biMiBH /BbT2`bBQM BM T`2/B+i2/ DBHBM; T`Q##BHBiB2b 7Q` i?2 ?B;?2bi@`BbF +b2bc bQK2 ?B;?@`BbF /272M/Mib ?p2 ?B;? DBHBM; T`Q##BHBiB2b r?BH2 Qi?2` +b2b rBi? bBKBH`Hv ?B;? `BbF ?p2 HQr T`Q##BHBiB2b Q7 DBHěi?i Bb- i?2v `2 i`2i2/ b B7 i?2v `2 HQr `BbFX h?mb- BM +QMi`bi iQ r?i r2 KB;?i ?p2 2tT2+i2/- Dm/;2b BM i?Bb +b2 /Q MQi b22K iQ bi`m;;H2 KQbi rBi? i?2 KB//H2 M/ }M/ i?2 iBHb i?2 2bB2biX AMbi2/ i?2v b22K iQ bi`m;;H2 KQbi rBi? QM2 iBH @ i?2 ?B;? `BbF +b2bX eX9Xk LQBbv T`2/B+iBQMb

Pm` T`2/B+iBQM Q7 i?2 Dm/;2Ƕb `2H2b2 /2+BbBQMb +M HbQ ;Bp2 mb bQK2 b2Mb2 7Q` r?v Dm/;2b KB;?i #2 ?pBM; i?Bb i`Qm#H2X _2+HH r2 /2MQi2/ Dm/;2 T`2/B+iBQMb Q7 /272M/Mi +`BK2 `BbF

b h(xi,zi)- r?B+? Bb 7mM+iBQM Q7 #Qi? Q#b2`p#H2b xi UHBF2 +`BKBMH `2+Q`/V M/ 7+iQ`b zi MQi Q#b2`p#H2 iQ i?2 H;Q`Bi?K UHBF2 i?2 /272M/MiǶb /2K2MQ` BM i?2 +Qmì`QQKVX h?2 #2?pBQ`H b+B2M+2 HBi2ìm`2 bm;;2bib i?i i?Bb 2ti` BM7Q`KiBQM +QmH/ #2 Tì Q7 i?2 T`Q#H2K M/ Kv #2 i?2 `2bQM Dm/;2b /Q TQQ`Hv `2HiBp2 iQ i?2 H;Q`Bi?KX 6Q` 2tKTH2- bQK2 bim/B2b bm;;2bi i?i ?B;?Hv bHB2Mi BMi2`T2`bQMH BM7Q`KiBQM Ubm+? b i?2 /2;`22 Q7 2v2 +QMi+i i?i Bb K/2V +M #2 Qp2`@r2B;?i2/c M/ i?i H2bb bHB2Mi #mi KQ`2 BM7Q`KiBp2 /i UHBF2 Tbi #2?pBQ`bV +M #2 mM/2`@r2B;?i2/X A7 z Bb //BM; mb27mH bB;MH iQ Dm/;2b BM ?2HTBM; i?2K T`2/B+i /272M/Mi `BbF BM Qm` #BH TTHB+iBQM- i?2M h(x ,z) b?QmH/ #2 #2ii2` T`2/B+iQ` i?M hˆ(x)=E[h(x, z) x]X A7 i i | z bBKTHv //b MQBb2 i?2M i?2 `2p2`b2 b?QmH/ #2 i`m2X q?BH2 r2 /Q MQi Q#b2`p2 h(xi,zi)- r2 /Q Q#b2`p2 R(h(xi,zi)) b r2HH b Qm` T`2/B+iBQM Q7 i?2 Dm/;2Ƕb `2H2b2 /2+BbBQM- Jˆ(xi)X

