���������
���
��������������
��� �!�#”%$’&)(*�,+.-!”/$�01�32406575701(,+’-98:$;�!$�<>=?$�<1$@2:A9BDCECEF6-*�6�*G3H@IJ�6(*KMLON�0 P,$�C75RQTS(*IUI?$�CWV X�Y[Z]\;^;_a`cbed.fW_Wghghikjl^]m�_Wgh_n\�befMo�p4_Wq>\rbhseZ�_Wj.s�tvu�wxuzy9\;{lg�|vm)_Egh_n\�befMo9}*~n�;��� fMo6�l�k�Rp4beik�’_�}
m�_n����\;jl��}1�R�@������� ~E|[�������6}!�a� t
��� ik�k�U\�Z�_Eshse_a�4j1ik�’_Ebeghi�s[�.}1���;���6sM\rse_
�6shbe_W_7sn}�� \;�k_WZ�}l�4mT���;�;� ~�}>�a�1t
���a� p���Y[m4�1u4} m��>� dr��_Eb4 �o>\��lghgh_W_
¡.},~r¢r£’¤;����_Ebe�kikj9} � _7beZ]\;j.�
¥ �.\;jlj*} �¦_Ed�j6{!§�¨)be_Wgh_n\�befMo9© \rshsn© fEd�Z�}>^;d;bhb7¨)��ik�k�¦\;Z�_Eshse_�© _n� �9}l� �¦\��lgM¨)ªlbegOsn© ^;Z]�*© �1_
d�bei¦^;ikj>\;�k����q1�l{l�kikghol_W��ikj
�)bhbn} � ©>\�j>� �#«�l�k�k_Ebn}�¬@©v[�4_E�1bM\;�*�4_7s[�®d�be�6gW¯1shbeikfM� g�d�°cseol_4shbM\;�1_W± }
� q1beikj1^�_Ebn}*~n�;��¤ ©
²]³c´WµW¶r·>¸;µ�¹ u®o1_�fWd�j6�’_Ebe^;_WjlfE_ºd�°�{>\�f7�.|»q1bed;q>\;^�\�seikd�j¼�k_n\rbejlikjl^#ikg�\;jl\;��� �W_n�
ghd�\;g4sed]_E½ q1�U\�ikjºfEd�Z�Z�d�j�q1ol_Wj1d�Z�_Wj1d�j�d;{lgh_Ebe��_n��{6��q1bM\�fEsei�sei¦d;jl_EbegW© � \�j6�
�1j>�1_EghikbM\�{l�k_]{�_Wo>\n�6ikd;beg
d;°�{>\�f7�6q bed�q�fn\�j#{�_]\n�’d�i¦�1_W�3��ikseo�shbeikfM�6g
seol\�sD\�be_
bM\rbe_W���¾_7½1q�d;gh_n�¾ikjºgh_Ebeikd��1g�se_Ef7o1jlikfn\;�%q1�l{l�kikfn\rsei¦d;jlgW©,u®olikgaq>\�q�_Eb�^�ik�’_Egaghd�Z�_
d�°cseold�gh_RshbeikfM�6gW}>\�j>��d�¿!_Ebeg�_E½ ql�¦\;jl\�seikd�j1g)d�°���o.�]seol_E�]�®d�be��©
� \�j6��\;� seold;begDo>\n�’_�gh�1^�^�_EgOse_n��seo>\�sDgh_WfWd;j>�6|Àd�bM�1_EbDd�q seikZ�i¦�W\�seikd�jÁZ�_Eseo1d6�1g
\rbe_®\�� ��\�j.sM\;^�_Ed��lg*°Jd�bcjl_W� bM\;�.j1_Es9shbM\�ikjlikjl^ ©rYÀs�ikg�gho1dn��j�seol\�s,Z�d�gOs)[fW�¦\;ghghikfn\��k±
gh_WfEd�j>�6|»d;bM�1_7bDZ�_7seold6�1gR\�be_�ikZ�q1bM\�fEseikfn\;�c°Jd�b
�U\rbe^�_]jl_E�1bM\;�%j1_Es[��d;be�6gW©�t�°J_E�
Z�_Eseo1d6�1g�\rbe_aq1bed�q�d;gh_n��seol\�s)�1dDjld;s�ol\r��_4seol_Wgh_a�kikZ�i�sM\�seikd�j1gW©
 ÃlÄ�Å�Æ!ÇaÈDÉ
Ê,Å!ËeÇ�Ä
24�1ÌWÍ>Î!C701Î*�6Ïl�.5E=U01�Á=?K���< $;C7ÐÁÎ,0 Î*(!I?� C]�!$;(!CE� I��!$�5eÑ)01C7ÍÁI?$;� C7�*=U�!Ï#� IUÏ10 CE=¦5EÒ!ÓÔP,$;Ì�� (*K7$
=¦5
=JK
Ì�0 �*Ì�$�Î�5E(*�6I?I?Ð3K7=UÓ�Î!I?$ -,Ìr01Ó�Î*(�5E�657=?0 �*� IUI?к$�Õ�Ì�=U$;�l5;-9� �*G�P,$;Ì�� (*K7$�=¦5
0 Ö×57$;�ÁÑ)01C7Í�K;A
Ø�0.Ñ4$�< $;C;-'Ï1$r5M5E=U�*Ï:=U5�570�Ñ40 CEÍ�Ñ4$�I?IÀ-6� �*G�KM01Ó�$�57=?Ó�$;K�570@Ñ40 CEÍÙ�.5�� IUI[- Ì�� ��K7$�$;ÓÚÓ�0 CE$R06Ö
�6���6C75�5EÒ*�6�º��K7Ì�=U$;�*Ìr$1A1ÛD$;K7=UÏ1�!=?�!ÏÙ�6�9G�57CW�6=?�!=?�!Ï]�]�!$�5eÑ)01C7Í�(*K7=U�!ÏÙP*� ÌWÍ>Î!CE0 Î�CE$;Ül(!=?C7$�K
Ó�� Í>=U�!Ï
Ó�� �>Ð@K7$�$;Ó�=U�!Ï1IUÐ@�6CEP!=U57CW�6CEÐDÌWÒ!01=?Ì�$;K�KM(9ÌWÒ]� K/57Ò!$)�l(*ÓÙP,$�C®�6�*G@5eÐ>Î,$;Kv06Ö!�!0�G�$�K�-
I?�’Ð1$�CWK�->I?$;�6CE�!=?�!Ï�CE�657$�K�-�5ECE� =U�*=U�!Ï�� �*G¾57$;KM5DK7$r5WK�-*� �*G�KM0�ÖÝ01CM5EÒ%A*ÞRÒ!$�KM$]ÌWÒ*0 =JÌr$;KaÌ;�6��P,$
ÌrCE=¦5E=?Ì;�6I[-�Ð $�5/5EÒ!$�CE$�=JK/�!0�ÖÝ0l01IUÎ*C70>06Ö�CE$;Ì�=UÎ,$�ÖÝ01CvG�$�Ìr=JG�=U�*Ïa57Ò!$;ÓßP9$�Ì�� (*KM$�57Ò!$;Ð@� C7$�I?� C7Ï1$�I?Ð
Î!C701P!I?$�Óà� �*G�G!�.5W�:G!$�Î,$��*G�$;�l5;A Ø
0.Ñ)$;< $�C�-�57Ò!$;C7$a� C7$RÒ!$;(!C7=JKM57=JÌ�K��6�9G�K70 Ó�$R(!�*G!$�CEIUÐ>=?�!Ï
57Ò!$;0 CEÐ�57Ò*�65
Ì�� �¾Ò!$;IUÎ�Ï1(!=?G!$@��Î!CW� Ìr57=U57=?0 �!$;CR570�Ó��6Í1$:P,$r5757$;C
ÌWÒ!0 =JÌr$�K�A
áh�Ù5EÒ!$Râ*CWKe5�K7$;Ìn5E=U01��P9$;IU0.ÑãÑ)$R=?�15EC70�G�(9Ìr$aKe5W�6�*G*�6CWGÙP*�1ÌWÍ>Î!C701Î*�6Ïl�.5E=U01�]�6�*G�G�=JK7Ì�(*K7K
���>(!ÓÙP,$�CD06Ö�K7=UÓ�Î!I?$]Ò!$;(!C7=JKM57=JÌ�K�01C�5EC7=JÌWÍ�KaÖÝ0 CD=UÓ�Î!CE0.<>=U�*Ï�=¦5WK�Î,$�C7ÖÝ0 CEÓ�� �*Ìr$1A*äå$Ù�!$�æ>5
G�=?KEÌr(9K7K�=JKEKM(!$�K]0 ÖaÌ�0 �>< $;C7Ï1$��*Ì�$ A�äå$�57Ò!$;�çG�$�K7Ì�C7=?P9$��#ÖÝ$�Ñéè7Ì�I?�1K7K7=?Ì;�6IJê¾K7$;Ì�0 �*G�L[01CEG�$;C
�!0 ��LOI?=U�!$��6C�01Î�57=?Ó�=Uë��.57=?0 �T5E$;ÌWÒ!�!=JÜl(!$;Kº�6�*GìK7Ò!0.Ñí5EÒ*�.5�5EÒ!$�=?C¾� Î!Î!I?=?Ì;�.5E=U01�ç5E0z�!$�(*CE� I
�!$r5eÑ40 CEͼ57CW�6=?�!=?�!ϼ=JK�< $;C7ÐzI?=?Ó�=U57$�Gc-RG�$;K7Î!=U57$#Ó��6�>ÐãÌ�I?� =UÓ�K�5E0¼57Ò*$ÁÌr0 �l5ECE� C7Ðz=?�ì57Ò*$
IU=U57$;CE�657(!CE$ A�î�=U�9�6I?IUÐ1-�Ñ)$�Î!CE$;K7$��l5��ÁÖÝ$;ÑïK7$;Ì�0 �*G�L[01CEG�$;CÙÓ�$r5EÒ!0�G!K�57Ò9�.5ºG�0¼� Ì;Ìr$;IU$;CE�657$
IU$��6CE�!=U�*Ï�=?��Ìr$�C75E� =U��Ì��1KM$�K�A
ð ñÙò%ó®Æ*Ä
Ë7Ä�ôõó�Ä
È÷öxò/Ä�ò%Æ*ó®ø7Ëeùcó�Å!ËeÇ�Ä
ÞRÒ!$�CE$��6CE$�KM$;< $�CW�6I�� Î!Î!CE01� ÌWÒ*$;K
570Á�6(!570 Ó��657=JÌ�Ó��1ÌWÒ!=?�!$�IU$��6CE�!=U�*Ï*-cP!(�5�ÓÙ(*ÌWÒú06Ö457Ò*$
KM(*Ì;Ìr$�K7KMÖÝ(!I>�6Î!Î!CE01�1ÌWÒ!$;K/Ì��6�ÙP9$4Ì��.5E$�Ï10 CE=Uë;$;G�� K�û6üEý þ.ÿ�������� �Wý�
��Wþ
���Wý.ü��9ÿ��lû����������;þ�
nA’ÞRÒ*$
IU$��6CE�!=U�*ÏÁÓ�� ÌWÒ!=?�!$ -®� KÙC7$;Î!CE$;K7$��l57$�Gú=U�çî�=?Ï (!CE$��1-�Ì�0 Ó�Î!(�5E$;K���ÖÝ(!�*Ìr57=?0 ������� ��
���
ÑaÒ!$�CE$�� �
=JK/5EÒ!$��!L[57Ò�=U�*Î!(�5�Î*�65M57$;C7�/-‘� �*G�� C7$;Î!CE$;K7$��l5EK/57Ò!$�Ì�0 I?IU$�Ìn5E=U01�Ù06Ö,� G��e(*KM5E� P!I?$
Î*�6CW�6Ó�$r5E$�CWK�=?�ú57Ò!$3KMÐ�KM57$�Ó�A���Ìr0lKe5]ÖÝ(*�*Ìn5E=U01����������� �!�”
#����� �$
#���%�r-/�$;�1KM(*C7$�K
57Ò!$�G�=JKEÌrCE$�Î*� �*ÌrÐ]P,$r5eÑ4$�$;�!� � -‘5EÒ!$�è7Ì�0 CEC7$�Ìn5Wê
01C®G!$;K7=UCE$;G�0 (!57Î!(�5�ÖÝ01C�Î*�.5757$;C7�&� � – � �*G
57Ò!$:0 (�5EÎ!(�5aÎ!CE0�G�(*Ìr$�G�P>Ð�57Ò!$@K7Ð>KM57$;Ó�AlÞRÒ!$@�’< $;CE� Ï $�Ì�01KM5�ÖÝ(!�*Ìr57=?0 �'��(*)
+-,/.0� ����=?K)57Ò*$
�'< $�CW�6Ï1$
0 Öv5EÒ!$�$�CEC701CEK1����0.< $�CR��K7$r5�06Ö�=U�*Î!(�5-2.0 (�5EÎ!(�5
Î9�6=?CEKRÌ�� IUI?$;G¾5EÒ!$@57CW�6=?�!=?�!Ï�KM$�53 ���:+�
#�¾+4�4
6575/5758���:9�
;�&9<�-=1A�áh�]5EÒ!$4K7=?Ó�Î*IU$�Ke5�KM$�5M5E=U�!Ï9-�57Ò!$4IU$��6CE�!=?�!Ï
Î!CE0 P*IU$;Ó Ì�0 �*K7=JKe5WK/=?�
â*�*G�=?�!Ï�57Ò*$]<.�6I?(!$�06Ö<� 57Ò*�65�Ó�=?�!=?Ó�=Uë;$;K:� (*)#+-,7. � ���rA*áh�#Î!CW� Ìr57=JÌr$1->57Ò!$]Î,$�C7ÖÝ0 CEÓ��6�*Ì�$
06Ö�5EÒ!$�KMÐ�KM57$�Ó 0 � �º57CW�6=?�!=?�!Ï�KM$�5@=JK:06Ö�I?=U5M57I?$�=?�15E$�CE$;KM5;AcÞRÒ!$�Ó�0 CE$ÙCE$�I?$�<.�6�l5@Ó�$;� K7(!CE$
=?KD57Ò*$�$;C7CE0 CDCE�657$Ù0 Ö�57Ò*$�K7Ð�Ke5E$�Ó =U� 57Ò!$�â*$;I?G%-,ÑaÒ*$�CE$Ù=U5:Ñ40 (!IJGÁP,$�(*KM$�GÁ=?� Î!CW� Ìr57=JÌr$1A
ÞRÒ!=?K]Î9$;CMÖÝ01C7Ó��6�9Ìr$�=?K]$;KM57=?Ó��657$�G P>ÐÁÓ�$�� K7(!C7=?�!Ï357Ò*$�� Ì�Ì�(!CW� ÌrÐ 0 �ú�#KM$�5]06ÖaK7� Ó�Î*IU$�K
G�=?K>�e0 =?�l5)ÖÝCE0 Óõ5EÒ!$:57CW�6=?�!=?�!Ï�K7$r5�->Ì;�6I?IU$�G�5EÒ!$:57$;KM5aKM$�5;A!ÞRÒ!$:Ó�01KM5RÌ�0 Ó�Ó�0 �!I?Ð�(*KM$�GºÌ�01KM5
ÖÝ(!�*Ìn5E=U01��=?KR5EÒ!$]Q#$��6�@?�Ül(*�6CE$;GBA�CEC701CDC
� � � �E �>� �GF ���H� �
#���;� F
��(*)
+-,7.��
�
I�J�6Kv+
� �
COST FUNCTION
LEARNING
MACHINE
Parameters
Output
E0, E1,….Ep
Error
Desired
Output
D0, D1,…Dp
Input
M(Z,W)
Z0, Z1,… Zp
W
L
ÞRÒ!=?K�ÌWÒ*�6Î�5E$�C�=JK�ÖÝ0�Ì�(*KM$�G�0 ��KM57CW�.57$;Ï =?$;K�ÖÝ01C�=?Ó�Î*C70.<>=?�!Ï:57Ò!$�Î*C70�Ìr$�K7K�06ÖcÓ�=U�!=?Ó�=Uë;=U�*Ï
57Ò!$ºÌ�01KM5�ÖÝ(!�*Ìr57=?0 �%A�Ø�0.Ñ4$�< $;C;-,5EÒ!$;K7$�Ke5ECE�657$;Ï =?$;K@ÓÙ(9Ke5ÙP,$�(*K7$;Gú=?�¼Ìr0 �Q�e(!�*Ìn5E=U01�úÑa=¦5EÒ
Ó�$�57Ò!0�G!K�ÖÝ0 C�Ó��.æ�=?Ó�=?ë�=?�!Ï357Ò*$��!$r5eÑ40 CEÍSR K@�6P*=UI?=¦5eÐÁ570Áû ��� ��ü7ý �kÿ/T �r-/57Ò*�65]=?K;-c570�Î!CE$;G!=?Ìr5
57Ò!$�Ìr0 CECE$;Ìn5R5W�6CEÏ $r5WKaÖÝ01C�Î*�.5757$;C7�*K�57Ò!$�IU$��6CE�!=?�!Ï�KMÐ�KM57$;Ó Ò*�1Ka�!0 5DÎ!CE$�<>=?0 (*K7IUÐ3KM$;$���ÖÝ01C
Ó�01C7$�G�$�5E� =UIU�nA
Þ/0 (!�*G�$;CEKM5E� �*G¼Ï $;�!$�CW�6I?=?ë;�.5E=U01�%-/I?$r5�(*K�Ìr01�*K7=?G�$;C�Ò*0.Ñ P*� ÌWÍ>Î!CE0 Î*� Ï1�657=?0 �úÑ)01C7Í�K;A
ä $#KM5E�6C75�Ña=¦5EÒT�úK7$r5�06Ö@K7� Ó�Î!IU$�K�$;�1ÌWÒç06Ö:ÑaÒ!=JÌWÒã=JK��6�ã=U�!Î*(�5-2.0 (�5EÎ!(�5�Î*� =UC�0 Ö
57Ò*$
ÖÝ(!�*Ìn5E=U01�º5E0�P,$@IU$��6CE�!$;G%A�?>=?�*Ì�$D5EÒ!$@Ó�$;� K7(!CE$�Ó�$��l54Î!C70�Ì�$;KEK�=JK406Ö×57$;�¾�*0 =JKMÐ1-15EÒ!$�CE$:Ó��’Ð
P9$ú$�CECE0 CWK�=?��57Ò*$úKE�6Ó�Î!I?$;K;A4ä $¼Ì�� � =?Ó��6Ï =?�!$ 57Ò*�65�=UÖ�Ñ4$úÌr0 I?I?$;Ìn5E$;GxÓ�(!IU57=?Î!IU$
�����
06Ö4KE�6Ó�Î!I?$;K:5EÒ!$��ú$�� ÌWÒúKM$�5@Ñ40 (*I?G IU0>01Í �3IU=U5M5EIU$�G�=/V�$�CE$��l5]P9$�Ì�� (*KM$�0 Ö�57Ò*$��!0 =JKM$�� �*G
P9$�Ì��6(9KM$R06Ö,57Ò*$�G�=WV�$�CE$��l5�Î,0 =?�l5EK�KE�6Ó�Î!I?$;GcAXA)� ÌWÒ�06Ö,57Ò!$�KM$�G!�65E�@K7$r5EK®Ñ40 (*I?G��6IJK70DCE$;K7(!IU5
=U���!$�5eÑ)01C7Í�K�Ña=¦5EÒ�Ó�=?�!=?Ó��:57Ò*�65��6CE$RK7I?=UÏ1Ò15EIUÐ�G�=WV�$�CE$��l5�ÖÝCE0 Ó�$;� ÌWÒ�065EÒ!$�C�� �*GÙÖÝC701ÓÚ57Ò*$
57CE(!$�ÖÝ(*�*Ìn5E=U01�%A.áh�]5EÒ!=?K®ÌWÒ*� Î�57$;C;-�Ñ4$4Ì�0 �*Ì�$��l57CW�.5E$�0 ��=UÓ�Î!CE0.<>=U�!Ï
57Ò!$4Î!CE0�Ìr$;KEKv06Ö!â*�9G�=U�*Ï
57Ò!$RÓ�=U�*=UÓ�(!ÓßÖÝ0 C�5EÒ!$)Î9�6C757=JÌr(!IJ�6C®KM$�5�06Ö*$�æ�� Ó�Î!IU$�Kv57Ò*�65�Ñ4$4� C7$4Ï =?< $;�%A.8:$��!$;CE� IU=?ë;�657=?0 �
57$;ÌWÒ*�!=?Ül(!$�K�5EC7Ð35E03Ì�0 CEC7$�Ìn5�ÖÝ01C�57Ò*$�$;C7CE0 CWKa=?�15EC70�G�(9Ìr$;G =U�l5E0�57Ò*$��!$�5eÑ)01C7Í�� KD��CE$;K7(!IU5
06Ö®0 (!CaÌWÒ!01=?Ì�$:0 Ö®G*�.5E�1KM$�5;A!24065EÒ3� C7$@=?Ó�Î901CM5W�6�l5;A?>$�<1$�CW�6Ia5EÒ!$�01C7$�57=JÌ��6ID$4V�0 C75EK¾Ò*�'< $Á� �*�6I?Ð>ë�$�GT57Ò!$åÎ!CE0>Ì�$;KEK�06Ö]I?$;� C7�*=U�!ÏçPlÐìÓ�=?�!=¦L
Ó�=?ë�=?�!Ï�5EÒ!$�$�CECE0 C�0 �¼�35ECE� =U�!=?�!ÏÁK7$r5 �À��Î!CE0>Ì�$;KEK�KM01Ó�$r57=?Ó�$;K�Ì��6I?I?$;G A�Ó�Î!=?C7=JÌ�� I�Na=JKMÍ
Q#=U�*=UÓ�=?ë;�.5E=U01� � � ��� – � ���OA?>0 Ó�$
0 Ö%57Ò*01K7$�57Ò*$�0 CE$r5E=?Ì;�6I��6�*� IUÐ�K7$;K)�6CE$�P*� K7$;G�0 �¾G!$;Ìr01Ó�Î90lKM=?�!Ï�5EÒ!$DÏ1$��!$;CE� IU=?ë;�6L
57=?0 ��$�CECE0 C�=?�l570@5eÑ40�57$;C7Ó�KDC P!=J� K)�6�*G�<.�6CE=J�6�*Ì�$ �»K7$�$�$1A Ï9A � � E �*�nAlÞRÒ!$�P!=J� K�=?K)��Ó�$;� K7(!CE$
06Ö9Ò*0.ÑzÓÙ(*ÌWÒÙ57Ò!$R�!$�5eÑ)01C7Í@01(�57Î!(!5;-6�'< $;CE� Ï $�G@0.< $�C®�6I?I>Î90lK7K7=?P!IU$RG!�65E�@KM$�5EK®G�=/V,$;CEKvÖÝCE0 Ó
57Ò!$
G!$;K7=UCE$;GÙÖÝ(!�*Ìr57=?0 �%AlÞRÒ!$�<.�6CE=?� �*Ìr$R=JK��@Ó�$;�1KM(!CE$R06Ö�Ò!0.ÑTÓÙ(*ÌWÒ�57Ò*$��!$r5eÑ40 CEÍ�0 (!57Î!(�5
<'� C7=?$;K)P,$r5eÑ4$�$��3G!�.5W� K7$r5WK�A$A�� C7I?Ð�=U�¾57CW�6=?�!=?�!Ï*-157Ò!$@P!=J� K)=JK)IJ�6CEÏ $DP9$�Ì�� (*KM$D57Ò*$D�!$�5eÑ)01C7Í
0 (�5EÎ!(�5D=JK
Ö»�6C�ÖÝCE0 Óï5EÒ!$�G�$�KM=?CE$;G3ÖÝ(!�*Ìr57=?0 �%A�ÞRÒ!$�<'� C7=J�6�9Ìr$]=JK�<1$�CEÐ3K7Ó��6I?I/P,$;Ì�� (*K7$]57Ò*$
G!�.5W��Ò*� K
Ò*� G3I?=¦5757I?$Ù=?���*(!$;�*Ìr$]Ð1$r5�A*"/�657$]=?��57CW�6=?�!=?�!Ï*-�5EÒ!$]P!=J� K�=?KDKMÓ��6I?I%P,$;Ì;�6(*K7$�57Ò*$
�!$r5eÑ40 CEÍ�Ò*� KDIU$��6CE�!$;GÁ57Ò!$�(!�*G!$�CEIUÐ>=?�!ϺÖÝ(*�*Ìn5E=U01�%A%Ø�0.Ñ4$�<1$�C�-*=UÖ�57CW�6=?�!$�G�570>03IU01�!Ï*-,57Ò*$
�!$r5eÑ40 CEÍ�Ña=?I?I�� I?K70]Ò*�’<1$�I?$;�6CE�!$�G�57Ò!$:�!01=?K7$DK7Î9$�Ìr=Uâ9Ìa5E0Ù5EÒ*�.5RG!�.5W� K7$r5�AlÞRÒ!=JK4=?K)CE$rÖÝ$�CECE$;G
570#� K:0.< $;CM5ECE� =U�*=U�!Ï9A*áh�¼K7(*ÌWÒ ��Ì��1KM$1-,57Ò!$�<.�6CE=?� �*Ìr$�Ña=?IUI�P,$�I?� C7Ï1$�P,$;Ì;�6(*K7$Ù5EÒ!$��!01=?K7$
<'� C7=?$;K�P,$r5eÑ4$�$;��G!�65E�1KM$�5EK;A�áO5�Ì;�6�ÙP,$aKMÒ*0.Ña�]57Ò9�.5�57Ò*$4Ó�=?�!=?ÓÙ(!Óß5E065W�6I�$�CECE0 C�Ña=UI?I�0�Ì�Ìr(*C
ÑaÒ!$��357Ò*$]KM(!Ó 06Ö�P!=?�1Ka�6�*G3<.�6CE=J�6�*Ì�$:� C7$@Ó�=U�*=UÓ��6I[A
ÞRÒ!$�CE$3� C7$#�å�>(!ÓÙP,$�C�0 Ö
5E$;ÌWÒ!�!=JÜl(!$;K��Ý$ A Ï*A�$��6CEIUÐzKM5701Î!Î!=?�!Ï*-�CE$�Ï1(!IJ�6CE=Uë��.57=?0 � ��ÖÝ01C
Ó��6æ�=UÓ�=?ë�=?�!Ï�57Ò!$�Ï1$��!$;CE� IU=?ë;�657=?0 �¾� P!=?IU=U5eÐ�06Ö����!$r5eÑ40 CEÍ�ÑaÒ!$;�3(9KM=?�!Ï�P*� ÌWÍ>Î!CE0 Î/A
ÞRÒ!$ú=?G�$��ç0 ÖÙ5EÒ!=?K#ÌWÒ9�6Î�5E$�C�-)5EÒ!$�CE$rÖÝ01C7$1-R=?K35E0TÎ*C7$�KM$;�15�Ó�=U�*=UÓ�=?ë;�.5E=U01� KM57CW�.5E$�Ï1=U$�K�ÝÏ =?< $;�Á�ºÌ�01KM5�ÖÝ(!�*Ìr57=?0 � �D�6�*G35EÒ!$]5EC7=JÌWÍ�K
�1K7K70�Ìr=J�.57$�G�Ña=¦5EÒÁ=?�*ÌrCE$;�1KM=?�!Ï�57Ò*$�K7Î9$;$;GÁ� �*G
Ü1(9�6I?=¦5eÐz0 Ö
5EÒ!$�Ó�=?�!=?Ó�=Uë��.57=?0 �/A�áO5�=?K�Ò!0.Ñ4$�<1$�C�ÌrI?$;�6C�5EÒ*�.5�5EÒ!$#ÌWÒ!0 =JÌr$306ÖD57Ò!$#Ó�0�G�$�I�ÝÓ�0�G�$�I%K7$�I?$;Ìr57=?0 � �r-15EÒ!$��6CWÌWÒ!=U57$;Ìr57(!CE$D� �*Gº57Ò!$�Ìr0lKe54ÖÝ(!�*Ìr57=?0 �3=?KRÌ�C7(*Ì�=?� I,ÖÝ0 CR0 P�5W�6=?�!=?�!Ï
���!$r5eÑ40 CEÍ]5EÒ*�.5)Ï $��*$�CW�6I?=Uë;$;K�Ñ4$�I?IÀA�?>0]Í1$�$�Î�=?��Ó�=U�9G�57Ò*�65)=UÖc57Ò!$
ÑaC701�!Ï�Ó�0>G!$�I�ÌrIJ� KEK�=?K
(*KM$�GÙ� �*G��!0:Î!CE0 Î,$�C�Ó�0�G�$;I�KM$;IU$�Ìn57=?0 �Ù=?K®G�01�!$ -;57Ò!$;��$;< $;�Ù�
K7(!Î,$�CEPÙÓ�=U�*=UÓ�=?ë;�.5E=U01�ÙÑa=?IUI
ÌrI?$;�6CEI?Ð��!065RÒ!$�I?Î�< $;C7Ð�ÓÙ(9ÌWÒ%A�áh�ºÖ»�1Ìn5�->57Ò!$@$ræ�=JKe5E$��*Ì�$@06Ö/0.<1$�C757CW�6=?�!=U�*ÏÙÒ*�1K)I?$;G3K7$�< $;CE� I
�6(�5EÒ!0 CWKR570¾KM(!Ï1Ï $�Ke5a5EÒ*�.5
=?�*�1Ì�Ìr(*CE�657$�Ó�=U�*=UÓ�=?ë;�.5E=U01� �6I?Ï 01C7=U57Ò*Ó�KaÌ;�6�#P,$]P,$r5M5E$�CD57Ò*� �
Ï 0>0�Gº01�!$;K;A
4Å>ó�ÄDÈ�ó®Æ*È��úó�Ê�
��DÆ!Ç��
ó®ô�ó�Å!ËeÇ)Ä
��IU57Ò!01(!Ï Òú5EÒ!$�5EC7=JÌWÍ�KÙ�6�9G¼�6�*� IUÐ�K7$;K�=?�ú57Ò!=JK�Î*�6Î,$�C��6CE$�Î!C7=?Ó��6CE=UI?Ð Î*C7$�KM$;�15E$;Gú=?�¼57Ò*$
Ìr0 �l5E$ræ>5Ù06Ö�èEÌrIJ� KEKM=JÌ�� I?ê3ÓÙ(*I¦5E=¦LOI?�’Ð1$�C�ÖÝ$;$;G>L[ÖÝ0 CEÑR�6CWG �*$�(!CW�6I��*$r5eÑ40 CEÍ>K;-%Ó��6�>Ðå06ÖR57Ò*$�Ó
�6IJKM0��6Î*Î!IUÐ�570�Ó�01KM5�0657Ò*$�CaÏ CW� G!=U$;�157L[P9� K7$;G�I?$;� C7�!=?�!Ï�Ó�$r5EÒ!0�G!K�A
ÞRÒ!$)K7=UÓ�Î!I?$;KM5/ÖÝ01C7Ó 0 Ö!ÓÙ(!IU57=?I?�’Ð1$�C%I?$;� C7�*=U�!Ï
Ó��1ÌWÒ!=?�!$�5ECE� =U�!$�G�Ña=U57Ò]Ï1CE�1G�=U$;�l5MLOP*� K7$;G
IU$��6CE�!=U�*ÏD=JK�K7=UÓ�Î!I?ÐÙ�@Ke5W� ÌWÍ]0 Ö9Ó�0�G�(!I?$;K;-6$;�1ÌWÒ�0 Ö9ÑaÒ!=JÌWÒ�=UÓ�Î!I?$�Ó�$��l5WK��DÖÝ(!�*Ìn5E=U01����. �
� . ��� .
�� .�� + �n-lÑaÒ!$�CE$�� . =?K)�]<1$;Ìn5E0 C�CE$�Î*C7$�KM$;�15E=U�*Ï@57Ò!$D0 (�5EÎ!(�5)0 Ö�57Ò!$DÓ�0�G�(*IU$1-�� .=?K)57Ò*$:<1$;Ìr570 C406Ö/57(!�*� P!I?$:Î9�6CW�6Ó�$r5E$�CWK�=?��5EÒ!$@Ó�0�G�(*IU$ �»��K7(!P*K7$r5R06Ö����r-��6�*G�� .�� + =?K57Ò!$:Ó�0>G!(!IU$ R K)=?�!Î!(�5R< $�Ìn5701C �À� K)Ñ)$;IUIc� K�57Ò!$:Î!CE$�<>=?0 (*K�Ó�0�G�(*IU$ R K40 (!57Î!(�5R< $�Ìn5E0 C-�nA1ÞRÒ*$
=U�!Î*(�5����:5E0Ù5EÒ!$:â*CEKM5RÓ�0�G�(*IU$@=JK�5EÒ!$@=U�*Î!(�5aÎ*�.5757$;C7�@�1��A>áOÖ/57Ò*$:Î9�6C757=J�6IcG�$�CE=?<'�657=?< $D06Ö���ÙÑa=¦5EÒºCE$;K7Î9$�Ìn54570�� . =?K4Í>�!0.Ña�%-157Ò*$��¾57Ò!$:Î*�6C757=J�6I�G�$;C7=?<.�.57=?< $�K�0 Ö ���ÙÑa=U57Ò¾C7$�KMÎ,$;Ìr5
570 � .¾� �*G � .�� + Ì�� �¾P,$]Ìr01Ó�Î*(�57$�G¾(9KM=?�!Ï�57Ò!$�P9� ÌWÍ>Ñ4� CEGºC7$�Ìr(!CECE$��*Ì�$
� � �
� � . �
� �
� � � � .
�� .�� + �
� � �
� � .
� ���
� � .�� + �
� �
� � � � .
� .�� + �
� �G�
� ��. � ���
ÑaÒ!$�CE$����
���
� � .
��.�� + �a=?K�57Ò!$ �l� Ì�0 P!=J�6��0 Ö � Ña=U57Ò#CE$;K7Î9$�Ìn5�5E0 � $�<.�6I?(*�657$;G#�65�57Ò*$
Î901=U�l5!����.
�� .�� + �n-��6�*G
������ � � .
