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aBim�iBQMb r?2`2 #Qi? T`QiQMb /BbbQHp2 BMiQ KQ`2 T�`iB+H2b �`2 +QMbB/2`2/ �b#�+F;`QmM/ U`B;?i /B;`�K BM 6B;X RXRVX "�+F;`QmM/ K�v �HbQ +QK2 7`QK /B7@72`2Mi bQm`+2bX 6Q` 2t�KTH2- r?2M irQ T�`iB+H2b ?Bi 2�+? Qi?2`- K�Mv M2rT�`iB+H2b �`2 +`2�i2/ �M/ K�v #2 /2i2+i2/ BM i?2 �6SX �HbQ- r?2M i?2 BMi�+iT`QiQM ?Bib bQK2 �6S +QKTQM2Mi- 2X;X K�;M2i Q` TBT2- Bi Bb bK�b?2/ �M/+`2�i2b � b?Qr2`b Q7 T�`iB+H2b r2 �`2 MQi BMi2`2bi2/ BMX �HH i?2b2 #�+F;`QmM/bBim�iBQMb M22/ iQ #2 }Hi2`2/ QmiX

RXk *�i+?BM; i?2 KmQMb6`QK i?2 [m�MimK T?vbB+b T2`bT2+iBp2- 2H2+i`QK�;M2iB+ BMi2`�+iBQM Bb /QM2#v b2M/BM; pB`im�H T?QiQMb γγ 7`QK #Qi? T�`iB+H2bX q?2M i?2b2 irQ T?QiQMbK22i- i?2v +`2�i2 � KmQM T�B` µ+µ− r?B+? Bb b?QrM BM 6B; RXRX h?2b2 KmQMb�`2 +�m;?i BM �hG�a �M/ �`2 2bb2MiB�H 7Q` }M/BM; /2~2+i2/ T`QiQMb �i i?2�6SX

q?2M irQ T`QiQMb BMi2``�+i i?2v #Qi? HQb2 � 7`�+iBQM Q7 i?2B` KQK2MimKf2M2`;vX6`QK i?2 H�r Q7 +QMb2`p�iBQM Q7 2M2`;v Bi Bb FMQrM i?�i i?Bb HQbi 2M2`;v Kmbi?�p2 i`�Mb7Q`K2/ BMiQ bQK2i?BM; 2Hb2X �M/ Bi Bb i?2b2 M2rHv +`2�i2/ KmQMbi?2 2M2`;v ?�b i`�Mb7Q`K2/ iQX 6`QK 1BMbi2BMǶb 2[m�iBQM E = mc2 r2 FMQri?2`2 Bb � `2H�iBQM #2ir22M 2M2`;v �M/ K�bbX h?�i K2�Mb i?�i r2 +�M +�H+mH�i2i?2 2M2`;v HQbb 7`QK 2H�biB+ BMi2`�+iBQM 7`QK i?2 K�bb Q7 i?2 KmQMbX 6Q` i?Bbr2 mb2 i?2 7QHHQrBM; 7Q`KmH� RXR (k) r?2`2 s Bb i?2 +2Mi`2 Q7 K�bb 2M2`;v Q7i?2 T`QiQM #2�Kb- �M/ η i?2 Tb2m/Q@`�TB/Biv �M;H2UrBi? `2bT2+i iQ i?2 #2�KTBT2V,