j8 LQiB+2 i?i BM KFBM; i?Bb T`2/B+iBQM r2 M2p2` mb2 /i QM +`BK2X aQ B7 i?2 T`2/B+i2/ Dm/;2 #2ib i?2 Dm/;2- Bi Kmbi QMHv #2 #2+mb2 i?2 Dm/;2 Bb KBbmbBM; UQM p2`;2V i?2 mMQ#b2`p2/ z p`B#H2bX AM 2bb2M+2- r2 rQmH/ HBF2 iQ +QKT`2 i?2 Dm/;2 iQ i?2 T`2/B+i2/ Dm/;2X q2 rBHH /Q i?Bb BM i?2 bK2 rv r2 +QKT`2/ BM a2+iBQM 9Xk i?2 Dm/;2 iQ i?2 H;Q`Bi?KX b #27Q`2- r2 #2;BM rBi? i?2 b2i Q7 +b2b `2H2b2/ #v i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2bX q2 i?2M DBH //BiBQMH /272M/Mib b r2 T`2/B+i i?2 Dm/;2b rQmH/ @ DBHBM; }`bi i?Qb2 /272M/Mib rBi? i?2 ?B;?2bi T`2/B+i2/ T`Q##BHBiv Q7 Dm/;2b DBHBM; i?2KX AM Qi?2` rQ`/b- r2 #2;BM #v DBHBM; i?Qb2 /272M/Mib r?Q `2 `2H2b2/ #mi r?QK r2 T`2/B+i2/ ?p2 i?2 ?B;?2bi T`Q##BHBiv Q7 #2BM; DBH2/ #v i?2 Dm/;2bX Uh?2 /Bz2`2M+2 rBi? Qm` T`2pBQmb +QKT`BbQM iQ i?2 Dm/;2b Bb i?i r2 ?/ 2`HB2` DBH2/ /272M/Mib #v i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbFXV

(6B;m`2 Rj #Qmi ?2`2X)

6B;m`2 Rj THQib i?2 `2bmHib Q7 i?Bb 2t2`+Bb2X q2 THQi T2`7Q`KM+2 Q7 Dm/;2b BM 2+? H2MB2M+v [mBMiBH2X q2 i?2M b?Qr r?i +`BK2 `i2 i?i rQmH/ `2bmHi B7 r2 DBH2/ b i?2 T`2/B+i2/ Dm/;2 rQmH/X q2 HbQ BM+Hm/2 7Q` +QKT`BbQM ?2`2 r?i rQmH/ ?TT2M B7 r2 DBH2/ ++Q`/BM; iQ T`2/B+i2/ +`BK2X q2 b22 ?2`2 +H2`Hv i?i i?2 T`2/B+i2/ Dm/;2 /Q2b #2ii2` i?M Dm/;2b i?2Kb2Hp2bX AM 7+i- bBKTHv DBHBM; ++Q`/BM; iQ Jˆ ;2ib mb `Qm;?Hv ?H7rv iQr`/b i?2 ;BM r2 ?/ 7`QK DBHBM; ++Q`/BM; iQ T`2/B+i2/ `BbFX

(h#H2 N #Qmi ?2`2X)

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8Rq2 ?p2 HbQ /QM2 i?2 `2@`MFBM; TQHB+v bBKmHiBQM mbBM; Jˆ BMbi2/ Q7 T`2/B+i2/ `BbF b #27Q`2X h?Bb T`Q/m+2b bBKBH` `2bmHib iQ r?i r2 `2TQ`i ?2`2, i?2 T`2/B+i2/ Dm/;2 /Q2b #2ii2` i?M i?2 Dm/;2 #mi MQi b r2HH b i?2 H;Q`Bi?K /2bB;M2/ iQ T`2/B+i `BbFX

je KQ`2 7B`Hv +QKT`2 Dm/;2b iQ T`2/B+i2/ p2`bBQMb Q7 i?2Kb2Hp2b- r2 #mBHi M2r b2i Q7 BM/BpB/mi2/ H;Q`Bi?Kb 2+? Q7 r?B+? Bb i`BM2/ QM bBM;H2 Dm/;2Ƕb +b2HQ/X8k q2 +M i?2M mb2 Mv QM2 Q7 i?2b2 BM/BpB/mH T`2/B+i2/ Dm/;2b iQ +QMi`+i /QrM i?2 `2H2b2/ b2i Q7 i?2 KQbi H2MB2Mi@[mBMiBH2 Dm/;2bǶ +b2HQ/ b BM 6B;m`2 8X AM 6B;m`2 R9- r2 b?Qr ?Qr 2+? Q7 i?2b2 BM/BpB/mH Jˆ QmiT2`7Q`Kb i?2 /2+BbBQMb Q7 +imH Dm/;2bX