��.�� + ��=?K
57Ò*$��l� Ìr01P!=J�6��06Ö � Ña=U57Ò CE$;K7Î,$;Ìn5
570 �çAÞRÒ!$
�1�1Ìr01P!=?� �º0 Ö®��<1$;Ìn5E0 C4ÖÝ(!�*Ìr57=?0 �#=JKa��Ó��.57CE=Uæ¾Ìr01�15W�6=?�!=?�!Ï�57Ò!$�Î*� CM5E=?� I%G�$�CE=?<'�657=?< $�K
06Ö]�6I?I�5EÒ!$Á0 (!57Î!(�5WKºÑa=U57ÒxCE$;K7Î,$;Ìn5º570ç� IUI
57Ò!$Á=?�!Î!(!5EK;A)äxÒ!$;�x57Ò*$ �6P,0.< $#$�Ü1(9�.57=?0 �9K
�6CE$3� Î!Î!I?=U$�Gz5E0 5EÒ!$#Ó�0�G�(!I?$;K�=?�ãCE$�<1$�CWKM$¾0 CWG�$�C�-�ÖÝC701Ó I?�'Ð1$�C�� 5E0úI?�'Ð1$�CB� -��6I?IR57Ò*$
Î*�6C757=J�6I,G�$�CE=U<.�657=?< $;K�06Öc5EÒ!$DÌ�01KM5�ÖÝ(!�*Ìr57=?0 �¾Ña=¦5EÒ�C7$�KMÎ,$;Ìr5�5E0��6I?I!5EÒ!$:Î*�6CW�6Ó�$r5E$�CWK�Ì�� ��P,$
Ìr0 Ó�Î!(!57$;G%A*ÞRÒ!$�ÑR�'Ð�06Ö�Ì�0 Ó�Î!(�5E=U�*Ï�Ï CW� G�=?$��l5EK4=JKaÍ>�!0.Ña��� K4P*� ÌWÍlLOÎ!CE0 Î*� Ï1�.5E=U01�%A
Þ/CW� G�=U57=?0 �9�6IlÓÙ(!IU57=UL[IJ�’Ð $;C/�!$;(!CW�6I>�!$r5eÑ40 CEÍ�K/� C7$4�DK7Î9$�Ìr=J�6I�Ì��1KM$)06Ö!5EÒ!$R�6P,0.< $)K7Ð�Ke5E$�Ó
ÑaÒ!$�CE$:57Ò!$�Ó�0�G�(!I?$;Ka� C7$��6IU57$;C7�9�.57$�G�IJ�'Ð $;CEK406Ö�Ó��.57CE=UæºÓÙ(!IU57=?Î!I?=?Ì;�.5E=U01�*K �×5EÒ!$�Ñ4$�=?Ï Òl5EK
�
�6�*G3Ìr01Ó�Î,0 �*$��l5MLOÑa=?K7$�KM=?Ï Ó�01=?GºÖÝ(!�*Ìr57=?0 �*K �Ý57Ò!$�(*�!=¦5WK#�4C
� . � � . � .�� + � E �
� .�� � ��� . � ��� �
ÑaÒ!$�CE$ ��.¾=JK���Ó��.57CE=UæºÑaÒ!01K7$@�>(!ÓÙP,$�C�0 Ö®Ì�0 I?(!Ó��*Ka=JKR57Ò*$]G�=UÓ�$;�*KM=?0 ��0 Ö � .�� + -*� �*G�l(*ÓÙP,$�CÙ0 ÖaC70.Ñ�K@=JK�5EÒ!$¾G�=?Ó�$��*K7=?0 �¼06Ö�� .,A �ï=JKÙ��<1$;Ìn5E0 C�ÖÝ(*�*Ìn5E=U01�ú57Ò*�65��6Î*Î!IU=?$;KÙ�
KM=?Ï Ó�0 =JG ÖÝ(!�*Ìr57=?0 �ú570#$�� ÌWÒúÌr01Ó�Î,0 �*$��l5]06Öa=U5EK�=?�!Î!(�5�A�� . =?K]57Ò!$�<1$;Ìn5E0 C�0 ÖRÑ4$�=?Ï Òl5E$;G
KM(!Ó�K;-!0 C
� ���hý��%ÿ������ �
n-�570�IJ�'Ð $�C���A��Î!Î!I?Ð>=U�*Ï�57Ò!$DÌWÒ*�6=?��C7(*IU$a5E0�57Ò*$�$;Ül(*�657=?0 ���6P,0.< $1-.57Ò*$
ÌrIJ� KEKM=JÌ�� I!P*�1ÌWÍlÎ*C701Î*�6Ïl�.57=?0 �
$;Ül(*�.5E=U01�*Ka�6CE$:0 P�5W�6=?�!$;G C
� ���
��� ,. ������� �
,. � � �G���� ,. � � �
� �G�
���
,! . � �
.�� +
� ���
��� ,. �#" �
� ���
����$.�� +
� J , �
, $. � ����%� ,. 5 ��& �
ÞRÒ!$]�6P,0.< $:$;Ül(*�657=?0 �*KaÌ;�6���6IJKM0�P9$�ÑaCE=U5M57$;��=U��Ó��.5EC7=Uæ�ÖÝ0 CEÓ'C
� ���
� � . � �'� �#� . �
� ���
� � . �)(X�
� ���
� � . � � .�� +
� �G�
� � . ��* �
� �G�
� � .�� + � �,+.
� ���
� � . 5 ��- �
ÞRÒ!$�KM=?Ó�Î!IU$�Ke5aI?$;� C7�!=?�!Ï'�ÝÓ�=?�!=UÓ�=?ë;�657=?0 � �4Î!CE0�Ìr$�G�(!CE$:=?��KM(*ÌWÒ���KM$�5M5E=U�!Ï�=JK457Ò!$�Ï1CE�6L
G�=U$;�l5
G�$;KEÌr$;�15�� IUÏ10 CE=¦5EÒ!Ó�ÑaÒ!$;C7$ � =JKa=U57$;CE�657=?< $�I?Ð�� GP�e(*Ke5E$;G�� K4ÖÝ01IUI?0.Ñ�KDC
���/.%� � ���/. F � � F10 � �
� � 5 �%� � �
áh� 5EÒ!$�KM=?Ó�Î!IU$�Ke5�Ì��1KM$1- 0 =?K@�3K7Ì;�6IJ�6C@Ìr01�*Ke5W�6�l5;A�Q#01C7$�KM01Î!Ò!=JKe5E=?Ì;�.5E$;GÁÎ*C70�Ìr$�G�(!CE$;KD(*K7$
<'� C7=J�6P*IU$ 0 A�áh�T065EÒ!$�C�Ó�$r5EÒ!0�G!K 0 5W�6Í $�K]5EÒ!$3ÖÝ0 CEÓ 06Ö@� G�=J�6Ï10 �*� I)Ó��657CE=¦æc-®0 C�=JK�� �
$;KM57=?Ó��657$¾06ÖR57Ò!$¾=U�><1$�CWKM$�Ø
$;KEKM=J�6�¼Ó��.5EC7=Uæú06Öa57Ò*$ºÌr0lKe5�ÖÝ(!�*Ìn5E=U01� �»K7$;Ì�0 �*G¼G!$�CE=U<.�.5E=U<1$
Ó��657CE=¦æ ��K7(*ÌWÒz�1K]=?�¼57Ò!$���$�ÑR5E0 �ç� �*G��D(*�1KM=UL��
$�ÑR5E0 �úÓ�$r57Ò*0>G*K�G�$�K7Ì�C7=?P,$;GúIJ�.57$;CÙ=?�
57Ò!$�ÌWÒ*� Î�57$;C;AS� Î!C701Î9$;C�ÌWÒ!0 =JÌr$�06Ö 0 =JK@=?Ó�Î,0 C75E� �l5@� �*GÁÑa=?IUI�P,$�G�=JK7Ì�(*K7K7$;G �.5@IU$;�!Ï65EÒ
I?�657$�C�A
� ���aò
�� Æ!ó�Ê,Å!ËMÊ�ó�ø�
�Æ9ËMÊ�
��
24�1ÌWÍ>Î!C701Î*�6Ïl�.5E=U01��Ì��6�3P,$�< $�CEÐ�K7IU0.Ñ�Î9�6C757=JÌr(!IJ�6CEIUÐ�ÖÝ01CaÓÙ(!IU57=?IJ�'Ð $�CE$;Gº�!$r5eÑ40 CEÍ�K4ÑaÒ!$�CE$
57Ò!$#Ìr0lKe5�KM(*CMÖ»�1Ìr$3=?K�5eÐ>Î!=JÌ��6I?I?Ðå�*0 ��LhÜl(*� G�CW�.5E=?Ì -v�*0 ��LhÌr01�l<1$ræc-v� �*GzÒ*=UÏ1ÒTG�=?Ó�$��*K7=?0 �*� I
Ña=¦5EÒ Ó��6�>Ð�I?0>Ì;�6I®Ó�=U�*=UÓ��3�6�*G 2.0 C �9�.5@CE$�Ï =?0 �9K�A�ÞRÒ!$�CE$�=?K:�!0¾ÖÝ0 CEÓÙ(!IJ��5E0¾Ï1(*�6CW�6�l5E$�$
57Ò*�65:� � �/5EÒ!$a�!$r5eÑ40 CEÍ�Ña=?IUI*Ì�0 �>< $;C7Ï1$�5E0@�:Ï10l0�G�KM01IU(!57=?0 �%-"� E �®Ìr01�>< $�CEÏ $;�*Ìr$)=?K�K7Ña=UÖ×5;-601C��� ��Ìr01�l<1$�CEÏ $;�*Ìr$a$;< $���0�Ì;Ìr(!CWK��654�6I?I[AlØ
0.Ñ)$;< $�C�-6=?��57Ò*=?K4KM$�Ìn5E=U01��Ñ)$DG�=?KEÌr(9K7K4���>(!ÓÙP,$�C
06Ö�5EC7=JÌWÍ�K�5EÒ*�.5�Ì�� �ÁÏ CE$;�657I?о=?Ó�Î!C70.<1$]5EÒ!$�ÌWÒ9�6�*Ì�$;KD06Ö�â*�*G!=U�!Ï���Ï10>0>G KM01IU(!57=?0 �ÁÑaÒ!=?I?$
�6IJKM0
G!$;ÌrCE$;�1KM=?�!Ïa5EÒ!$)Ì�0 �>< $;C7Ï1$��*Ì�$®57=?Ó�$)0 Ö×57$��ÙPlÐ@01CEG�$;CEK%06Ö*Ó��6Ï1�!=U57(*G�$1A�QÁ0 CE$�G�$r5W�6=?IU$�G
57Ò!$;0 CE$r57=JÌ�� I��e(*KM57=Uâ9Ì��657=?0 �*KRÑa=?IUI/P9$�Ï1=U<1$��3=U��IJ�.57$;C�KM$�Ìn5E=U01�*K�A
����� �����������! ���"��$#&%(') �*� ,+��!���-�/.0%1�2')3�"03�4��
�45º$;�1ÌWÒx=¦5E$�CW�.57=?0 �/-�$;Ül(*�657=?0 ��� � � ��CE$;Ül(!=?C7$�K��zÌ�0 Ó�Î!I?$r57$#Î9� KEK�57Ò*C701(!Ï ÒT57Ò*$Á$��l57=?CE$
G!�.5W� K7$r5�=?�#0 CWG�$�Ca5E0ºÌr01Ó�Î!(�57$]57Ò!$¾ý65���ü7ý;û �
0 Ca5EC7(*$]Ï CW� G�=?$��l5�A*ÞRÒ!=JK�=JKaC7$�ÖÝ$�CEC7$�G¾570º�1K
P*�.5WÌWÒ�I?$;� C7�*=U�!Ï�K7=U�9Ìr$��6��$��l5E=UCE$�èMP*�65EÌWÒ*ê:0 Ö�G!�65E�:ÓÙ(9Ke5�P,$�Ìr01�*K7=?G�$;C7$�GÙP,$rÖÝ01C7$aÑ4$�=?Ï Òl5WK
�6CE$ (!�G!�.5E$;GcA �
I¦5E$�CE�*�.5E=U<1$�I?Ð -R0 �*$ Ì�� � (*K7$úKe5E0>ÌWÒ9� KM57=JÌ��Ý01�!I?=U�!$��¾IU$��6CE�!=U�*ÏçÑaÒ!$;C7$å�
Wÿ��>û � �a$ræ!� Ó�Î*IU$ 3 � (
;� ( =�=JK�ÌWÒ!01K7$�� �Ý$1A Ï9A!CW�6�*G�01Ó�IUД�)ÖÝCE0 Ó 5EÒ!$�57CW�6=?�!=?�!Ï�KM$�5
�.5�$�� ÌWÒ
=¦5E$�CW�.57=?0 ��.nAX�
� ��
��[ÿ���ý � ��06Ö,57Ò!$�57CE(!$aÏ CW� G�=?$��l5�=JK®57Ò!$;��Ìr01Ó�Î*(�57$�G�P9� K7$;G�0 ��57Ò*$�$�CEC701C� ( 0 Öv5EÒ*�.5a$ræ!� Ó�Î*IU$1-*�6�*Gº57Ò*$��357Ò!$�Ñ4$�=?Ï Òl5WKa�6CE$D(!Î�G!�657$;G C
����.�7 � �<� ���/.%� F10 � � (
� � 5 �%�X���
2)$�Ì�� (*KM$�57Ò!=JK/$�Ke5E=UÓ��657$�0 Ö�57Ò!$)Ï CW� G�=?$��l5/=JK%�*0 =JKMÐ1-�5EÒ!$�Ñ4$�=?Ï Òl5EK/Ó��'ÐD�!0 5vÓ�0.< $�Î!C7$�Ìr=JKM$;IUÐ
G�0.Ña��57Ò*$)Ï1CE�1G�=U$;�l5v�.5�$;� ÌWÒÙ=¦5E$�CW�.57=?0 �/A �DK/Ñ4$)K7Ò*�6I?I>KM$;$ -;57Ò!=JK:èM�!01=?K7$;ê��65v$�� ÌWÒ]=U57$;CE�657=?0 �
Ì��6� P9$�� G�<.� �15W�6Ï1$�0 (9K�AS?l570�ÌWÒ*�1Ke5E=?ÌÙIU$��6CE�!=U�*Ϻ=JK
Ï1$��!$;CE� IUI?Ð357Ò!$�Î!CE$rÖÝ$�CECE$;G�Ó�$r5EÒ!0�GÁÖÝ01C
P*� K7=?Ì:P*�1ÌWÍ>Î!C701Î*�6Ïl�.5E=U01��ÖÝ0 CR5EÒ!$@ÖÝ0 I?IU0.Ña=?�!Ï�57Ò!CE$�$�CE$;�1KM01�*KDC
8�9 #!�:3;���!4<%1 =�&>?�����������! ���”��A@B%1�2′)3C”�3C4� A ?l5E0>ÌWÒ9� KM57=JÌ�I?$;�6CE�!=?�!Ï�=?K4(*K7(*�6I?I?Ð ���:D �@Ö»�1Ke5E$�C457Ò9�6�3P*�.5WÌWÒºI?$;�6CE�!=?�!Ï*AE A ?l5E0>ÌWÒ9� KM57=JÌDI?$;� C7�*=U�!Ï��6IJK70�0 Ö×57$;�3CE$;K7(!IU5EKR=?�¾P,$r5757$;C
KM01IU(!57=?0 �*K;A
�!A ?l5E0>ÌWÒ9� KM57=JÌDI?$;� C7�*=U�!Ï�Ì�� �¾P,$�(*K7$;G¾ÖÝ0 CR5ECE�1ÌWÍ>=U�!Ï�ÌWÒ*� �!Ï $�K�A
?l570�ÌWÒ*�1Ke5E=?Ì�IU$��6CE�!=U�*Ï
=JK/Ó�01KM5®06Ö×57$;� � �:D �aÖ»� KM57$;C/5EÒ*�6��P*�.5WÌWÒÙI?$;� C7�!=?�!Ï�Î9�6C757=JÌr(!IJ�6CEIUÐ
0 ��IJ�6CEÏ $aCE$;G�(*�*G!�6�l5)G*�.5E�1KM$�5EK;AlÞRÒ*$
CE$;� K70 ��ÖÝ01C�57Ò*=?K)=?K4K7=UÓ�Î!I?$�5E0�K7Ò!0.Ñ�A>&)01�*KM=JG�$;C�57Ò*$
KM=?Ó�Î!IU$3Ì��1KM$¾ÑaÒ!$�CE$¾��5ECE� =U�*=U�!ÏåKM$�5�0 Ö
KM=?ë�$ � � ��� =JKÙ=?�*� G!< $�C757$;�l57I?ÐåÌ�0 Ó�Î90lKM$�G¼06Ö � �
=?G�$;�l57=JÌ��6IvÌr0 Î*=U$�Ka06Ö���K7$r5
Ña=U57Ò � � � K7� Ó�Î!IU$�K�A ��< $;CE� Ï =?�!Ï�57Ò!$]Ï1CE�1G�=?$��l5�0.< $;C��6I?I<� ��� �
Î*�.5757$�CE�*KÙÏ =?< $;K]57Ò!$¾$ræ!� Ìr5�KE�6Ó�$�CE$;K7(!I¦5�� K�Ìr0 Ó�Î!(!57=?�!Ï#57Ò*$ºÏ CW� G!=U$;�15�P*� K7$;Gú01�'�e(*Ke5
57Ò!$3â*CWKe5@� � � A�ÞRÒ>(*K;-�P*�.5WÌWÒçÏ1CE�1G�=U$;�l5�G�$�K7Ì�$��l5�=?K�ÑR� KM57$�ÖÝ(!IaP,$;Ì�� (*K7$¾=U5�C7$�Ìr01Ó�Î*(�57$�K
57Ò!$�KE�6Ó�$�Ül(*�6�l5E=¦5eÐ � � 57=?Ó�$�K�P,$rÖÝ0 CE$�0 �*$�Î*�6CW�6Ó�$r5E$�C@(!Î�G!�.5E$ A�BD� 5EÒ!$�065EÒ!$�C�Ò9�6�*Gc-
Ke5E0>ÌWÒ9� KM57=JÌÁÏ CW� G!=U$;�153Ña=UI?I�KM$;$å�zÖÝ(!I?I�$�Î,0>ÌWÒ � K � � =¦5E$�CW�.57=?0 �9K�5EÒ!C701(!Ï Ò�� � � � LOI?0 �!Ï
57CW�6=?�!=U�*Ï�K7$r5�A%áh�úÎ!CW� Ìn5E=?Ì�$ -c$�æ�� Ó�Î!IU$�K@CE� C7$;IUÐÁ� Î!Î,$;�6C@Ó�0 CE$�57Ò*� �ú0 �*Ì�$�=?�¼�#G!�.5W� K7$r5�-
P!(�5:57Ò!$;C7$Ù� C7$Ù(*KM(9�6I?IUÐ#ÌrI?(*KM57$;CEK
06Ö�Î*�65M57$;C7�9K�5EÒ*�.5@�6CE$]< $;C7Ð�KM=?Ó�=UIJ�6C�A9î*0 CD$ræ!�6Ó�Î!I?$Ù=?�
Î!Ò!0 �*$�Ó�$�ÌrIJ� KEKM=Uâ9Ì��657=?0 �%-�� IUIc0 Ö/57Ò*$:Î9�.5M5E$�CE�*K4ÖÝ0 CR5EÒ!$@Î!Ò!01�!$�Ó�$ 2��:2ÙÑa=?IUI<�»Ò!0 Î,$rÖÝ(!I?I?Ð$�
Ìr0 �l5W�6=?�]ÓÙ(*ÌWÒ�06Ö!5EÒ!$RK7� Ó�$4=?��ÖÝ0 CEÓ��.57=?0 �/A;áO5�=JK/5EÒ!=JKvCE$;G!(!�*G!� �*ÌrÐ:57Ò9�.5�Ì��6��Ó��6Í $)P*�.5WÌWÒ
IU$��6CE�!=U�*Ï�Ó�(*ÌWÒ�KMI?0.Ñ)$;C457Ò*� �¾01��L[I?=?�!$ A?l570�ÌWÒ*�1Ke5E=?Ì
IU$��6CE�!=U�*Ï�� I?K70Ù0 Ö×57$��¾C7$�KM(*I¦5WK)=?�3P9$�5M57$;CaKM01IU(�5E=U01�*K4P9$�Ì�� (*KM$:06Ö/57Ò!$@�!01=?K7$
=U��5EÒ!$:(!Î,G*�.57$�K�A1��01�!I?=U�!$��6C)�!$r5eÑ40 CEÍ�K�(*K7(*�6I?I?Ð�Ò*�'<1$�ÓÙ(*I¦5E=UÎ!I?$:IU0�Ì�� I*Ó�=?�!=UÓ��Ù06Ö/G�=/V,$;CML
=U�!Ï�G�$�Î�5EÒ*K;AlÞRÒ!$DÏ 0l�6I!0 Öc57CW�6=?�!=U�*Ï�=?K�570]I?0�Ì��657$�01�!$�06Öc5EÒ!$;K7$�Ó�=?�!=UÓ��*Al2R�.5WÌWÒ�IU$��6CE�!=?�!Ï
Ña=UI?I%G�=JK7Ì�0.< $�C�57Ò!$@Ó�=?�!=UÓ�(!Ó�0 Ö/ÑaÒ*�.5E$�<1$�C4P*� K7=U�¾57Ò*$DÑ4$�=?Ï Òl5EKR� C7$D=U�!=U57=J�6I?I?Ð�Î!IJ� Ìr$�GcA>áh�
Ke5E0>ÌWÒ9� KM57=JÌ�IU$��6CE�!=U�*Ï*-c5EÒ!$��!01=?K7$�Î!CE$;K7$��l5]=U�ú5EÒ!$�(!Î�G!�657$;K�Ì�� �åCE$;K7(!IU5Ù=?�ú57Ò!$�Ñ4$�=?Ï Òl5WK�e(!Ó�Î!=U�*Ïå=?�l570 57Ò!$�P*�1KM=?�ç0 Ö:� �!065EÒ!$�C�-vÎ,01KEK7=UP!I?ÐçG�$;$�Î,$�C�-®IU0�Ì�� IRÓ�=?�!=?ÓÙ(!Ó�A�ÞRÒ!=JK�Ò*�1K
P9$;$��#G�$�Ó�01�*Ke5ECE�657$�Gº=?�#Ìr$�C75E� =U��K7=UÓ�Î!I?=¦â9$;G�Ì��1KM$�K � ��”!- � � �[A?l570�ÌWÒ*�1Ke5E=?ÌDIU$��6CE�!=?�!Ï�=JKa�6IJK70�(*K7$rÖÝ(*I%ÑaÒ!$��¾57Ò*$DÖÝ(*�*Ìn5E=U01�3P,$�=?�!Ï�Ó�0�G�$�I?$;G¾=?KaÌWÒ9�6�!Ï L
=U�!Ïã0.< $;C�57=?Ó�$ -R�çÜl(!=U57$ Ì�0 Ó�Ó�0 ��KEÌr$;�*�6CE=U0ç=U��=?�*G�(9Ke5EC7=J�6I:�6Î!Î!I?=JÌ��.5E=U01�*K�ÑaÒ*$�CE$Á57Ò*$
G!�.5W��G�=JKe5EC7=?P!(�5E=U01�ÁÌWÒ*�6�!Ï1$;KRÏ1CE�1G�(*�6I?I?Ð�0.< $;Ca57=?Ó�$ �Ý$1A Ï9A9G�(!$]570�Ñ4$;� C
�6�*G¾5E$;�6CD06Ö®57Ò*$
Ó��1ÌWÒ!=?�!$;K
�nAcáOÖ)57Ò!$�I?$;� C7�!=?�!ϾÓ��1ÌWÒ!=?�!$�G�0>$;K@�!0 5�G!$r57$�Ìn5]�6�9GÁÖÝ01IUI?0.Ñß57Ò*$�ÌWÒ*�6�!Ï1$�=U5�=?K
=UÓ�Î,01KEKM=?P!I?$
5E0�I?$;� C7�º57Ò!$�G!�65E��Î!CE0 Î,$�CEIUÐ��6�9G�IJ�6CEÏ $:Ï $��*$�CW�6I?=Uë��.57=?0 ��$;C7CE0 CWK�Ña=?I?IcC7$�KM(!IU5;A
äx=¦5EÒzP*�.5WÌWÒúIU$��6CE�!=U�*Ï*-%ÌWÒ*� �!Ï $�K�Ï 0�(!�*G!$r57$�Ìn5E$;Gz� �*GåÑ)$�01P�5E� =U�¼CW�.5EÒ!$�C�P*�1GúC7$�KM(*I¦5WK
KM=?�*Ìr$¾Ñ)$��6CE$�I?=UÍ1$�I?Ðå570ú�’< $�CW�6Ï1$�0.< $;CÙKM$;< $;CE� I�CE(!IU$�K�-�ÑaÒ!$;C7$�� K�0 ��LOIU=?�!$¾IU$��6CE�!=U�*Ï��å=UÖ
0 Î,$�CW�.57$�G#Î!CE0 Î,$�CEIUÐ �ÀKM$;$ÙP,$�I?0.ÑÚ=U�åKM$�Ìn5E=U01� � A!(Q����Ña=?IUIv57CW� ÌWÍ35EÒ!$�ÌWÒ9�6�!Ï1$;K
� �*GÁÐ>=?$�IJG
Ï 0>0�G¾� Î!Î!CE0’æ>=?Ó��.5E=U01�ºCE$;K7(!I¦5WK�A
Û
$�KMÎ!=U57$
57Ò!$:� G�<.� �15W�6Ï1$;K®06Ö/KM570�ÌWÒ*�1Ke5E=?ÌRI?$;� C7�*=U�!Ï9-65EÒ!$�CE$
�6CE$
KM57=?IUI,CE$;� K70 �9K®ÑaÒlÐ�0 �*$
Ó�=?Ï Òl5
Ì�0 �*K7=?G!$�CR(*K7=U�!Ï�P*�65EÌWÒ�I?$;�6CE�!=?�!Ï C
8 9 #!�!3;���:4&%1 =�<>�+��!���-�/@B%1�2′)3�”03�4�1A�&)01�*G�=U57=?0 �*KR0 Ö®Ì�0 �>< $;C7Ï1$��*Ì�$D� C7$:Ñ)$;IUI/(!�*G�$;CEKM570>0�GcAE ARQ �6�>Ð:�1Ì�Ì�$�I?$�CW�.57=?0 �@5E$;ÌWÒ!�*=?Ül(!$�K �Ý$1A Ï9A�Ì�0 �P�e(*Ï1�.5E$�Ï1CE�1G�=U$;�l5
��01�!IUÐ:0 Î!L
$;CE�657$@=?�3P9�.5EÌWÒ3I?$;�6CE�!=?�!Ï*A
�*ARÞRÒ*$�0 CE$r5E=?Ì;�6I�� �*�6I?Ð�KM=JK�0 Öa57Ò!$�Ñ4$�=?Ï Òl5�G!Ðl�9�6Ó�=?Ì;KÙ� �*G¼Ìr01�l<1$�CEÏ $;�*Ìr$
CW�.5E$;Ka� C7$@KM=?Ó�Î!I?$�C�A
ÞRÒ!$;K7$º� G!<'� �l5E�6Ï1$;K�KM57$;Ó÷ÖÝCE0 Ó÷57Ò*$ºK7� Ó�$��!0 =JK7$�57Ò*�65ÙÓ��6Í1$ºKe5E0�ÌWÒ*� KM57=JÌ�IU$��6CE�!=?�!Ï
� G�<.�6�l5W�6Ï $;0 (*K;A.ÞRÒ!=JK®�!0 =JKM$1-.ÑaÒ!=JÌWÒ�=JK�K70@Ì�C7=U57=JÌ�� I>ÖÝ0 C®â*�9G�=U�*Ï�P9$�5M57$;C�I?0>Ì;�6I�Ó�=?�!=UÓ���� I?K70
Î!C7$;< $;�15WK@ÖÝ(!I?I4Ì�0 �>< $;C7Ï1$��*Ì�$Ù5E0#57Ò*$ºÓ�=U�*=UÓ�(!Ó�Aváh�*KM57$�� Gú0 ÖaÌ�0 �>< $;C7Ï1=U�*Ϻ5E0#57Ò!$¾$ræ!� Ìr5
Ó�=?�!=?ÓÙ(!Ó�-�5EÒ!$�Ìr01�l<1$�CEÏ $;�*Ìr$
KM5E� IUIJK40 (�5�G�(*$D5E0�57Ò!$@Ñ4$�=?Ï Òl5 �9(*Ìn5E(*�.5E=U01�*K�A!ÞRÒ*$@K7=?ë�$:06Ö
57Ò!$ �*(*Ìn5E(*�.5E=U01�*KÙG!$�Î,$��*G¼01�ú57Ò!$¾G�$�Ï1C7$;$�06Ö��!01=?K7$�06ÖR57Ò*$¾KM570�ÌWÒ*� KM57=JÌ�(!Î�G!�.5E$;K;A�ÞRÒ*$
<'� C7=J�6�9Ìr$º0 Ö
5EÒ!$ �9(*Ìn5E(*�.5E=U01�*K��6CE0 (!�9Gú57Ò!$�I?0�Ì��6I4Ó�=U�*=UÓ�(!Ó =JK�Î!C701Î901CM5E=U01�*�6I�570å57Ò*$
IU$��6CE�!=U�*Ï3CW�.5E$ 0 � E **- E (�- & �OA0?>0#=?�å01CEG!$�C@570#CE$;G!(*Ìr$�57Ò*$ �*(*Ìr57(*�657=?0 �*K�Ñ4$�Ì�� �å$;=¦5EÒ!$�C
G�$;Ì�C7$�� K7$G�À�6�!�*$;�6IU�v57Ò*$�IU$��6CE�!=?�!Ï�CE�657$R0 C�Ò*�’< $a�6���1G!�6Î�5E=U<1$aP*�.5WÌWÒ�KM=?ë�$1A6áh��57Ò!$;0 CEÐ � � �*-
� � - � &!- � " ��=U54=JKRKMÒ!0.Ña��57Ò*�65)5EÒ!$D01Î�57=?Ó��6I��6�!�*$;�6I?=?�!Ï�KEÌWÒ!$;G!(!IU$:06Öc5EÒ!$:IU$��6CE�!=U�*ÏÙCW�.57$D=?K
06Ö�57Ò!$@ÖÝ01C7Ó
0����
.
�%� E �
ÑaÒ!$�CE$ .®=?K�57Ò!$D�>(!ÓÙP,$�C)06ÖcÎ*�.5757$;C7�*K�Î!CE$;K7$��l57$�G��6�*G
�
=JK��]Ì�0 �*KM5E� �l5;A áh��Î*CE�1Ìn57=JÌr$1-65EÒ!=?K
Ó��’кP9$@5E0l0�Ö»�1Ke5
���!0 57Ò!$;C�Ó�$r5EÒ!0�G�570�C7$;Ó�0.< $a�!01=?K7$�=JK�5E0Ù(*K7$ºè7Ó�=?�!=UL[P9�.5EÌWÒ*$;KEê!-.5EÒ*�.54=?K;-lKM5E� CM5)Ña=¦5EÒ
�#KMÓ��6I?I�P9�.5EÌWÒ¼K7=Uë;$º�6�9G =?�*Ì�C7$�� K7$�57Ò!$ºK7=?ë�$º�1K@57CW�6=?�!=?�!Ï#Î!CE0>Ì�$�$�G!K�AvQ��6I?IU$;CÙG�=JK7Ì�(*KEKM$�K
0 �!$�Ó�$r5EÒ!0�G ÖÝ01C]G�0 =?�!Ͼ57Ò!=JK � E ” ���6�*G¼BDC7C � �”� ��G!=?KEÌr(*KEK7$;K:57Ò*=?K:ÖÝ01C�IU=?�!$;� C�Î!CE0 P!I?$�Ó�K;A
Ø�0.Ñ4$�< $;C;-lG�$;Ì�=?G!=U�!ÏÙ57Ò!$:CW�.57$:�.5RÑaÒ!=JÌWÒ�570�=U�9ÌrCE$;� K7$a5EÒ!$DP9�.5EÌWÒ¾KM=?ë�$:�6�*GºÑaÒ!=?ÌWÒº=U�!Î*(�5EK
570�=U�*Ì�IU(9G�$@=U�¾57Ò!$�K7Ó��6I?I,P9�.5EÌWÒ*$;K4=?Ka�1KRG�=¦Õ�Ì�(!I¦5��1K4G!$r57$;C7Ó�=?�!=?�!Ï�57Ò!$:Î!CE0 Î,$�CRIU$��6CE�!=?�!Ï
CE�657$ A A V�$;Ìr57=?< $�I?Ð357Ò!$�KM=?ë�$�06Ö�5EÒ!$ÙI?$;� C7�!=?�!Ï�CW�.5E$Ù=?� KM570�ÌWÒ*� KM57=JÌ�I?$;� C7�!=?�!ϺÌ�0 CEC7$�KMÎ,0 �9G!K
570�57Ò*$:CE$;K7Î,$;Ìn5E=U<1$�KM=?ë�$�0 Ö/57Ò*$�Ó�=?�!=%P9�.5EÌWÒ/A
��065E$º�6IJK70�57Ò*�65]57Ò!$¾Î!CE0 P!I?$�Ó÷06ÖaC7$;Ó�0.