ξµµ = mµµ√s

e±η URXRV

RXj 1tT2`BK2Mi�H b2i@mT�i G>*- i?2 #2�K Bb BM 7�+i b2T�`�i2/ BMiQ #mM+?2b Q7 T`QiQMb r?B+? �`2 k8Mb �r�v 7`QK 2�+? Qi?2`X 1�+? b2;K2Mi +QMi�BMb �#Qmi 1014 T`QiQMbX �iBMi2`�+iBQM TQBMiUASV i?2b2 b2;K2Mib �`2 7Q`+2/ iQ +`Qbb 2�+? Qi?2` mbBM; i?2K�;M2iB+ }2H/b �M/ T�`iB+H2b BMi2`�+i i?2`2- �M/ bQK2 +QMiBMm2 iQ i?2 �6Sbi�iBQMbX �6S +QMi�BMb 9 bi�iBQMb Ĝ irQ bi�iBQMb QM i?2 H27i bB/2 7`QK i?2 AS�M/ irQ QM i?2 `B;?i bB/2X h?2b2 irQ bi�iBQMb QM #Qi? bB/2b �`2 B/2MiB}2/ �bL1�_ �M/ 6�_ bi�iBQMX L1�_ bi�iBQM Bb bBim�i2/ ky8 K �r�v 7`QK AS �M/6�_ bi�iBQM kRd K �r�v 7`QK ASX 1�+? �6S bi�iBQM +QMi�BMb 9 bBHB+QM TH�M2b-2�+? ?�pBM; � `2bQHmiBQM Q7 jjet3y TBt2Hb Ĝ 2H2+i`Q@b2MbBiBp2 mMBibX h?2 �`2�Q7 i?2b2 TH�M2b Bb 8ytk8y m2X 1�+? TH�M2 Bb TH�+2/ �#Qmi k KK �r�v 7`QKi?2 #2�K �tBb iQ /2i2+i QMHv /2~2+i2/ T�`iB+H2bX aBM+2 i?2 `2bQHmiBQM Q7 i?2/2i2+iQ` BM s /B`2+iBQM Bb Km+? ?B;?2` i?�M BM u /B`2+iBQM- p2`v Q7i2M QMHv s

9

RXjX 1tT2`BK2Mi�H b2i@mT

/B`2+iBQM Bb i�F2M BM �++QmMi BM i?2 �M�HvbBbX

�MQi?2` �bT2+i Q7 i?2 �6S �`2 i?2 K�;M2ib �HQM; i?2 #2�K TBT2X h?Bb K�;@M2iB+ }2H/ �`2 mb2/ iQ �ii`�+i T�`iB+H2b r?B+? 2b+�T2 i?2K #2�K 2p2HQT2X S�`@iB+H2b rBi? HQr2` KQK2MimK +?�M;2 i?2B` i`�D2+iQ`v KQ`2 bB;MB}+�MiHv �M/?�p2 ?B;?2` #B�b 7`QK #2�K �tBbX "�b2/ QM i?2 T`QT2`iB2b Q7 K�;M2ib i?27QHHQrBM; (k) 7Q`KmH� r�b /2`Bp2/,

x(ξ) = −119ξ − 164ξ2 URXkV

lbBM; i?Bb 7Q`KmH� r2 +�M +�H+mH�i2 i?2 X TQbBiBQM Q7 � T�`iB+H2 B7 r2 FMQr BiǶbKQK2MimK HQbb ξX "v X TQbBiBQM Bb K2�Mi i?2 T`QiQM ?Bi QM i?2 �6S TBt2H/2i2+iQ`X h?Bb Bb �HbQ ?Qr r2 }M/ Qm` bB;M�H +�M/B/�i2b bBM+2 r2 +�M +�H+mH�i2i?2 KQK2MimK HQbb Q7 /2~2+i2/ T`QiQMb 7`QK KmQMbX 6B;m`2 RXk b?Qrb i?2r?QH2 �6S b2imT,

6B;m`2 RXk, 1tT2`BK2Mi�H b2i@mT rBi? /2b+`BTiBQMX (k)

8

RX �6S 2tT2`BK2Mi

RX9 *m``2Mi +`Bi2`B� 7Q` bB;M�Hf#�+F;`QmM/b2T�`�iBQM

h?2 bQHmiBQM Q7 i?2 [m�/`�iB+ 2[m�iBQM RXk Bb,

ξReco = −119 ± 656x

328 URXjV

q2 +QMbB/2` QMHv bQHmiBQM rBi? + bB;M BM i?2 7Q`KmH�- #2+�mb2 i?2 Qi?2` bQ@HmiBQM ;Bp2b mMT?vbB+�H p�Hm2bX h?Bb p�Hm2 Bb +�HH2/ ξRecoX Ai 2[m�Hb iQ �M2tT2+i2/ KQK2MimK HQbb Q7 T`QiQMb #�b2/ QM i?2 X TQbBiBQMX