(6B;m`2 R9 #Qmi ?2`2X)

Pm` `2bmHib iF2M iQ;2i?2` bm;;2bib QM2 `2bQM r?v Dm/;2 `2H2b2 /2+BbBQMb +M #2 BKT`Qp2/ mTQM, h?2B` +imH /2+BbBQMb `2 MQBbv `2HiBp2 iQ K2M (Jˆ) i?i +QMiBMb Km+? KQ`2 bB;MHX AM T`iB+mH`- i?Bb ǳMQBb2Ǵ TT2`b iQ #2 /m2 iQ mMQ#b2`p#H2 p`B#H2b- r?B+? mM/mHv BM~m2M+2 i?2b2 /2+BbBQMbX eX9Xj _2H2b2 pbX #BH KQmMi

6BMHHv- i?2`2 Bb [m2biBQM Q7 r?i 2t+iHv Dm/;2b `2 KBb@T`2/B+iBM;X aQ 7` BM Qm` MHvbBb r2 ?p2 K/2 i?2 bBKTHB7vBM; bbmKTiBQM i?i Dm/;2b `2H2b2 Q` DBH- r?2M BM 7+i i?2v b2i #BH KQmMi b r2HHX Ai Bb HQ;B+HHv TQbbB#H2 i?i BM i?2 `2bmHib r2 T`2b2Mi2/ #Qp2- i?2 Dm/;2 +imHHv BMi2M/2/ iQ DBH ?B;?@`BbF T2QTH2 #mi bBKTHv KBb@T`2/B+i2/ r?i #BH KQmMi i?2v rQmH/ #2 #H2 iQ KF2 M/ bbB;M2/ i?2K #BH KQmMib i?i r2`2 ǵiQQ HQrXǶ Smi /Bz2`2MiHv- Bi Bb TQbbB#H2 i?i Dm/;2b `2 +imHHv KBb@T`2/B+iBM; ǵ#BHBiv iQ TvǶ ì?2` i?M `BbFX hQ 2tKBM2 i?Bb TQbbB#BHBiv r2 +M 2tKBM2 i?2 /2;`22 Q7 T`2/B+i#H2 `BbF r2 }M/ KQM; /272M/Mib i?2 Dm/;2b `2H2b2 Qmi`B;?i @ i?i Bb- T2QTH2 i?2 Dm/;2b bbB;M iQ `2H2b2 QM `2+Q;MBxM+2 U_P_VX 6Q` i?Bb ;`QmT i?2`2 Bb MQ TQbbB#BHBiv Q7 KBb@T`2/B+iBM; #BHBiv iQ Tv- bBM+2 i?2`2 Bb MQ #BH KQmMi i?i Bb `2[mB`2/ 7Q` `2H2b2c T2QTH2 `2 bBKTHv `2H2b2/ rBi?Qmi Mv `2[mB`2K2Mi Q7 +b? Q` Qi?2` +QHHi2`HX q2 b22 i?i 2p2M KQM; i?2 b2i Q7 T2QTH2 i?2 Dm/;2b `2H2b2/ Qmi`B;?i U_P_Ƕ/V- i?2`2 `2 T2QTH2 rBi? ?B;? ì2b Q7 T`2/B+i#H2 `BbF, i?2 +`BK2 ì2 7Q` i?2 `BbFB2bi RW Q7 /272M/Mib `2H2b2/ Qmi`B;?i #v i?2 Dm/;2 Bb bBKBH` iQ r?i r2 b22 KQM; i?2 7mHH `2H2b2/ b2i Uy¯ =59.2W p2`bmb y¯ =56.3WVX8j