IU01�!Ï
P9$�ÖÝ0 CE$D5EÒ!$��!01=?K7$@C7$;Ï =?Ó�$@=JKa$�<1$��3C7$�� ÌWÒ!$�GcA���!0 57Ò!$;CD� G!<'� �l5E�6Ï1$�06Ö�P*�65EÌWÒ�5ECE� =U�!=?�!Ï�=JKa5EÒ*�.5:0 �!$�=?KD�6P!I?$�5E0º(*K7$ÙK7$;Ìr01�*G�0 CWG�$;C
Ó�$�57Ò!0�G!K�5E0åK7Î,$�$;Gç57Ò*$3I?$;� C7�*=U�!ÏåÎ!CE0�Ìr$;KEK;A�?>$�Ìr01�*Gz01CEG�$;C�Ó�$�57Ò!0�G!K�K7Î9$;$;GãIU$��6CE�!=?�!Ï
PlÐ $;KM57=?Ó��657=?�!Ï��!065��e(9Ke5�5EÒ!$�Ï CW� G�=?$��l5@P!(�5Ù� I?K70º5EÒ!$�Ìr(*C7<.�.5E(!CE$�0 Ö�5EÒ!$�Ìr0lKe5]K7(!CMÖ»�1Ìr$1A
8:=U<1$��ú57Ò*$ºÌr(!CE<.�.5E(!C7$1-%0 �*$ºÌ�� �å$�Ke5E=UÓ��657$�5EÒ!$º�6Î*Î!C70'æ�=?Ó��.57$�I?0�Ì��.5E=U01�ú06ÖR57Ò!$3� Ìr57(*� I
Ó�=?�!=?ÓÙ(!Ó�A
Û
$�KMÎ!=U57$�57Ò!$
�1G�<.�6�l5E� Ï $�K�06Ö�P*�.5WÌWÒ�(!Î�G!�.5E$;K;-1KM570�ÌWÒ*� KM57=JÌRI?$;�6CE�!=?�!Ï�=JK�KM57=?IUI906Ö×57$;��57Ò*$
Î!C7$�ÖÝ$�CEC7$�G�Ó�$r5EÒ!0�GºÎ*� CM5E=?Ì�(!IJ�6CEIUÐ�ÑaÒ!$;�¾G�$��6I?=U�!Ï�Ña=U57Òº<1$�CEÐ�I?� C7Ï1$DG!�65E��KM$�5EK4P9$�Ì�� (*KM$:=U5
=?K�K7=?Ó�Î*IUÐ�Ó�(*ÌWÒ3Ö»� KM57$;C;A
����� ���
*�� "�3C4 ���C%�� ����
� .0%1
��$r5eÑ40 CEÍ�K]I?$;� C7�ú5EÒ!$ºÖ»�1Ke5E$;KM5ÙÖÝCE0 Ó 57Ò*$¾Ó�01KM5�(*�!$ræ�Î,$;Ìn5E$;GãK7� Ó�Î*IU$1A�ÞRÒ!$;C7$�ÖÝ0 CE$ -v=¦5�=?K
� G�<>=JK7� P!IU$�570 ÌWÒ*0l0lKM$3�ÁKE�6Ó�Î!I?$¾�.5�$;�1ÌWÒ¼=¦5E$�CW�.5E=U01�¼57Ò*�65�=JK]5EÒ!$3Ó�0lKe5�(!��Ö»� Ó�=?I?=?� CÙ5E0
57Ò!$úKMÐ�KM57$;Ó3A��
0657$1-457Ò!=JK#�6Î!Î*IU=?$;K¾0 �!I?Ðì570ìKM570�ÌWÒ*� KM57=JÌÁI?$;� C7�*=U�!ÏTKM=?�*Ì�$ 5EÒ!$ 01CEG!$�C306Ö
=U�!Î*(�5�Î!CE$;K7$��l5E�657=?0 �ç=JK�=?C7CE$�I?$�<.�6�l5�ÖÝ0 C�P*�65EÌWÒ,+.A)B
Ö:Ìr01(!CWKM$1-v5EÒ!$�CE$�=?K��!0¼K7=UÓ�Î!I?$�Ñ4�'Ð
570åÍl�*0.Ñ ÑaÒ!=?ÌWÒç=U�!Î*(�5EK�� C7$¾=U��ÖÝ01C7Ó��657=?0 �zCE=?ÌWÒ/-vÒ!0.Ñ4$�<1$�C�-v� < $�CEмKM=?Ó�Î!I?$º5EC7=JÌWÍå57Ò*�65
ÌrCE(*G�$�I?Ð =?Ó�Î!I?$�Ó�$��l5EK]57Ò!=JK�=JG�$;��=JK�5E0ÁKM=?Ó�Î!I?Ð ÌWÒ!0>01K7$�K7(*Ì�Ì�$;KEKM=?< $�$ræ!� Ó�Î*IU$�K:57Ò*�65��6CE$
ÖÝC701Ó þ.ÿ � �rü �����4ÌrIJ� KEKM$�K�KM=?�*Ì�$�57CW�6=?�!=?�!Ï#$ræ!�6Ó�Î!I?$;K]P9$;IU01�!Ï =?�!Ï�570�5EÒ!$ºKE�6Ó�$�ÌrIJ� KEK�Ña=?IUI
Ó�0lKe5aI?=UÍ1$�I?оÌ�0 �l5E� =U�3KM=?Ó�=UIJ�6Ca=?��ÖÝ0 CEÓ��.5E=U01�%A���!0 57Ò!$;C�Ò!$;(!C7=JKM57=JÌaÖÝ0 C �e(*G�Ï1=U�*ÏÙÒ!0.ÑìÓÙ(9ÌWÒ��!$�Ñx=?��ÖÝ01C7Ó��.5E=U01����5ECE� =U�!=?�!Ï]$�æ!�6Ó�Î!I?$
Ìr0 �l5W�6=?�*K/=JKv570D$ræ!�6Ó�=?�!$�5EÒ!$4$�CEC701C/P,$r5eÑ4$�$��]57Ò!$R�!$�5eÑ)01C7Í:0 (�5EÎ!(�5��6�*G]57Ò!$)5E� C7Ï1$r5�<'� IU(*$
ÑaÒ!$���57Ò*=?K�=?�!Î!(!5�=?K®Î*C7$�KM$;�15E$;GcA �ìI?� C7Ï1$)$;C7CE0 C®=?�*G�=JÌ��.5E$;K®5EÒ*�.5�5EÒ!=JK�=U�*Î!(�5�Ò*�1K��!065�P,$�$;�
IU$��6CE�!$;G#P>Ð357Ò*$��*$r5eÑ40 CEÍ3� �*GÁK703Ì�0 �l5E� =U�*KD�ºI?065:06Ö��*$�ÑÚ=?��ÖÝ0 CEÓ��.5E=U01�%A,ÞRÒ*$�CE$rÖÝ0 CE$ -,=U5
Ó�� Í $�KvK7$��*K7$)570:Î!C7$�KM$;�l5v5EÒ!=?K�=?�!Î!(�5�Ó�0 CE$�ÖÝCE$;Ül(!$;�l57I?Ð A B
Ö,Ì�0 (!CWKM$1-;P>Ð#è7I?� C7Ï1$;êRÑ4$)Ó�$;� �
C7$;I?�657=?< $�5E0
�6I?I10 Ö�57Ò!$)065EÒ!$�C/57CW�6=?�!=U�*Ï�$ræ!�6Ó�Î!I?$;K;A��
Kc5EÒ!$4�!$r5eÑ40 CEÍ�5ECE� =U�*K;-r5EÒ!$;K7$�CE$�IJ�.5E=U<1$
$�CEC701CEK
Ña=UI?I�ÌWÒ*�6�*Ï $��6�*G KM0�KMÒ*0 (!IJGÁ5EÒ!$�ÖÝC7$�Ül(!$��*Ì�Ð#06Ö�Î*C7$�KM$;�15W�.5E=U01�ÁÖÝ0 C��¾Î*�6C757=JÌr(*I?� C
=U�!Î*(�5�Î*�.5757$�CE�%A � Ó�$�57Ò!0�Gç57Ò*�65�Ó�0�G�=Uâ*$;K�5EÒ!$¾Î*C701P*�6P!=?I?=¦5eÐú06Ö:�6Î!Î,$;� CE� �*Ìr$¾06Ö
$�� ÌWÒ
Î*�.5757$�CE�3=?K�Ì;�6I?IU$�G¾� � ��� � �!ý�
nÿ/Trÿ��>û
D ��� � �rA
� �C���& �%�������
��.�%1 ��,” ����� ����”�
*�
�� 3C>��&’�
�2��”��&3 � �<3;��%13;��1A�?�Òl(���$Á57Ò!$ 57CW�6=?�!=U�*ÏzKM$�5¾KM0z57Ò*�65¾KM(9Ì�Ìr$�K7K7=?< $�57CW�6=?�!=?�!Ïz$�æ�� Ó�Î!IU$�K
�*$�< $;C �ÝCW�6CE$�I?Ð"��P,$�I?0 �!Ï�5E0�57Ò!$]KE�6Ó�$�ÌrIJ� KEK�AE A���C7$�KM$;�l5�=?�!Î!(�5�$ræ!� Ó�Î*IU$�KÙ5EÒ*�.5�Î!CE0�G�(*Ìr$�� I?� C7Ï1$º$�CECE0 CÙÓ�01C7$ºÖÝC7$�L
Ül(!$;�l57I?Ð�57Ò*� ��$ræ!�6Ó�Î!I?$;K45EÒ*�.5�Î!CE0�G�(*Ì�$@��K7Ó��6I?I%$�CEC701C;A
X�u®ol_�d�bM�1_Ebvikj:��olikfMo�^;bM\�� ik_Wj.seg�\rbe_�gh�1Z�Z�_n�Dikj@{l\�sefMo�Z]\W�D{�_�\r¿!_WfEse_n�:{.�
bed��1j>�1d�¿Ù_Ebhbed;b
i�°�seol_7be_ai¦g�\:ghik^;jli�ª>fn\�j.s�bM\�jl^;_ad;°%^;bM\;�1ik_Wj.s���\��k�l_WgW©
Ø�0.Ñ4$�< $;C;-®01�!$ÁÓÙ(9Ke5ºP,$ Ì;�6CE$rÖÝ(!I�ÑaÒ*$��xÎ,$�C757(!CEP!=?�!ϼ57Ò*$Á�!0 CEÓ��6IaÖÝCE$;Ül(!$;�*Ìr=?$;K�06Ö =U�!Î*(�5�$ræ!�6Ó�Î!I?$;K:P,$;Ì�� (*K7$�5EÒ!=JK�ÌWÒ*�6�!Ï1$;K 57Ò!$�CE$�IJ�.5E=U<1$Ù=?Ó�Î,0 C75E� �*Ìr$�57Ò9�.5@57Ò!$��!$�5eÑ)01C7Í Î!I?�1Ìr$�K/01�ÙG�=/V,$;C7$;�15�$ræ!�6Ó�Î!I?$;K;A'ÞRÒ!=?KvÓ��'Ð@0 C/Ó��'Ð@�!0 5vP,$4G�$�KM=?CW�6P!I?$ A�î!0 C�$ræ!� Ó�Î*IU$1- � �>ÿ
� � D � �*ÿ�� ����ý � � �¦ÿ��Eþ � �#þ ý��hý D ��� �Oý6ÿ��*ÿ��>û ��� ���kÿ���ü
,DWý�� � ��þ6ÿ
�ý�
��Àü ���
P,$;Ì;�6(*K7$�01(�57I?=?$�CWK
Ì��6�åÎ!CE0�G�(*Ìr$�IJ�6CEÏ $�$�CECE0 CWK
Ð1$r5ÙK7Ò!0 (!IJG �!065]P,$�Î!CE$;K7$��l57$�GÁÖÝCE$;Ül(!$;�15EIUÐ1AvBD�å57Ò!$�0 57Ò!$;C
Ò*�6�*G%-15EÒ!=JK�5E$;ÌWÒ!�!=JÜl(!$@Ì��6�ºP9$:Î*�6C757=JÌr(*I?� C7I?Ð�P,$��*$râ9Ì�=?� I*ÖÝ01C)P,0>01KM57=?�!Ï]5EÒ!$DÎ,$�C7ÖÝ0 CEÓ��6�*Ì�$
ÖÝ0 Ca=?��ÖÝC7$�Ül(!$��l57I?к0�Ì;Ìr(!CEC7=?�!Ï�=U�*Î!(�5EK;-!$1A Ï9A 2’ë�2Ù=?��Î!Ò!0 �*$�Ó�$@C7$�Ìr0 Ï1�!=U57=?0 �
����� �A�&’�
�!.0″�� “�3C4 ����%�� 3 ��*C��
&)0 �>< $;C7Ï1$��*Ì�$)=JK�(*K7(*� IUI?Ð]Ö»�1Ke5E$�C�=UÖ�57Ò!$
�'<1$�CW�6Ï1$)0 Ö,$�� ÌWÒ�=U�*Î!(�5�<.�6CE=J�6P!I?$a0.< $;C®57Ò!$a5ECE� =U�!L
=U�!Ï�K7$r5®=?K�Ì�IU0lKM$)570@ë;$�CE0*A'Þ/0�K7$�$)57Ò!=JK�-6Ì�0 �*K7=JG�$�C�57Ò*$4$�æ>57CE$�Ó�$aÌ�� K7$4ÑaÒ!$�CE$4� IUIl5EÒ!$R=U�!Î*(�5EK
�6CE$)Î,01K7=¦5E=U<1$ A'äå$�=?Ï Òl5EKv570��DÎ*�6C757=JÌr(*I?� Cv�!0�G�$R=?�Ù5EÒ!$4â*CWKe5®Ñ)$;=UÏ1Òl5�IJ�'Ð $;C�� C7$)(!Î,G*�.57$�GÙP>Ð
�6�º� Ó�01(!�l5�Î!CE0 Î,0 C757=?0 �*� I�570�� � ÑaÒ*$�CE$ �@=?K�57Ò*$ �»KEÌ�� I?� C
��$�CEC701C��.5)57Ò*�65)�!0�G�$:�6�*G � =?K
57Ò!$:=U�*Î!(�5R< $;Ìr5701C �»K7$�$:$;Ül(*�657=?0 �*K �#" ��� �*G�� � � �;�nA>äxÒ!$��3�6I?I90 Öc57Ò!$@Ìr01Ó�Î901�!$��l5EK)06Ö/� �
=U�!Î*(�54<1$;Ìr570 C4�6CE$
Î,01K7=¦5E=U<1$ ->�6I?I90 Öc57Ò!$:(!Î�G!�.5E$;K406Ö%Ñ4$�=?Ï Òl5WK�5EÒ*�.5)ÖÝ$�$;Gº=U�l5E0��]�*0>G!$DÑa=?IUI
P9$�57Ò!$�KE�6Ó�$�K7=?Ï ���»=ÀA $ AcK7=UÏ1�0���Q�;�nA �
K:�¾C7$�KM(!IU5;-957Ò*$;K7$�Ñ4$�=?Ï Òl5EK:Ì�� � 01�!IUÐ#� IUI®G�$;Ì�C7$�� K7$
0 C
� IUI%=?�*Ì�C7$�� K7$ � �Eû ��� � ��ü)ÖÝ01C
��Ï =?< $;��=U�!Î*(�5DÎ*�65M5E$�CE�%A*ÞRÒ>(*K;-*=UÖ���Ñ4$�=?Ï Òl5�<1$;Ìn5E0 C�Ó�(*KM5
ÌWÒ*�6�!Ï1$ºG�=?C7$�Ìn5E=U01�z=¦5�Ì�� �z0 �!I?ÐúG�0 K70ÁP>Ðúë�=?Ï ë;� Ï Ï1=U�!Ï#ÑaÒ*=?ÌWÒz=JK�=U�!$�Õ�Ìr=?$��l5�� �*Gú57Ò>(*K
< $�CE�K7IU0.�A
áh�º5EÒ!$]�6P,0.< $@$ræ!� Ó�Î*IU$1->57Ò!$�=?�!Î!(�5WKaÑ4$�CE$:� IUI%Î,01K7=U57=?< $ A!Ø
0.Ñ)$;< $;C;->=?�3Ï1$��!$;CE� IÀ-�� �lÐ
KMÒ!=UÖ×5�06Ö)57Ò!$��’< $;CE� Ï $]=?�!Î!(�5]�'ÑR�'Ð3ÖÝC701Ó�ë�$�CE0ºÑa=?I?I�P!=?�1KD57Ò!$�(!Î�G!�.5E$;K@=?� �¾Î*�6C757=JÌr(*I?� C
G�=UCE$;Ìr57=?0 �Á� �*G357Ò>(*KDKMI?0.Ñ G!0.Ña�#IU$��6CE�!=U�*Ï*A*ÞRÒ!$;C7$�ÖÝ0 CE$ -!=U5D=JK�Ï10>0>G35E0ºK7Ò!=¦Ö×5D57Ò!$Ù=U�!Î*(�5EK
KM0�5EÒ*�.5D57Ò!$Ù�’<1$�CW�6Ï1$:0.<1$�CR5EÒ!$�57CW�6=?�!=?�!ϺK7$r5
=JK
Ì�IU0lKM$@5E0�ë�$;C709AÁÞRÒ!=JK�Ò!$;(!C7=JKM57=JÌ]KMÒ*0 (!IJG
P9$º� Î!Î!I?=U$�G¼�.5�� IUI)I?�'Ð1$�CWK@ÑaÒ!=JÌWÒ¼Ó�$��6�*K]57Ò*�65ÙÑ4$�Ñ4� �l5�57Ò!$º�'<1$�CW�6Ï1$�0 Ö45EÒ!$ ��� �!��� ��
06Ö4�¾�!0�G�$�570�P,$�Ì�IU0lKM$Ù570�ë�$;C70¾P9$�Ì�� (*KM$�57Ò*$;K7$�01(�57Î*(�5EK�� C7$Ù57Ò!$�=?�!Î!(�5WK:570357Ò!$��!$�æ>5
I?�’Ð1$�C � ��- �OA/ÞRÒ!=JK�Î!CE0 P!I?$�Ó÷Ì��6�úP,$�� G!G!C7$�K7K7$;G P>Ð Ìr0>01CEG�=?�*�657=?�!Ï�Ò!0.ÑÚ5EÒ!$�=U�*Î!(�5EK��6CE$
57CW�6�*KMÖÝ0 CEÓ�$;GúÑa=U57Ò¼5EÒ!$¾ÌWÒ!01=?Ì�$�06Ö
K7=?Ï Ó�0 =JG!�6I4� Ìr57=?<'�657=?0 �úÖÝ(!�9Ìn57=?0 �/A®Ø
$�CE$�Ñ4$ºG�=JK7Ì�(*K7K
57Ò!$�=?�!Î!(�5a5ECE� �*KMÖÝ0 CEÓ��657=?0 �%A�ÞRÒ!$]G!=?KEÌr(*KEK7=U01�¾0 Ö/57Ò*$]KM=?Ï Ó�0 =JGºÖÝ0 I?IU0.Ñ�K;A
&)0 �>< $;C7Ï1$��*Ì�$�=JK�Ö»�1Ke5E$�C]�!0 5Ù0 �*IUÐ =¦ÖR57Ò*$�=U�*Î!(�5EK��6CE$�KMÒ*=¦Ö×5E$;Gz�1K]G�$;KEÌrCE=?P9$�Gå� P90.<1$
P!(�5a�6IJKM0]=UÖ%5EÒ!$�Ð��6CE$DKEÌ�� IU$�G�KM0Ù57Ò*�654� IUI,Ò*�'< $D�6P,0 (�5457Ò!$:K7� Ó�$DÌr0.<.� C7=J�6�*Ì�$ - � , ->ÑaÒ!$�CE$
� ,�� �I
9
J�6Kv+
��
�, � F 5 �%� � �
Ø�$�CE$ – I =?K�57Ò!$D�>(!ÓÙP,$�C)06Öc57CW�6=?�!=?�!Ï�$ræ!� Ó�Î*IU$�K�-�� , =JK�57Ò*$DÌr0.<.� C7=J�6�*Ì�$a06Ö�57Ò*$ � (�� =?�!Î!(�5 <'� C7=J�6P*IU$ � �*G �, =JK�57Ò!$�� (�� Ì�0 Ó�Î901�!$��l5406Öc57Ò*$ � (�� 57CW�6=?�!=?�!ÏÙ$�æ!�6Ó�Î!I?$ A$?�Ì�� IU=?�!ÏÙK7Î9$;$;G!K IU$��6CE�!=U�*Ï�P9$�Ì��6(9KM$D=¦54Ò!$�I?Î*K�5E0ÙP*� I?� �*Ìr$a01(�5�5EÒ!$ CW�.5E$ �.5)ÑaÒ!=?ÌWÒ�57Ò!$DÑ)$;=UÏ1Ò15WK�Ìr01�!�!$�Ìn57$�G 570357Ò!$�=?�!Î!(�5]�*0>G!$;K:IU$��6CE�%AcÞRÒ!$�<.�6I?(!$�06Ö�5EÒ!$�Ìr0.<.�6CE=J�6�*Ì�$�K7Ò!0 (!IJG P9$�Ó��.5WÌWÒ!$;G Ña=¦5EÒ 57Ò*�65�0 Öa57Ò!$�KM=?Ï Ó�01=?Gú(*K7$;G%A®î*0 CÙ57Ò!$�KM=?Ï Ó�01=?GúÏ1=U<1$��zP,$�I?0.Ñ�-�� Ìr0.<.�6CE=J�6�*Ì�$�06Ö �º=JK�� Ï 0>0�G¾ÌWÒ!01=?Ì�$ A
ÞRÒ!$�$ræ!Ìr$;Î�57=?0 �35E0ºK7Ì;�6I?=U�*Ï�� IUI�Ìr0.<.�6CE=J�6�*Ì�$;K)570�5EÒ!$ÙKE�6Ó�$�<.�6I?(!$]0�Ì�Ì�(!CEKRÑaÒ*$��#=U5
=?K
Íl�*0.Ña� 5EÒ*�.5ÙK70 Ó�$�=U�*Î!(�5EKÙ�6CE$�0 Ö4I?$;KEK�K7=UÏ1�!=¦â,Ì��6�9Ìr$�57Ò*� � 0 57Ò!$;CEK;Acáh�¼KM(9ÌWÒå�#Ì;� K7$ -c=U5
Ì��6��P,$]P,$��!$�â9Ìr=J�6Ic5E0ºKEÌ��6I?$:57Ò!$ÙIU$�K7K�K7=?Ï �!=Uâ9Ì�� �l5�=U�!Î*(�5EKDG�0.Ña�3K70�57Ò9�.5�5EÒ!$�Ð��6CE$�èMI?$;KEK
� ‘)�!3� �>��&’�
“03�4 ����%�� 3 ��*C�� �1ARÞRÒ*$D�’< $;CE� Ï $406Ö%$�� ÌWÒ�=?�!Î!(�54<'� C7=J�6P*IU$�0.<1$�C�5EÒ!$�5ECE� =U�*=U�!Ï�KM$�5)KMÒ*0 (!IJG�P,$DÌrI?01K7$
5E0�ë�$�CE0*AE A�?!Ì��6I?$@=U�*Î!(�5�<.�6CE=?� P!I?$;KaK70�5EÒ*�.5a5EÒ!$�=?C�Ìr0.<.� C7=J�6�*Ì�$;K4�6CE$��6P,0 (�5a5EÒ!$]K7� Ó�$ A
�*A4áh�*Î!(�5�<.�6CE=?� P!I?$;KaK7Ò!0 (!IJG¾P9$�(!�9Ìr0 CECE$�IJ�.57$�G�=UÖ�Î,01KEK7=UP!I?$ A
ÞRÒ!$��6P,0.< $�5eÑ)0357CE=JÌWÍ>K:0 ÖRK7Ò!=UÖ×57=?�!ÏÁ�6�*GåKEÌ��6I?=?�!Ϻ5EÒ!$�=?�!Î!(�5WK]�6CE$�Ü1(*=¦5E$�KM=?Ó�Î!IU$�5E0
=UÓ�Î!I?$�Ó�$��l5�A”���!0 57Ò!$;CR57CE=?ÌWÍ�5EÒ*�.5a=JKaÜ1(*=¦5E$:$6V,$�Ìn5E=U<1$:P*(�5aÓ�01C7$@G�=UÕ�Ìr(!IU5a570�=UÓ�Î!I?$�Ó�$;�15
=?K
570ºG!$;Ìr01C7CE$�IJ�.5E$@57Ò!$�=U�*Î!(�5EK;A%&)0 �*K7=?G!$�C�5EÒ!$�K7=?Ó�Î*IU$��!$r5eÑ40 CEͺ=?� î�=UÏ1(!CE$ E A9áOÖ�=U�!Î*(�5EK
�6CE$Ù(!�*Ì�0 CEC7$;I?�657$�G357Ò!$;� =U5:=JK:Î90lK7K7=?P!IU$�570�K70 I?< $�ÖÝ01CD5EÒ!$�<'� IU(*$�0 Ö � + 5EÒ*�.5�Ó�=U�*=UÓ�=?ë�$;K57Ò!$�$;C7CE0 C@Ña=U57Ò!01(�5Ù�6�>Ð Ì�0 �*Ì�$�CE�ÁÖÝ0 C � F -/�6�9G <>=JÌr$�< $;CEKE�!A�áh�å065EÒ!$�C�Ñ40 CWG!K;-�57Ò!$�5eÑ40<'� C7=J�6P*IU$�K��6CE$a=U�9G�$�Î,$��*G!$��l5��Ý57Ò!$:KMÐ�KM57$�Ó 06Öc$�Ü1(9�.57=?0 �9K�=JK�G�=J�6Ï10 �*� I8�rA6äx=¦5EÒºÌr01C7CE$�IJ�.5E$;G
=U�!Î*(�5EK;-101�!$�Ó�(*Ke5RKM01IU<1$RÖÝ0 C)P90 57ÒºK7=UÓ�(!IU5E�6�*$�0 (9KMI?Ð�ÑaÒ*=?ÌWÒ�=JK)�]ÓÙ(*ÌWÒ�Ò*� CEG!$�C�Î!CE0 P*IU$;Ó3A
��CE=U�*Ì�=UÎ9�6IRÌr0 Ó�Î,0 �!$;�l5�� �*�6I?Ð�KM=JK �À�6IJKM0 Í>�!0.Ña�ç� K�5EÒ!$3H�� C7Ò>(!�*$���Lh”%0>$�<1$�$ræ�Î*� �*K7=U01� �
Ì��6�3P,$�(*KM$�G¾570�C7$;Ó�0.< $ �kÿ�� �Wý.üaÌ�0 CEC7$;I?�657=?0 �*K)=U��=?�!Î!(�5WK � � � �OA
áh�!Î!(�5WK�57Ò9�.53� C7$#I?=?�!$;� C7I?ÐTG!$�Î,$��*G�$;�l5 �×5EÒ!$ $�æ>57CE$�Ó�$ÁÌ��1KM$Á0 Ö]Ìr0 CECE$�IJ�.57=?0 � ��Ó��’Ð
�6IJKM0@Î!CE0�G�(*Ìr$�G!$�Ï $;�!$�CW� Ì�=U$�K�ÑaÒ!=?ÌWÒ�Ó��’ÐÙK7I?0.ÑçI?$;�6CE�!=?�!Ï*A1&)01�*K7=?G�$;C�57Ò*$�Ì�� K7$aÑaÒ!$;C7$R0 �*$
=U�!Î*(�5�=JK��6I?Ñ4�’Ð�Kv5eÑa=JÌr$R57Ò*$�065EÒ!$�C�=?�!Î!(�5���
F � E
+ �nA1ÞRÒ!$a�!$r5eÑ40 CEÍ]01(�57Î!(!5�=?K�Ìr0 �9Ke5W�6�l5�6I?0 �!Ï�IU=?�!$�K � F ��� F �%��� E �%� + -�ÑaÒ!$;C7$���=JKa��Ì�0 �*KM5E� �l5;A�ÞRÒ>(*K�->5EÒ!$@Ï CW� G�=?$��l5R=?KRë;$�CE0�6I?0 �!Ï@5EÒ!$;K7$DG�=?CE$;Ìn5E=U01�*K:�ÀKM$;$Dî�=?Ï (!CE$ E �rA1Q#0.<>=?�!ÏÙ� IU01�!Ï@57Ò!$�KM$DIU=?�!$�K�Ò*�1K��6P9KM01IU(�5E$�I?Ð��*0
$4V�$;Ìn5�01�ÁIU$��6CE�!=?�!Ï*A�äå$�� C7$Ù57CEÐl=?�!Ͼ570�KM01IU<1$Ù=?� E LOÛ ÑaÒ*�65:=JK:$4V�$;Ìn5E=U<1$�I?Ð#0 �!I?ÐÁ����LOÛ
Î!C701P!I?$�Ó�AúáeG�$;� IUI?Ð�Ñ)$�Ñ4� �l5
570¾C7$;Ó�0.< $]01�!$�0 Ö�57Ò!$�=?�!Î!(�5WK@ÑaÒ!=?ÌWÒ Ña=UI?I�G�$;Ì�C7$�� K7$]57Ò*$
KM=?ë�$@06Ö�57Ò*$��!$r5eÑ40 CEÍ�A
îv=?Ï (*C7$ �¾KMÒ*0.Ñ�K�5EÒ!$�$;�l57=?C7$�Î!C70�Ì�$;KEK�06Ö�5ECE� �*KMÖÝ0 CEÓ�=?�!Ï�=?�!Î!(!5EK;A�ÞRÒ*$�KM57$;Î*KD� C7$B� ���
KMÒ!=UÖ×5
=?�!Î!(�5WK�K70�57Ò!$�Ó�$;� ��=?Kaë;$�CE0*- � E �RG�$�Ìr0 CECE$�IJ�.57$:=?�!Î!(�5WK�-,�6�*G ��� �R$;Ül(*� IU=?ë�$�Ìr0.<.� C7=UL
�6�*�$;K;A
z1 z2
y
ω1 ω2
ω2
ω1
Lines of
constant E
L
îv=?Ï (*C7$ � A ?>=UÏ1Ó�0 =JG!K®57Ò9�.5)� C7$�K7Ð>Ó�Ó�$�57CE=?Ìa� P901(�5�57Ò*$�0 CE=UÏ1=U�@�»$ A Ï*A1K7$�$�î�=?Ï (!CE$ � P ���6CE$
Î!C7$�ÖÝ$�CEC7$�G]ÖÝ01C®57Ò!$DK7� Ó�$RCE$;�1KM01�Ù5EÒ*�.5�=?�!Î!(�5WK�K7Ò!0 (!IJG�P9$
�!0 CEÓ��6I?=Uë;$;Gc-.�*� Ó�$�I?Ð -.P,$;Ì�� (*K7$
57Ò!$;Ðç�6CE$ºÓ�0 CE$ºI?=?Í $�I?Ðú570åÎ!CE0�G�(*Ìr$30 (!57Î!(�5WK@�ÝÑaÒ!=JÌWÒì�6CE$ ÿ������ ��
�5E0 5EÒ!$��!$ræ>5�I?�’Ð1$�C-�
57Ò*�654�6CE$a0 �¾�’< $�CW�6Ï1$4Ì�IU0lKM$�570]ë;$�CE0*A1ÞRÒ*=?K�=?K)=U�¾Ìr0 �l5ECE�1Ke5�- K7�'Ð1-.570Ù57Ò!$DIU01Ï =JKe5E=?Ì4ÖÝ(*�*Ìn5E=U01�
ÑaÒ!01K7$@0 (�5EÎ!(�5EK
�6CE$:� IUÑR�'Ð�K)Î,01K7=U57=?< $��6�*G�K70�ÓÙ(*KM5aÒ*�'< $���Ó�$;�6�¾57Ò9�.5�=JKaÎ90lKM=U57=?< $1A
��"04
�&" 9 �1A�?�ÐlÓ�Ó�$r5EC7=J̺K7=?Ï Ó�0 =JG!K]K7(*ÌWÒz� KÙÒ>ÐlÎ,$�CEP,0 I?=?Ì�5W�6�!Ï1$��l5Ù0 Ö×57$��ãÌr0 �><1$�CEÏ $�Ö»� KM57$;C
5EÒ*�6�35EÒ!$]Ke5W�6�*G*�6CWG�I?0 Ï =JKM57=JÌ
ÖÝ(*�*Ìn5E=U01�%AE A � CE$;Ìr01Ó�Ó�$;�*G�$�GzKM=?Ï Ó�01=?G � � - �)=JK6C ��� � � � �X5!(�� "�- 5W�6�!Ò�
F V � � A>=?�*Ì�$�57Ò*$5W�6�!ÒÁÖÝ(!�*Ìn5E=U01�Á=JKDK70 Ó�$r5E=UÓ�$�K
Ìr01Ó�Î!(�5E�657=?0 �*� IUI?Ð3$ræ�Î9$;�*K7=U<1$ -��6�Á�6Î*Î!C70'æ�=?Ó��.L
5E=U01��06Öv=U5�P>к��CW�.57=?0�06Ö®Î901IUÐ>�!01Ó�=J�6IJKRÌ�� �3P,$�(*K7$;G¾=U�9Ke5E$;� G%A
�*A�?�0 Ó�$r5E=UÓ�$;K�=U5�=JK�Ò!$�I?Î�ÖÝ(!I>5E0:�1G!GÙ�:K7Ó�� IUIlI?=U�!$��6C�57$;C7Ó�-‘$ A Ï*A���� � � �x5E�6�*Ò0� � ��7
� K70�� K4570��’<10 =JG �9�65
KMÎ,065WK�A
-6 -4 -2 2 4 6
0.2
0.4
0.6
0.8
1
-3 -2 -1 1 2 3
-1.5
-1
-0.5
0.5
1
1.5
(a) (b)
L
$�CEC701C4K7(!C7Ö»� Ìr$@Ì�� �ºP,$,5���ü����,�.5a�!$;� C457Ò!$@0 CE=?Ï =?�%A�î!0 C45EÒ!=?KRCE$;�1KM01�º=U5a=?KRÏ10l0�G�570��’< 01=?G
=U�!=U57=J�6I?=?ë�=?�!ϾÑa=U57Òå< $;C7Ð#K7Ó��6I?I�Ñ4$�=?Ï Òl5WK�Ac24$;Ì;�6(*K7$Ù0 Ö�57Ò!$�KE�.5E(!CE�657=?0 �Á0 Ö�57Ò*$�K7=?Ï Ó�0 =JG!K;-
57Ò!$�$�CEC701CDK7(!C7Ö»� Ìr$�=JKD� I?K70 �9�65DÖ»� C:ÖÝC701Ó 5EÒ!$�0 CE=UÏ1=U�/A �DG!G�=?�!Ï3�¾KMÓ�� IUI®I?=U�!$��6CD57$;C7Ó 5E0
57Ò!$]K7=UÏ1Ó�0 =JG¾Ì;�6��KM01Ó�$�57=?Ó�$;KRÒ!$;IUÎ#�'< 01=?G�57Ò!$ �,�.5�CE$�Ï =?0 �9K�A
����� � �����& �"03�4 � �2')4<% �
�!.�*C%1
áh��ÌrIJ� KEK7=¦â9Ì;�.5E=U01�]Î!CE0 P!I?$�Ó�K;-;5W�6CEÏ $�5v<.�6I?(!$;K®� C7$�5eÐlÎ*=?Ì;�6I?IUÐ�P!=?�*� C7Ð �Ý$1A Ï9A 3 L
� - 7 �Q=P�nA'&)01Ó�L
Ó�01�ºÑa=JK7G!0 Ó Ó�=UÏ1Òl5RK7$�$;Óõ570�KM(*Ï Ï $�Ke5)57Ò*�65)5EÒ!$:5E� C7Ï1$r5)<.� IU(!$�K4P9$�K7$r5a�.5457Ò!$@<.�6I?(!$:06Ö
57Ò!$]K7=UÏ1Ó�0 =JG R Ka�1KMÐ>Ó�Î�5E0657$�K�A!Ø
0.Ñ)$;< $;C;-157Ò!=JKaÒ*�1KaKM$;< $;CE� I�G!CE�'ÑaP*�1ÌWÍ�K�A
îv=?CWKe5�-;=?�*KM5E�6P*=UI?=¦5E=U$�K®Ì��6�ÙC7$�KM(!IU5;A.ÞRÒ!$)57CW�6=?�!=?�!Ï