6Q` i?2 b2T�`�iBQM Q7 bB;M�Hf#�+F;`QmM/ 7QHHQrBM; +`Bi2`B� �`2 mb2/ (k),

Ç m < 70 :2o �M/ m > 105 :2p

Ç 0.02 < ξµµ < 0.1

Ç (ξµµ − ξReco)/ξµµ < 0.1

Ç QM2 i`�+F �i L1�_ bi�iBQM �M/ QM2 i`�+F �i 6�_ bi�iBQM rBi? +HQb2 XTQbBiBQMb

h?2 `2�bQM 7Q` i?2 }`bi +QM/BiBQM Bb i?�i K�bb BM i?2 BMi2`p�H (70, 105) Bb �bbQb@bB�i2/ rBi? z #QbQM BMi2`�+iBQMbX h?2 b2+QM/ +QM/BiBQM Bb b2i #2+�mb2 T`QiQMbrBi? ξµµ Qmi Q7 i?Bb BMi2`p�H �`2 �HbQ Qmi Q7 i?2 �6S �++2Ti�M+2 @ i?2v /Q MQi?Bi i?2 b2MbQ` TH�M2X h?2 i?B`/ +QM/BiBQM b�vb i?�i `2+Q`/2/ KQK2MimK HQbb�M/ 2tT2+i2/ KQK2MimK HQbb Kmbi #2 +HQb2 iQ;2i?2`X h?2 H�bi +QM/BiBQM Bbmb2/ iQ #2 +H2�` i?�i i`�+Fb +QK2 QMHv 7`QK QM2 T�`iB+H2X

h?2 �#Qp2 +`Bi2`B� �`2 p2`v bi`B+iX h?2v /QMǶi +QMbB/2` �Mv Qi?2` b�KTH2brBi? +HQb2 ξ p�Hm2b- 2p2M i?Qm;? i?2`2 �`2 biBHH K�Mv b�KTH2b r?B+? /Q MQi7mH}HH i?2 b2+QM/ 7Q`KmH� #mi �`2 biBHH ?B;?Hv T`Q#�#H2 iQ #2 � bB;M�HX h?2+m``2Mi bQHmiBQM /Q2b MQi 2t�KBM2 Qi?2` p�`B�#H2b r?B+? +QmH/ #2 � ;QQ/ T`2@/B+iQ` Q7 #2BM; � bB;M�H @ HBF2 bT2+B}+ X TQbBiBQMb Q` bT2+B}+ KmQM r2B;?ib 7Q`bB;M�Hf#�+F;`QmM/X hQ BKT`Qp2 i?2 b2H2+iBQM �M/ }M/ KQ`2 +�M/B/�i2b i?2K�+?BM2 H2�`MBM; �H;Q`Bi?K ?�b #22M /2p2HQT2/X

e

*?�Ti2` kJ�+?BM2 H2�`MBM;

kXR q?�i Bb K�+?MBM2 H2�`MBM;

h?2 K�BM Tm`TQb2 Q7 K�+?BM2 H2�`MBM; K2i?Q/b Bb iQ }M/ `2H�iBQMb BM +QH@H2+i2/ /�i� rBi? FMQrM QmiTmi #�b2/ QM r?B+? i?2 K2i?Q/ Bb �#H2 iQ T`2/B+i-rBi? +2`i�BM T`Q#�#BHBiv- QmiTmi 7Q` bQK2 M2r Q` MQM@+H�bbB}2/ /�i�X qBi?ǴQmiTmiǴ Bb mbm�HHv K2�Mi � #2HQM;BM; iQ bQK2 +H�bb Q` bQK2 `2�H MmK#2`Xh�bF BM r?B+? r2 i`v iQ �bbB;M /�i� � +Q``2bTQM/BM; +H�bb �`2 +�HH2/ +H�bbB@}+�iBQM T`Q#H2K Ub?Q`iHv +H�bbB}+�iBQMV- i�bF r?2`2 r2 M22/ iQ �bbB;M /�i�� `2�H p�Hm2 Bb +�HH2/ `2;`2bbBQM T`Q#H2K Ub?Q`iHv `2;`2bbBQMVX �b � ivTB+�H+H�bbB}+�iBQM T`Q#H2K +QmH/ #2 T`2/B+iBM; r?2i?2` T2`bQM ?�bf?�b MQi ?�p2 �bT2+B}+ BHHM2bb- #�b2/ QM i?2 `2TQ`i2/ bvKTiQKb #v T�+B2Mi- K2�bm`2/ i2KT2`@�im`2 2i+X �b � ivTB+�H 2t�KTH2 Q7 `2;`2bbBQM Bb T`2/B+iBM; i?2 T`B+2 Q7 � ?Qmb2#�b2/ QM i?2 HQ+�iBQM Bi Bb bBim�i2/- �++QKQ/�iBQM bT�+2- MmK#2` Q7 `QQKb 2i+X