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jd d LiBQMH `2THB+iBQM

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99 6B;m`2 k, Pmi+QK2b 7Q` i?2 _2Hb2/ _MF2/ #v S`2/B+i2/ _BbF

LQi2b, h?2 };m`2 #Qp2 b?Qrb i?2 `2bmHib Q7 M H;Q`Bi?K #mBHi mbBM; kkR-3de Q#b2`piBQMb BM Qm` Lu* i`BMBM; b2i- TTHB2/ iQ i?2 RRy-Nj3 Q#b2`piBQMb BM Qm` i2bi b2i Ub22 6B;m`2 RVX q2 `2TQì i?2 Q#b2`p2/ Dm/;2Ƕb `2H2b2 ì2 Uv@tBbV ;BMbi #Qi? i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbF 7Q` 2+? Q#b2`piBQM M/ i?2 Q#b2`p2/ +`BK2 ì2 UQ#b2`p2/ QMHv 7Q` i?Qb2 /272M/Mib BM i?2 i2bi b2i `2H2b2/ #v i?2 Dm/;2bV 7Q` R-yyy #BMb bQì2/ #v T`2/B+i2/ `BbFX h?2 +QHQ`BM; b?Qrb b?`2 Q#b2`piBQMb BM 2+? #BM rBi? T`BQ` 7BHm`2 iQ TT2`X h?2 #QiiQK M/ #+F TM2Hb b?Qr i?2 T`QD2+iBQM Q7 i?2 };m`2 QMiQ i?2 irQ /BK2MbBQMH T`2/B+i2/ +`BK2 `BbF- Q#b2`p2/ +`BK2 ì2 bT+2 M/ i?2 T`2/B+i2/ +`BK2 `BbF-Dm/;2 { } { `2H2b2 ì2 bT+2X }

98 6B;m`2 j, q?Q Bb CBH2/ b Cm/;2b "2+QK2 JQ`2 ai`BM;2Mi\

LQi2b, h?2 #` BM i?2 KB//H2 Q7 i?2 };m`2 b?Qrb r?Q i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2b DBH UiQTV M/ `2H2b2 U#QiiQKV BM Qm` Lu* /ib2iX h?2 +QHQ` b?/BM; b?Qrb i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbFX h?2 #` i i?2 `B;?i b?Qrb ?Qr i?2 kM/ KQbi H2MB2Mi [mBMiBH2 Dm/;2b BKTHB+BiHv b2H2+i i?2B` K`;BMH /2iBM22b iQ ;2i 7`QK i?2 KQbi H2MB2Mi [mBMiBH2Ƕb `2H2b2 ì2 /QrM iQ i?2B` QrM `2H2b2 ì2X h?2 ``Qrb b?Qr r?2`2 rBi?BM i?2 `BbF /Bbi`B#miBQM Q7 i?2 H2MB2Mi [mBMiBH2Ƕb `2H2b2/ b2i i?2 bi`B+i2` Dm/;2b `2 b2H2+iBM; i?2 K`;BMH /2iBM22bX h?2 #` i i?2 H27i b?Qrb ?Qr i?2 H;Q`Bi?K rQmH/ b2H2+i K`;BMH /2iBM22b iQ +?B2p2 i?2 bK2 `2/m+iBQM BM `2H2b2 ì2X