Î*C70�Ìr$�K7K/Ña=UI?Il57CEÐ@570:G�C7=?< $�57Ò!$40 (!57Î!(�5
� KaÌrI?01K7$@� KRÎ,01KEKM=?P!I?$D5E0�57Ò!$:5W�6CEÏ $r5a<.�6I?(!$�K�-�ÑaÒ!=JÌWÒ#Ì�� �¾01�!IUкP9$�� ÌWÒ*=U$;< $;G3� K7Ð>Ó�Î�570 57=UL
Ì��6I?I?Ð A �DK)�ÙC7$�KM(*I¦5�- 5EÒ!$
Ñ4$�=?Ï Òl5EK �Ý01(�57Î!(!5R� �*G�$�<1$���Ò!=JG!G�$;� ��� C7$DG�C7=?< $;��570�I?� C7Ï1$�C�� �*G
I?� C7Ï1$�C�<'� IU(*$;K�ÑaÒ!$�CE$)57Ò!$�K7=UÏ1Ó�0 =JGÙG�$;C7=?<.�.57=?< $)=?K�Ì�IU0lKM$)570@ë;$�CE0*A'ÞRÒ!$R< $�CEÐ�IJ�6CEÏ $�Ñ4$�=?Ï Òl5WK
=U�*Ì�C7$�� K7$�5EÒ!$DÏ1CE�1G�=?$��l5EK;- Ò!0.Ñ4$�<1$�C�-65EÒ!$;K7$DÏ1CE�1G�=?$��l5EK)�6CE$�57Ò*$��ºÓ�(!IU57=?Î!IU=?$;G¾P>Ð��6�º$�æ�Î90 L
�!$��l57=J�6I?I?Ð�K7Ó��6I?I9K7=UÏ1Ó�01=?G�G!$�CE=U<.�.5E=U<1$ �Ý$�æ!Ìr$�Î!5�ÑaÒ!$��¾�@5eÑa=?KM57=?�!Ï�5E$�CEÓ�F�=JK�� G*G�$;G�5E0]57Ò*$
KM=?Ï Ó�0 =JG �4Î!CE0�G�(*Ì�=U�!Ï���Ñ4$�=?Ï Òl5�(!Î�G!�.5E$]ÌrI?01K7$@570�ë;$�CE0*A"�
K
��C7$�KM(!IU5;-!57Ò!$�Ñ4$�=?Ï Òl5EK�Ó��'Ð
P9$�Ìr0 Ó�$]KM57(*ÌWÍ�A?>$;Ì�0 �*Gc-,ÑaÒ!$;�#57Ò!$�0 (!57Î!(�5WKDKE�.5E(!CW�.57$1-*5EÒ!$Ù�*$r5eÑ40 CE;Ï1=U<1$;K��*0º=?�*G�=JÌ��.5E=U01�Á06Ö4Ìr0 �!L
â9G�$��9Ìr$]I?$�<1$�I[A*äxÒ!$;�Á�6�#=?�!Î!(�5
Î9�.5M5E$�CE��Ö»�6I?I?K
�!$;� C
��G�$�Ìr=JKM=?0 ��P,0 (!�9G!�6CEÐ�5EÒ!$]0 (!57Î!(�5
ÌrIJ� KEK�=?K�(*�*Ìr$;CM5W�6=?�%A�áeG�$;� IUI?Ðz5EÒ!=JK�KMÒ*0 (!IJGTP9$#CE$��*$�Ìn5E$;GT=U�T5EÒ!$#�!$r5eÑ40 CEÍzP>Ðã� �ã01(�5ML
Î!(�5@<'� IU(*$]57Ò9�.5D=JKD=U�ÁP,$r5eÑ4$�$;�#57Ò*$]5eÑ40�Î90lK7K7=?P!IU$Ù5E� C7Ï1$r5
<.�6I?(!$�K�-,=ÀA $ A,�!0 5D�!$��6C
$;=¦5EÒ!$�C
� K7ÐlÓ�Î�5E065E$ A'Ø�0.Ñ4$�< $;C;-�I?� C7Ï1$�Ñ)$;=UÏ1Òl5EK/57$��9G�570
ÖÝ0 CWÌr$4�6I?I101(�57Î!(!5EKv570
57Ò!$)5E� =UIJK/0 Ö�57Ò!$RK7=UÏ L
Ó�01=?G�CE$�Ïl�6CWG�I?$;KEK®06Ö,57Ò!$D(!�*Ìr$;CM5W�6=?�l5eÐ A ÞRÒ>(*K;-65EÒ!$��!$�5eÑ)01C7Í�Ó��’Ð�Î!CE$;G�=JÌn5)�@ÑaCE0 �*Ï]ÌrIJ� KEK
Ña=¦5EÒ!0 (�5:Ï =?<>=U�!Ͼ�6�>о=?�*G�=JÌ��657=?0 �Á0 Ö�=¦5WK�I?0.ÑÚÌr01��â9G�$;�*Ìr$]=?�#5EÒ!$ÙCE$;K7(!IU5;A�”/�6CEÏ $�Ñ4$�=?Ï Òl5WK
57Ò*�65DK7�657(!CW�.5E$:57Ò!$]�*0>G!$;KaÓ��6Í1$@=¦5
=?Ó�Î90lK7K7=?P!IU$@5E0ºG�=/V,$;C7$;�l57=J�.57$�P,$r5eÑ4$�$;�35eÐlÎ*=?Ì;�6I/� �*G
�!0 �l5eÐ>Î!=JÌ��6Ic$�æ!�6Ó�Î!I?$;K;A��KM01IU(�5E=U01�ç5E0ú57Ò!$�KM$#Î*C701P!IU$;Ó�K�=?K�570¼KM$�5�57Ò!$Á5E�6CEÏ $�5�<'� IU(*$;K�5E0åP,$ÁÑa=U57Ò!=?�ì57Ò*$
CE� �!Ï $�0 Öc57Ò!$:KM=?Ï Ó�01=?Gc-1CE�657Ò!$;C�5EÒ*�6�º�65�5EÒ!$:�1KMÐ>Ó�Î�5E0657=JÌa<.�6I?(!$�K�A!&4�6CE$�ÓÙ(9Ke54P9$D5E� Í $��/-
Ò!0.Ñ)$;< $;C;->5E0�=U�9KM(!CE$�5EÒ*�.5�5EÒ!$]�!0�G�$Ù=?K
�!065
CE$;KM57CE=JÌn57$�G3570�01�!I?Ð�57Ò*$ÙI?=U�!$��6C�Î9�6C75
06Ö®57Ò*$
KM=?Ï Ó�0 =JGcAQ?>$�5M57=?�!Ï:57Ò*$�5W�6CEÏ $r5®<.�6I?(!$;Kv5E0
5EÒ!$RÎ901=U�l5�06Ö!5EÒ!$RÓ��.æ�=UÓ�(!ÓÚK7$;Ìr01�*GÙG!$�CE=U<.�.5E=U<1$
0 �ú57Ò*$3K7=UÏ1Ó�0 =JG =JKÙ57Ò!$¾P9$�Ke5�Ñ4�'Ð 570#5W�6Í1$º� G�<.� �15W�6Ï1$�06Öa57Ò*$º�!01�!IU=?�!$��6CE=¦5eÐåÑa=¦5EÒ!0 (!5
K7�657(!CW�.5E=U�!Ï 57Ò*$ÁKM=?Ï Ó�0 =JGcA�ÞRÒ!=JK�=JK��6�!0 57Ò!$;C�C7$�� K70 �ç57Ò!$ÁK7=UÏ1Ó�0 =JGç=?�xîv=?Ï (*C7$ � PT=JK��
Ï 0>0�G#ÌWÒ!0 =JÌr$1A*áO5
Ò*�1K�Ó��.æ�=?ÓÙ(!Ó�K7$;Ì�0 �*G�G�$;C7=?<.�.57=?< $��.5 � �]ÑaÒ*=?ÌWÒÁÌ�0 CEC7$�KMÎ,0 �*G¾5E0�57Ò*$
P!=U�9�6CEÐ�5E� C7Ï1$r5a<.�6I?(!$;K45eÐ>Î!=JÌ�� Ic=U�#ÌrIJ� KEK7=¦â9Ì;�.5E=U01�ºÎ!CE0 P!I?$�Ó�K;A
� �2′)4&%(��
&)Ò!0>0lKM$R5W�6CEÏ $r5�<.� IU(!$�K��.5�57Ò!$�Î,0 =?�l5�06Ö,57Ò*$�Ó��.æ�=UÓ�(!ÓõKM$�Ìr0 �9G�G!$�CE=U<.�.5E=U<1$a0 ��57Ò*$
K7=UÏ1Ó�0 =JG¾K70�� K4570��'<10 =JGºKE�.57(*CE�657=?�!ÏÙ5EÒ!$�0 (!57Î!(�5D(!�!=U5EK;A
� t s[��ikgOseikjl^Ôse_EbeZ ikgõ\�ghZ]\;�k�ì�kikjl_W\�bõse_EbeZ \;�l�1_W� sedÔseo1_�jld6�1_íd�� seql� sn}ú_�© ^1©
� � � ��
åsM\;j1o � � �
�� � ©
����� � 3�" ��"0�!.�"�� "03�4 ���C%���%("�4&�;��
ÞRÒ!$�Ke5W�6C757=?�!Ϻ<.�6I?(!$�KD0 Ö�5EÒ!$�Ñ4$�=?Ï Òl5WK:Ì;�6� Ò*�'< $��¾K7=UÏ1�!=Uâ9Ì�� �15@$4V�$;Ìr5�0 �Á5EÒ!$�57CW�6=?�!=?�!Ï
Î!C70�Ì�$;KEK�A®äå$�=?Ï Òl5EK�K7Ò!0 (!IJGzP,$ÁÌWÒ!0lKM$;�zCE� �*G�01Ó�I?мP!(�5�=?�TK7(*ÌWÒT� ÑR�'Ðå57Ò*�65�57Ò!$#K7=UÏ L
Ó�01=?Gº=?K4Î!CE=?Ó�� C7=?I?Ð��1Ìn57=?<.�.5E$;G�=?�º=U5EK4I?=U�*$;�6C4CE$�Ï =?0 �/A1áOÖ/Ñ4$�=?Ï Òl5WK)� C7$:�6I?I9<1$�CEÐ�IJ�6CEÏ $�57Ò!$;�
57Ò!$�K7=UÏ1Ó�01=?G Ña=UI?I�KE�.57(*CE�657$�C7$�KM(!IU57=?�!Ï3=U�úK7Ó�� IUI�Ï1CE�1G�=?$��l5EK
57Ò*�65�Ó�� Í $�IU$��6CE�!=?�!Ï3K7I?0.Ñ�A
áOÖ
Ñ)$;=UÏ1Òl5EK��6CE$º< $;C7ÐúK7Ó�� IUI)57Ò*$��TÏ CW� G�=?$��l5EKÙÑa=UI?Ia�6IJKM0 P9$�< $;C7ÐúK7Ó�� IUI[A�áh�15E$�CEÓ�$;G�=J�.5E$
Ñ)$;=UÏ1Ò15WK457Ò*�65
CW�6�!Ï1$D0.<1$�CR57Ò*$]KM=?Ï Ó�0 =JG R KRIU=?�!$��6C�CE$�Ï1=U01�ºÒ*�'<1$D5EÒ!$Ù�1G�<.�6�l5E� Ï $D57Ò*�65 � ���
57Ò!$�Ï1CE�1G�=?$��l5EK�� C7$�IJ�6CEÏ $�$��!01(!Ï Òå5EÒ*�.5]I?$;� C7�!=?�!Ï#Ì�� �úÎ!C70�Ì�$�$;Gú� �*G�� E �@57Ò!$��!$�5eÑ)01C7Í
Ña=UI?I!I?$;�6CE��57Ò!$�I?=?�!$;� C�Î*�6C75�06Ö,57Ò!$�Ó�� Î!Î!=?�!Ï@P9$�ÖÝ0 CE$R57Ò!$aÓ�0 CE$�G�=UÕ�Ìr(!IU5��!0 �*IU=?�!$;� C�Î*�6C75;A�
ÌWÒ!=?$�<>=?�!Ï]5EÒ!=?K4CE$;Ül(!=?C7$�K)Ì�0>0 CWG�=U�9�.57=?0 �ºP9$�5eÑ)$;$���5EÒ!$D57CW�6=?�!=U�*Ï�K7$r5a�!0 CEÓ��6I?=Uë��.5E=U01�%-
57Ò!$
ÌWÒ*0 =JÌr$�0 ÖcK7=?Ï Ó�0 =JGc- � �*G�57Ò!$DÌWÒ!0 =JÌr$�0 ÖcÑ)$;=UÏ1Ò15�=?�!=U57=J�6I?=Uë��.5E=U01�%A äå$
KM5E�6C75�P>ÐÙCE$;Ül(!=?C7L
=U�!Ï�5EÒ*�.5a5EÒ!$]G�=JKe5EC7=?P!(�5E=U01��06Ö/5EÒ!$�0 (!57Î!(�5WKa06Ö®$;�1ÌWÒ¾�*0>G!$�Ò*�’< $@��Ke5W�6�*G*�6CWG¾G�$;<>=?�657=?0 ���� �D06ÖR�6Î!Î!CE0’æ�=UÓ��657$�I?Ð � AcÞRÒ!=JK@=?K@� ÌWÒ*=U$;< $;G �.5:57Ò!$�=?�!Î!(�5�IJ�'Ð $�C:P>Ð#�!0 CEÓ��6I?=Uë;=U�*Ï�57Ò*$
57CW�6=?�!=U�*Ï KM$�5�� K�G�$;KEÌrCE=?P9$�G¼$;� C7I?=U$;C;AvÞ/0Á01P�5E� =U�z� Ke5W�6�*G!� CEG¼G!$�<>=?�657=?0 �zÌ�IU0lKM$�5E0 �º�65
57Ò!$@0 (!57Î!(�5a0 Ö%57Ò!$:â*CWKM54Ò!=JG!G�$;�¾IJ�’Ð $;C)Ñ4$ �e(*Ke5a�!$;$;G�570�(*KM$:5EÒ!$��6P,0.< $
CE$;�0 ��$��*G!$;G
KM=?Ï Ó�0 =JG�5701Ï $�57Ò!$;C�Ña=U57Ò�5EÒ!$
CE$;Ül(!=?C7$;Ó�$��l5�57Ò9�.5�5EÒ!$
=?�!Î!(!5)5E0�57Ò!$:KM=?Ï Ó�01=?G�� I?K70]Ò*�'<1$��
Ke5W�6�*G!� CEG�G�$;<>=?�657=?0 ������� � A �
KEKM(!Ó�=?�!Ï�5EÒ!$Ù=?�!Î!(�5WK�- � , -*5E0º��(!�!=U5:� C7$�(*�*Ìr01C7CE$�IJ�.5E$;G
Ña=¦5EÒ3<.� C7=J�6�*Ì�$�� ->57Ò*$]Ke5W�6�*G!� CEG¾G�$�<>=J�.5E=U01�¾0 Öv5EÒ!$�(!�!=U5EKaÑ4$�=?Ï Òl5E$;G3KM(!Ó Ña=UI?IcP,$
� ��� �
J � F,! ��
+��EF
5 �%� � �
ÞRÒl(9K�-‘5E0:=?�*K7(!CE$�5EÒ*�.5®57Ò*$�� ��� � C7$R�6Î!Î*C70’æ�=?Ó��657$;IUÐ��457Ò!$RÑ4$�=?Ï Òl5EK®K7Ò!0 (*I?G�P9$RCW�6�*G!0 Ó�IUÐ
G�CE�’Ña�¾ÖÝCE0 Óí��G�=JKe5EC7=?P!(�5E=U01��Ña=¦5EÒ3Ó�$��6�3ë�$�CE0��6�*G3��Ke5W�6�*G*�6CWG¾G�$;<>=?�657=?0 �3Ï =?< $��3P>Ð��� ��� � +��7F �%��” �
ÑaÒ!$�CE$��Ô=?K45EÒ!$��>(!ÓÙP,$�Ca0 Ö�=?�!Î!(!5EKR5E0�57Ò!$�(!�*=¦5�A
� 3�” ��”��!.0″�� “�3C4�� %1″04<�;�� �DK7K7(!Ó�=U�*Ï�5EÒ*�.5 C
�1A)5EÒ!$@57CW�6=?�!=?�!Ï�KM$�5aÒ*� KRP,$�$;�3�*0 CEÓ�� IU=?ë�$�Gc-!�6�9GE A)5EÒ!$]K7=UÏ1Ó�01=?GºÖÝCE0 Óíî�=?Ï (!CE$ � P3Ò*� KRP,$�$;�3(9KM$�G
5EÒ!$���Ñ4$�=?Ï Òl5EKRK7Ò!0 (!IJG¾P9$�CW�6�*G!0 Ó�IUÐ�G!CE�'Ña�ºÖÝC701Óí��G�=?KM57CE=?P!(�57=?0 � �Ý$1A Ï9A!(!�!=UÖÝ0 CEÓ&�
Ña=U57Ò�Ó�$;� �¾ë;$�CE0�� �*G3Ke5W�6�*G!� CEG3G�$;
����� � �����& �”03�4 @ %1�2′)3C”�3C4 ‘)�2��%(
ÞRÒ!$�CE$Ù=JKD�65DI?$;�1Ke5:0 �!$�Ñ)$;IUIUL[Î*C7=?�*Ìr=?Î!I?$;G#Ó�$�57Ò!0�G��ÀG�$;KEÌrCE=?P9$�G#=U�åKM$�Ìn5E=U01� -!A E �4ÖÝ01CD$�Ke5E=¦L
Ó��657=?�!Ï�57Ò!$@=JG�$;� I,I?$;� C7�*=U�!Ï�CE�657$ 0 A!Q �6�>Ð�0657Ò*$�CaK7ÌWÒ*$�Ó�$;KG�ÝÓ�0lKe5R06Ö%5EÒ!$�ÓíCE�657Ò!$;C)$;Ó�L
Î!=UCE=JÌ��6IU�vÒ*�’< $4P,$�$���Î!CE0 Î,01K7$;GÙ=U��57Ò*$4I?=U57$�CW�.5E(!CE$�5E0@� (�5701Ó��.57=JÌ�� IUI?Ð]� GP�e(*Ke5�5EÒ!$RIU$��6CE�!=?�!Ï
CE�657$ AcQ#0lKe5@06Ö�57Ò!0lKM$�K7ÌWÒ*$�Ó�$;K:G�$;Ì�C7$�� K7$]5EÒ!$�IU$��6CE�!=U�*ϺCW�.57$�ÑaÒ!$;�Á57Ò*$�Ñ4$�=?Ï Òl5:< $;Ìr5701C
èM01KEÌr=?I?I?�657$;KEê!-c� �*G =?�*Ì�C7$�� K7$�=U5]ÑaÒ!$;� 5EÒ!$�Ñ4$�=?Ï Òl5�< $;Ìr5701CDÖÝ01IUI?0.Ñ�K��3C7$;I?�657=?< $;IUÐ KM57$�� G�Ð
G�=UCE$;Ìr57=?0 �%A'ÞRÒ!$4Ó��6=?�ÙÎ!CE0 P!I?$�Ó Ña=U57Ò�57Ò!$�KM$)Ó�$r57Ò*0>G*Kv=JKv57Ò*�65v5EÒ!$�Ð]� C7$)�!065��6Î*Î!C701Î!CE=?�657$
ÖÝ0 C�Ke5E0�ÌWÒ*� KM57=JÌÙÏ1CE�1G�=?$��l5D01C:01��LOIU=?�!$�IU$��6CE�!=U�*ϾP,$;Ì;�6(*K7$Ù5EÒ!$�Ñ)$;=UÏ1Òl5:<1$;Ìn5E0 C �*(*Ìr57(*�657$;K
�6I?I�57Ò!$@5E=UÓ�$ A
2)$;Ð 01�*G#ÌWÒ!0>01K7=U�*Ͼ�ºK7=?�!Ï I?$�Ï1IU01P*�6IvIU$��6CE�!=?�!ϺCW�.5E$ -,=¦5@=?K@Ì�IU$��6CD57Ò*�65:Î!=JÌWÍ>=U�*Ͼ�3G�=¦Ö×L
ÖÝ$�CE$��l5�IU$��6CE�!=?�!ϼCE�657$ 0 ,�ÖÝ0 C�$�� ÌWÒìÑ)$;=UÏ1Òl5ºÌ��6�ì=?Ó�Î!C70.<1$357Ò!$ Ì�0 �>< $;C7Ï1$��*Ì�$ A<��Ñ4$�I?IUL
Î!C7=?�*Ì�=UÎ!I?$;G�ÑR�'Ð:0 Ö,G�01=U�*Ï
5EÒ!=?K;-.P*�1KM$�GÙ01��Ìr01Ó�Î!(�57=?�!Ï�K7$;Ìr01�*GÙG!$�CE=U<.�.5E=U<1$;K;-'=?K®G�$�K7Ì�C7=?P9$�G
=U� K7$;Ìr57=?0 � -*A/�1A9ÞRÒ!$�Ó��6=?�#Î!Ò!=?IU0lKM01Î!Ò>о=JK�5E0ºÓ��6Í1$ÙK7(!C7$]57Ò*�65:�6I?I%5EÒ!$�Ñ)$;=UÏ1Ò15WK�=?�#57Ò*$
�!$r5eÑ40 CEÍ�Ìr01�l<1$�CEÏ $DC701(!Ï Ò!I?к�6545EÒ!$]KE�6Ó�$�KMÎ,$�$�GcA
Û
$;Î9$;�*G�=?�!Ï@(!Î901�Ù5EÒ!$�Ìr(*C7<.�.5E(!CE$)0 Ö!57Ò!$a$;C7CE0 C®K7(!CMÖ»�1Ìr$1-'K70 Ó�$4Ñ)$;=UÏ1Òl5EK�Ó��'Ð�C7$�Ü1(*=UCE$
�aKMÓ��6I?I6I?$;� C7�!=?�!ÏRCW�.57$�=?��0 CWG�$;C�570��'< 01=?G:G�=?< $;C7Ï1$��*Ì�$ -nÑaÒ!=?IU$�0657Ò*$�CWK�Ó��'ÐDC7$�Ül(!=UCE$��RI?� C7Ï1$
IU$��6CE�!=U�*Ï
CW�.57$4=?��01CEG�$;C/5E0�Ìr0 �><1$�CEÏ $��65®�DC7$�� K70 �*� P!I?$)K7Î9$;$;GcA.24$;Ì;�6(*K7$)0 Ö!57Ò*=?K;-.IU$��6CE�!=?�!Ï
CE�657$;K�=U��57Ò!$:IU0.Ñ4$�C�I?�'Ð1$�CWK�KMÒ*0 (!IJG�Ï $;�!$�CW�6I?I?ÐÙP,$
IJ�6CEÏ $�C�57Ò*� ��=U�º57Ò!$DÒ!=?Ï Ò!$;C�IJ�'Ð $�CWK �ÀKM$;$
îv=?Ï (*C7$ E � �nA9ÞRÒ!=?KDÌr01C7CE$;Ìr5EK4ÖÝ0 C�57Ò!$�Ö»�1Ìn5a5EÒ*�.5
=?�#Ó�01KM5
�!$;(!CE� Ic�!$r5:�6CWÌWÒ!=¦5E$;Ìr57(!CE$;K;-�57Ò*$
KM$�Ìr0 �9G�G�$�CE=U<.�657=?< $
0 Ö�57Ò!$@Ìr0lKe5�ÖÝ(*�*Ìn5E=U01�ºÑa=U57Ò�CE$;K7Î9$�Ìn5)570ÙÑ4$�=?Ï Òl5WK�=?��57Ò!$:I?0.Ñ)$;C�I?�'Ð1$�CWK
=?K:Ï $;�!$�CW�6I?I?Ð3K7Ó��6I?IU$;C
5EÒ*�6� 57Ò*�65:0 Ö�57Ò!$�Ò!=?Ï Ò!$;CDIJ�'Ð $;CEK;A9ÞRÒ*$�CW�.5E=U01�*�6I?$]ÖÝ01C
5EÒ!$�� P90.<1$
Ò!$�(!CE=JKe5E=?Ì;KvÑa=?I?I�P9$aG�=JK7Ì�(*KEKM$�G]=?��Ó�0 CE$)G!$r5E� =UI�=?��I?�657$�C®K7$;Ìn5E=U01�*K®�6I?0 �!Ï:Ña=U57Ò�KM(!Ï1Ï $�Ke5E=U01�*K
ÖÝ0 C�Ò!0.Ñ 5E0�ÌWÒ!0>01K7$@57Ò!$Ù�1Ìn5E(*�6Iv<'� IU(*$�06Ö®57Ò!$ÙIU$��6CE�!=U�*Ï�CE�657$@ÖÝ0 C
57Ò!$�G�=WV�$�CE$��l5
Ñ4$�=?Ï Òl5WK�»K7$�$]K7$;Ìn5E=U01� -*A/���nA
áOÖ
KMÒ*� C7$�GúÑ)$;=UÏ1Òl5EKÙ� C7$�(9KM$�GzKM(9ÌWÒç� KÙ=U�¼5E=UÓ�$�LOG�$;I?�'Ðå�!$;(!CE� I��!$�5eÑ)01C7Í�K&�ÀÞaÛ � � �
� � E �v01CDÌ�0 �>< 01IU(�5E=U01�*�6I/�!$r5eÑ40 CEÍ�K � E � �O-!5EÒ!$ÙI?$;� C7�!=?�!Ï�CW�.5E$ÙK7Ò!0 (!IJG#P,$ÙÎ!CE0 Î,0 C757=?0 �9�6Ic5E0
57Ò!$�KEÜl(*�6CE$�CE0>065�06Ö)57Ò!$��>(!Ó�P9$;C�06ÖaÌr01�!�!$;Ìr57=?0 �*K�K7Ò*� C7=?�!Ͼ57Ò*�65@Ñ4$�=?Ï Òl5�-cP9$�Ì��6(9KM$�Ñ4$
Íl�*0.Ñ�57Ò9�.5a57Ò*$�Ï CW� G�=?$��l5EKR� C7$@��KM(*Ó�06Ö®Ó�0 CE$rLO0 C7L[I?$;KEK�=?�*G�$;Î9$;�*G�$;�15a5E$�CEÓ�K�A
���
*��!.0″�� %A���C%A@ %1�2′)3C”�3C4 � �B%1% 9
� Ï1=U<1$@$;� ÌWÒ¾Ñ)$;=UÏ1Òl5R=U5EK�0.Ña�¾I?$;� C7�!=?�!Ï�CW�.57$
� I?$;� C7�*=U�!Ï�CE�657$�K4K7Ò!01(!I?GºP9$@Î!CE0 Î,0 C757=?0 �9�6I9570�57Ò!$�KEÜ1(9�6CE$
CE0l0 540 Ö%57Ò*$
�>(!Ó�P9$;Ca06Ö®=U�*Î!(�5EKa570�57Ò!$�(*�!=¦5
� Ñ4$�=?Ï Òl5WK@=U�¼I?0.Ñ)$;C�I?�’Ð1$�CWK�KMÒ*0 (!IJG 5eÐlÎ*=?Ì;�6I?IUÐ P9$�IJ�6CEÏ $;C:57Ò*� �¼=U�å57Ò*$
Ò*=UÏ1Ò!$�CaIJ�’Ð $;CEK
B
57Ò!$;CR57CE=?ÌWÍ�K)ÖÝ0 Ca=?Ó�Î!C70.<>=?�!Ï�57Ò!$]Ì�0 �>< $;C7Ï1$��*Ì�$
=?�*ÌrI?(*G�$ C
� �
�%(3;��*
Q#01Ó�$��l57(!Ó
��� ��.�7 � �<� 0 � ��(�� +
���
7�� ��� �/.%�6
Ì��6��=?�*ÌrCE$;�1KM$RKMÎ,$�$�GÙÑaÒ*$���57Ò!$�Ì�01KM5�K7(!C7Ö»� Ì�$)=JK®Ò!=?Ï Ò!I?Ð]�!01�*KMÎ*Ò!$�CE=?Ì;�6I>P,$;Ì�� (*K7$4=U5�G!�6Ó�Î*K
57Ò!$#K7=Uë;$¾0 Ö�57Ò!$#KM57$;Î*K��6I?0 �!ÏåG�=UCE$;Ìr57=?0 �*K�0 Ö
Ò!=?Ï ÒãÌ�(!CE<'�657(!CE$¾57Ò>(*K�Ð>=U$;I?G�=?�!Ïú� IJ�6CEÏ $;C
$4V�$;Ìn5E=U<1$ÙI?$;� C7�!=?�!Ï�CW�.5E$Ù�6I?0 �*Ï�57Ò!$�G�=?C7$�Ìn5E=U01�*K�0 Ö�IU0.ÑÚÌ�(!C7<.�657(!CE$ � � � � ���çG!$��!0 57$;K
57Ò*$
Ke5EC7$;�!Ï65EÒ�0 Ö95EÒ!$aÓ�0 Ó�$��l57(*ÓÚ57$;C7Ó&�rA6áO5�Ò*� K�P9$;$���ÌrIJ�6=?Ó�$;GÙ57Ò*�65�Ó�01Ó�$��l57(!Ó Ï $;�!$�CW�6I?I?Ð
Ò!$�I?Î*K�Ó�01C7$�=?�ÁP*�65EÌWÒ#Ó�0�G�$�57Ò9�6�#=?�ÁKe5E0>ÌWÒ9� KM57=JÌ@Ó�0�G�$1-9P*(�5
�!0ºK7Ð�Ke5E$�Ó��.5E=?ÌÙKe5E(*G�Ð306Ö
57Ò!=JK��6CE$@Í>�!0.Ña��5E0�57Ò!$]� (�57Ò!01CEK;A
8 9 ���C��” #<% .�%(�!'-3�"03�4 ')�2��%1 QÁ� �>Ð �6(�5EÒ!0 CWK;-c=U�*Ì�IU(9G�=U�*Ï�?>0 Ó�Î,0 I?=U�*K7Í>ÐÁ$r5Ù� IÀA � � ( �O-
ÛD� C7Í1$���� Q#0>0>G!Ð � – �[->(!5M5701� � � * �[-�Q#(*CE�65E� $r5��6I[A � E * �aÒ*�’< $3Î!CE0 Î,01K7$;G¼CE(!I?$;K�ÖÝ01C
�6(�5E0 Ó��.5E=?Ì;�6I?IUÐ�� G!� Î�57=?�!Ï�5EÒ!$
I?$;� C7�*=U�!Ï�CW�.5E$;K �»K7$�$D� I?K70 � � & �*�nA>ÞRÒ!$�KM$�CE(!I?$;K)Ìr0 �l5EC701I!57Ò*$
KMÎ,$�$�G¾0 Ö�Ì�0 �>< $;C7Ï1$��*Ì�$
P>Ð�=?�*ÌrCE$;�1KM=?�!Ï�0 C�G�$�ÌrCE$;� K7=?�!ÏÙ5EÒ!$@IU$��6CE�!=?�!Ï�CE�657$@P*� K7$;Gº0 �357Ò*$
$�CEC701C;A
ä $�� KEKM(!Ó�$�5EÒ!$]ÖÝ01IUI?0.Ña=?�!Ï�Ö»� Ìr5EK
ÖÝ0 C:��IU$��6CE�!=?�!Ï�CW�.57$�� G!� Î�5E�657=?0 �Á�6I?Ï 01C7=U57Ò*ÓBC�� ���
57Ò!$�K7Ó��6I?IU$�Ke5%$;=UÏ1$��><.�6I?(!$®06Ö>57Ò*$�Ø�$�K7K7=?� � �»K7$�$(!ÓÙP,$�CD06Ö�=U57$�CW�.5E=U01�*K;-
57Ò!$ Î*�6CW�6Ó�$r5E$�C�<1$;Ìn5E0 C � �/.%�ºÑa=UI?ID� Î!Î!CE01� ÌWÒã57Ò*$ Ó�=U�*=UÓ�(!Ó ÖÝC701Ó 5EÒ!$ G�=?C7$�Ìn5E=U01�x06Ö
57Ò!$3Ó�=U�!=?ÓÙ(*Ó $�=?Ï $��><1$;Ìn5E0 C]0 Öa57Ò!$�Ø�$�K7K7=J�6� �»K7$�$BA�Ü,A8� E (X�n-®î�=UÏ1(!C7$ "X�rA��
�*G�$�C�57Ò*$;K7$
Ìr0 �9G�=¦5E=U01�*K�57Ò!$:$�<10 I?(�57=?0 ��0 Ö%57Ò*$D$�Ke5E=UÓ��.5E$;G�Î9�6CW�6Ó�$r5E$�C)Ì;�6�¾P9$D57Ò!01(!Ï Òl5406Öv�1K)�Ù0 �!$�L
G�=UÓ�$;�*KM=?0 �9�6I�Î!C70�Ì�$;KEK
�6�9G�57Ò!$�Ó�=U�!=?ÓÙ(*Ó�$�=?Ï $��><1$;Ìn5E0 C # Ì�� �ÁP9$��6Î*Î!C70'æ�=?Ó��.57$�G �×ÖÝ0 C
��IJ�6CEÏ $:�>(!ÓÙP,$�C
06Öv=U57$;CE�657=?0 �*KDC!K7$�$�î�=UÏ1(!C7$
” �4PlÐ
# ��� � �
����� � �
�
� �
����� �P
ÑaÒ!$�CE$��
�:G�$;�!065E$;KR5EÒ!$���F:�!01C7Ó�A!Ø
$��*Ì�$�Ñ)$�Ì�� �3�1G�0 Î!5
��Î*C70X�e$;Ìn5E=U01�
� ��� # + � �
��� � ���
�
� �
��� � �
570¾57Ò!$��6Î*Î!C70’æ�=?Ó��.57$�G�Ó�=U�!=?ÓÙ(*Ó A�=?Ï $;�l<1$;Ìr570 C # �1K:�¾0 �*$�G�=?Ó�$��*K7=U01�*�6I®Ó�$;�1KM(*C7$�06Ö
57Ò!$
G!=?KM5E� �*Ìr$R5E0�57Ò!$
Ó�=?�!=?ÓÙ(!Ó�AßÞRÒ!=JK�G�=JKM5E�6�9Ìr$�Ì�� ��P9$�(9KM$�G�570]Ìr01�l57CE0 I>57Ò*$�IU$��6CE�!=?�!Ï
CE�657$ �×ÖÝ01C�G�$r5W�6=?I?K�K7$�$ � E * �U�
� �/.C7 � �<� � �/.�7 � � F10 ( � ��(
���
�%� (X�
' �/.�7 �D� � � � F �Q� ' �/.%��7 � � ��(
���
� ��� � � ��� �%� * �
0 �/.�7 �D� � 0 �/.%��7�� 0 ��.%� ����� ' �/.�7 � ��� F10 �/.%�;�
�%� - �
ÑaÒ!$�CE$��ÙÌr0 �l5EC701I?K�57Ò!$@I?$;� Í�K7=?ë�$:06Ö/5EÒ!$@�'< $�CW�6Ï1$ -��
��å� C7$:Ìr0 �9Ke5W�6�l5EK4�6�*G ' =JK)(9KM$�G¾�1K
�6(�æ�=?IU=J�6CEÐ�<.�6CE=?� P!IU$:5E0�Ì;�6IJÌr(!IJ�.5E$:57Ò!$�I?$;� Ílо�'< $�CW�6Ï1$
0 Ö/57Ò*$�Ï CW� G�=?$��l5 ���
� � A
��065E$º5EÒ*�.5�5EÒ!=JK�KM$�5�0 Ö
CE(!IU$�K�=?K�$�� K7Ðú570¼Ìr01Ó�Î*(�57$#�6�9GçKM57CW�6=?Ï Òl5MÖÝ01C7ÑR�6CWGå570ú=?Ó�L
Î!IU$;Ó�$��l5;Acäå$�KM=?Ó�Î!IUÐ Ò*�'< $�570�Í $;$�Î 57CW� ÌWÍ#06Ö4�6�ú� G!G�=U57=?0 �9�6I®< $�Ìn5701C@=U� A�Ü,A8� � * �-C,57Ò*$