hQ #2 �#H2 iQ /Q bQ- r2 ivTB+�Hv M22/ iQ +QHH2+i � HQi Q7 /�i� rBi? FMQrMQmiTmiX h?2M r2 bTHBi i?2 /�i� BMiQ i`�BMBM; �M/ i2biBM; b2iX PM i?2 i`�BM@BM; b2i r2 i`�BM i?2 K2i?Q/X h?2M r2 H2i i?2 K2i?Q/ iQ T`2/B+i +H�bb2b U7Q`+H�bbB}+�iBQMV Q` `2�H MmK#2`b U7Q` `2;`2bbBQMV QM i?2 i2biBM; b2iX "2+�mb2 r2FMQr r?�i i?2 b�KTH2b BM i2biBM; b2i /Q 2[m�H iQ- r2 �`2 �#H2 iQ +�H+mH�i2?Qr bm++2b7mH Qm` K2i?Q/ BbX 6Q` +H�bbB}+�iBQM r2 mbm�HHv Dmbi +�H+mH�i2 i?2T2`+2Mi�;2 Q7 +Q``2+iHv �bbB;M2/ b�KTH2b iQ iQi�H MmK#2` Q7 b�KTH2bX 6Q` `2@;`2bbBQM r2 mbm�HHv mb2 Ja1X

aQK2iBK2b Bi ?�TT2Mb i?�i � K2i?Q/ ?�b � T2`72+i b+Q`2 QM � i`�BMBM; b2i#mi TQQ` b+Q`2 QM i2biBM; b2iX _2�bQM 7Q` i?Bb Bb i?�i i?2 b2T�`�iBQM `mH2b Q7i?2 K2i?Q/ �`2 iQQ +QKTH2t iQ #2bi }i i?2 i`�BM b2iX h?Bb T`Q#H2K Bb +�HH2/Qp2`}iiBM; �M/ i?2`2 �`2 K�Mv i2+?MB[m2b ?Qr iQ `2/m+2 Bi- 2X; +`Qbb p�HB/�@iBQM- `2;mH�`Bx�iBQM- 2i+X

d

kX J�+?BM2 H2�`MBM;

6Q` bQK2 K2i?Q/b r2 �HbQ +`2�i2 � p�HB/�iBQM b2i QM r?B+? r2 }M/ i?2 #2bi?vT2`T�`�K2i2`b Q7 i?2 K2i?Q/ 7Q` +m``2Mi T`Q#H2KX 1�+? K2i?Q/ ?�b BibQrM ?vT2`T�`�K2i2`bX 6Q` M2m`�H M2ib BiǶb ivTB+�HHv MmK#2` Q7 M2m`QMb- 7Q`HQ;BbiB+ `2;`2bbBQM `2;mH�iBx�iBQM ivT2- 7Q` /2+BbBQM i`22b BiǶb i?2 /2Ti? Q7 i?2i`22- 2i+X

AM Qm` �M�HvbBb r2 ?�p2 QMHv � bK�HH /�i�b2i r2 +�M rQ`F rBi?X aBM+2 r2 ?�p2QMHv eN bB;M�H b�KTH2b- Bi Bb MQi bi�iBbiB+�HHv TQbbB#H2 iQ b�v r?B+? K2i?Q/ Bb/2}MBi2Hv i?2 #2biX h?�iǶb r?v A �K �HbQ K2�bm`BM; �p2`�;2 /Bz p�Hm2 7Q`;Bp2M T`Q#�#BHBiv BMi2`p�H BM M2ti b2+iBQMb �b �MQi?2` +`Bi2`B� 7Q` }M/BM; i?2#2bi K2i?Q/X

kXk L2m`�H M2irQ`FbL2m`�H M2irQ`F Bb � K�+?BM2 H2�`MBM; i2+?MB[m2 BMbTB`2/ #v ?mK�M #`�BMXh?2v rQ`F r2HH 7Q` #Qi? `2;`2bBQM �M/ +H�bbB}+�iBQMX Aib K�BM mMBi Bb � T2`@+2Ti`QM r?B+? vQm +�M b22 QM i?2 TB+im`2 #2HQrX

6B;m`2 kXR, JQ/2H Q7 � T2`+2Ti`QMX (j)