9e 6B;m`2 9, q?Q /Q ai`B+i2` Cm/;2b CBH\ S`2/B+i2/ _BbF Q7 J`;BMH .272M/Mib

LQi2b, h?Bb };m`2 b?Qrb r?2`2 2+? Q7 i?2 [mBMiBH2b Q7 bi`B+i2` Dm/;2b BM Lu* b2H2+i i?2B` K`;BMH /272M/Mib U`2HiBp2 iQ i?2 KQbi H2MB2Mi [mBMiBH2V- +QKT`2/ iQ ?Qr i?2 H;Q`Bi?K rQmH/ b2H2+i K`;BMH /2iBM22bX qBi?BM 2+? TM2H- r2 /BpB/2 i?2 bKTH2 mT BMiQ ky #BMb #v T`2/B+i2/ +`BK2 `BbF Ub?QrM QM i?2 t@tBbVX h?2 #H+F b2;K2Mi i i?2 iQT Q7 2+? #` b?Qrb i?2 b?`2 Q7 2+? #BM i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2b DBHX AM i?2 iQT `B;?i@?M/ TM2H- r2 b?Qr r?B+? /272M/Mib i?2 b2+QM/@KQbi@H2MB2Mi [mBMiBH2 Dm/;2b BKTHB+BiHv b2H2+i iQ DBH iQ ;2i 7`QK i?2 KQbi H2MB2Mi Dm/;2Ƕb `2H2b2 `i2 /QrM iQ i?2B` QrM HQr2` `2H2b2 `i2 U#Hm2V- M/ r?Q i?2v +QMiBMm2 iQ `2H2b2 Ur?Bi2VX h?2 H27i@?M/ iQT TM2H b?Qrb r?QK i?2 H;Q`Bi?K rQmH/ b2H2+i BMbi2/X 1+? Q7 i?2 `2KBMBM; `Qrb b?Qrb i?2 bK2 +QKT`BbQM #2ir22M i?2 Dm/;2 M/ H;Q`Bi?K /2+BbBQMb 7Q` i?2 Qi?2` H2bb@H2MB2Mi Dm/;2 [mBMiBH2bX

9d 6B;m`2 8, *QKT`BM; AKT+i Q7 .2iBMBM; BM Q`/2` Q7 S`2/B+i2/ _BbF hQ q?i Cm/;2b +?B2p2

LQi2b, h?Bb };m`2 HQQFb i T2`7Q`KM+2 r?2M //BiBQMH /272M/Mib `2 DBH2/ ++Q`/BM; iQ T`2/B+iBp2 KQ/2H Q7 r?Q Dm/;2b rQmH/ DBHX Ai +QKT`2b +`BK2 ì2b M/ `2H2b2 ì2b iQ i?2 /2+BbBQMb Q7 bi`B+i2` Dm/;2bX h?2 `B;?i@KQbi TQBMi BM i?2 ;`T? `2T`2b2Mib i?2 `2H2b2 ì2 Q7 i?2 KQbi H2MB2Mi [mBMiBH2 Q7 Dm/;2b- rBi? i?2 +`BK2 ì2 i?i `2bmHibX h?2 `2/ HBM2 b?Qrb i?2 +`BK2 `2/m+iBQMb i?i `2HBx2 B7 r2 DBH //BiBQMH /272M/Mib 7`QK i?Bb TQQH ++Q`/BM; iQ T`2/B+i2/ #2?pBQ` Q7 Dm/;2bX "v +QKT`BbQM- i?2 HB;?i /b?2/ HBM2 b?Qrb i?2 /2+HBM2 BM +`BK2 Ub T2`+2Mi;2 Q7 i?2 H2MB2Mi [mBMiBH2Ƕb +`BK2 ì2- b?QrM QM i?2 v@tBbV i?i `2bmHib 7`QK `M/QKHv b2H2+iBM; //BiBQMH /272M/Mib iQ /2iBM 7`QK rBi?BM i?2 H2MB2Mi [mBMiBH2Ƕb `2H2b2/ +b2b- rBi? i?2 +?M;2 BM `2H2b2 ì2 `2HiBp2 iQ i?2 H2MB2Mi [mBMiBH2 b?QrM QM i?2 t@tBbX b MQi?2` +QKT`BbQM- i?2 ;`22M +m`p2 b?Qrb i?2 +`BK2 ì2 f `2H2b2 ì2 i`/2Qz i?i +QK2b 7`QK DBHBM; //BiBQMH /272M/Mib rBi?BM i?2 H2MB2Mi [mBMiBH2Ƕb `2H2b2/ b2i BM /2b+2M/BM; Q`/2` Q7 i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbFX h?2 7Qm` TQBMib QM i?2 ;`T? b?Qr i?2 +`BK2 ì2 f `2H2b2 ì2 Qmi+QK2b i?i `2 Q#b2`p2/ 7Q` i?2 +imH /2+BbBQMb K/2 #v i?2 b2+QM/ i?`Qm;? }7i? KQbi H2MB2Mi [mBMiBH2 Dm/;2b- r?Q b22 bBKBH` +b2HQ/b QM p2`;2 iQ i?Qb2 Q7 i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2bX