�'< $�CW�6Ï1$;G:Ï CW� G!=U$;�15 ' A.ÞRÒ!$)�!0 CEÓ 06Ö�5EÒ!=?K�<1$;Ìn5E0 C/57Ò!$;��Ìr01�l57CE0 IJKc57Ò*$4K7=Uë;$�0 Ö�57Ò!$4IU$��6CE�!=?�!Ï
CE�657$ �»K7$�$�A�Ü,A8� � - �%�rA ÞRÒ!$
� IUÏ10 CE=¦5EÒ!ÓÚÖÝ01IUI?0.Ñ�K�5EÒ!$
K7=UÓ�Î!I?$�=?�15E(!=U57=?0 � C1Ö»�6C4�'Ñ4�'Ð�ÖÝCE0 Ó�57Ò*$
Ó�=?�!=?ÓÙ(!Ó �»I?� C7Ï1$ÙG�=JKe5W�6�*Ì�$ � �
=U5DÎ!CE0�Ìr$�$�G!KD=U� P!=UÏ3Ke5E$�Î*K:�6�9G ÌrI?01K7$�5E0�57Ò*$�Ó�=?�!=UÓ�(!Ó
=¦5
� �!�!$;� I?K45EÒ!$�I?$;�6CE�!=?�!Ï�CE�657$ �×ÖÝ01CR57Ò!$;0 CE$r57=JÌ�� I%G�$r5W�6=?I?K
KM$;$ � E * �U�rA
����� �� 9 "��!. +��! �"0 "!C*C3��6��"0�<3C #� ��"04
�&" 9�# 3C"0��
��IU57Ò!01(!Ï Ò¼Ó�01KM5�K7Ð�Ke5E$�Ó�K�(*K7$��!0�G�$;KÙP*� K7$;Gå01�zG�065ÙÎ*C70�G�(*Ìr5EK]� �*G¼K7=UÏ1Ó�01=?G*K�-%Ó�� �lÐ
0657Ò*$�CR5eÐ>Î9$�KR06Ö�(!�!=U5EK �Ý01CaI?�’Ð1$�CWK#��Ì�� �¾P,$�(*K7$;GcA”� Ìr01Ó�Ó�01�3� I¦5E$�CE�*�.5E=U<1$D=JK457Ò*$:CW� G!=?� I
P*� K7=?K�ÖÝ(!�*Ìr57=?0 ���ÀN�2Rî ���!$�5eÑ)01C7Í'�»K7$�$ � (�- E &!- "!- � E �U��áh�ºN�2Rîå�!$r5eÑ40 CEÍ�K�- 57Ò!$:G�065RÎ!CE0>G�L
(*Ìn5�0 Ö95EÒ!$aÑ)$;=UÏ1Òl5�� �*G�=U�*Î!(�5�< $�Ìn5E0 C®=?K�C7$;Î!I?�1Ìr$�GÙÑa=U57Ò��GA�(*Ì�IU=JG�$��6��G�=JKe5W�6�*Ì�$4P,$r5eÑ4$�$;�
L
\n�’_EbM\;^;_��>dn�Tikg
\�qlq bedr½ ikZ]\�se_E�k�]d;jl_a� ikZ�_Wjlghikd�jl\;��sedn��\rbM�1g®seol_)Z�ikjlikZ:�1Z����R\;jl�Ùi�s�ikg�\D^;d.d6��\;q1q1bedn½ ikZ]\�|
seikd;j�d;°�seo1_aZ�ikjlikZ:�1Z�_Wik^;_Wj6��\��¦�1_��1i�be_WfEseikd;j�d;°cseo1_ � _Wghghi¦\�j9©
57Ò!$D=U�!Î*(�54� �*G�Ñ)$;=UÏ1Òl5)�6�*G�5EÒ!$DK7=?Ï Ó�0 =JG�=?K�C7$;Î!IJ� Ìr$�G�P>Ð�� ��$ræ�Î901�!$��l5E=?� IÀAlÞRÒ!$�0 (!57Î!(�5
� Ìn5E=U<>=U5eÐ�=JK�Ìr01Ó�Î*(�57$�Gc-!$ A Ï*A>ÖÝ01Ca0 �!$@01(�57Î!(!5;-*�1K
� � � � � J , Kv+ � , $ræ�Î�
F �E � F, � � F
� , � F��
ÑaÒ!$�CE$ � , ��� , ��=JK�5EÒ!$
Ó�$��6���»KM5E� �*G!� CEG�G�$;
Ìr0 Ó�P!=?�*�.5E=U01�30 Ö�Ï CW� G�=?$��l5
G�$�K7Ì�$��l5 �×ÖÝ01C
0 (!57Î!(�5:(!�!=U5EK
�a�6�9G�(!�*K7(!Î9$;C7<>=JKM$�G#ÌrI?(*KM57$�CE=?�!Ï
ÖÝ0 C�G�$�57$�CEÓ�=U�*=U�!Ï�5EÒ!$�Ó�$;� �*Ka�6�*G¾Ña=JG>57Ò*K�06Ö�57Ò!$]N�2Rî¼(*�!=¦5WK�A
���!I?=UÍ1$�K7=?Ï Ó�0 =JG!�6I�(!�!=U5EK@ÑaÒ*=?ÌWÒåÌ��6�åÌr0.<1$�C�5EÒ!$�$��l57=?CE$�K7Î*� Ì�$ -��¾K7=?�!Ï I?$�N
24îì(*�!=¦5
Ìr0.< $;CEK:01�!IUÐå�#KMÓ�� IUI)IU0�Ì�� I�C7$;Ï =?0 �ú06Ö457Ò*$�=U�*Î!(�5�K7Î*� Ì�$ A/ÞRÒ*=?K]Ì;�6�úP,$º�6�z�1G�<.�6�l5E� Ï $
P9$�Ì��6(9KM$�I?$;�6CE�!=?�!Ï#Ì�� � P,$�Ö»� KM57$;C;A%N�2Rî (!�!=U5EK�Ó��'Ð � I?K70ºÖÝ01C7Ó÷��P9$�5M57$;CÙK7$r5�06ÖRP*� K7=JK
ÖÝ(!�*Ìn5E=U01�*K:5703Ó�0�G�$�I�57Ò*$�=?�!Î!(!5�K7Î*�1Ìr$�57Ò*� � K7=UÏ1Ó�01=?G (!�!=U5EK;-%�6IU57Ò!01(!Ï ÒÁ57Ò!=JK@=?K:Ò!=?Ï Ò*IUÐ
Î!C701P!I?$�ÓõG�$�Î,$��*G!$��l5;A*BD��57Ò*$D�!$;Ï1�657=?< $�K7=?G�$1- 5EÒ!$
I?0�Ì�� IU=U5eÐ�Î*C701Î9$;CM5eÐ�06Ö/N�2Rî®K)Ó��'Ð�P,$
�ÁG�=JK7�1G�<.�6�l5E� Ï $�Î*� CM5E=?Ì�(!I?� C7I?Ð =?�zÒ!=?Ï ÒzG!=UÓ�$��9KM=?0 �*� I4K7Î*�1Ìr$;K]P9$�Ì��6(9KM$�Ó��'Ðå(!�!=U5EK��6CE$
�!$�$�G�$;Gç570úÌr0.<1$�C�57Ò!$#K7Î*� Ì�$;K;A®N
24î®K��6CE$3Ó�01C7$3�6Î!Î*C701Î!C7=J�.5E$º=?� �»IU0.Ñ G�=UÓ�$;�*KM=?0 �9�6IU�
(!Î!Î,$�C�IJ�'Ð $;CEK4�6�*G�K7=UÏ1Ó�0 =JG!K4=U� �ÝÒ*=UÏ1Ò�G!=UÓ�$��9KM=?0 �*� I8�)I?0.Ñ)$;CRI?�'Ð1$�CWK�A
� � Ç)Ä��)ò%Æ!ô�ò/ÄDÊ�ò Ç��#öxÆ!ó�È
ËMò/Ä)Å��xò��>Ê�ò/Ä)Å
�
��� 8 @B”0� ��.0% � ��%1�:’��
áh�Ù5EÒ!=?K®K7$;Ìr57=?0 �ÙÑ4$4$ræ!�6Ó�=?�!$4K70 Ó�$406Ö957Ò!$)57Ò!$;0 CEÐ�P9$;Ò!=?�*G]5EÒ!$457CE=?ÌWÍ�K�Î!CE$;K7$��l57$�G�$;� C7I?=?$�C�A
ä $�P,$�Ï1=U��=?�301�!$]G�=?Ó�$��*K7=U01�¾ÑaÒ*$�CE$D5EÒ!$](!Î�G!�657$�$;Ül(*�657=?0 �¾ÖÝ0 CaÏ1CE�1G�=U$;�l5aG!$;KEÌr$��l5�Ì�� �
P9$�ÑaCE=¦5757$;���1K
����.�7 � �<� ���/.%� F 0�� �&� ���� � 5 � E � �
ä $]Ñ40 (*I?G�I?=UÍ1$@570�Í>�!0.Ñ Ò!0.Ñ 57Ò*$]<.�6I?(!$]06Ö 0 �PV�$;Ìr5EK
Ì�0 �>< $;C7Ï1$��*Ì�$:� �*G357Ò*$]IU$��6CE�!=?�!Ï
KMÎ,$�$�GcA/î�=UÏ1(!CE$ &3=?IUI?(*KM57CW�.57$�K:57Ò!$�I?$;� C7�*=U�!Ï3P,$�Ò*�'<>=?0 C:ÖÝ0 C]K7$�<1$�CW�6I�G�=/V,$;C7$;�15ÙK7=?ë�$;K:0 Ö 0
ÑaÒ!$��º57Ò!$DÑ)$;=UÏ1Ò15�� Ke5W�6C75EK)0 (�54=U�º57Ò!$D<>=?Ì�=U�!=U5eÐ�06Öv�ÙIU0�Ì;�6I*Ó�=?�!=?ÓÙ(!Ó�A>áh�º01�!$DG�=?Ó�$���L
KM=?0 �%-v=¦5�=?KÙ$;� K7ÐÁ5E0 G�$�â*�!$�5EÒ!$º01Î�57=?Ó��6I�I?$;� C7�!=?�!Ï#CW�.5E$ – 0�� � (W-v�1K]P,$�=?�!Ï#57Ò*$�IU$��6CE�!=?�!ÏCE�657$¾57Ò*�65�Ña=UI?IaÓ�0.< $¾57Ò!$�Ñ4$�=?Ï Òl5�5E0å57Ò!$�Ó�=U�*=UÓ�(!Ó�- � � ,7.c-�=?�ãÎ!CE$;Ì�=?K7$�I?м0 �*$�KM57$;Î�»K7$�$@îv=?Ï (*C7$ & �»=8�eP �nA!áOÖ 0 =?KaK7Ó��6I?IU$;C�5EÒ*�6� 0�� � (�57Ò!$;�º5EÒ!$�Ke5E$�Î*K7=?ë�$:Ña=UI?IcP9$�K7Ó��6I?IU$;C4� �*GÌr0 �><1$�CEÏ $��9Ìr$aÑa=?IUI,5E� Í $�Ó�(!IU57=?Î!IU$D57=?Ó�$;KM57$;Î*K�A>áOÖ 0 =JK)P9$�5eÑ)$;$�� 0 � � ( �6�*G E 0 � � ( 57Ò!$;��57Ò*$Ñ)$;=UÏ1Ò15RÑa=?IUI�01KEÌr=?I?I?�657$D� C701(!�*G � � ,/. P!(�5aÑa=?IUI�$;< $��l5E(*�6I?IUÐ�Ì�0 �>< $;C7Ï1$ �»î�=?Ï (!CE$ & �Ý=U�eÌ �nA�áOÖ
0 =JK�Ó�0 CE$@57Ò9�6�#5eÑa=JÌr$@5EÒ!$�K7=Uë;$]06Ö 0 � � ( �Àî�=UÏ1(!C7$�& �Ý=U�eG �457Ò!$;�#57Ò*$ÙKe5E$�Î*K7=?ë�$]=JK
K70�I?� C7Ï1$57Ò*�65a57Ò!$�Ñ4$�=?Ï Òl5a$��*G*KR(!Î3Ö»�6C757Ò!$;CRÖÝC701Ó � � ,7. 57Ò*� �3P,$rÖÝ01C7$1A!Û
=?< $;C7Ï1$��*Ì�$@C7$�KM(!IU5EK;A
E
(
ω
)
ω
η > η
opt
ω
min
E
(
ω
)
ω
η < η
opt
ω
min
a)
c)
E
(
ω
)
ω
η = η
opt
ω
min
E
(
ω
)
ω
η > 2 η
opt
ω
min
b)
d)
E
(
ω
)
ω
η = η
opt
ω
∆ω
dE/d
ω
ω
c
ω
min
ω
c
ω
min
d
E(
ω
c
)
d
ω
� i � � iki �
L
ÖÝ(!�*Ìn5E=U01�%- 0 � � ( Ì;�6�#P,$�G�$;C7=?< $�G�PlÐ3â*CWKM5D$ræ�Î*� �*G�=?�!Ï � =?� ��Þ��'Ð>IU01C
K7$�CE=U$�K
�6P,0 (!5
57Ò*$Ìr(!CEC7$;�l5RÑ4$�=?Ï Òl5�- � �DC
� � ���<� �&� � � ��7 ��� F � � � � �&� �
�-�� � 7
�
E � � F � � � F � F6�&��� �-�� � F 7 565D54
� E ���
ÑaÒ!$�CE$]Ñ4$](*K7$]57Ò*$�K7Ò!0 C757Ò*� �*G�� ��
�����
� � �
� �
� �
�� � K � � A,áOÖ � =JK
Ül(*�1G�CE�657=JÌ@57Ò*$�K7$;Ìr01�*G0 CWG�$�C]G�$;C7=?<.�.5E=U<1$�=JK]Ì�0 �*KM5E� �15]� �*G 57Ò!$�Ò!=?Ï Ò*$�C]01CEG�$;C:57$�CEÓ�K�<.�6�!=JK7Ò%A/ÛD=WV�$�CE$��l57=J�.5E=U�*Ï
P90 57Ò#KM=JG�$�KRÑa=¦5EÒ3CE$;K7Î,$;Ìn5a5E0&� 5EÒ!$���Ï =?< $�K
� �&� ���� � � �
�&� �
�-�
� � 7 � � F �
�-� �
F6�&��� �-�
� � F 5 � EXE �
?>$r5757=?�!ÏB� � � � ,7.#�6�*G#�*0657=?�!Ï�5EÒ*�.5 � �&��� � ,7. � � � � � � -9Ñ)$��6CE$]IU$�Ö×5:�6Ö×57$�CDC7$��6C7LCE� �!Ï =?�!Ï�Ña=¦5EÒ
� � ,7.&� � � F
� FD� � �
�-�� � F �
� + � � � �
�-�� � 5 � E � �
&)0 Ó�Î*�6CE=?�!Ïå57Ò!=JK�Ña=U57Òì57Ò*$Á(!Î�G!�.5E$Á$;Ül(*�657=?0 � � E � �n-�Ñ4$�â*�*GT5EÒ*�.5¾Ñ)$ÁÌ;�6�TC7$�� ÌWÒì�
Ó�=?�!=?ÓÙ(!Ó =U��01�!$�Ke5E$�Î�=¦Ö
0�� � (<�
� F �&� � � �� � F �
� + 5 � E � �
�®$�CEÒ*�6Î*K®� ��$;� K7=?$�C�ÑR�'Ð]570�01P�5E� =U��5EÒ!=?K)K7� Ó�$aC7$�KM(!IU5�=JK�=?IUI?(*KM57CW�.57$�G�=U��î�=?Ï (!CE$ & �»=U=U�nA
ÞRÒ!$¼P90 5M5E0 Ó Ï1CE� Î!Ò Î*IU0 5EK357Ò*$¼Ï CW� G�=?$��l5#06Ö�� �1K#�ãÖÝ(!�*Ìn5E=U01� 06Ö&� A ?>=?�*Ìr$ � =?K
Ü1(9� G�CW�.5E=?Ì -v5EÒ!$#Ï CW� G!=U$;�15�=JK�KM=?Ó�Î!IUÐã� KM57CW�6=?Ï Òl5�IU=?�!$#Ña=U57ÒT<'� IU(*$3ë;$�CE0å�65�57Ò!$#Ó�=?�!=¦L
ÓÙ(!Óõ�6�*G ����
� � �
���
�.5�5EÒ!$
Ì�(!C7CE$��l5�Ñ4$�=?Ï Òl5 � � A � FD� � � F6� =JK�K7=UÓ�Î!I?Ð]5EÒ!$
K7IU01Î9$R06Ö�5EÒ!=?K
IU=?�!$]�6�9Gº=JK�Ìr01Ó�Î!(�57$�G3(*KM=?�!Ï�57Ò*$]Ke5W�6�*G!� CEG¾KMI?0 Î,$@ÖÝ0 CEÓÙ(*I?�
� F � � � F � � � �&� � � � � � � F �� � F � � ,/. 5 � E " �
?>0 I?<>=U�!Ï�ÖÝ01C:� � ,7.º5EÒ!$���Ï1=U<1$;K4$;Ül(*�657=?0 � � E � �nAäxÒ!=UI?$#5EÒ!$ÁI?$;�6CE�!=?�!ϼCW�.57$�5EÒ*�.5¾Ï =?< $;K�Ö»� KM57$;KM5¾Ì�0 �>< $;C7Ï1$��*Ì�$¾=JK 0 � � ( -�57Ò*$ÁI?� C7Ï1$;KM5IU$��6CE�!=U�*ÏTCW�.5E$å57Ò*�65 Ì��6� P,$¼(*K7$;G Ña=¦5EÒ!0 (!5 Ì�� (*KM=?�!ÏìG�=?< $�CEÏ $;�*Ìr$ú=JK �»� I?K70xKM$;$¼îv=?Ï6L
(!C7$'& �Ý=U�eG �
0 � + � � E 0�� � (
5 � E & �
áOÖ1� =?K@�!0 5�$ræ!� Ìr57I?ÐÁÜ1(9� G�CW�.5E=?ÌÙ57Ò!$;� 5EÒ!$�Ò!=?Ï Ò!$;C@0 CWG�$�CD57$;C7Ó�K@=?� $�Ü1(9�.57=?0 � � E � �:�6CE$
�!065�Î!CE$;Ì�=?K7$�I?мë�$;C70ú�6�*G � E � �Ù=?K�01�!I?Ðz�6�ì�6Î!Î!CE0'æ�=UÓ��657=?0 �%A�áh�TK7(*ÌWÒì� Ì;� K7$ -®=U5�Ó��'Ð
5E�6Í1$]ÓÙ(*I¦5E=UÎ!I?$Ù=U57$;CE�657=?0 �*K�570¾IU0�Ì��657$�5EÒ!$�Ó�=?�!=?ÓÙ(!Ó $;< $��#ÑaÒ*$��Á(*K7=?�!Ï 0 � � ( -9Ò!0.Ñ4$�<1$�C�-Ìr0 �><1$�CEÏ $��9Ìr$DÌ;�6��Ke5E=UI?I%P,$]Ül(!=¦5E$@Ö»� KM5;A
áh� ÓÙ(*I¦5E=UÎ!I?$�G�=UÓ�$;�*KM=?0 �9K�-cG�$�57$�CEÓ�=U�*=U�!Ï 0�� � (a=?K@�¾P!=¦5@Ó�0 CE$�G�=UÕ�Ìr(!IU5�P9$�Ì�� (*KM$�57Ò*$C7=?Ï Òl5
K7=?G�$�0 Ö � E � �4=?K���Ó��657CE=¦æ�� � +DÑaÒ!$;C7$�� =JK
Ì;�6I?IU$�Gº5EÒ!$]Ø�$�K7K7=J�6��ÑaÒ!01K7$]Ìr01Ó�Î90 L
�!$��l5EK
�6CE$DÏ1=U<1$��3PlÐ
��,!
�
� FD�
� � , � � � E (X�
Ña=¦5EÒ ��� �
���� �¼-*� �*G � $�Ü1(9�6I�570�5EÒ!$@570 5E�6I/�l(*ÓÙP,$�Ca06Ö®Ñ4$�=?Ï Òl5EK;A
��=JK��
Ó�$;�1KM(*C7$406Ö957Ò!$aÌr(*C7<.�.5E(!CE$)0 Ö ��A.áh��5eÑ)0@G�=?Ó�$��*K7=U01�*K;-'57Ò!$RI?=U�!$�K®06Ö�Ìr0 �9Ke5W�6�l5��ÖÝ01C®�:Ül(*� G!CE�657=JÌ�Ìr0lKe5��6CE$40.<'� I>=U��KMÒ*� Î9$a�1K�K7Ò!0.Ña�]=?��îv=?Ï (*C7$ (>A.ÞRÒ!$R$�=?Ï $;�>< $;Ìr5701CEK/06Ö
� Î901=U�l5)=?��5EÒ!$DG�=?CE$;Ìn5E=U01�*K�0 Ö�57Ò!$DÓ��Q�e0 C�� �*G�Ó�=?�!0 C4�.æ�$;K;A ÞRÒ!$D$�=?Ï $��><.�6I?(!$�K�Ó�$;� K7(!CE$
57Ò!$]KM57$;$�Î!�!$�K7KR0 Ö�� �6I?0 �*Ï�5EÒ!$]Ìr01C7CE$;K7Î,0 �*G�=?�!Ï�$�=?Ï $��9G�=UCE$;Ìr57=?0 �%A
������
��.�%&� áh�z57Ò!$¾IU$�� KM5ÙÓ�$;�6�ãK7Ül(*� C7$��À"/Q�? �]�6I?Ï 01C7=U57Ò*Ó3-vÑ)$ºÒ*�'< $º� KM=?�!Ï I?$ºIJ�'Ð $;C
IU=?�!$;� Ca�!$r5eÑ40 CEÍ�Ña=U57Ò�$�CEC701C4ÖÝ(!�*Ìn5E=U01�
�&����� � �E I
9
J�6Kv+
� � � F J , � , � � , � F � E * �
Eigenvectors
of H
ω
min,1
ω
min,2
ν
1
ν
2
ω
1
ω
2
P
E
� \ � � {��
L
ghq be_n\���d;°�seo1_ai¦j1ql� seg�i¦j�ikjlql� s�ghq>\�fW_�©
�
K7=U�!Ï���KEÌ��6IJ�6CRI?$;� C7�!=?�!Ï�CW�.57$@=JKRÎ!CE0 P!I?$�Ó��.5E=?Ì:=?��ÓÙ(!IU57=?Î!I?$]G�=UÓ�$;�*KM=?0 �9K�A!äå$�ÑR�6�l5
0 5E0ÙP,$DIJ�6CEÏ $�K70]5EÒ*�.5RÌr01�l<1$�CEÏ $;�*Ìr$a=JK�Ö»�1Ke5R�6I?0 �!Ï@5EÒ!$@KMÒ*� IUI?0.ÑxG�=?C7$�Ìn57=?0 �9K�06Ö0� �»K7Ó�� IUI
$�=?Ï $��><.�6I?(!$�KD0 Ö ���r-cÒ!0.Ñ)$;< $;C;-,=¦Ö 0 =JKD570>0�I?� C7Ï1$]57Ò*$�Ñ)$;=UÏ1Ò15WK
Ña=?I?I�G�=?< $�CEÏ $��6I?0 �!Ͼ57Ò*$
Ke5E$�$�ÎìG�=?C7$�Ìn5E=U01�*K'�ÝIJ�6CEÏ $3$�=?Ï $��><.�6I?(!$�KÙ0 Ö ���rA�Þ/0¼K7$�$¾57Ò!=JK�Ó�0 CE$3K7Î9$�Ìr=Uâ9Ì�� IUI?Ð -�I?$r5�(*K
�6Ï1� =U�¾$ræ�Î*� �*G'��-!P!(�5a5EÒ!=JKR57=?Ó�$]�6P,0 (�5���Ó�=U�!=?ÓÙ(*Ó
�&� ��� � �&��� � ,7. ��7 �E � � F � � ,7. � + �
��
�
� � � � F � � ,7. �-5 �#� � �
Û
=/V,$;C7$;�l57=J�.57=?�!Ï��#� � �4� �*Gº(9KM=?�!Ï�57Ò*$�C7$�KM(!IU5a=U�35EÒ!$�(!Î�G!�.5E$�$;Ül(*�.5E=U01� � E � ��Ï1=U<1$;K
���/.�7 � �<� ���/.%� F10 � � �/.%�
� � �#�"���� ���/.%� F10 �
�
�
� � � ����.%� F � � ,/. �-5 �#� E �
?>(!P�5ECE�1Ìn57=?�!Ï&� � ,7.¾ÖÝC701Ó�P,0657Ò#K7=?G!$;KRÏ =?< $�K
� ����.�7 � � F � � ,/. �<� ��� F 0 � ��� � ,7. �%�6� ����.%� F � � ,/. �-5 �#� � �
áOÖ/57Ò*$:Î*C7$�Ö»� Ìn5E0 CG��� F 0 � ��� � ,7. �%�)=JKa�ÙÓ��.5EC7=Uæ�57CW�6�9KeÖÝ01C7Ó��.5E=U01��57Ò9�.5a�6I?Ñ4�'Ð�K4KMÒ!CE=?�!Í�K�Á< $�Ìn5E0 C �»=ÀA $ A®=U5EK�$�=?Ï $;�><'� IU(*$;KÙ� IUIRÒ*�'<1$�Ó��6Ï1�!=¦5E(*G�$¾IU$�K7K�57Ò9�6� ����5EÒ!$��ç57Ò!$3(!Î�G!�.5E$
$;Ül(*�.5E=U01�¾Ña=?I?I/Ìr01�l<1$�CEÏ $1A
Ø�0.Ñ G�0>$;KÙ57Ò!=JK�Ò!$�I?ÎzÑa=U57ÒãÌWÒ*0l0lKM=?�!Ï#5EÒ!$ºI?$;� C7�*=U�!Ï CE�657$;K �ºáeG�$;� IUI?ÐúÑ)$�ÑR�6�l5�G�=¦Ö×L
ÖÝ$�CE$��l5ºI?$;�6CE�!=?�!ÏúCE�657$�K��6I?0 �!Ïú5EÒ!$ G�=/V�$�CE$��l5º$�=?Ï $;�*G�=?C7$�Ìn5E=U01�*K�A�ÞRÒ*=?Kº=?K�K7=?Ó�Î*IU$Á=UÖ�57Ò*$
$�=?Ï $��9G�=UCE$;Ìr57=?0 �*K:�6CE$ÙI?=?�!$;G (!Î Ña=U57Ò 57Ò!$�Ì�0l01CEG!=U�*�657$��.æ�$;KD06Ö�5EÒ!$�Ñ)$;=UÏ1Ò15WK�A,áh�úKM(*ÌWÒ �
Ì�� K7$ ->5EÒ!$�Ñ4$�=?Ï Òl5EKR�6CE$@(!�*Ì�0 (!Î!I?$;G3�6�9G¾Ñ4$�Ì�� �3�1K7K7=UÏ1�º$�� ÌWÒ3Ñ)$;=UÏ1Ò15a=U5EKR0.Ña�3IU$��6CE�!=?�!Ï
CE�657$
P9� K7$;G�01��57Ò*$:Ì�0 CEC7$�KMÎ,0 �*G!=U�!ÏÙ$�=?Ï $��><.�6I?(!$1AlØ
0.Ñ)$;< $�C�- =UÖ%5EÒ!$DÑ4$�=?Ï Òl5WK)� C7$:Ìr0 (*Î!IU$�G
57Ò!$;��Ñ)$aÓ�(*Ke5�â*CEKM5�CE065E�657$ � K7(*ÌWÒ�57Ò*�65 � =?K�G�=?� Ï 01�*�6I[-.=ÀA $ A 57Ò!$DÌr0>0 CWG�=?�*�.5E$R�6æ�$;K�I?=U�*$
(!Î�Ña=U57Ò�5EÒ!$
$;=UÏ1$��*G!=UCE$;Ìr57=?0 �*K �»K7$�$Dî�=?Ï (!CE$ (.P �nA>ÞRÒ!=JK�=JK�57Ò!$DÎ!(!CEÎ90lKM$D06Ö/G�=J�6Ï10 �*� IU=?ë�=?�!Ï
57Ò!$]Ø
$;KEKM=J�6��G�=JK7Ì�(*K7K7$;G¾$;� C7I?=?$�C�A
“%$r5���P,$@57Ò!$�CE065W�.57=?0 �¾Ó��.57CE=Uæ¾KM(9ÌWÒº5EÒ*�.5
� ��� ��� + �#� � �
ÑaÒ!$�CE$ � =?K�G!=?� Ï 0 �9�6Ic�6�*G�� + � ���9A!ÞRÒ!$]Ìr0lKe5RÖÝ(!�*Ìr57=?0 �357Ò*$��ÁÌ�� �¾P,$�ÑaCE=¦5757$��#�1K
�&����� � �&��� � ,7. ��7 �E � � � F � � ,7. � + � +�
� � �
��
�
� � � +�
� ����� F � � ,7. � � 5�#� ” �
QÁ�6Í>=?�!Ïã�ãÌWÒ*�6�!Ï1$Á06Ö�Ìr0>0 CWG�=?�*�.5E$;K�5E0 � �
����� F � � ,7. �¾KM=?Ó�Î!IU=Uâ*$�K�5EÒ!$å� P90.<1$$;Ül(*�.5E=U01�º5E0
�&� � � � �&� � ��7 �E � + � � �#� & �
�6�*Gº57Ò!$@5ECE� �*KMÖÝ0 CEÓ�$�Gº(*Î,G!�657$�$�Ü1(9�.57=?0 �3P,$;Ìr01Ó�$;K
� �/.�7 � �<� ��� F 0 � � � ��.%�-5 �#� (X�
��065E$�57Ò9�.5�� F 0 � =?KDG�=J�6Ï 01�*�6IcÑa=U57Ò G�=?� Ï 01�*�6I/Ì�0 Ó�Î,0 �!$;�15WK � F 0�� , A�ÞRÒ!=?K
$;Ül(*�657=?0 �
Ña=UI?I%Ìr01�l<1$�CEÏ $�=UÖ � � F 0�� , � � � ->=ÀA $ A 0 � F� � ÖÝ0 Ca�6I?I �WA>áOÖ�Ìr01�*KM57CW�6=?�!$;G�5E0�Ò*�’< $:�
nÿ��lû ���K7Ì;�6IJ�6CRIU$��6CE�!=?�!Ï�CW�.5E$:ÖÝ0 C��6I?I%Ñ4$�=?Ï Òl5EK)5EÒ!$���Ñ4$�ÓÙ(*KM5aC7$�Ü1(*=UCE$
0 � E� � + � �#� * �
=U�ì0 CWG�$;C�5E0z�'< 01=?GãG�=U<1$�CEÏ $;�*Ìr$1-�ÑaÒ*$�CE$ � � + � =JK�57Ò!$#IJ�6CEÏ $�Ke5�$;=UÏ1$��><.�6I?(!$¾0 Ö �zA�î!01CÖ»� KM57$;KM5
Ìr01�>< $�CEÏ $;�*Ìr$DÑ)$@Ò*�'<1$
0�� � (�� �� � + � 5 �#� - �
áOÖ � � ,/.3=JK���IU0 5
KMÓ�� IUI?$�CR5EÒ*�6� � � + ��57Ò!$;��Ì�0 �>< $;C7Ï1$��*Ì�$DÑa=?I?I%P9$�<1$�CEкK7IU0.Ñ �6I?0 �!Ï�57Ò*$� � ,7.ÙG�=?C7$�Ìn5E=U01�%A;áh�ÙÖ»� Ìr5;-.Ìr01�l<1$�CEÏ $;�*Ìr$�5E=UÓ�$4=?K�Î!CE0 Î,0 C757=?0 �9�6I65E0�5EÒ!$aÌr0 �9G�=¦5E=U01�]�>(!ÓÙP,$�C
� �
� � + � � � � ,/.ÁK70�5EÒ*�.5:=¦5:=?K:G�$;K7=?CE� P!IU$]570�Ò*�’<1$Ù� KDKMÓ�� IUI��6�Á$;=UÏ1$��><.�6I?(!$ÙK7Î!C7$�� G#�1KÎ90lK7K7=UP*IU$1A Ø�0.Ñ4$�< $;C;-cK7=U�9Ìr$�Ñ4$�Ò*�'< $�CE065E�657$�G � 5E0#P9$º� IU=?Ï �*$;GåÑa=¦5EÒú57Ò!$¾Ìr0>0 CWG�=?�*�.5E$��6æ�$;K;-��� (X�aÌr01�*K7=?KM5EK��1Ìn5E(*�6I?IUÐ306Ö �à=U�*G!$�Î,$��*G�$;�l5 �rLhG�=?Ó�$��*K7=U01�*�6I/$;Ül(*�.5E=U01�*K;A*ÞRÒ!$�CE$rÖÝ01C7$1-!Ñ4$
Ì��6�ãÌWÒ!0>01K7$º�ÁI?$;� C7�!=?�!ÏÁCW�.5E$�ÖÝ01C�$�� ÌWÒ¼Ñ4$�=?Ï Òl5�=?�*G�$;Î9$;�*G�$��l5�06Öa5EÒ!$¾0 57Ò!$;CEK;A�ä $3KM$;$
57Ò*�65a57Ò!$�01Î�57=?Ó��6IcCW�.57$:ÖÝ01CR57Ò!$ � (�� Ñ4$�=?Ï Òl5 � , =JK 0 � � ( � , � +� � A
�
��� � ����
� .0%1
@B”03�%1�2′ �A%(� � �&’�� îv=?Ï (*C7$ � � G�=JKMÎ!IJ�’Ð�K��åK7$r5�0 Ö � ��� $�æ!�6Ó�Î!I?$;K�G�CW�’Ña�zÖÝCE0 Ó 5eÑ40
8@�6(*KEKM=J�6��G�=?KM57CE=?P!(�57$�GÙÌ�I?�1K7K7$;KvÌr$��l5E$�CE$;G]�65 �ÝL � A � – L � A * ��� �*G � � A � – � A * �nA’ÞRÒ!$)$�=?Ï $��><.�6I?(!$�K
06Ö�57Ò*$)Ìr0.<.� C7=J�6�*Ì�$�Ó��.57CE=Uæ@� C7$ � A * � �6�*G � A � � &*Aräå$�57CW�6=?�Ù��K7=?�!Ï I?$�IJ�'Ð $�C/IU=?�!$;� C/�!$�5eÑ)01C7Í
Ña=¦5EÒ E =?�!Î!(�5WK�- ��0 (!57Î!(�5�- E Ñ4$�=?Ï Òl5WK�-c�6�9G���P!=J� K��»K7$�$�î�=?Ï (!CE$B�#- �;�
(9KM=?�!Ï357Ò!$�"vQ�?