�b vQm +�M b22- T2`+2Ti`QM �++2Tib b2p2`�H BMTmib �M/ ;Bp2b QM2 QmiTmiX Ai�HbQ ?�b Bib QrM r2B;?i w p2+iQ` rBi? QM2 r2B;?i 7Q` QM2 BMTmiX h?2`2 Bb �HbQ� bT2+B�H r2B;?i w0 r?B+? Bb +�HH2/ BMi2`+2Ti �M/ ?�b � +QMbi�Mi BMTmi x0 = 1X

q?2M i?2 M2m`QM �++2Tib �M BMTmi 7`QK i?2 /�i�UQM2 `Qr Q7 i?2 /�i�b2iV-r2 KmHiBTHv �HH i?2 BMTmib rBi? Bib +Q``2bTQM/BM; r2B;?i �M/ bmK i?2K mT�++Q`/BM; i?2 7QHHQrBM; 7Q`KmH�,

p =n!

i=0wixi UkXRV

3

kXkX L2m`�H M2irQ`Fb

h?2M i?2 QmiTmi p ;Q2b BMiQ �M �+iBp�iBQM 7mM+iBQM 7`QK r?B+? r2 ;2i i?2QmiTmi Q7 � M2m`QMX �M 2t�KTH2 Q7 �+iBp�iBQM 7mM+iBQM Bb � bB;KQB/ 7mM+iBQMr?B+? Bb /2}M2/ �b,

σ(x) = 11 + e−x

= ex

ex + 1 UkXkV

:`�T? Q7 bB;KQB/ 7mM+iBQM, q2 +�M �HbQ mb2 ?vT2`#QHB+ i�M;2Mi i�M? Q` B/2M@

6B;m`2 kXk, :`�T? Q7 bB;KQB/ 7mM+iBQMX (9)

iBiv 7mM+iBQMX A/2MiBiv 7mM+iBQM Bb �HbQ mb2/ �b QmiTmi 7mM+iBQM 7Q` `2;`2bbBQMT`Q#H2KbX

kXkXR q?�i QM2 M2m`QM �+im�HHv /QPm` Tm`TQb2 Bb iQ }M/ i?2 #2bi r2B;?ib 7Q` r?B+? r2 ;2i i?2 #2bi b+Q`2 QMi`�BMBM; b2iX "2+�mb2 i?2 /�i�b2i rBi? M@+QHmKMb K�F2b mT M@/BK2MbBQM�H/�i� bT�+2- r2 �`2 BM 7�+i HQQFBM; 7Q` i?2 #2bi +Q2{+B2Mib Q7 ?vT2`TH�M2 r?B+?b2T�`�i2b i?2 /�i�bT�+2 KQbi 2z2+iBp2HvX "2HQr Bb b?QrM �M 2t�KTH2 Q7 bm+?� b2T�`�iBQM 7Q` Rk /�i�TQBMib BM irQ@/BK2MbBQM�H /�i�bT�+2X

N

kX J�+?BM2 H2�`MBM;

6B;m`2 kXj, GBM2�`v b2T�`�#H2 T`Q#H2KX

� T`Q#H2K Bb r?2M /�i� �`2 TH�+2/ BM i?2 /�i�bT�+2 7QHHQrBM;Hv,

6B;m`2 kX9, GBM2�`v MQM@b2T�`�#H2 T`Q#H2KX

"2+�mb2 r2 +�MMQi b2T�`�i2 i?2b2 /�i�TQBMib 2z2+iBp2Hv QMHv rBi? QM2 HBM2r2 +�HH i?2K HBM2�`v BMb2T�`�#H2X J2i?Q/ r?B+? +�M T2`7Q`K QMHv HBM2�` b2T@�`�iBQM �`2 +�HH2/ HBM2�` b2T�`�iQ`bX "2bB/2 M2m`QM r2 +�M HQ;BbiB+ `2;`2bbBQM(e) Q` aoJ UamTTQ`i o2+iQ` J�+?BM2V (e)X

Ry

kXkX L2m`�H M2irQ`Fb

kXkXk G2�`MBM; QM2 M2m`QM�b K2MiBQM2/ T`2pBQmbHv- Qm` ;Q�H Bb iQ }M/ i?2 #2bi r2B;?ib 7Q` r?B+? i?2QmiTmi p2+iQ` 7Q` �HH i?2 b�KTH2b z ?�p2 i?2 H2�bi #B�b 7`QK i?2 `2�H QmiTmidX J�i?2K�iB+�Hv r2 r�Mi iQ KBMBKBx2 7Q`KmH� r?B+? Bb +�HH2/ +Qbi 7mM+iBQMXPM2 Q7 i?2 KQbi +QKKQM HQbb 7mM+iBQMb Bb Ja1 UK2�M b[m�`2/ 2``Q`V /BpB/2/#v MmK#2` Q7 b�KTH2b (8),

P (w) = 1n

n!

i=1(d− z)2 UkXjV

hQ /Q i?Bb r2 M22/ iQ }M/ � ;`�/B2Mi 7Q` r2B;?i p2+iQ` (8),

∇wP = ( ∂P

∂w1, ...