93 6B;m`2 e, S`2/B+iBM; BM G2bb G2MB2Mi ZmBMiBH2b lbBM; .i 7`QK JQbi G2MB2Mi

LQi2b, h?Bb };m`2 i2bib 7Q` r?2i?2` i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2b BM Qm` Lu* /ib2i `2 #2ii2` i mbBM; ǵmMQ#b2`p#H2bǶ BM KFBM; `2H2b2 f /2iBM /2+BbBQMb i?M `2 i?2 H2bb@H2MB2Mi [mBMiBH2 Dm/;2bX h?2 iQT TM2H `2T`Q/m+2b i?2 +HB#ìBQM +m`p2 7`QK 6B;m`2 k- THQiiBM; i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbF ;BMbi Q#b2`p2/ +`BK2 ì2b rBi?BM i?2 i2bi b2iX 6Q` i?2 `2KBMBM; TM2Hb- r2 i`BM M H;Q`Bi?K mbBM; Dmbi i?2 b2i Q7 /272M/Mib `2H2b2/ #v i?2 KQbi H2MB2Mi [mBMiBH2 Dm/;2b- M/ i?2M mb2 i?i H;Q`Bi?K iQ ;2M2ì2 T`2/B+i2/ +`BK2 `BbF iQ +QKT`2 iQ Q#b2`p2/ +`BK2 ì2b 7Q` i?2 b2i Q7 /272M/Mib `2H2b2/ #v i?2 H2bb@H2MB2Mi [mBMiBH2b Q7 Dm/;2bX

9N 6B;m`2 d, aBKmHiBM; 1z2+ib Q7 q`MBM; avbi2K

LQi2b, h?2 };m`2 #Qp2 bBKmHi2b i?2 +?M;2 BM Qmi+QK2b i?i rQmH/ `2bmHi BM Lu* 7`QK TTHvBM; M 2`Hv r`MBM; bvbi2K i?i rQmH/ r`M Dm/;2b r?2M i?2v `2 #Qmi iQ `2H2b2 bQK2QM2 rBi? T`2/B+i2/ +`BK2 `BbF #Qp2 bQK2 i?`2b?QH/- bbmKBM; T2`72+i Dm/;2 +QKTHBM+2X q2 THQi /Bz2`2Mi +M/B/i2 i?`2b?QH/b THQii2/ HQM; i?2 t@tBbX h?2 iQT TM2H b?Qrb i?2 T2`+2Mi;2 TQBMi +?M;2 BM i?2 /2i2MiBQM `i2 i?i rQmH/ `2bmHi- r?BH2 i?2 #QiiQK TM2H b?Qrb i?2 T2`+2Mi +?M;2 BM +`BK2 `i2 i?i rQmH/ `2bmHiX