�6I?Ï 0 CE=U57Ò!Ó =?�ìP*�.5WÌWÒãÓ�0�G�$1A)î�=UÏ1(!CE$ � �#G�=?K7Î!IJ�'Ð�K�57Ò!$#Ñ4$�=?Ï Òl5�57CW�P�e$�Ìn5701C7Ðz� �*GT$�CEC701C
G�(!CE=U�!Ï�I?$;� C7�!=?�!Ï3ÑaÒ!$��ú(*K7=?�!Ï#�¾I?$;� C7�*=U�!Ï3CW�.57$�K:06Ö 0 � �X5 "¾� �*G E A "�A���0 57$�57Ò9�.5�57Ò*$
IU$��6CE�!=U�*Ï�CW�.5E$��ÀKM$;$ A�Ü,A � * � 0 � + � � E � � � + � � E �$5 * � � E 5 � *�Ña=?IUI/Ì;�6(*K7$�G�=?< $�CEÏ $;�*Ìr$�K� KR=JKR$�<>=?G!$��l5aÖÝ0 C 0 � E 5 “!A
ω1ω0
ω2
χ0
y
χ1
L
îv=?Ï (*C7$’� E K7Ò!0.Ñ�K:5EÒ!$ºKE�6Ó�$�$ræ!�6Ó�Î!I?$�(*K7=U�*ÏÁKe5E0>ÌWÒ9� KM57=JÌ�=?�*KM57$�� Gå06ÖaP*�65EÌWÒúÓ�0>G!$
IU$��6CE�!=U�*Ï*A6Ø�$;C7$1- �@I?$;�6CE�!=?�!Ï@CE�657$R06Ö 0 � � 5 E =JK�(*K7$;GcAlBD�*$�Ì��6��K7$�$R5EÒ*�.5�5EÒ!$a57CW�P�e$�Ìn5E0 CEÐ
=?K�ÓÙ(9ÌWÒç�!01=?K7=U$;CÙ5EÒ*�6�ã=U�ãP*�.5WÌWÒçÓ�0�G�$�KM=?�*Ìr$30 �*IUÐz� �ç$;KM57=?Ó��.5E$¾0 Ö�57Ò!$3Ï CW� G!=U$;�15�=?K
(*KM$�Gã�65�$;� ÌWÒT=U57$�CW�.5E=U01�%A�ÞRÒ!$#Ìr0lKe5�=JK�Î!I?065M5E$;Gì� K�� ÖÝ(!�*Ìr57=?0 �ì06Ö:$�Î,0�ÌWÒ%A<���ì$�Î,0�ÌWÒ
Ò!$�CE$@=?K�K7=?Ó�Î*IUкG!$râ*�!$�G�� KG� ��� =?�!Î!(!5
Î!CE$;K7$��l5E�657=?0 �*K4ÑaÒ!=JÌWÒ%->ÖÝ0 C�KM570�ÌWÒ*�1Ke5E=?Ì:I?$;� C7�!=?�!Ï9-
Weight space
−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Log MSE (dB)
0 1 2 3 4 5 6 7 8 9 10
−20
−15
−10
−5
0
epochs
Weight space
−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Log MSE (dB)
0 1 2 3 4 5 6 7 8 9 10
−20
−15
−10
−5
0
epochs
� \ � � { �
L
í~�� ¡º\;jl� � {��
�
z¢ � ¡6©
Ìr0 CECE$;K7Î901�*G!Kc5E0 � � � Ñ)$;=UÏ1Ò15�(!Î�G!�.5E$;K;A.áh�ÙP*�65EÌWÒ%-.�6��$�Î,0�ÌWÒ�Ìr01C7CE$;K7Î,0 �*G!K%570:0 �!$4Ñ4$�=?Ï Òl5
(!Î,G*�.57$1A
Weight space
−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Log MSE (dB)
0 1 2 3 4 5 6 7 8 9 10
−20
−15
−10
−5
0
epochs
batch
L
� � ¢6©
Log MSE (dB)
0 1 2 3 4 5 6 7 8 9 10
−20
−15
−10
−5
0
Weight space
−2 −1.6 −1.2 −0.8 −0.4 0 0.4 0.8 1.2 1.6 2 2.4
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
epochs
L
seikfa�k_n\�bej1i¦j1^1©
� *C.0��”�.0� �&%(‘ �A%(� � �:’�� î�=UÏ1(!C7$�� � K7Ò!0.Ñ�K)57Ò*$]�6CWÌWÒ!=¦5E$;Ìr57(!CE$:ÖÝ0 C���< $;C7Ð�K7=?Ó�Î*IU$�Ó�(!I¦L
57=?I?�'Ð1$�C®�!$r5eÑ40 CEÍ�A.áO5�Ò*� K �a=?�!Î!(!5;-"�aÒ!=JG!G�$;�%- � �*GB�401(�57Î*(�5��!0�G�$1A6ÞRÒ!$�CE$��6CE$ E Ñ4$�=?Ï Òl5WK
�6�*G E P!=J� K7$;K;A*ÞRÒ!$�� Ìn5E=U<.�657=?0 �3ÖÝ(!�*Ìr57=?0 �#=JK ��� � �1� � 5 ($�c5E� �!Ò �%� E ��� � � �nA9ÞRÒ*$�57CW�6=?�!=?�!Ï
KM$�5:Ìr01�l5E�6=?�*K � � $�æ�� Ó�Î!IU$�KaÖÝCE0 Óï$;�1ÌWÒ#06Ö E Ì�I?�1K7K7$;K;A924065EÒÁÌrIJ� KEKM$�K
� C7$Ù8@� (*K7K7=J�6�ÁG�=JKeL
57CE=UP!(!57$;GºÑa=¦5EÒ3KM5E� �*G!� CEG�G!$�<>=?�657=?0 � � A � A�&)IJ� KEK �DÒ*�1K)�ÙÓ�$;�6�¾06Ö%L
�D� �*GºÌ�I?�1K7K E Ò9� K4�
Ó�$��6�¾06Ö 7 �1A>Þ��6CEÏ $�5)<.�6I?(!$�K4� C7$
L#�DÖÝ0 CRÌrIJ� KEK��:� �*G 7 �
ÖÝ0 CaÌrIJ� KEK E A�î�=UÏ1(!C7$!� ��KMÒ*0.Ñ�K
57Ò!$]KM570�ÌWÒ*�1Ke5E=?ÌD57CW�P�e$�Ìn5E0 CEÐ�ÖÝ0 CR57Ò*$�$ræ!�6Ó�Î!I?$ A
ω1
ω0
ω2
ω3
χ
y
L
�2��”0�<3C �!3 9 �?'-')�:' ��*C'->��!� % � ‘)�!3C �>��:’�
�!��”0�<3�
�% #�"� �"0��% 9
ä $#Ì�� �ç(*K7$¾57Ò!$�CE$;K7(!I¦5WK�06Ö�5EÒ!$�Î!C7$;<>=U01(*K�K7$;Ìr57=?0 �ç570B�e(*KM57=UÖÝÐçKM$;< $;CE� I)0 Ö�57Ò!$35EC7=JÌWÍ�K
G�=?KEÌr(9K7K7$;G¾$;� C7I?=U$;C;A
��* � � ')�!� �=����%�
%1�!3� >�’)�
����% “�3�� *�� #!�2′)”�� � .�%1
ÞRÒ!$DCE$;�1KM01��ÖÝ0 CR5EÒ!$��6P,0.< $
57CE=?ÌWÍ�=JK457Ò*�65��Ù�!01�!ë�$;C70�Ó�$;�6�3=?�º5EÒ!$@=U�!Î*(�5a<'� C7=J�6P*IU$�K
ÌrCE$;�.5E$;K��$5���ü�� �Uý.ü[û �
$�=?Ï $;�l<.� IU(!$1A*ÞRÒ!=JK�Ó�$;� �*KR5EÒ!$ÙÌr01�*G�=U57=?0 �#�>(!Ó�P9$;C�Ña=UI?I/P,$]IJ�6CEÏ $1-
=ÀA $ A.5EÒ!$
Ì�01KM5�K7(!C7Ö»� Ì�$aÑa=UI?I!P,$�Ke5E$�$�Î�=?��KM01Ó�$RG!=UCE$;Ìr57=?0 �*K�� �*G�KMÒ9�6I?IU0.Ñã=U��065EÒ!$�CWK�K70@57Ò*�65
Ìr0 �><1$�CEÏ $��9Ìr$ÙÑa=?I?I�P9$�<1$�CEÐÁKMI?0.Ñ�AcÞRÒ!$�KM01IU(�5E=U01� =JK:570#K7=UÓ�Î!I?ÐÁÎ!CE$�Î*C70�Ìr$�K7KD5EÒ!$�=U�!Î*(�5EK
PlоKM(!P!57CW� Ìn5E=U�*Ï�5EÒ!$�=?C�Ó�$;� �*K;A
î!0 C���K7=U�*Ï I?$:I?=?�!$;� Ca�!$�(!CE0 �/->57Ò!$�$;=UÏ1$��>< $�Ìn5701CEK40 Ö/57Ò*$]Ø�$;KEK7=?� � �»Ña=¦5EÒ�Ó�$��6�*KaK7(!P�L
57CW� Ìn5E$;G ��Î901=U�l5�� IU01�!Ï�57Ò!$¾Î!CE=U�*Ì�=UÎ9�6I��6æ>$�K�06ÖR5EÒ!$¾Ì�IU01(*Gú06ÖR57CW�6=?�!=?�!Ï#< $�Ìn5E0 CWK&�ÝCE$;Ì;�6I?I
îv=?Ï (*C7$ * �nA>áh�!Î*(�5EK45EÒ*�.5RÒ*�’< $:�ÙIJ�6CEÏ $
<'� C7=J�.5E=U01��=?�3K7Î!CE$;� Gº�6I?0 �!Ï�G�=WV�$�CE$��l5aG�=?C7$�Ìn57=?0 �9K
06Ö%5EÒ!$D=?�!Î!(!5RK7Î*� Ì�$
Ña=?IUI�Ò*�'<1$
�]IJ�6CEÏ $DÌr0 �9G�=¦5E=U01�º�>(!Ó�P9$;C4� �*G�K7IU0.ÑxI?$;� C7�!=?�!Ï9A ���9G¾K70
Ñ)$@CE$;Ìr01Ó�Ó�$;�*G C
�A�&’
��!.0″�� % ����%$#!�2′)”0�!3�� %1 =�<>����C%A”�3�� *�� #!�2′)”�� � .�%1 �
áOÖ:5EÒ!$Á=?�!Î!(�53<.�6CE=?� P!IU$�K��6CE$ÁÌr01C7CE$�IJ�.5E$;Gc-®5EÒ!=?KºÑa=UI?I
�*065ºÓ��6Í1$�57Ò!$ $�CEC701C�KM(!C7Ö»� Ì�$
KMÎ!Ò*$�CE=?Ì;�6I[-�P!(�5�=U5�Ña=UI?I%Î,01KEKM=?P!I?Ð�C7$�G�(*Ì�$:=U5EK�$;Ì�Ì�$��l57CE=JÌr=U5eÐ A
&)0 CEC7$;I?�657$;G�=U�!Î*(�5a<'� C7=J�6P*IU$�K)(9KM(*� IUI?Ð�Ì�� (*K7$D5EÒ!$@$�=?Ï $;�l<1$;Ìr570 CWK�0 Ö � 570�P,$:CE065W�.5E$;G
�'Ñ4�'Ð:ÖÝCE0 Ó 57Ò*$�Ìr0>0 CWG�=?�*�.5E$)�.æ�$�K1�Àî�=UÏ1(!C7$ (6�
<1$�CWKM(*K ('P �%5EÒ>(*K®Ñ)$;=UÏ1Òl5�(!Î�G!�657$;K�� C7$4�!0 5
G�$;Ì�0 (!Î!I?$;G%A*Û
$�Ìr01(!Î!I?$;G3Ñ)$;=UÏ1Òl5EKRÓ��6Í1$D5EÒ!$Áè70 �!$@I?$;�6CE�!=?�!Ï�CE�657$@Î,$�C�Ñ4$�=?Ï Òl5Eê�Ó�$r5EÒ!0�G
0 Î�5E=UÓ��6I[-�5EÒl(9K�-�Ñ4$@Ò*�’< $:57Ò*$@ÖÝ0 I?IU0.Ña=?�!Ï�57CE=?ÌWÍSC
� %(� �:'-')%1.0�2��%A����% "�3�� *�� #!�2')"�� � .�%1 �
��0.ÑõKM(!Î*Î90lKM$�5EÒ*�.5�57Ò!$º=U�!Î*(�5�<.�6CE=J�6P!I?$;K�0 Ö��#�!$�(*C701�¼Ò*�'< $�P,$�$;�çG�$;Ì�0 CEC7$;I?�657$�Gc-
57Ò!$]Ø
$;KEKM=J�6�3ÖÝ0 CR5EÒ!=JK��!$;(!C701�¾=JKR5EÒ!$��#G�=J�6Ï10 �*� I%�6�*G3=U5EKa$;=UÏ1$��><.�6I?(!$;KRÎ,0 =?�l5
�6I?0 �!Ï�57Ò*$
Ìr0>0 CWG�=?�*�.5E$º�.æ�$;K;A/áh�TKM(9ÌWÒç� Ì;� K7$�57Ò!$3Ï CW� G!=U$;�15�=?K��!065�57Ò!$3P,$;KM5�G�$�K7Ì�$��l5�G�=?CE$;Ìn5E=U01�
� K�Ì��6�¼P,$�KM$;$��z=?�çî�=UÏ (‘P%A��45Ù5EÒ!$3Î901=U�l5 �®-®�6�ã�6CEC70.ÑõKMÒ*0.Ñ�K�57Ò9�.5�Ï1CE�1G�=?$��l5�G�0>$;K
�!065@Î901=U� �6CWG!K�57Ò!$�Ó�=U�*=UÓ�(!Ó�A%Ø�0.Ñ4$�< $;C;-,=UÖ�Ñ)$�=?�*Ke5E$;�1G �1K7K7=UÏ1�Á$;�1ÌWÒÁÑ4$�=?Ï Òl5:=U5EK
0.Ña� I?$;�6CE�!=?�!Ï3CE�657$'�Ý$;Ül(*� I�57Ò!$�=?�l<1$�CWKM$�06Ö�57Ò!$�Ìr01C7CE$;K7Î,0 �*G�=?�!Ͼ$�=?Ï $��><.�6I?(!$��a5EÒ!$��å57Ò*$
G�$;KEÌr$;�15�G�=?CE$;Ìn5E=U01�¾Ña=?I?IcP9$�=?�º5EÒ!$]G�=?C7$�Ìn5E=U01�º06Ö�57Ò*$:0 57Ò!$;C��6CEC70.Ñì5EÒ*�.5aÎ,0 =?�l5EKaG�=?C7$�Ìn5EIUÐ
570.ÑR�6CWG!K)57Ò!$�Ó�=?�!=UÓ�(!Ó'C
# �% � �% ���!'-�!��% .�%1�2')3C"�3C4 ')�2��% > �&’ %1�!�-��� %1″�4&�;� �
� �åøMó �(�>Ë7Ê�ó®ø �lò/Ê�Ç�ÄDÈ Ç�Æ*È�ò/ÆTÇ ��Å!Ë��õËeùcó�Å!ËeÇ)Ä�� òcÅ���ÇaÈ?�
áh�Ù5EÒ!$4ÖÝ0 I?IU0.Ña=?�!Ï:Ñ)$RÑa=?IUI�P!CE=?$��*Ð�=?�l57CE0>G!(*Ìr$457Ò*$ �
$�ÑR5E0 �%-6Ì�0 �P�e(!Ïl�.5E$)Ï1CE�1G�=U$;�l5;-68@�6(*KEKML
��$�ÑR5E0 �%-l”%$;< $��>P,$�CEÏ�QÁ�6CWÜl(*�6CWG>5��6�9GÙ5EÒ!$ �D(*�1KM=UL ��$�ÑR5E0 �@�»2Rî�8 ?”�®Ó�$r5EÒ!0�G@�»K7$�$
� I?K70
� � � – � � – �*- ” �*�nA
����� �A% � ���<3 8 .04<�&'-"0����
Þ/0�Ï $�5@� � (*�*G�$�CWKM5E�6�9G�=U�*Ͼ0 Ö�57Ò*$ �
$�ÑR5E0 �åÓ�$�57Ò!0�GåI?$r5�(*K@CE$;Ì�� Î!=U57(!IJ�.5E$Ù5EÒ!$�C7$�KM(*I¦5WK
ÖÝC701Ó�K7$;Ìn5E=U01� "�A7� AX�DK7K7(!Ó�=U�*Ï]��Ü1(9� G�CW�.5E=?Ì4I?01KEK�ÖÝ(!�*Ìn5E=U01�&� �»K7$�$ A)Ü9A8� E � �;�®� K�G�$;Î!=JÌn57$�G
=U��î�=UÏ1(!C7$ & �Ý=?=8�r-6Ñ)$RÌ�� ��Ì�0 Ó�Î!(�5E$457Ò!$aÑ4$�=?Ï Òl5®(!Î,G*�.57$�� IU01�!ÏD57Ò!$RI?=U�!$�K�06ÖSA�Ü,A8� E ���OL-� E � �
��� � 0
� FD�
��� F
� � + � �
���
� 0 ��� � � � + � �
���
� ��� �
ÑaÒ!$�CE$ 0 Ó�(*KM5]570#P,$ºÌWÒ!0lKM$;�å=?�ú57Ò*$�CE� �!Ï $ � � 0 � �ºKM=?�*Ì�$&� =?K�=?�¼Î!CW� Ìr57=JÌr$��!0 5
Î9$;CMÖÝ$�Ìn57I?Ð#Ül(*� G�CW�.5E=?Ì A!áh�#5EÒ!=?K
$;Ül(*�657=?0 �#=?��ÖÝ0 CEÓ��.57=?0 �Á� P901(�5�5EÒ!$�Ø
$;KEKM=J�6� �é=JK�5W�6Í1$��
=U�l570��1Ì�Ìr01(!�l5;A>áOÖ/5EÒ!$�$�CECE0 C)ÖÝ(!�*Ìn5E=U01�¾ÑR� KRÜl(*�1G�CE�657=JÌ
01�!$�Ke5E$�Î3Ñ)01(!IJGºP,$�KM(�Õ�Ì�=U$;�15R5E0
Ìr0 �><1$�CEÏ $ A
�
K7(*�6I?IUÐç57Ò!$ $��!$;C7Ï1ÐãK7(!CMÖ»�1Ìr$Á� C701(!�*Gç57Ò!$ Ó�=?�!=?ÓÙ(!Ó =JK�CW�.57Ò*$�C�$�I?I?=UÎ*K70 =JGc-)0 C�=?�
57Ò!$�$ræ>5EC7$;Ó�$�I?=UÍ1$��º5E�1Ìr0�KMÒ!$;IUI[-cG�$�Î,$��9G�=U�*Ï301� 5EÒ!$�Ìr0 �9G�=¦5E=U01�!=?�!Ͼ0 Ö�5EÒ!$�Ø�$;KEK7=?� �%A �
ÑaÒ!=¦5E$��!=?�!Ïa5ECE� �*KMÖÝ0 CEÓ3-nÑ4$�I?I Í>�!0.Ña�:ÖÝCE0 Ó KM=?Ï �*� I6Î!CE0�Ìr$;KEK7=U�!ÏRI?=¦5E$�CW�.5E(!C7$ � E – �1Ì�� ��ÌWÒ*�6�!Ï1$
57Ò!=JK�$;IUI?=UÎ9KM01=?G�K7Ò*�6Î,$R570Ù��K7Î!Ò!$;C7=JÌ�� I!KMÒ9�6Î,$R57Ò!CE0 (!Ï1Ò��B� � � +��EF � �»K7$�$
î�=?Ï (!CE$ ��”:� �*GA�Ü,A7�#� � �%�nAP?>0D57Ò!$4=?�l<1$�CWKM$)Ø�$;KEK7=?� �Ù=?� A�Ü,A8� � � ��P*�1KM=JÌ�� IUI?Ð�KMÎ*Ò!$�CE$;Kv0 (�5�57Ò*$)$;C7CE0 C�KM(!C7Ö»� Ì�$
IU0�Ì�� IUI?Ð AlÞRÒ!$aÖÝ01IUI?0.Ña=U�*Ï@5eÑ)0Ù� Î!Î!CE01�1ÌWÒ!$;K�Ì;�6��P9$:KMÒ*0.Ña��5E0ÙP,$�$;Ül(!=?<.�6I?$��l5DC �»� ��(*K7$a57Ò*$
��$�ÑR5E0 �Á� IUÏ10 CE=¦5EÒ!Óí=?�Á�6�#(!�l5ECE� �*KeÖÝ01C7Ó�$�G¾Ñ4$�=?Ï Òl5
K7Î*� Ì�$]�6�*G �»P ��G!0�(*K7(*�6I%Ï1CE�1G�=?$��l5
G�$;KEÌr$;�15a=?�#��ÑaÒ*=¦5E$��!$�G#Ìr0>0 CWG�=?�*�.5E$:K7Ð�Ke5E$�Ó �ÀKM$;$]îv=?Ï (*C7$���” � � ��- �OA?>(!Ó�Ó��6CE=Uë;=U�!Ï9->57Ò!$ �
$�ÑR5E0 �#�6I?Ï 01C7=U57Ò!Ó�Ì�0 �>< $;C7Ï1$;K)=U��01�!$]Ke5E$�Î�=UÖv5EÒ!$�$�CEC701C4ÖÝ(!�*ÌnL
57=?0 �ç=JK�Ül(*� G!CE�657=J̺�6�9G �Ý(*�!IU=?Í $�Ï1CE�1G�=U$;�l5�G�$�K7Ì�$��l5
�Ù=¦5�=JK�=U�><.�6CE=?� �l5�Ña=U57ÒTC7$�KMÎ,$;Ìr5�5E0
IU=?�!$;� C�57CW�6�*KMÖÝ0 CEÓ��.57=?0 �9KÙ0 Ö�57Ò!$�=?�!Î!(�5�<1$;Ìr570 CWK;A�ÞRÒ!=JK�Ó�$;�6�9K�57Ò*�65�5EÒ!$#Ìr0 �><1$�CEÏ $��9Ìr$
57=?Ó�$#=JK��!0 5��QV,$�Ìn5E$;GTP>ÐçKMÒ*=¦Ö×5WK�-�KEÌ�� IU=?�!ϼ�6�*GãCE065E�657=?0 �ã06ÖD=?�!Î!(!5�< $;Ìr5701CEK;A�Ø�0.Ñ4$�< $;C
0 �!$¾06Öa57Ò*$ºÓ��6=?�çG�CW�'ÑaP*� ÌWÍ�K�=JKÙ57Ò*�65��6� � � � Ø
$;KEKM=J�6�zÓ��657CE=¦æúÓÙ(*KM5�P,$�Ke5E0 CE$;G
�6�*G�=?�>< $�C757$�Gc-!ÑaÒ!=JÌWÒ�5E� Í $�K�
����ÁV��aÎ,$�C�=U57$;CE�657=?0 �*K
�6�*G�=JKa5EÒ!$�CE$rÖÝ01C7$�=?Ó�Î!CE�1Ìn5E=?Ì;�6IcÖÝ01C
Ó�01C7$@5EÒ*�6�#��ÖÝ$;Ñ <.� C7=J�6P!I?$;K;A ?>=?�*Ìr$]57Ò!$]$;C7CE0 C4ÖÝ(!�9Ìn57=?0 �#=JK�=?�#Ï $;�!$�CW�6Ic�*0 ��LhÜl(*� G�CW�.5E=?Ì –
57Ò!$;C7$�=JK��!0�Ï (9�6CW�6�l57$;$�0 Ö4Ì�0 �>< $;C7Ï1$��*Ì�$ A�áOÖ)5EÒ!$ºØ
$;KEKM=J�6�å=?K]�!065]Î,01K7=¦5E=U<1$�G�$râ9�!=¦5E$��Ý=UÖ
=¦5:Ò*� KDKM01Ó�$Ùë�$�CE0�01C
$�<1$��#�!$;Ï1�657=?< $ A�=?Ï $;�><'� IU(*$;KaÑaÒ!$;C7$]57Ò!$�$�CEC701C
KM(*CMÖ»�1Ìr$]=JK��9�65D01C
KM01Ó�$:G�=?C7$�Ìn57=?0 �9K4� C7$DÌr(!CE< $�GºG�0.Ña�>ÑR�6CWG �n- 57Ò!$;��57Ò*$ �
$�ÑR5701�¾� IUÏ10 CE=¦5EÒ!ÓõÑa=UI?IcG�=U<1$�CEÏ $1-
KM0�57Ò*$]Ø�$;KEK7=?� � � �
�� � �RÎ,01K7=¦5E=U<1$�G�$râ*�*=¦5E$ A�B
Ö�Ìr01(!CWKM$D57Ò!$]Ø
$;KEKM=J�6��Ó��.5EC7=Uæº0 Ö�Ó�(!I¦5E=¦L
I?�'Ð1$�C
�*$r5eÑ40 CEÍ>K
=?K:=?� Ï1$��!$;CE� I/�!0 5:Î,01K7=¦5E=U<1$�G!$râ*�!=U57$�$�<1$�CEÐ>ÑaÒ!$�CE$ A,î!0 CD57Ò*$;K7$�CE$;�1KM01�*K
57Ò!$,��$;ÑR5701� �6I?Ï 01C7=U57Ò*Ó�=U� =¦5WK@0 CE=UÏ1=U�*� I/ÖÝ01C7Ó�=JK:�!065@(*KE�6P!I?$�ÖÝ0 C@Ï $;�!$�CW�6I��!$�(*CE� I��*$r5ML
Ñ)01C7Í�I?$;� C7�!=?�!Ï9AlØ
0.Ñ)$;< $�C4=U5�Ï =?< $;K4Ï10l0�Gº=U�*K7=?Ï Òl5EK)ÖÝ0 C�G!$�< $;IU01Î!=?�!ÏÙÓ�0 CE$�KM01Î!Ò!=JKe5E=?Ì;�.5E$;G
�6I?Ï 0 CE=U57Ò!Ó�K;->�1KaG�=JK7Ì�(*K7K7$;G¾=?�¾5EÒ!$@ÖÝ0 I?I?0.Ña=U�!Ï9A
ω -½Λ Θ′
-½ΘΛ
U
Network
input
output
ω Network
ω
input
output
Θ-½ΛU
Newton Algorithm here …… ….is like Gradient Descent
there
L
570�â*�9G#G�$;KEÌr$;�15:G�=UCE$;Ìr57=?0 �*Ka57Ò*�65�57CEк5E0�Ó�=U�*=UÓ��6I?I?Ð3K7Î901=UI/57Ò!$ÙC7$�KM(!IU5D�1ÌWÒ!=U$;< $�Gº=?�#57Ò*$
Î!C7$;<>=U01(*K�=U57$;CE�657=?0 �*K;- � � ��=¦5R(*K7$;K4�]I?=U�*$:K7$;� CEÌWÒ%-��6�9G�Ó�01KM54=?Ó�Î901CM5W�6�l57I?Ð -S�#” ��=U54Ñ40 CEÍ�K
0 �!I?Ð�ÖÝ0 CaP9�.5EÌWÒ�I?$;� C7�!=?�!Ï9A
ÞRÒ!$�5EÒ!=UCWG�Î!CE0 Î,$�C75eÐ:=?K�KMÒ*0.Ña��=U��îv=?Ï (*C7$ ��&!A �
KEKM(!Ó�$)Ñ)$)Î!=?ÌWÍ��DG�$;KEÌr$;�15�G�=UCE$;Ìr57=?0 �%-
$ A Ï*A,57Ò!$�Ï1CE�1G�=U$;�l5;-957Ò!$;� Ñ4$�Ó�=?�!=?Ó�=?ë�$�� IU01�!Ͼ�¾I?=U�!$�=?�Á5EÒ!=?K�G!=UCE$;Ìr57=?0 � �»IU=?�!$�K7$;�6CWÌWÒ �rA?>(!P*K7$;Ül(!$;�15EIUÐúÑ4$ºK7Ò!0 (!IJGå57CEÐå570#â9�*Gz� G!=UCE$;Ìr57=?0 �z�6I?0 �*Ï#ÑaÒ!=?ÌWÒz57Ò!$¾Ï CW� G�=?$��l5ÙG�0>$;K
�!065�ÌWÒ*� �!Ï $3=¦5WK�G�=?C7$�Ìn57=?0 �/-�P!(�5�Ó�$�CE$�I?Ðz=¦5WK�IU$;�!Ï65EÒ �ÀÌr01�P�e(!Ï1�657$#G�=?C7$�Ìn5E=U01� �n-®P,$;Ì�� (*K7$
Ó�0.<>=?�!Ï � IU01�!Ï�57Ò!=JK�G�=UCE$;Ìr57=?0 �zÑa=?I?I)�!0 5�K7Î901=UI�57Ò!$3CE$;K7(!I¦5�06Öa57Ò*$ºÎ!CE$�<>=?0 (*KÙ=¦5E$�CW�.57=?0 �/A
ÞRÒ!$�$�<10 I?(�57=?0 �¾06Ö�57Ò!$]G�$�K7Ì�$��l5�G�=?C7$�Ìn57=?0 �9K�� $ �.5a=U57$;CE�657=?0 ���º=JKRÏ =?< $;�3�1K
� $ � F � � � � $ ��7 � $ � $ � +
� � ���
ÑaÒ!$�CE$457Ò!$
ÌWÒ*0 =JÌr$R06Ö � $ Ì�� ��P,$�G�01�!$R$�=U57Ò!$;C�� Ì;Ìr0 CWG�=?�!ÏD570]î�IU$�5EÌWÒ!$;C��6�*G�Na$;$�<1$;K � � � �
first descent
direction gradients
conjugate
directionL M/N ¹PO �*¹ � ��_Esef7oÙd;°�fWd�j �O�l^�\�se_�^;bM\;�1ik_Wj.s)�1i�be_WfEseikd;jlg�i¦j�\�¢�px_7bhbed;b�gh�1bh°J\;fW_�©
� $ � � �&� � $ � + � �&� � $ �� �&� � $ � + � + � �&� � $ � + � � � E �
0 C �®0 IJ�6Í�� �*G3Na=UP*=U$;C7$
� $ � � � �&� � $ � F � �&� � $ � + �;� + � � � � $ �� �&� � $ � + � + � � � � $ � + � 5 � � � �
ÞRÑ)0�G�=?C7$�Ìn5E=U01�*K�� $ �6�9G � $ � + �6CE$@G!$râ*�!$�G�� KaÌr01�P�e(!Ïl�.57$:=UÖ
� + $ � � $ � + � �
=ÀA $ A�Ìr0 �Q�e(!Ï1�657$ºG�=?CE$;Ìn5E=U01�*KÙ� C7$�01CM5EÒ!0 Ï10 �*� I�G�=?C7$�Ìn57=?0 �9K]=?�¼57Ò!$3KMÎ9� Ìr$�0 Ö
�6�¼=JG�$��l5E=¦5eÐ
Ø�$;KEK7=?� �]Ó��.57CE=Uæ��ÀKM$;$)î�=UÏ1(!CE$:� (X�nA���$�CEÐ@=UÓ�Î,0 C75E�6�l5%ÖÝ01C�Ì�0 �>< $;C7Ï1$��*Ì�$�=U�ÙP90 57Ò�ÌWÒ*0 =JÌr$;K/=?K
ρ
κ−1
ρ
κ
κ
ω
L M/N ¹PO �!¹ � ��_Esef7oÙd;°�fWd�j �O�l^�\�se_�^;bM\;�1ik_Wj.s)�1i�be_WfEseikd;jlg�i¦j�\�¢�px_7bhbed;b�gh�1bh°J\;fW_�©
�
Ï10l0�GÙIU=?�!$RKM$��6CWÌWÒ]Î!CE0>Ì�$;G�(*C7$1A�î*0 C��
Î,$�C7ÖÝ$;Ìr57I?Ð]Ül(*� G�CW�.5E=?Ì�ÖÝ(!�*Ìr57=?0 ��Ña=¦5EÒ �í<'� C7=J�6P*IU$�K
��Ì�0 �>< $;C7Ï1$��*Ì�$aÑa=¦5EÒ!=U� �ÔKM57$;Î*KRÌ��6�ºP9$@Î!CE0.< $�GcA1î*0 C4�!0 ��LhÜl(*� G!CE�657=JÌaÖÝ(!�*Ìr57=?0 �*K��®01I?� Í
�6�*GTNa=?P!=U$;C7$ R K�ÌWÒ!01=?Ì�$3K7$�$;Ó�K�Ó�01C7$3C701P!(*KM5;A�&)0 �Q�e(!Ï1�657$�Ï CW� G�=?$��l5'� � ����Ì��6�T�6IJKM0åP,$
�!$r5eÑ40 CEÍ�5ECE� =U�!=?�!Ï9A*áO5@Ò*� K
P9$;$�� � Î!Î!I?=U$�G#Ña=¦5EÒÁIJ�6CEÏ $]K7(*Ì�Ì�$;KEK�=?�ÁÓÙ(!IU57=ULOI?�’Ð1$�C��!$�5eÑ)01C7Í
57CW�6=?�!=U�*Ï�0 ��Î!CE0 P!I?$�Ó�K®5EÒ*�.5R�6CE$aÓ�0>G!$�CW�.57$�K7=?ë�$;G�Ña=U57ÒºCE�657Ò!$;C�IU0.ÑTCE$;G�(!�9G!�6�*Ì�ÐÙ=?��57Ò*$
G!�.5W�!A/Þ)Ð>Î!=?Ì;�6I�� Î!Î!I?=?Ì;�.5E=U01�*K�CW�6�!Ï1$�ÖÝCE0 Ó ÖÝ(!�*Ìr57=?0 �ç� Î!Î!CE0’æ>=?Ó��.5E=U01�%-�C701P90 57=JÌ�Ìr0 �l5EC701I
� � – �O->57=?Ó�$�LOK7$�CE=?$;KRÎ!CE$;G�=JÌn5E=U01�3� �*G3065EÒ!$�CaCE$;� I,<.� IU(!$�G3Î!C701P!I?$�Ó�KRÑaÒ!$�CE$@Ò!=?Ï Ò#� Ì;Ìr(!CW� Ì�Ð
=?KÙÑ4� �15E$;GcA�&)IU$��6CEIUÐ 0 �¼IJ�6CEÏ $�� �*GúC7$�G�(!�*G*�6�l5 �»Ì�I?�1K7K7=Uâ9Ì��657=?0 � �:Î!CE0 P*IU$;Ó�K�Ke5E0�ÌWÒ*� KM57=JÌ
P*� ÌWÍ>Î!CE0 Î*� Ï1�657=?0 � =JK@Ö»�1Ke5E$�C�A ��IU57Ò*0 (!Ï1Òz�.5M5E$�Ó�Î�5WK]Ò*�’<1$�P,$�$;�zÓ�� G�$�5E0 G�$�â*�!$�Ó�=?�!=¦L
P*�.5WÌWÒ!$;K � E " �O-.57Ò!$DÓ��6=?��G�=?KE� G!<'� �l5E�6Ï1$a06Ö%Ìr01�P�e(!Ïl�.57$
Ï CW� G�=?$��l5�Ó�$r5EÒ!0�G!K�CE$�Ó��6=?�*K�57Ò*�65
=¦5�=JK��åP*�65EÌWÒãÓ�$�57Ò!0�G �ÝÎ*� CM5EIUÐzG!(!$3570 57Ò!$�Î!CE$;Ì�=?K7=U01�çCE$;Ül(!=?C7$;Ó�$��l5EK�=U�TI?=U�!$#K7$;� CEÌWÒ
Î!C70�Ì�$;G�(!CE$ �rA
����� �=*C�! �"�� �A% � ���&3�� +
! �A���
ÞRÒ!$ �D(*� K7=¦L ��$;ÑR5701� �À24î�8 ?"�)Ó�$r57Ò*0>G �%� �4=U57$�CW�.5E=U<1$�I?Ð�Ìr01Ó�Î*(�57$�Ka�6�3$;KM57=?Ó��657$@06Ö�57Ò*$
=U�>< $;CEK7$��$�K7K7=?� �%-<� E �:=?K�6�
���� F �@�6I?Ï 01C7=U57Ò*Ó3-<�#� �:CE$;Ül(!=?C7$�K@IU=?�!$�K7$;� CEÌWÒú�6�*G � � �@=U5
Ñ)01C7Í�K40 �!I?Ð�ÖÝ01CaP*�.5WÌWÒ3I?$;� C7�*=U�!Ï9A
ÞRÒ!$
Î,01K7=¦5E=U<1$
G�$�â*�!=U57$:$;KM57=?Ó��657$�0 Öc57Ò!$:=?�l<1$�CWKM$�Ø
$;KEKM=J�6��=JK4G�0 �!$:G�=?C7$�Ìn57I?Ð�Ña=¦5EÒ!0 (!5
C7$�Ü1(*=UCE=U�*Ï�Ó��657CE=¦æ3=U�><1$�CWKM=?0 �#�6�9G¾P>Ð30 �!I?Ð3(*KM=?�!Ï�Ï1CE�1G�=U$;�l5�=U��ÖÝ01C7Ó��657=?0 �%A ��I?Ï 0 CE=U57Ò!Ó�=UL
Ì��6I?I?Ð#57Ò!=JKÙÌ;�6�åP9$�G!$;KEÌrCE=UP,$;Gú� K:ÖÝ01IUI?0.Ñ�KDC<� � �Dâ9CEKM5Ù�3Î90lKM=U57=?< $�G�$�â*�!=U57$�Ó��.5EC7=Uæ � =?K
ÌWÒ!01K7$��%-�$1A Ï9A � � �*- � E �)5EÒ!$��35EÒ!$]KM$��6CWÌWÒ¾G�=?CE$;Ìn5E=U01�¾=JK�K7$r5R570
� ��.%� � ����.%� � �&� � �/.%�%�4
��� �®�@I?=?�!$
K7$;�6CWÌWÒÙ=JK�Î,$�C7ÖÝ0 CEÓ�$;G��6I?0 �!Ï �,- ÑaÒ!=JÌWÒ�Ï =?< $�K�57Ò!$�(*Î,G!�657$RÖÝ01C�57Ò!$
Î*�6CW�6Ó�$r5E$�CWK
�.5a57=?Ó�$'.