∂P

∂wn) UkX9V

q?2M i?2 ;`�/B2Mi Bb +�H+mH�i2/- r2 +�M mb2 � H2�`MBM; i2+?MB[m2 +�HH2/;`�/B2Mi /2b+2MiX :`�/B2Mi /2b+2Mi Bb � K2i?Q/ r?2`2 r2 +�H+mH�i2 �M �p2`�;22``Q` i?`Qm;? � b2i Q7 b�KTH2b- +�H+mH�i2 ;`�/B2Mi 7Q` r2B;?i p2+iQ` �M/ ǴK�F2bi2TǴ BM i?2 /B`2+iBQM Q7 i?2 ;`�/B2MiX J�FBM; bi2T K2�Mb r2 mT/�i2 i?2r2B;?i p2+iQ` rBi? ;`�/B2Mi KmHiBTHB2/ #v bQK2 ivTB+�Hv bK�HH MmK#2` η r?B+?Bb +�HH2/ H2�`MBM; `�i2X "2HQr Bb i?2 K�i?2K�iB+�H MQi�iBQM Q7 ;`�/B2Mi /2b+2Mi(8),

w← w− η∇wP UkX8Vq?2M r2 `mM i?Bb Bi2`�iBQM K�Mv iBK2b r2 ;2i iQ � HQ+�H KBMBK�X q?B+?

Bb `2�HHv MQi bQ ;QQ/ #2+�mb2 r2 M22/ iQ }M/ � ;HQ#�H KBMBK�X h?�MF7mHHv- 7Q`M2m`�H M2ib rBi? ?B;? MmK#2` Q7 M2m`QMb �HH i?2 HQ+�H KBMBK�b �`2 �i bBKBH�`H2p2H �b ;HQ#�H KBMBK�- bQ 7Q` i?2 b�K2 MmK#2` Q7 M2m`QMb r2 b?QmH/ ;2ibBKBH�` `2bmHib `2;�`/H2bb i?2 HQ+�H KBMBKmK r2 ;2i bim+F BMX

RR

kX J�+?BM2 H2�`MBM;

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6B;m`2 kX8, 1t�KTH2 Q7 j@H�v2` M2m`�H M2iX

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kXkX L2m`�H M2irQ`Fb

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∂y1∂p1

∂p1∂wi

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AM i?2 CmTvi2` MQi2#QQF A �K rQ`FBM; rBi? H�i2bi Svi?QM p2`bBQMX 6Q` �M�HvbBbA �K mbBM; i?2 7QHHQrBM; Svi?QM HB#`�`B2b,

Ç T�M/�b (3) @ HB#`�`v 7Q` rQ`FBM; rBi? /�i�b2ib

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jX _2�HBb�iBQM

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A biBHH H2�`M2/ i?2 _PPh +QKK�M/b- #2+�mb2 �HH i?2 +m``2Mi `2bmHib /QM2rBi? `QQi mb�;2X �HbQ i?2 /�i�b2i Bb b�p2/ BM bT2+B�H _PPh }H2 bQ A M22/2/iQ +QMp2`i Bi iQ X+bp }H2X

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h`22b +�M #2 b�p2/ BMiQ � X`QQi }H2X �M �/p�Mi�;2 Q7 � X`QQi }H2b Bb i?�i r2+�M QT2M Bi rBi? _PPhb #`Qrb2` Ur?B+? Bb QT2M2/ #v +�HHBM; M2r h"`Qrb2`7`QK _PPh i2`KBM�HV �M/ b22 i?2 i`22b BMbB/2 i?2 }H2 �M/ i?2B` #`�M+?2bX �M@Qi?2` �/p�Mi�;2 Q7 X`QQi }H2b Bb i?�i r?2M r2 QT2M Bi BM i?2 _PPh #`Qrb2`-i?2v �`2 �miQK�iB+�HHv +QMp2`i2/ BMiQ ?BbiQ;`�KbX � /Bb�/p�Mi�;2 Bb i?�i QMHvi?2 `QQi 7`�K2rQ`F +�M rQ`F rBi? i?Bb 7Q`K�iX