8y 6B;m`2 3, aBKmHiBQM Q7 *`BK2 _i2 @ _2H2b2 h`/2Qz H;Q`Bi?K HHQrb

LQi2b, h?2 +m`p2 BM i?2 iQT TM2H b?Qrb i?2 +`BK2 ì2 M/ `2H2b2 ì2 +QK#BMiBQMb i?i rQmH/ #2 TQbbB#H2 BM Lu* B7 Dm/;2b r2`2 ;Bp2M `BbF iQQH i?i +QmH/ `2@`MF HH /272M/Mib #v i?2B` T`2/B+i2/ +`BK2 `BbF M/ `2+QKK2M/ i?2K 7Q` /2i2MiBQM BM Q`/2` Q7 `BbFX aBM+2 r2 rQmH/ HBF2 +`BK2 ì2 i?i +M #2 K2MBM;7mHHv +QKT`2/ +`Qbb `2H2b2 ì2b- i?2 v@tBb b?Qrb i?2 ìBQ Q7 +`BK2b +QKKBii2/ #v `2H2b2/ /272M/Mib iQ i?2 iQiH MmK#2` Q7 /272M/Mib- MQi Dmbi i?2 MmK#2` `2H2b2/Xh?2 +m`p2 b?Qrb r?i ;BMb rQmH/ #2 TQbbB#H2 `2HiBp2 iQ +imH +m``2Mi Dm/;2 /2+BbBQMb- bbmKBM; T2`72+i +QKTHBM+2 rBi? i?2 M2r iQQHX h?2 +m`p2 BM i?2 #QiiQK TM2H b?Qrb i?2 `BbF H2p2H Q7 i?2 K`;BMH T2`bQM /2iBM2/ i 2+? TQbbB#H2 `2H2b2 ì2 mM/2` i?2 H;Q`Bi?KB+ `2H2b2 `mH2X

8R 6B;m`2 N, :BMb 6Q` 1+? Q7 k8 Cm/;2b 6`QK _2@_MFBM;

LQi2b, h?Bb };m`2 b?Qrb i?2 TQi2MiBH ;BMb 7`QK M H;Q`Bi?KB+ `2H2b2 `mH2 p2`bmb +m``2Mi Dm/;2 /2+BbBQMb b2Tì2Hv 7Q` 2+? Q7 i?2 k8 Dm/;2b BM Qm` Lu* /ib2i rBi? i?2 H`;2bi +b2HQ/b rBi?BM Qm` i2bi b2iX q2 mb2 i?2 H;Q`Bi?K i`BM2/ QM /i 7`QK HH Dm/;2b M/ +b2b BM i?2 i`BMBM; b2i- M/ i?2M +QKT`2 TQi2MiBH ;BMb Q7 i?2 H;Q`Bi?K p2`bmb 2+? Q7 i?2b2 Dm/;2b QM2 i iBK2 U2+? #` `2T`2b2Mib +QKT`BbQM iQ b2Tì2 Dm/;2V BM i2`Kb Q7 ;BMb BM `2H2b2 ì2b ?QH/BM; +`BK2 ì2 +QMbiMi UiQT TM2HV M/ `2/m+iBQM BM +`BK2 ì2b ?QH/BM; `2H2b2 ì2b +QMbiMi U#QiiQK TM2HVX

8k 6B;m`2 Ry, .2+QKTQbBM; SQHB+v aBKmHiBQM :BMb, :BMb 7`QK _2H2bBM; M/ CBHBM;