� ��.%� � � �/. F � � F10 ��.%� �S�/.%�45
îv=?�*� IUI?Ð � � ��57Ò*$#$;KM57=?Ó��657$#0 ÖD5EÒ!$Á=?�l<1$�CWKM$�Ø�$�K7K7=J�6�T=?K�(*Î,G!�657$�GcAR&)01Ó�Î9�6CE$;Gç570ú57Ò*$
��$�ÑR5E0 �º� IUÏ10 CE=¦5EÒ!ÓÚ5EÒ!$ �D(9� K7=¦L ��$;ÑR570 ��� Î!Î!CE01� ÌWÒ�0 �*IUÐ��!$�$�G!K�Ï1CE�1G�=?$��l5�=?��ÖÝ0 CEÓ��.57=?0 �/A
ÞRÒ!$
Ó�01KM5)K7(*Ì�Ì�$;KEKeÖÝ(*I;�D(*�1KM=UL��
$�ÑR5E0 ���6I?Ï 01C7=U57Ò*Óà=JK�5EÒ!$
24C70.Ð�G�$;��LhîvI?$r5WÌWÒ!$�C7Le8:0 IJG>Ö»�6CEP�L?>Ò*�6�*�!0 �»2Rîv8 ?”��Ó�$�57Ò!0�GcA1ÞRÒ!$a(!Î�G!�.5E$aC7(!I?$4ÖÝ0 C®5EÒ!$a$;KM57=?Ó��.57$a0 Ö*5EÒ!$a=U�><1$�CWKM$aØ�$�K7K7=J�6�
=?K
���/.%�<� ���/. F ���
� 7�� + � �
� + �
� � � +
� + �
F
� � + � 7�� � � +
� + �
�
� � � �
ÑaÒ!$�CE$�KM01Ó�$�� P!P!CE$�<>=?�657=?0 �*K4Ò*�’<1$@P9$;$���(*K7$;GºÖÝ0 CR57Ò*$@ÖÝ0 I?IU0.Ña=?�!Ï � � �@< $�Ìn5E0 CWK
� � � �&� � �/.%�;� F � � � � ��. F ���%�
� � � ��.%� F � �/. F � �45 � � " �
��IU57Ò!01(!Ï Ò%-®� KÙÓ�$��l57=?0 �!$�G¼�6P,0.< $1-%57Ò*$¾Ìr01Ó�Î!IU$�æ�=¦5eÐå=?KÙ0 �!I?Ð
����ÁF��n-�Ñ)$¾�6CE$ºKe5E=UI?I4C7$�L
Ü1(*=UCE$;Gz570¼Ke5E0 CE$3�1� � � Ó��657CE=¦æc-�KM0 57Ò*$�� IUÏ10 CE=¦5EÒ!Ó =JK�01�!I?ÐzÎ!CW� Ìn5E=?Ì;�6I)ÖÝ0 C�K7Ó�� IUI
�!$r5eÑ40 CEÍ�K]Ña=U57Òç�*0 ��LOC7$�G�(!�*G*�6�l5]57CW�6=?�!=?�!Ï K7$r5WK�A®Na$�Ìr$��l5EIUмK70 Ó�$º<.�6CE=J�6�l5EKÙ$ræ�=?KM5�57Ò*�65
�6=?Ó 570�CE$;G�(9Ìr$�Ke5E0 CW�6Ï1$DCE$;Ül(!=?C7$;Ó�$��l5EKG�»K7$�$�$1A Ï9A � � �U�rA
��� � � �!*� � � �A% � ���&3 �!3 9 @B%(#&%13 � %(')4
� �2' �
*��2' 9 �
8@�6(*KEKeL ��$;ÑR5701�ú� �*G¼"%$;< $;�lP,$�CEÏ#QÁ�6CWÜl(*�6CWG>5Ù� IUÏ10 CE=¦5EÒ!Ó �%� �@(*K7$�5EÒ!$ºKEÜ1(9�6CE$ �1�1Ìr0 P*=
�6Î!Î!CE0’æ�=UÓ��657=?0 �%-�� E �v� C7$4Ó��6=?�!I?Ð]G�$;K7=UÏ1�!$;G]ÖÝ0 C�P*�65EÌWÒ�IU$��6CE�!=U�*Ï*-$��� �/Ò9�’< $)�@Ì�0 Ó�Î!I?$ræ�=¦5eÐ
06Ö
��#�ÁV �D�6�9G � � ��Ó�01KM5@=UÓ�Î,0 C75E�6�l5�-*5EÒ!$�Ð#Ñ40 CE;01�!I?Ð�ÖÝ0 C:Ó�$��6�åK7Ül(*� C7$�G�$�CEC701C
I?01KEK
ÖÝ(!�*Ìn5E=U01�*K;A,ÞRÒ!$�8@�6(*KEKML��
$�ÑR5701�Á�6I?Ï 01C7=U57Ò!Óï=JK
I?=UÍ1$]5EÒ!$��
$�ÑR5701� �6I?Ï 01C7=U57Ò*Ó3-9Ò!0.Ñ4$�< $;C
57Ò!$]Ø
$;KEKM=J�6��=JK��6Î!Î*C70'æ�=?Ó��657$�G�P>Ð�5EÒ!$ÙKEÜ1(9�6CE$D0 Öv5EÒ!$ �l� Ìr01P!=J�6� �ÀKM$;$]�6IJKM0�K7$;Ìr57=?0 � (>A E
ÖÝ0 C���ÖÝ(!C757Ò!$;C
G�=JK7�(*K7K7=?0 � �
��� � � J � � ��� �
� � ��%�
+ � ��� �
� � �
��� �
� +
� �&� � �-5 � � & �
ÞRÒ!$:”/$�<1$��>P9$;C7Ï�QÁ�6CWÜl(*�6CWG>5�Ó�$r5EÒ!0�G�=JK4IU=?Í $
57Ò!$�8@�6(*KEKML��
$�ÑR5701�º�6P,0.< $1- P!(!54=U54Ò9� K4�
C7$;Ï (!IJ�6CE=Uë��.5E=U01�ÙÎ*� CE� Ó�$�57$;C �¾5EÒ*�.5)Î!C7$;< $;�15WK®=¦5�ÖÝC701Ó�P!I?0.Ña=?�!Ï@(!Î%- =UÖ%KM01Ó�$a$�=?Ï $��><.�6I?(!$�K
�6CE$@K7��6I?I
��� � � J � � ��� �
� � ����
+ � ��� �
� � �
���
7���� �
� +
� �&� � �-
� � (X�
ÑaÒ!$�CE$ � G�$��*0657$�K#5EÒ!$ã(*�!=¦5eÐ Ó��.5EC7=UæcADÞRÒ!$x8@�6(9K7K ��$�ÑR5E0 �ÚÓ�$�57Ò!0�GÚ=JKÁ<.� IU=JGßÖÝ01C
Ü1(9� G�CW�.5E=?Ì:Ìr0lKe54ÖÝ(!�*Ìr57=?0 �*KaÒ*0.Ñ)$;< $�C4��KM=?Ó�=UIJ�6CRÎ!CE0�Ìr$;G!(!C7$@�6IJK70�Ñ40 CEÍ�K�Ña=U57Ò�H@(!I?IUP*�1ÌWÍlL
"%$�=?P!I?$�C�Ì�01KM5a� �*G3=?KaÌ;�6I?IU$�G��D�.5E(!CE� I/8:CE�1G�=?$��l5 �»K7$�$�$ A Ï*A � � - � � - E �*�nA
�
�Æ*Ë7Ê�
���Å>Ç Ê�Ç � �DÉ�Å>òíÅ���ò���ò��1�>Ëeó�Ä ËMÄ �WÇ�Æ ��ó�Å!ËeÇ)Ä ËMÄ
�ÚÉDøhÅ!ËMøMó���ò%ÆzÄ
òcÅ6 úÇ�Æ�
��
ä $)Ña=UI?I1�*0.ÑúG!=?KEÌr(*KEK/K7$�<1$�CW�6I.5E$;ÌWÒ!�*=?Ül(!$�Kv� =UÓ�$;G��65�Ì�0 Ó�Î!(�5E=U�!Ï
ÖÝ(!I?I101C/Î*� CM5E=?� I1Ø�$�K7K7=J�6�
=U��ÖÝ01C7Ó��657=?0 �3PlÐ �»� ��â9�!=¦5E$ÙG�=/V,$;C7$;�*Ìr$@Ó�$r5EÒ!0�Gc- �»P �RKEÜ1(9�6CE$ �l� Ì�0 P!=J�6�3�6Î!Î*C70'æ�=?Ó��657=?0 ��×ÖÝ0 C38@�6(*KEKeL ��$;ÑR5701�ì� �*Gì"%$;< $��>P,$�CEÏ6LhQÁ�6CWÜl(*�6CWG>5��6I?Ï 0 CE=U57Ò!Ó&�n- �»ÌD��Ìr0 Ó�Î!(!5E�.5E=U01�ì06Ö
57Ò!$�G�=?� Ï 01�*�6I%0 Ö®57Ò!$�Ø�$;KEK7=?� �Á�6�*G �ÀG �aP>Ð30 P�5W�6=?�!=?�!Ϻ��Î!CE0�G�(*Ìr5D06Ö®5EÒ!$�Ø
$;KEKM=J�6�Á� �*G
��< $;Ìr5701CaÑa=¦5EÒ!0 (�5:Ìr0 Ó�Î!(!57=?�!Ï�57Ò!$]Ø
$;KEKM=J�6�/A,B
57Ò!$;C
K7$�Ó�=¦Lh�6�9�6I?Ð15E=?Ì;�6I�5E$;ÌWÒ!�!=JÜl(!$;Ka57Ò*�65
�6I?IU0.Ñß5EÒ!$�Ìr01Ó�Î*(�5E�657=?0 �å06Ö�5EÒ!$�ÖÝ(!I?I�Ø�$�K7K7=?� � � C7$�0 Ó�=U5M57$�G P,$;Ì;�6(*K7$�57Ò!$;Ð �6CE$�CE�657Ò!$;C
Ìr0 Ó�Î!I?=JÌ��.5E$;G3�6�*G�� I?K70�CE$;Ül(!=?CE$:Ó�� �lÐ�ÖÝ0 CEÑ4� CEG 2.P*� ÌWÍ>ÑR�6CWG�Î!C701Î*�6Ïl�.5E=U01�ºKe5E$�Î*K � “!- * �OA
�
��� !�”�3C”0��% � ” �B%(‘)%(3�� %
ä $]Ì;�6�3ÑaC7=U57$@5EÒ!$ �lL[57Ò3IU=?�!$�06Ö�57Ò*$]Ø�$;KEK7=?� �
�
$ � � � � � �&� � �%�
��� $
�
� �&� � 7 � � $ � F � �&� � �
�
ÑaÒ!$�CE$ � $ � � �
�
�
65D565-
D�X
65D5654
� ��=?KD��< $�Ìn5E0 C�0 Ö�ë�$�CE01K
�6�*G#01�!I?о01�!$&��65
57Ò*$ÙÍlLÀ5EÒÎ90lKM=U57=?0 �%A�ÞRÒ!=JKDÌ;�6�ÁP,$Ù=?Ó�Î!I?$�Ó�$��l57$�GÁÑa=U57Òå��KM=?Ó�Î!I?$ÙCE$;Ìr=?Î,$XC�� � �DÌr01Ó�Î!(�57$Ù57Ò!$Ù570 5E�6I
Ï CW� G�=?$��l5)P>Ð�Ó�(!I¦5E=UÎ*IU$:ÖÝ0 CEÑR�6CWG��6�*GºP*� ÌWÍ>ÑR�6CWG�Î!CE0 Î*� Ï1�.5E=U01��Ke5E$�Î*K;A � E � �DG!G �@570�57Ò*$
�lLÀ5EÒ Î9�6CW�6Ó�$r5E$�C��6�*GåÌr01Ó�Î!(�57$�� Ï1�6=?� 57Ò!$�Ï CW� G!=U$;�15�-c�6�*G â*�*� IUI?Ð���� �@KM(*P�57CW� Ìr5@P,065EÒ
C7$�KM(!IU5EK4�6�9G�G�=?
(*$
5E0Ù�>(!Ó�$�CE=?Ì;�6I9$�CEC701CEK�=?��5EÒ!=JK)Ì�0 Ó�Î!(�5W�.57=?0 �¾K7ÌWÒ!$;Ó�$�57Ò*$
C7$�KM(!IU57=?�!ÏåØ�$;KEK7=?� �zÓ�=UÏ1Ò15��!065�P,$¾Î,$�C7ÖÝ$;Ìr57I?ÐúK7Ð>Ó�Ó�$�57CE=?Ì Aváh�ç57Ò!=JK�Ì��1KM$�=U5�KMÒ!01(!IJGzP,$
��� � � �[ünÿ/T �Eþ@�1KaG�$;KEÌrCE=?P9$�G¾P,$�I?0.Ñ�A
�
��� � �
*C�!’-%����!� � � “0�:3 ��� ��’)� ��”�
�!��”0�<3 > �&’A����% � �!*� � � �A% � ���<3 �:3 9
@ % #<%13 � %('-4 � � �2' �
*C�2' 9 �=�!.04<�&'-"0����
�
KEKM(!Ó�=?�!Ï���Ó�$;�6��KEÜ1(9�6CE$;GºÌ�01KM5aÖÝ(!�*Ìr57=?0 �
�&� � � � �E J �
� � � F ��� �
� � �;� +1� � � F ��� �
� � �;� � � * �
57Ò!$;�¾5EÒ!$�Ï CW� G!=U$;�15a=JK
� �&� � �
���
� F J �
� � � F ��� �
� � �%� + � ��� �
� � ��%� � � - �
�6�*Gº57Ò!$]Ø
$;KEKM=J�6�¾ÖÝ0 I?I?0.Ñ�Ka� K
� � � � � J �
� ��� �
� � �
���
+ � ��� �
� � �
���
7 J �
� � � F ��� �
� � �;� + � F���� �
� � ���� ��� 5 �)" � �
� K7=?Ó�Î*IU=UÖÝÐ>=U�!Ï�� Î!Î!CE0’æ>=?Ó��.5E=U01��06Öv57Ò!$�Ø�$�K7K7=J�6�º=JK457Ò*$@KEÜl(*�6CE$:06Ö/5EÒ!$’�1�1Ìr01P!=?� ��ÑaÒ!=JÌWÒ
=?K���Î,01K7=¦5E=U<1$�KM$;Ó�=ULhG�$râ*�*=¦5E$�Ó��657CE=¦æ¾06Ö�G!=UÓ�$��9KM=?0 � C%� �
� � � � � J �
� ��� �
� � �
���
+ � ��� �
� � �
���
�)"$���
ÑaÒ!$�CE$�5EÒ!$aKM$�Ìr01�*G�5E$�CEÓ ÖÝC701Ó A�Ü,A8�#" � �cÑR� K®G�CE0 Î!Î,$;G%A'ÞRÒ*=?K®=JK�$;Ül(!=?<'� IU$;�l5v5E0@�1K7K7(!Ó�=?�!Ï
57Ò*�65�57Ò!$��!$r5eÑ40 CEÍ�=JK
��I?=?�!$;� CaÖÝ(!�*Ìr57=?0 �Á0 Ö�5EÒ!$]Î*� CE� Ó�$r57$;CEK � A �
Ï1�6=?��57Ò*=?K
=?K
C7$�� G�=?IUÐ
=UÓ�Î!I?$�Ó�$��l5E$;G#ÖÝ01C�5EÒ!$ �>LÀ5EÒ Ìr01IU(!Ó��Á0 Ö�57Ò!$ �1�1Ìr01P!=?� � C!ÖÝ01CD� IUIv57CW�6=?�!=?�!Ï�Î*�65M57$;C7�9K�-�� ���
Ñ)$RÖÝ01C7ÑR�6CWGÙÎ*C701Î*�6Ïl�.57$1-’57Ò!$;��� E �®KM$�5�57Ò*$
� Ìr57=?
$;KEKM=J�6���6CE$aÑ4$�I?I*Í>�!0.Ña�
� ��*!- � -4� – �[A9áO5D=JK
� KEK7(!Ó�$;G357Ò9�.5D$�� ÌWÒ#IJ�’Ð $;Ca=U�#5EÒ!$Ù�*$r5eÑ40 CEͺÒ*�1Ka57Ò*$]ÖÝ(!�*Ìr57=?0 �*� I%ÖÝ01C7Ó
� , �,��� � , � �,����� � , � � � �»K7$�$Ùî�=?Ï (!CE$ � *�ÖÝ01C�5EÒ!$�K7=UÏ1Ó�0 =JG!�6I%�*$r5eÑ40 CEÍ$�rA �
K7=?�!Ï�57Ò*$
8@�6(*KEKeL ��$;ÑR5701�Ù�6Î!Î*C70’æ�=?Ó��657=?0 � �ÀG�CE0 Î!Î!=?�!Ï
57Ò!$457$;C7Ó 5EÒ*�.5�Ìr01�l5E�6=?� � � � � � �%�/Ñ4$)01P�5E� =U� C
� F6�
��� F
$
� � F4�
��� F
$
�)��� � � $ �%� F
�)” � �
� F6�
��� F
$ , �
� FD�
�%� F
$
� F, �)” ” �
�6�*G
� F6�
��� F, J
$
� F6�
��� F$
� F
$ , 5 �)”�& �
äx=¦5EÒ1�úP,$�=?�!Ͼ�38@�6(*KEK7=?� �Á�!0 �*IU=?�!$;� C7=U5eÐ�� K:KMÒ!0.Ña� =U�åîv=?Ï (*C7$ � *�ÖÝ01C
5EÒ!$�N
24îì�*$r5ML
Ñ)01C7Í�K4Ñ)$@01P�5E� =U�
� F �
��� F
$ , �
� F �
��� F
$
� � , F � $ , � F �)” (X�
�6�*G
� FD�
��� F, � J
$
� F4�
��� F
$
� � , F � $ , � F 5 �)”�* �
ÞRÒ!$�Ìr01KM5@06Ö4Ì�0 Ó�Î!(�5E=U�*Ϻ5EÒ!$�G�=?� Ï 01�*�6I�K7$;Ìr01�*G G!$�CE=U<.�.5E=U<1$;KDP>ÐÁC7(*�!�!=?�!Ϻ5EÒ!$;K7$�$;Ül(*�6L
57=?0 �*K@ÖÝCE0 Ó 57Ò!$�IJ� KM5]IJ�’Ð $�C:5E0�57Ò!$�â9CEKM5�0 �!$�=JK�$;KEK7$��l57=J�6I?IUÐÁ57Ò!$�KE�6Ó�$�� K:5EÒ!$�CE$�Ï1(!I?� C
P*� ÌWÍ>Î!CE0 Î*�657=?0 ��Î9� KEKR(*KM$�G�ÖÝ01CR57Ò!$�Ï1CE�1G�=?$��l5;-�$�æ�Ì�$�Î�5R5EÒ*�.5a5EÒ!$]K7Ül(*� C7$:06Öv57Ò!$�Ñ4$�=?Ï Òl5WK
�6CE$�(*KM$�G#=?�#57Ò!$ÙÑ)$;=UÏ1Ò15E$;G#K7(!Ó�K�A�ÞRÒ!=JKa5E$;ÌWÒ!�!=JÜl(!$]=JKD� Î!Î!I?=U$�G�=U�Á57Ò!$ èM0 Î!57=?Ó�� I/P!CW�6=?�
G!�6Ó��6Ï1$;ê�Î!CE(!�!=?�!Ï�Î!C70�Ì�$;G�(!CE$ �»K7$�$ � E ���*�nA
||ω−x ||2
y
x
f( )
ωx
x
ω
y
z
1/2
L
�
��� � �
��*C��”�3C4 ����%���’-� 9 *��6�,�<>�����% �A%1 � �”0�:3 �!3 9 � #&%1�6���:’
áh�ÙÓ��6�>Ð�Ó�$r5EÒ!0�G!Kv57Ò*�65®Ó�� Í $�(9KM$406Ö!5EÒ!$aØ�$�K7K7=?� �%-;57Ò!$aØ�$�K7K7=J�6�]=JK®(*K7$;G]$�æ!ÌrI?(*KM=?< $;IUÐ@=?�
Î!C70�G�(9Ìn5EK�Ña=¦5EÒ¾��<1$;Ìr570 C�A áh�l5E$�CE$;KM57=?�!Ï I?Ð - 57Ò!$;C7$�=JK4��Ñ4�'Ð�06Ö%Ì�0 Ó�Î!(�5E=U�!Ï�KM(9ÌWÒ�Î!C70�G�(9Ìn5EK
��ÿ�������� �RÏ 01=U�!Ï 57Ò!CE0 (*Ï Òz5EÒ!$¾57CE0 (!P!I?$306ÖDÌ�0 Ó�Î!(�5E=U�!Ï 57Ò*$�Ø
$;KEKM=J�6�ç=¦5WKM$;I¦ÖeA�ÞRÒ!$¾â*�!=U57$
G�=WV�$�CE$��9Ìr$�Ó�$r5EÒ!0�G3Ì;�6�¾ÖÝ(!IUâ*IUI%57Ò!=JKR5E�1KMÍ�ÖÝ0 C��6�#� C7P!=U57CW�6CEÐ�< $�Ìn5701C��
��� �
�
�
� ���� � � 7����:� F � ���� � � � �
�)"�- �
(*KM=?�!Ïå0 �!I?Ðú5eÑ40 Ï CW� G!=U$;�15�Ìr01Ó�Î*(�5E�657=?0 �*K'�»�65�Î,0 =?�l5 � �6�9G � 7 ���íCE$;K7Î9$�Ìn57=?< $;IUÐ"�r-
ÑaÒ!=?ÌWÒ#Ì;�6�3P9$�CE$;�1G�=UI?Ð�Ìr01Ó�Î!(�57$�G3Ña=¦5EÒ3P9� ÌWÍ>Î!CE0 Î � �z=JKa��KMÓ��6I?I/Ì�0 �*KM5E� �15-�nA
ÞRÒ!=?K)Ó�$r5EÒ!0�GºÌ�� ��P,$:� Î!Î!I?=U$�G�570�Ìr01Ó�Î*(�57$D57Ò!$:Î!CE=U�9Ìr=?Î*�6I,$�=?Ï $;�l<1$;Ìr570 C)�6�*Gº$�=?Ï $��!L <'� IU(*$�06Ö �÷P>Ð�5EÒ!$�Î90.Ñ4$�CRÓ�$r5EÒ!0�GcA*24к=U57$;CE�657=?�!Ï��6�*G3K7$r5M5E=U�*Ï
� �/.�7 � �<� ��� ��.%���� �/.%� �
�#& � �
57Ò!$�< $;Ìr5701C�� �/.%��Ña=UI?I�Ì�0 �>< $;C7Ï1$:570�5EÒ!$ÙIJ�6CEÏ $�Ke5�$;=UÏ1$��>< $�Ìn5701Ca06Ö � � �*G ��� ��.%���:5E0�57Ò*$
Ìr0 CECE$;K7Î901�*G�=?�!Ïú$�=?Ï $��><.�6I?(!$ � E �*-4� � -4� � �[A1?>$�$ � I?K70 � � � ��ÖÝ0 C3�6�x$�<1$��xÓ�0 CE$Á� Ì;Ìr(!CW�.5E$
Ó�$�57Ò!0�G¾57Ò9�.5 � ���RG�0>$;KR�!0 5�(*K7$Dâ9�!=¦5E$]G�=/V,$;C7$;�*Ìr$�K��6�*G � E �4Ò*� KaK7=?Ó�=?IJ�6C�Ìr01Ó�Î!IU$�æ�=¦5eÐ1A
� �xÄ
ó®ø � �lË �¼Ç���Å��
ò ��ò��1�>Ëeó�Ä ËMÄ �ÚÉDøhÅ!Ë
.øeó���ò/ÆçÄ�òcÅ åÇ�Æ
�
áO5�=?K�=U�l57$;C7$�Ke5E=U�*Ï@570](!�9G�$�CWKe5W�6�*G�Ò!0.ÑìK70 Ó�$a06Ö,57Ò!$�57CE=?ÌWÍ�K�K7Ò!0.Ña��Î!C7$;<>=U01(*KMI?ÐÙ=?���*(*$��*Ì�$
0 ��57Ò!$DØ�$;KEK7=?� �%-.=ÀA $ A1Ò!0.ÑãG!0l$�K®57Ò*$
Ø�$�K7K7=?� ��ÌWÒ9�6�!Ï1$4Ña=U57Ò�� CEÌWÒ*=¦5E$;Ìn5E(!CE$R� �*G�G�$r5W�6=?I?K�06Ö
57Ò!$�=UÓ�Î!I?$�Ó�$;�15W�.5E=U01�%A,Þ)Ð>Î!=JÌ��6I?I?Ð -!5EÒ!$�$�=?Ï $��><.�6I?(!$ÙG!=?KM57CE=UP*(�57=?0 �Á0 Ö�57Ò!$�Ø�$�K7K7=?� �ÁI?0l01Í�K
IU=?Í $�5EÒ!$]01�!$]KMÍ1$r5WÌWÒ!$;G3=?� î�=UÏ1(!C7$ E � C*��ÖÝ$;ÑÚKMÓ�� IUI%$;=UÏ1$��><.�6I?(!$;K;-!Ó��6�>оÓ�$�G�=?(!Ó 0 �!$�K
�6�*G�ÖÝ$;Ñ�< $;C7Ð�IJ�6CEÏ $
01�!$;K;A äå$:Ña=UI?I��!0.Ñ��6CEÏ (!$�57Ò*�65)5EÒ!$ �?ý.üÀû ����ÿ¦û ���:5.ý��!���
�Ña=?IUIcÌ;�6(*K7$
57Ò!$@5EC701(!P!I?$:=?�357Ò!$@5ECE� =U�*=U�!Ï�Î!CE0�Ìr$�K7K4P,$;Ì�� (*K7$ � E �!- E E �
� �!0 �!L[ë;$�CE0�Ó�$;� �¾=?�!Î!(!5EK�01CR�!$�(!CE0 ��KM5E�.5E$;K � EXE �
� Ña=?G!$�<'� C7=J�.5E=U01�*K406Ö�57Ò!$]K7$;Ì�0 �*G3G�$;C7=?<.�.57=?< $�K)ÖÝC701Ó�I?�'Ð1$�C4570�IJ�'Ð $;C
� Ìr01C7CE$�IJ�.5E=U01�ºP,$r5eÑ4$�$���KM5E�.5E$�<.�6CE=?� P!IU$�K�A
Þ/0ã$ræ�$�Ó�Î!I?=¦ÖÝÐì5EÒ!=JK�-4Ñ)$åKMÒ*0.Ñ 57Ò!$ $�=?Ï $��><.�6I?(!$åG�=?KM57CE=?P!(�57=?0 � 06Ö��¼�*$r5eÑ40 CEÍç5ECE� =U�!$�G
0 �çB�&4NõG!�.5W��=U�zî�=?Ï (!CE$ E � Av&)IU$��6CEIUÐ1-c57Ò!$;C7$�=JK]��Ña=JG�$ºK7Î!CE$;� G 06Öa$;=UÏ1$��><.�6I?(!$;K �ÀKM$;$
îv=?Ï (*C7$!� - ��� �*GºÑ4$:0 P*K7$�CE< $
57Ò*�6545EÒ!$@CE�657=?0�P,$r5eÑ4$�$;�º$1A Ï9A15EÒ!$:â*CWKe5��6�9G�57Ò*$:$;IU$;< $;�15EÒ
$�=?Ï $��><.�6I?(!$R=JK��6P,0 (�5 *!A6ÞRÒ!$�I?0 �*ÏD5W�6=?I!06Ö�5EÒ!$a$�=?Ï $;�l<.� IU(!$�G!=?KM57CE=UP*(�57=?0 �@�»K7$�$�î�=?Ï (!CE$ E � �
=?K:CW�.57Ò*$�C:Î*�6=?��ÖÝ(!I�P,$;Ì;�6(*K7$Ù5EÒ!$�CE�657=?0¾P,$r5eÑ4$�$;�Á57Ò*$�IJ�6CEÏ $�Ke5@�6�*G KMÓ��6I?I?$;KM5:$;=UÏ1$��><.�6I?(!$
Ï =?< $;K:5EÒ!$ºÌ�0 �*G�=U57=?0 �*=U�!Ï�0 Ö45EÒ!$�I?$;�6CE�!=?�!Ï�Î!CE0 P!I?$�Ó�A0� IJ�6CEÏ $�CW�.5E=U0#Ìr01C7CE$;K7Î,0 �*G!KD5E0Á�
P!=UÏ�G!=WV�$�CE$��*Ì�$]=?��57Ò!$Ù�6æ�=?KR0 Ö�5EÒ!$]$;IUI?=UÎ9KM01=?G!� I/K7Ò*�6Î,$;G3$�CECE0 CRÖÝ(!�*Ìr57=?0 � C*57Ò!$ÙI?� C7Ï1$�CR57Ò*$
CE�657=?0*-957Ò!$�Ó�0 CE$]Ñ)$�â*�*G ��5W� Ìr0 LOK7Ò!$;IUI�KMÒ*� Î9$�GÁÓ�=?�!=UÓ��*-,ÑaÒ*=?ÌWÒ � C7$�$ræ>57CE$�Ó�$;IUÐ#KM57$�$;Î
570.ÑR�6CWG!K)57Ò!$]K7Ó��6I?I%�.æ�=?Ka� �*G¾< $�CEÐ �9�65��6I?0 �!Ï�57Ò*$�IU01�!Ï��6æ�=?K;A���!0 57Ò!$;CDÏ1$��!$;CE� IvÌWÒ*� CE�1Ìn57$;C7=JKM57=JÌ�06Ö�5EÒ!$�Ø
$;KEKM=J�6� =U� ÓÙ(!IU57=UL[IJ�'Ð $;C
�!$�5eÑ)01C7Í�K
=?KD57Ò*$
KMÎ!CE$;�1GçP,$r5eÑ4$�$;�ãIJ�'Ð $;CEK;A®áh�Tî�=?Ï (!CE$ E ��Ñ4$3CE0 (*Ï Ò!I?ÐzKMÍ1$r5WÌWÒãÒ!0.Ñí57Ò!$ÁK7Ò*� Î9$�06Ö:57Ò*$
Ø�$;KEK7=?� �¼<'� C7=?$;K]ÖÝC701Ó÷P,$�=?�!Ï CE�657Ò!$;C �9�65Ù=U�z57Ò!$ºâ*CEKM5�IJ�'Ð $;C�570 P9$;=U�!ÏåÜl(!=¦5E$¾KM57$;$�Îz=?�
0 100 200 300 400 500 600 700 800
−6
−5.5
−5
−4.5
−4
−3.5
−3
−2.5
−2
−1.5
−1
−0.5
0
Eigenvalue order
1
0
L
o
g
E
ig
e
n
va
lu
e
the ratio between the 1st and
the 11th eigenvalues is 8
L
57Ò!$3I?�1Ke5�IJ�’Ð $�C�A ÞRÒ!=?K��QV,$�Ìn5EKÙ57Ò*$3I?$;� C7�*=U�!Ï KMÎ,$�$�Gç�6�9GçÌ�� �zÎ!CE0.<>=?G�$3�6�ã=U�!Ï1C7$�G�=?$��l5
5703$ræ�Î!IJ�6=?�#57Ò!$�K7IU0.ÑßI?$;� C7�!=?�!Ͼ=U� IU0.Ñ4$�CDI?�’Ð1$�CWK
�6�9G�57Ò!$�Ö»� KM5 �»K70 Ó�$r5E=UÓ�$�01KEÌr=?IUIJ�.5E=U�!Ï��
IU$��6CE�!=U�*Ï�=U��5EÒ!$
IJ� KM5�I?�’Ð1$�C�AX�ì5EC7=JÌWÍ]5E0ÙÌr01Ó�Î,$��9K7�657$a5EÒ!=?K)G�=/V,$;C7$;�154K7Ì;�6I?$a06ÖcIU$��6CE�!=?�!Ï�=?K
570�(*K7$
5EÒ!$@=U�>< $;CEK7$DG!=?� Ï 0 �9�6IcØ�$�K7K7=?� ��5E0�Ì�0 �l57CE0 I,57Ò*$:I?$;� C7�*=U�!Ï�CE�657$��»K7$�$��6IJK70�K7$;Ìn5E=U01�
&!A
� � � �Dø ��Ë7Ä�ô
4òvÊ�Ç�Ä
È��zÆ*È�ò%Æ
òcÅ���ÇaÈ?� Å�Ç� É
øhÅ!Ë7øeó���ò/Æ
� òcÅ6 úÇ�Æ�
��
2)$�ÖÝ0 CE$ÙÑ4$�Ì�0 �*Ì�$��l57CW�.5E$Ù=?� 5EÒ!=JK:K7$;Ìr57=?0 � 0 � Ò*0.Ñ 57035E� =UI?0 C@KM$�Ìr01�*G#0 CWG�$;C
5E$;ÌWÒ!�!=JÜl(!$;K
ÖÝ0 C�57CW�6=?�!=?�!ÏDIJ�6CEÏ $)�!$r5eÑ40 CEÍ�K�-�I?$r5�(*Kvâ*CWKe5�CE$�Î,$;�65®K70 Ó�$4CE�657Ò!$;C�Î,$;KEK7=UÓ�=JKe5E=?Ì�Ö»� Ìr5EK��6P,0 (!5
�6Î!Î!I?Ð>=U�*Ï�ÌrIJ� KEK7=?Ì;�6I9K7$;Ì�0 �*G�0 CWG�$�C)Ó�$�57Ò!0�G!K;A�Þ/$�ÌWÒ!�!=JÜl(!$;K)(*K7=U�!ÏÙÖÝ(!I?I�Ø
$;KEKM=J�6�º=U��ÖÝ01C7Ó��6L
57=?0 � �À8@�6(9K7K4L ��$;ÑR570 �/-!”%$�<1$��>P,$�CEÏ6LhQÁ�6CWÜl(*�6CWG>5)� �*G¾2Rî�8 ?”�4Ì��6�30 �*IUÐ�� Î!Î!I?Ð�570�< $;C7Ð
KMÓ��6I?IR�!$r5eÑ40 CEÍ�K]5ECE� =U�*$;Gz=?�TP*�.5WÌWÒçÓ�0�G�$ -®Ò!0.Ñ4$�<1$�C�57Ò!0lKM$�KMÓ�� IUIR�!$�5eÑ)01C7Í�K��6CE$º�!0 5