6Q` #2ii2` rQ`F rBi? i`22 i?2`2 Bb � K2i?Q/ +�HH hh`22,,GQQTUV r?B+? +`2�i2b� +H�bb 7Q` i?2 i`22X *`2�iBM; �M BMbi�M+2 Q7 i?Bb +H�bb HQ�/b i?2 +Q``2bTQM/BM;

Re

jXkX :2iiBM; /�i� 7`QK X`QQi }H2

i`22 �M/ �bbB;Mb #`�M+?2b HQ+�H p�`B�#H2b- r?B+? ?�b b�K2 M�K2 �b i?2 #`�M+?X*H�bb T`QpB/2b h`22*H�bb,,GQQT r?B+? HQQTb Qp2` i?2 r?QH2 i`22X >2`2 r2+�M Tmi Qm` QrM +Q/2 �M/ /Q r?�i r2 rBb? iQ /Q rBi? 2�+? `2+Q`/X aQ A HQ�/2/2�+? `Qr BMiQ � bBKTH2 X+bp }H2- r?B+? Dmbi +QMi�BM2/ i?2 p�Hm2b b2T�`�i2/ #v^c^ +?�`�+i2`X

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jX _2�HBb�iBQM

jXj .�i�b2ijXjXR J2�MBM; Q7 2�+? +QHmKMh?2 /�i�b2i r2 �`2 rQ`FBM; rBi? HQQFb HBF2 i?Bb,

6B;m`2 jXR, .�i�b2i r2 rQ`F rBi?X

6Q` #2ii2` mM/2`bi�M/BM; Q7 i?2 /�i�b2i A rBHH /BbiBM;mBb? i?`22 /Bz2`2Mi +QH@mKM ivT2b #�b2/ QM ?Qr r2`2 i?2 /�i� r2`2 Q#i�BM2/X h?2 }`bi ivT2 Bb i?2+QHmKMb r?B+? `2T`2b2Mi /�i� +QHH2+i2/ �i i?2 �hG�a /2i2+iQ`- b2+QM/ QM2Bb i?2 /�i� +QHH2+i2/ �i QM2 bBM;H2 �6S bi�iBQM �M/ i?2 i?B`/ Bb i?2 +QHmKMr?B+? r�b +`2�i2/ mbBM; i?2 BM7Q`K�iBQMb 7`QK irQ /Bz2`2Mi �6S bi�iBQMbX

jXjXRXR .�i� +QHH2+i2/ BM �hG�a

Ç K @ K�bb Q7 i?2 KmQM T�B` /2i2+i2/ �i �hG�a r?B+? +QK2b 7`QK 2H�biB+BMi2`�+iBQM @ Qm` bB;M�HX Pm` Tm`TQb2 rBHH #2 iQ }M/ � K�i+?BM; T`QiQMfb#v r?B+? i?2b2 KmQMb r2`2 +`2�i2/X

Ç �+Q @ �+QTH�M�`Biv- �M;H2 #2ir22M irQ +`QbbBM; #2�K �t2b �i BMi2`�+iBQMTQBMi 7Q` ;Bp2M 2p2MinMX

Ç tBG- tB_ @ KQK2MimK HQbb Q7 � T`QiQM ;QBM; iQ i?2 H27if`B;?i bB/2 Q7�6SX h?Bb p�Hm2 Bb +�H+mH�i2/ 7`QK KmQMb +�m;?i BM �hG�a mbBM; TQb@BiBp2fM2;�iBp2 η p�Hm2X

R3

jXjX .�i�b2i

Ç `mMnM- 2p2MinM @ B/2MiB}+�iBQM MmK#2`b Q7 �M 2tT2`BK2MibX _2H�iBQM#2ir22M i?2b2 B/2MiB}2`b Bb i?�i 7Q` QM2 `mMnM K�Mv 2p2MinMb �`2 T2`@7Q`K2/X 2p2MinM +�M #2 b22M �b B/2MiB}+�iBQM Q7 irQ bT2+B}+ #mM+?2b Q7T`QiQMb r?B+? +QHHB/2 �i ASX `mMnM Bb i?2 B/2MiB}+�iBQM MmK#2` Q7 i?2r?QH2 2tT2`BK2Mi @ 2X;X B/2MiB}+�iBQM Q7 �HH #mM+?2b Q7 T`QiQMb �++2H2`@�i2/ BM i?2 b�K2 /�vX

jXjXRXk .�i� +QHH2+i2/ �i QM2 �6S bi�iBQM

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Ç bB/2 @ bB/2 r?2`2 `2+Q`/BM;b r2`2 K�/2X G16h bB/2 +Q``2bTQM/b iQ y-_A:>h bB/2 +Q``2bTQM/b iQ RX qBi? T`2pBQmb FMQrH2/;2 �i r?B+? bB/2Bb 2�+? bi�iBQM HQ+�i2/- i?Bb +QHmKM Bb `2/mM/�MiX