LQi2b, h?Bb };m`2 b?Qrb r?2`2 i?2 iQiH +`BK2 ;BMb +QK2 7`QK BM Qm` Lu* /i rBi? i?2 H;Q`Bi?KB+ `2H2b2 `mH2 i?i `2@`MFb HH /272M/Mib #v T`2/B+i2/ `BbF- BM i2`Kb Q7 `2H2bBM; /272M/Mib i?2 Dm/;2b DBH2/ p2`bmb /2iBMBM; /272M/Mib i?2 Dm/;2 `2H2b2/X q2 +H+mHi2 i?2 iQiH b2i Q7 /2iBM f `2H2b2 ǳbrTbǴ i?2 H;Q`Bi?KB+ `mH2 KF2b +QKT`2/ iQ +m``2Mi Dm/;2 /2+BbBQMb M/ THQi i?2 b?`2 Q7 i?Qb2 brTb K/2 QM i?2 t@tBb BM #Qi? i?2 iQT M/ #QiiQK TM2HbX h?2 v@tBb BM i?2 iQT TM2H Bb ěi?2 Qp2`HH +`BK2 ì2- biìBM; rBi? i?2 +`BK2 ì2 Q#b2`p2/ 7Q` +m``2Mi Dm/;2 /2+BbBQMb ;QBM; /QrM iQ i?2 +`BK2 ì2 r2 Q#b2`p2 mM/2` i?2 H;Q`Bi?KB+ `2H2b2 `mH2X h?2 #QiiQK TM2H b?Qrb i?2 `2/m+iBQM BM +`BK2 i?i Bb +?B2p2/ 7Q` 2+? K`;BMH T2`bQM /2iBM2/ #v i?2 H;Q`Bi?K `2HiBp2 iQ DBHBM; bQK2QM2 rBi? i?2 bKTH2 p2`;2 `BbF- b r2HH b i?2 `2/m+iBQM BM +`BK2 i?i `2bmHib 7`QK `2H2bBM; i?2 K`;BMH /272M/Mi 7`QK DBH +QKT`2/ iQ `2H2bBM; bQK2QM2 rBi? i?2 bKTH2 p2`;2 `BbFX

8j 6B;m`2 RR, Cm/;2bǶ _2bTQMb2 iQ _BbF hQQHb BM S?BH/2HT?B

LQi2b, h?Bb };m`2 T`2b2Mib `2bmHib 7`QK i?2 S?BH/2HT?B #BH 2tT2`BK2Mi U:QH/FKT M/ :Qii7`2/bQM- RN39V b?QrBM; Dm/;2 +QKTHBM+2 rBi? i?2 `BbF iQQH i?i rb `M/QKHv bbB;M2/ iQ bQK2 Dm/;2b #mi MQi Qi?2`bX 1+? #` b?Qrb i?2 b?`2 Q7 ;Bp2M Dm/;2Ƕb `2H2b2 /2+BbBQMb i?i HB;M rBi? i?2 `BbF iQQHǶb `2+QKK2M/iBQM- b?/2/ #v r?2i?2` i?2 Dm/;2 rb ;Bp2M i?2 `BbF iQQH Ui`2iK2Mi ;`QmT BM Tm`TH2V Q` MQi U+QMi`QH BM ;QH/VX h?2 ?Q`BxQMiH HBM2b BM i?2 };m`2 b?Qr i?2 p2`;2 b?`2 Q7 /2+BbBQMb i?i +QKTHv rBi? i?2 `BbF iQQH `2+QKK2M/iBQMb 7Q` i?2 i`2iK2Mi ;`QmT Qp2`HH U/b?2/ HBM2V M/ +QMi`QH ;`QmT UbQHB/ HBM2VX

89 6B;m`2 Rk, .Bbi`B#miBQM Q7 S`2/B+i2/ CBH S`Q##BHBiB2b "v S`2/B+i2/ *`BK2 _BbF

LQi2b, h?Bb };m`2 b?Qrb i?2 `2HiBp2 ǳbT`2/Ǵ BM i?2 T`2/B+i2/ Dm/;2 DBH T`Q##BHBiB2b 7Q` +b2b BM Qm` Lu* i2bi b2i ;`QmT2/ iQ;2i?2` #v i?2 H;Q`Bi?KǶb T`2/B+i2/ +`BK2 `BbFX AM 2+? T`2/B+i2/ `BbF [mBMiBH2 r2 ;`T? i?2 /Bbi`B#miBQM UmbBM; pQH+MQ THQiV Q7 i?2 +QM/BiBQMH /Bbi`B#miBQM Q7 T`2/B+i2/ Dm/;2 DBHBM; T`Q##BHBiB2bX q2 7mì?2` +QHQ` 2+? TQBMi #v i?2 `2HBx2/ `2H2b2 ì2 i 2+? ì2X

88 6B;m`2 Rj, 1z2+i Q7 .2iBMBM; .272M/Mib Cm/;2b lbmHHv .2iBM

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