Ç tGQ+�H- vGQ+�H @ +QQ`/BM�i2b Q7 � i`�+F �i ;Bp2M bi�iBQMX

Ç taHQT2- vaHQT2 @ i?2b2 p�`B�#H2b �`2 �bbQ+B�i2/ rBi? i`�+F@+`2�i2 T`Q+2bb7`QK i?2 7Qm` TH�M2b �i QM2 bi�iBQMX h?2 bHQT2 Bb rBi? `2bT2+i iQ i?2BMBiB�H T`QiQM #2�KX

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RN

jX _2�HBb�iBQM

jXjXRXj .�i� +`2�i2/ mbBM; i?2 BM7Q`K�iBQMb 7`QK L1�_ �M/6�_ bi�iBQM

Ç MS`QiQMb @ MmK#2` Q7 `2+QMbi`m+i2/ T�`iB+H2b mbBM; i?2 BM7Q`K�iBQMb 7`QKL1�_ �M/ 6�_ bi�iBQMb �i i?2 b�K2 bB/2X _2+QMbi`m+iBQM Bb /QM2 #v+QKT�`BM; +QQ`/BM�i2b Q7 � i`�+Fb �i L1�_ �M/ 6�_ bi�iBQMX q?2MirQ +QQ`/BM�i2b �`2 +HQb2 iQ;2i?2` i?2v �`2 #2HB2p2/ iQ Q`B;BM�i2 7`QKQM2 T�`iB+H2X MS`QiQMb �HbQ BM+Hm/2b �HH +QK#BM�iBQMb Q7 TQbbB#H2 i`�+Fi`�D2+iQ`vX 6Q` 2t�KTH2- B7 r2 ?�p2 QM2 i`�+F �i L1�_ bi�iBQM rBi?xLocal = −5 �M/ i?2M irQ i`�+Fb �i 6�_ bi�iBQM rBi? xLocal1 = −5.5�M/ xLocal2 = −4.5- MS`QiQMb 2[m�Hb iQ kX

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jX8X aB;M�Hf#�+F;`QmM/ /2}MBiBQM

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A �HbQ `2TH�+2/ tBG �M/ tB_ +QHmKMb rBi? tBJJ �M/ tBJJQi?2`.B` +QHmKMbiQ K�F2 Bi +H2�` rBi? r?B+? ξ p�Hm2 r2 �`2 rQ`FBM; rBi?X tBJJ Bb i?2 KQ@K2MimK HQbb +�H+mH�i2/ 7`QK KmQM �bbQ+B�i2/ rBi? i?2 +Q``2bTQM/BM; bB/2-tBJJQi?2`.B` Bb i?2 KQK2MimK HQbb +�H+mH�i2/ 7`QK � KmQM +Q``2bTQM/BM;iQ i?2 Qi?2` bB/2X 6Q` side = 0- tBJJ 2[m�Hb iQ tBG- 7Q` side = 1 tBJJ 2[m�HbiQ tB_X

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diff = xiMM − xiRecoAFPxiMM UjXRV

h?Bb +�H+mH�i2b ?Qr /Bz2`2Mi Bb i?2 +�H+mH�i2/ ξ 7`QK KmQMb �M/ +�H+mH�i2/ξ p�Hm2 7`QK � i`�+FX

LQr 7Q` ;2iiBM; bB;M�H b�KTH2b A Tmi 7QHHQrBM; +`Bi2`B�,

RX m < 70 :2o Q` m > 105 :2o

kX diff < 0.1

6Q` #�+F;`QmM/ A ?�p2 mb2/ bBKBH�` +`Bi2`B�- QMHv rBi? /Bz = RXyX

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kR

jX _2�HBb�iBQM

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kk

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jX _2�HBb�iBQM

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z = x− µ

σUjXkV

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k9

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k8

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kd

jX _2�HBb�iBQM

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p(diff ) = le−ldiff

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p = (pe + pm)/2 UjX9V

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