57Ò!$�01�!$;K@5EÒ*�.5]�*$�$;GúK7Î9$;$;G�=?�!Ï#(!Îú5EÒ!$�Ó�01KM5;A/QÁ01KM5ÙKM$�Ìr0 �9G 01CEG�$;C�Ó�$r57Ò*0>G*K&�»Ì�0 �P�e(�L
Ï1�.5E$�Ï CW� G�=?$��l5�-%24î�8 ?�-�A;A�A#�:CE$;Ül(!=?CE$���I?=?�!$rLhKM$��6CWÌWÒå� �*GúÌ�� � 5EÒ!$�CE$rÖÝ01C7$��!0 5]P9$º(*KM$�G
=U�ú5EÒ!$ºKM570�ÌWÒ*� KM57=JÌ�Ó�0�G�$ A/Q �6�>Ð 0 Ö45EÒ!$�5EC7=JÌWÍ�K�G�=?KEÌr(9K7K7$;GåÎ!CE$�<>=?0 (*K7IUÐå�6Î!Î*IUÐ 0 �!I?ÐÁ5E0
P*�.5WÌWÒ#IU$��6CE�!=U�*Ï*A9î*C701Ó 01(!C
$�æ�Î9$;C7=?$��*Ì�$ÙÑ4$]Í>�!0.Ñ 57Ò*�65:��Ì;�6CE$rÖÝ(!I?I?к5E(!�!$;G Ke5E0�ÌWÒ*� KM57=JÌ
Ï CW� G�=?$��l5�G�$;KEÌr$;�15�=JK�Ò*�6CWGç570úP9$��.5�01�ãIJ�6CEÏ $�ÌrIJ� KEKM=Uâ9Ì;�.57=?0 �ãÎ!CE0 P!I?$�Ó�K;A®î*0 C�K7Ó��6I?IU$;C
Î!C701P!I?$�Ó�Ka5EÒ*�.5@C7$�Ül(!=UCE$Ù�1Ì�Ìr(*CE�657$�CE$;�6IULO<'� IU(*$;G�0 (!57Î!(�5WK:IU=?Í $]=?�ÁÖÝ(*�*Ìn5E=U01� �6Î!Î*C70'æ�=?Ó��6L
57=?0 �ì0 C�Ì�0 �l57CE0 IRÎ!CE0 P!I?$�Ó�K;-�Ñ)$#K7$�$�5EÒ*�.5ºÌ�0 �P�e(!Ïl�.5E$3Ï1CE�1G�=?$��l5'�»Ña=¦5EÒ��®0 IJ�6ÍlLON�=UP!=?$�CE$
0 2 4 6 8 10 12 14 16
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Eigenvalue magnitude
N
u
m
b
e
r
o
f
E
i
g
e
n
v
a
l
u
e
s
Big killers
L
L
A�Ü,A7� � � �%�)0QV�$�CWK457Ò!$�P,$;KM5DÌ�0 ÓÙP*=U�*�657=?0 �306Ö�KMÎ,$�$�Gc-!CE$�I?=?� P!=?IU=U5eк�6�9G¾K7=UÓ�Î!I?=JÌr=U5eÐ A ?>$;< $;CE� I
�.5M5E$�Ó�Î�5WK@(*KM=?�!ÏTèMÓ�=?�!=�P*�.5WÌWÒ!$;KEê�=?�ú�6Î!Î!I?Ð>=U�*Ï3Ì�0 �P�e(!Ïl�.5E$�Ï1CE�1G�=U$;�l5
5703IJ�6CEÏ $�� �*G C7$�L
G�(!�*G!� �l5@Î*C701P!IU$;Ó�KDÒ9�’< $ÙP,$�$;� Ó��1G�$�CE$;Ì�$��l57I?Ð � � (>– E “�- �”���OA � <'� C7=J�6�l5:06Ö4Ì�0 �P�e(*Ï1�.5E$
Ï CW� G�=?$��l5a0 Î�5E=UÓ�=?ë;�657=?0 � �»Ì�� IUI?$;G�KEÌ�� IU$�G�&R8 �RK7$�$;Ó�K�=U�l57$;C7$�Ke5E=U�*Ï C�Ò!$;C7$:57Ò*$�IU=?�!$ÙK7$;� CEÌWÒ
Î!C70�Ì�$;G�(!CE$@=?KRCE$�Î*I?�1Ìr$;G¾P>к�B�;ÛÚ”/$�<1$��>P9$;C7Ï�QÁ� CEÜl(*� CEG>545eÐ>Î9$]� IUÏ10 CE=¦5EÒ!Ó � E � �OA
����� 8 ������-���! ��”0� 9 “��!4<�&3��!. @B%(#&%13 � %(')4
� �2' �
*��2' 9 �
%(����� 9
Þ/030 P�5W�6=?� �3Ke5E0�ÌWÒ*� KM57=JÌÙ<1$�CWKM=?0 �#0 Ö�5EÒ!$�"%$�<1$��>P,$�CEϺQÁ�6CWÜl(*�6CWG>5@�6I?Ï 0 CE=U57Ò!Ó 5EÒ!$�=JG�$��
=?K]570 Ì�0 Ó�Î!(�5E$�57Ò*$ºG�=J�6Ï 01�*�6I)Ø�$;KEK7=?� �ú57Ò!CE0 (!Ï1Ò¼�#C7(*�!�!=?�!ÏÁ$;KM57=?Ó��.5E$�06ÖR57Ò*$¾K7$;Ìr01�*G
G�$�CE=U<.�657=?< $@Ña=¦5EÒ#C7$�KMÎ,$;Ìr5R570�$;�1ÌWÒ¾Î9�6CW�6Ó�$r5E$�C�A!ÞRÒ!$�=U�9Ke5W�6�l5E� �!$�01(*KaKM$�Ìr01�*G¾G!$�CE=U<.�.5E=U<1$
Ì��6�#P,$Ù01P�5E� =U�*$;G�<>=?��P9� ÌWÍ>Î!CE0 Î*� Ï1�.5E=U01�3�1K�K7Ò!0.Ña�#=U��5EÒ!$]ÖÝ01C7Ó�(!IJ� Ka0 Ö�K7$;Ìr57=?0 � (�A �
K
KM0>0 ���1K�Ñ4$aÒ*�’< $R5EÒ!01K7$aC7(*�!�!=?�!Ï]$;KM57=?Ó��.5E$;K�Ñ4$�Ì�� ��(*K7$a57Ò!$;Óà5E0ÙÌr01Ó�Î!(�57$
=U�*G!=U<>=JG�(*�6I
IU$��6CE�!=U�*Ï�CW�.5E$;K)ÖÝ0 Ca$�� ÌWÒ3Î*�6CW�6Ó�$�57$�C
0 $ , � �� � � �
� � �� � � 7 �
�#&”���
ÑaÒ!$�CE$ � G�$��!0 57$�K�5EÒ!$�Ï I?0 P9�6I*I?$;� C7�*=U�!Ï�CW�.5E$ -l�6�*G � ��� �� � �� � � =JK��ÙC7(!�*�!=U�*Ï]$;KM57=?Ó��.57$
06Öc57Ò*$G�=?� Ï 01�*�6I/K7$;Ì�0 �*G�G�$;C7=?<.�.5E=U<1$�Ña=¦5EÒÁC7$�KMÎ,$;Ìr5�570 � $ , A �ú=?KD��Î*�6CW�6Ó�$�57$�CR5E0�Î!CE$�<1$��l5 0 $ ,ÖÝC701ÓßP!IU0.Ña=?�!Ï:(!Î�=U��Ì�� K7$)57Ò!$aK7$;Ìr01�*GÙG!$�CE=U<.�.5E=U<1$�=JK�KMÓ�� IUI[-'=ÀA $ A.ÑaÒ!$;�]5EÒ!$R0 Î�5E=UÓ�=?ë;�.5E=U01�
Ó�0.<1$;K4=?���,�.5�Î*� CM5WKR06Ö/5EÒ!$�$�CECE0 C4ÖÝ(!�*Ìr57=?0 �%A*ÞRÒ*$�C7(!�*�!=U�*Ï�$�Ke5E=UÓ��657$@=?K
Ìr0 Ó�Î!(!57$;G��1K
� � F6�
��� F$ , � .�� � ���%� F�� ��� � F6���� F$ , � ��� � 7 � � F6�G���� F$ ,
�#& E �
ÑaÒ!$�CE$ � =?K3�çK7Ó��6I?I:Ì�0 �*KM5E� �l5�57Ò*�65�G!$r57$;C7Ó�=?�!$;Kº57Ò*$å� Ó�01(!�l5¾0 Ö]Ó�$;Ó�0 CEÐã5EÒ*�.53=?K
P9$;=U�!Ͼ(*K7$;GcA,ÞRÒ!$�K7$;Ì�0 �*G#G�$;C7=?<.�.5E=U<1$;K
Ì;�6�#P,$�Ì�0 Ó�Î!(�5E$;G#Î!CE=?0 Ca5E0�57CW�6=?�!=?�!Ï�0.<1$�Ca$ A Ï*A
��KM(*P*KM$�5D0 Ö�5EÒ!$]5ECE� =U�*=U�!ϾKM$�5;A ?�=U�*Ì�$]5EÒ!$�Ð#ÌWÒ*� �!Ï $�01�!IUÐ3< $;C7Ð�K7IU0.ÑaI?Ð�5EÒ!$�Ð�0 �*IUÐ3�!$�$�G
5703P9$�C7$;$;KM57=?Ó��.57$�G#$�<1$�CEÐ3ÖÝ$�ÑÚ$;Î90�ÌWÒ*K;A<�
065E$Ù5EÒ*�.5:57Ò!$�� G*G�=¦5E=U01�*�6I�Ì�01KM5D0.< $;C
CE$�Ï1(!I?� C
P*� ÌWÍ>Î!CE0 Î*� Ï1�657=?0 �#=JKD�*$�Ï I?=?Ï =?P!IU$�� �*G Ì�0 �>< $;C7Ï1$��*Ì�$Ù=JK � �1K:�¾CE(!IU$�0 Ö�57Ò>(!Ó�P �Á�6P,0 (!5
57Ò!CE$�$:57=?Ó�$;KRÖ»�1Ke5E$�CR5EÒ*�6�#��Ì�� C7$�ÖÝ(!IUI?Ð�5E(!�!$;G�KM570�ÌWÒ*�1Ke5E=?Ì:Ï CW� G!=U$;�15�� IUÏ10 CE=¦5EÒ!Ó�A
áh��îv=?Ï (*C7$ E E �6�*G E �@Ñ)$DKM$;$a57Ò!$DÌr0 �><1$�CEÏ $��9Ìr$R06Ö�57Ò*$DKM570�ÌWÒ*� KM57=JÌaG�=J�6Ï10 �*� I*"%$;< $��!L
P9$;C7Ï�QÁ� CEÜl(*� CEG>54Ó�$r57Ò*0>G �#&”� ��ÖÝ01C��]5E0.Ð�$ræ!�6Ó�Î!I?$@Ña=¦5EÒº5eÑ40�G�=/V,$;C7$;�15�K7$r5WKR06ÖvI?$;� C7�!L
=U�!Ï�CW�.5E$;K;AlBDP><>=U01(*KMI?Ð�5EÒ!$�$ræ�Î,$�CE=UÓ�$;�154KMÒ!0.Ña��î�=?Ï (!CE$ EXE Ìr01�l5E�6=?�*K®ÖÝ$;Ñ)$;C �*(*Ìr57(*�657=?0 �*K
57Ò*� �3=?�#î�=UÏ1(!C7$ E ��G�(*$@570�K7Ó�� IUI?$�CRI?$;� C7�!=?�!Ï�CW�.57$�K�A
����� � �
��*C��”�3C4 ����%���’-“�3C� ” � �!.�� “�4&%13;#!�!.�*C%
!#&%1�6���:’=�<>����C% �A%1 � �”��!3
áh��57Ò!$aÖÝ01IUI?0.Ña=?�!Ï@Ñ)$�Ï1=U<1$457Ò!CE$�$a5EC7=JÌWÍ�K�ÖÝ0 C4Ìr0 Ó�Î!(!57=?�!Ï@57Ò!$
Î!C7=?�*Ì�=UÎ*� I!$�=?Ï $;�!<.�6I?(!$�2 ��$;ÌrL
570 C¾06Ö�5EÒ!$ Ø
$;KEKM=J�6�xÑa=U57Ò!01(�5¾Ò9�'
$�=?Ï $��><1$;Ìn5E0 C�06Ö:57Ò!$ÁØ
$;KEKM=J�6� �ÝÑa=U57Ò!01(�5ºÒ*�'<>=?�!Ï 570¼Ìr01Ó�Î*(�57$�5EÒ!$ÁØ�$�K7K7=?� � �Ù57Ò!CE0 (*Ï Ò
�’< $�CW�6Ï1=U�*Ï �»K7$�$�� I?K70 � E * �*�nA
Weight space
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Log MSE (dB)
0 1 2 3 4 5 6 7 8 9 10
−20
−15
−10
−5
0
Hessian
largest
eigenvalue:
λ = 0.84
max
η = 2.38max
epochs
Learning
rates:
η0 = 0.12
η1 = 0.03
η2 = 0.02
Maximum
admissible
Learning
rate (batch):
L
ghi¦\�jlg)��i�seo�~W����_E½1\;Z�q1�¦_EgW©>u®o1_
j1_Es[��d;be��o>\;g�d�j1_��¦ikj1_n\�b)�lj1iksn}�¢:ikjlql� seg�\;j>�3~�d;�1seq1�1sn}1iÝ© _�©
seo be_W_aq>\rbM\;Z�_Ese_7beg � ¢
�®_Wik^;o6segW}9~a{li¦\�g �7©
Weight space
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Log MSE (dB)
0 1 2 3 4 5 6 7 8 9 10
−20
−15
−10
−5
0
Hessian
largest
eigenvalue:
λ = 0.84
max
η = 2.38max
epochs
Learning
rates:
Maximum
admissible
Learning
rate (batch):
η0 = 0.76
η1 = 0.18
η2 = 0.12
L
ghi¦\�jlg)��i�seo�~W����_E½1\;Z�q1�¦_EgW©>u®o1_
j1_Es[��d;be��o>\;g�d�j1_��¦ikj1_n\�b)�lj1iksn}�¢:ikjlql� seg�\;j>�3~�d;�1seq1�1sn}1iÝ© _�©
seo be_W_aq>\rbM\;Z�_Ese_7beg � ¢
�®_Wik^;o6segW}9~a{li¦\�g �7©
� � � %(‘ � % ���C� 9 ä $�CE$�Î,$;�65a57Ò!$�CE$;K7(!IU5�06Ö®0 (!C�G�=JKEÌr(*KEKM=?0 ��=?�#KM$�Ìn57=?0 � (�A “”C!Ke5W�6C757=?�!Ï
ÖÝC701Óí��CE� �*G�0 Óí=U�!=U57=J�6I/< $;Ìr5701C ��-!57Ò!$�=U57$;CE�657=?0 �
� .�� � � � � ��� �� � ��� � �
Ña=UI?I*$;< $��l5E(*�6I?IUÐ�Ìr01�l<1$�CEÏ $4570]57Ò!$�Î*C7=?�*Ìr=?Î*� I*$�=?Ï $;�>< $;Ìr5701C �»0 C4�@< $;Ìr5701C�=U��5EÒ!$�Î!CE=?�*Ìr=?Î*�6I
$�=?Ï $��9KMÎ*�1Ìr$��)� �*G ��� � � � �
Ña=?I?I/Ìr01�l<1$�CEÏ $D570�57Ò*$]Ìr0 CECE$;K7Î901�*G�=?�!Ï�$;=UÏ1$��><.�6I?(!$ � � � -4� � �OA
� � ��.0�&' � � ���!3� �"0�<3 �
�!065EÒ!$�C@Ó�$r5EÒ!0�GÁÓ��6Í1$;KD(*KM$�06Ö�5EÒ!$�Ö»� Ìn5:57Ò9�.5�KMÓ��6I?I�Î9$;CM5E(!CML
P*�.5E=U01�*KR06Ö�57Ò!$�Ï1CE�1G�=?$��l5R� I?K70�IU$�� Gº570�57Ò*$�Î!C7=?�*Ì�=UÎ*� Ic$�=?Ï $;�l<1$;Ìr570 CR0 Ö �
� .�� � � ��
� ��%� � � 7 � � � � ���� � � � � � F � ���� � � � �
�#& � �
ÑaÒ!$�CE$ �#=?K��@K7Ó��6I?I!Ìr0 �9Ke5W�6�l5;A1BD�!$R=U57$;CE�657=?0 ��06Ö*5EÒ!=JK�Î!CE0>Ì�$;G�(*C7$4C7$�Ül(!=UCE$;Kv5eÑ40:ÖÝ0 CEÑ4� CEG
�6�*Gº5eÑ)0�P*�1ÌWÍ>Ñ4� CEGºÎ!C701Î*�6Ïl�.5E=U01�ºKe5E$�Î*KaÖÝ0 Ca$;�1ÌWÒ¾Î9�.5M5E$�CE�¾=?�357Ò!$@5ECE� =U�*=U�!Ï�K7$r5�A
� 3�.0″03�% � �
� *����2��”��&3 �&>�� ÞRÒ!$�ÖÝ0 I?IU0.Ña=?�!Ï�CE(!I?$ÙÓ��6Í1$;KD(*KM$�06Ö�5EÒ!$�CE(!�!�*=U�!Ï3�’
Î!CE0 Î*� Ï1�.5E=U01�%-�Ke5E$�Î3=?K�Î9$;CMÖÝ01C7Ó�$;G3�6�9G�5EÒ!$�Ï CW� G�=?$��l5WK�� � � �a� C7$@KM570 CE$;G%-
�!A ��� ��
�
� � ��
� �
=?Ka�1G!G�$�Gº5E0�57Ò!$]Ì�(!C7CE$��l5aÑ4$�=?Ï Òl5a< $;Ìr5701C � -
� Aa��ÖÝ01C7ÑR�6CWG��6�*G#P9� ÌWÍ>Ñ4� CEG3Î!CE0 Î9�6Ï1�657=?0 ��Ke5E$�Î =?K
Î9$;CMÖÝ01C7Ó�$;GÁÑa=¦5EÒ#57Ò!$�Î,$�C757(!CEP9$�G
Ñ)$;=UÏ1Òl5R<1$;Ìr570 Ca� �*G¾57Ò!$�Ï1CE�1G�=U$;�l5EK�� � � � �R� C7$�KM570 CE$;G%-
"�A457Ò!$�G!=WV�$�CE$��*Ì�$ � � �1��� � � � � F � � � �;�@=?K�Ì�0 Ó�Î!(�5E$;Gå�6�*G 57Ò*$�CE(!�!�*=U�!Ï#�'<1$�CW�6Ï $Ù06Ö
57Ò!$�$;=UÏ1$��>< $�Ìn5E0 CR=?KR(*Î,G!�657$�Gc-
&!ARÑ)$@I?0>0 Î3ÖÝC701Ó � E �OL-��& ��(*�15E=UIv��C7$�� K70 �*� P!IUÐ�KM5E� P!IU$@CE$;K7(!IU5�=?KR01P�5E� =U�!$�G�ÖÝ01C���-
(>A457Ò!$�01Î�57=?Ó��6I%I?$;� C7�*=U�!Ï�CW�.57$@=JK457Ò!$;�#Ï =?< $;�¾� K
0 � � ( � �� � � 5
áh��î�=?Ï (!CE$ E � Ñ4$aKM$;$457Ò!$R$�<10 I?(�57=?0 ��06Ö957Ò!$R$�=?Ï $;�><'� IU(*$4�1K��DÖÝ(!�9Ìn57=?0 ��06Ö957Ò!$R�>(!Ó�P9$;C�06Ö
Î*�.5757$�CE��Î!CE$;K7$��l5E�657=?0 �*K,ÖÝ01Cv�R�!$;(!CW�6I6�!$�5eÑ)01C7ÍD=U�]��Ò*�6�*G!ÑaC7=U5M5E$��]ÌWÒ*� CE�1Ìn57$;C�C7$�Ìr0 Ï1�!=U57=?0 �
5E� K7Í�A�áh� Î!CW� Ìr57=JÌr$�Ñ)$�� G*�6Î�5@57Ò*$�I?$;� ÍÁKM=?ë�$�06Ö)57Ò!$�CE(!�!�!=?�!Ï��’< $;CE� Ï $]=?� 01CEG!$�C:5703Ï $�5
ÖÝ$�Ñ4$�C��*(*Ìr57(*�657=?0 �*K@�À� K��6IJK70 =?�*G�=JÌ��657$;Gã0 �ç57Ò!$�â9Ï (!CE$ �rA�áh�ã57Ò*$¾â9Ï (!CE$�Ñ)$�KM$;$357Ò*�65
�.Ö×57$;C]ÖÝ$;Ñ)$;CÙ5EÒ*�6� � � � Î*�65M5E$�CE�zÎ!CE$;K7$��l5E�657=?0 �*K@5EÒ!$¾Ì�0 CEC7$�Ìn5Ù01CEG!$�C]0 Ö�Ó�� Ï �!=U57(9G�$�ÖÝ01C
57Ò!$¾$�=?Ï $��><.�6I?(!$1-%=ÀA $�5EÒ!$�I?$;� C7�!=?�!ÏÁCW�.5E$�=?KÙC7$�� ÌWÒ!$�GcAvî*C701ÓÔ5EÒ!$º$�æ>Î,$�CE=?Ó�$;�l5EK]Ñ4$º� I?K70
0 P*K7$�CE< $D57Ò*�65a57Ò!$ �9(*Ìn5E(*�.5E=U01�*KR06Ö�57Ò!$]�'<1$�CW�6Ï1$DØ�$�K7K7=J�6�30.< $�C)57CW�6=?�!=?�!Ï��6CE$�KMÓ��6I?I[A
0 50 100 150 200 250 300 350 400
0
10
20
30
40
50
60
70
80
Number of pattern presentations
e
ig
e
n
v
a
lu
e
γ=0.1 γ=0.03
γ=0.01
γ=0.003
L
sM\rseikd�jlg@°?d;b]\�gho>\rbe_n�#�®_Wik^�o.s]j1_Es[��d;be�3��i�seo塺�¦\W�._EbegW} �;£ ���;¤3fWd�j1jl_Wf7sei¦d;jlg�\�j>�¼~r¢;�;¤º°Ube_W_
ql\�bM\�Z�_Ese_EbegW©lu®ol_RshbM\;ikj1i¦j1^@gh_Es�fWd;jlghikgOseg)d�°®~n�;����o>\�j>�6��beikshse_Ej��1ik^;iksegW©
áh� î�=UÏ1(!C7$ E “º�6�*G E &�Ñ4$�KM5E� CM5:Ña=¦5EÒÁ5EÒ!$�KE�6Ó�$�=U�!=U57=J�6I�Ì�0 �*G�=U57=?0 �9K�-��6�*G Î9$;CMÖÝ01C7Ó
��â!æ�$;G3�>(!ÓÙP,$�C�0 Ö�$;Î90�ÌWÒ*K�Ña=¦5EÒ3I?$;� C7�*=U�!Ï�CW�.5E$;K�Ì�0 Ó�Î!(�5E$;G3P>кÓÙ(*I¦5E=UÎ!I?Ð>=U�*Ï�57Ò!$]Î*C7$�L
G�=?Ìr57$�G�I?$;� C7�*=U�!Ï:CW�.57$4P>ÐÙ�:Î!CE$;G�$�â*�!$;G�Ìr01�*KM5E�6�l5�A6&)Ò*0l0lKM=?�!Ï@Ìr01�*Ke5W�6�l5����»=ÀA $ A (*KM=?�!Ï:57Ò*$
Î!C7$�G�=JÌn57$�G�0 Î�5E=UÓ�� I/CW�.57$��a�6I?ÑR�’Ð>K�Ï =?< $;K�C7$�KM=JG�(*� I%$�CEC701CEKRÑaÒ*=?ÌWÒ � C7$�<1$�CEоÌ�IU0lKM$@5E0�57Ò*$
$�CEC701C�� ÌWÒ!=?$�<1$;G�P>Ð�57Ò!$DP9$�Ke5RÌWÒ!0 =JÌr$�0 Ö�57Ò!$:Ìr0 �9Ke5W�6�l5;A1áh��065EÒ!$�C)Ñ)01CEG!K;-.5EÒ!$ºè7Î!C7$�G�=JÌn57$�G
0 Î�5E=UÓ��6IcCW�.5E$;ê�=JKR0 Î�5E=UÓ��6I/$��!01(!Ï Ò%A
0 0.250.50.75 1 1.251.51.75 2 2.252.52.75 3 3.253.53.75 4
0
0.5
1
1.5
2
2.5
LEARNING RATE
PREDICTED OPTIMAL LEARNING RATE
M
E
A
N
S
Q
U
A
R
E
D
E
R
R
O
R
1 epoch
2 epochs
3 epochs
4 epochs
5 epochs
L
q be_n�1ikfEse_W� d;q1seikZ]\;���k_n\rbejlikjl^ºbM\�se_�°?d;bÙ\�°J�l�k���ÁfWd;jljl_EfEse_n�Ájl_EsÀ�®d;be� � ��¤;£ �#�;� � ~n� �7©�u®o1_
shbM\�ikjlikjl^@gh_7s)fEd�jlghikgOseg�d;°/�;���:ol\;j>�6��bei�shse_Wj��1ik^;iksegW©
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
0
0.5
1
1.5
2
2.5
LEARNING RATE
PREDICTED OPTIMAL LEARNING RATE
M
E
A
N
S
Q
U
A
R
E
D
E
R
R
O
R
1 epoch
2 epochs
3 epochs
4 epochs
5 epochs
L
q be_n�1ikfEse_W�åd�q sei¦Z]\��)�k_n\rbejlikjl^�bM\rse_�°Jd;b�\�gho>\rbe_n� ��_Wik^�o.s�j1_Es[��d;be�Á��i�seoz¡3�¦\n�’_Ebeg � ~W�’¢r£ �
~n¡��;¤ �Á����¢ �#£���� �å~n��� �ú~n� �7} ��£ ���;¤ � �kd.fn\�� �ÙfWd;jljl_EfEseikd�jlg�\;jl�ã~r¢;�;¤�°?be_E_ºql\�bM\�Z�_Ese_Ebeg
� ghol\�be_n�Ù�®_Wik^�o.seg �7©lu®ol_RshbM\�i¦j1ikjl^�gh_Es�fWd;jlghikgOseg�d;°�~n�;���@ol\;j>�6��bei�shse_Wj�� i¦^;i�segW©
Â�� � Ë �>ÊcÉ?�1�>ËeÇ�Äïó�Ä
È �åÇ�Ä
Êcø7É?�>ËeÇ�Ä
�
Ì�Ì�0 CWG�=?�!ϼ570ã57Ò*$ CE$;Ì�0 Ó�Ó�$��*G!�657=?0 �*KºÓ�$��l57=?0 �!$�G��6P,0.< $1-)�çÎ!CE�1Ìn5E=¦5E=U01�!$�CºÖ»� Ìr=?�!ÏT�
ÓÙ(!IU57=UL[IJ�'Ð $;CR�!$�(!CW�6Ic�*$r5a57CW�6=?�!=?�!Ï�Î!CE0 P!I?$�Ó�Ñ40 (*I?G¾Ï 0�57Ò*C701(!Ï Ò¾57Ò!$@ÖÝ01IUI?0.Ña=?�!Ï�KM57$;Î*KDC
� KMÒ>(���$@5EÒ!$�$ræ!�6Ó�Î!I?$;K
� Ìr$;�15E$�CR5EÒ!$�=U�*Î!(�5
<.�6CE=J�6P!I?$;K4P>кK7(!P�57CW� Ìr57=?�!Ï�57Ò!$�Ó�$��6�
� �!0 CEÓ��6I?=Uë;$:57Ò!$�=?�!Î!(�5�<.� C7=J�6P!I?$:570���Ke5W�6�*G*�6CWG¾G�$;<>=?�657=?0 �306Ö �
� =¦Ö®Î,01KEKM=?P!I?$ -*G�$�Ìr01C7CE$�IJ�.5E$�57Ò*$�=U�!Î*(�5
<.�6CE=?� P!I?$;K;A
� Î!=JÌWͺ���!$r5eÑ40 CEÍ�Ña=U57Ò357Ò!$]K7=?Ï Ó�0 =JG�ÖÝ(*�*Ìn5E=U01��K7Ò!0.Ña�3=U�3â*Ï1(!CE$ �
� KM$�5a57Ò!$@5W�6CEÏ $�54<.�6I?(!$�KaÑa=¦5EÒ!=?�¾5EÒ!$�CW�6�!Ï1$D0 Öv5EÒ!$]KM=?Ï Ó�01=?Gc->5eÐ>Î!=JÌ�� IUI?Ð 7 �@�6�*G¾L
� A
� =U�*=¦5E=?� IU=?ë�$@5EÒ!$�Ñ)$;=UÏ1Òl5EK4570�CW�6�*G!0 Ó�<.�6I?(!$�Ka� KRÎ!CE$;KEÌrCE=UP,$;G¾P>Ð�� &*A
ÞRÒ!$@Î!C7$�ÖÝ$�CEC7$�GºÓ�$�57Ò!0�G¾ÖÝ0 CR5ECE� =U�!=?�!Ï�57Ò*$��!$r5eÑ40 CEÍ�KMÒ*0 (!IJGºP,$�Î!=JÌWÍ $�G¾�1K4ÖÝ0 I?IU0.Ñ�KDC
� =¦Ö957Ò!$)57CW�6=?�!=?�!Ï@KM$�5�=JK�I?� C7Ï1$:�ÝÓ�0 CE$)57Ò*� ���
ÖÝ$�ÑzÒ>(!�*G!C7$�GÙKE�6Ó�Î!I?$;K
�%�6�9G]CE$;G�(!�9G!�6�l5;-
�6�*G�=UÖ�57Ò*$]5E�1KMÍ3=JK
ÌrIJ� KEK7=¦â9Ì;�.5E=U01�%-*(*K7$ÙKM570�ÌWÒ*�1Ke5E=?Ì�Ï1CE�1G�=?$��l5�Ña=¦5EÒ Ì�� C7$�ÖÝ(!I%5E(!�!=?�!Ï*-
0 Ca(*K7$:57Ò!$]KM570�ÌWÒ*�1Ke5E=?Ì@G�=J�6Ï10 �*� Ic”%$�<1$��>P,$�CEÏ�QÁ� CEÜl(*� CEG�54Ó�$r5EÒ!0�GcA
� =¦Ö�57Ò*$@57CW�6=?�!=U�*Ï�K7$r5a=JKR�!065a5E0l0�IJ�6CEÏ $ ->01Ca=¦Öv57Ò!$@5W� K7Í�=?KRCE$�Ï1C7$�K7K7=?0 �%-l(*K7$@Ì�0 �P�e(*Ï1�.5E$
Ï CW� G�=?$��l5�A
&)I?�1K7K7=?Ì;�6IcK7$;Ìr01�*G>LO0 CWG�$�C4Ó�$r5EÒ!0�G!K��6CE$@=UÓ�Î!CW� Ìr57=JÌ�� Ic=U�#�6I?Ó�01KM5��6I?Ic(*KM$�ÖÝ(!I/Ì;� K7$;K;A
ÞRÒ!$D�*0 ��LOIU=?�!$��6CRG�Ð>�*�6Ó�=JÌ�K)06Ö�KM570�ÌWÒ*�1Ke5E=?Ì
Ï CW� G�=?$��l5RG�$;KEÌr$;�15R=?�ºÓÙ(*I¦5E=¦LOI?�’Ð1$�C4�!$�(*CE� I
�!$r5eÑ40 CEÍ�K�-6Î9�6C757=JÌr(!IJ�6CEIUÐ�� K�=¦5RÎ9$;CM5W�6=?�*K�5E0ÙÏ1$��!$;CE� IU=?ë;�657=?0 �%-.=JK)KM57=?I?I*Ö»� C�ÖÝCE0 Ó P9$;=U�!Ï�Ñ)$;IUI
(!�*G�$;CEKM570>0�GcA1QÁ0 CE$a57Ò!$;0 CE$r5E=?Ì;�6I!Ñ40 CEÍ�� �*G�KMÐ�KM57$;Ó��657=JÌa$ræ�Î,$�CE=UÓ�$;�15W�6I9Ñ)01C7Í�=?K��!$�$�G�$;GcA
8 � ��3C� �,.�% 9 4<% �%(3;� ��A "�A � "�A 2:A ��H�A LhN�A6Q¼A6Ï1CE�657$�ÖÝ(!IUI?ÐÙ�1ÌWÍl�*0.ÑaIU$�G�Ï $4ÓÙ(�5E(*�6I $ræ!ÌWÒ*�6�*Ï $:Ï CW�6�l5EK)ÖÝCE0 Ó Û:�:� Ûà�6�*G$� ?!î)A � ò �Eò/Æ!ò/Ä Ê�òC� ~�© ��©!t)Z]\rbeiש4�)_W�1bM\����k_n\�bej1i¦j1^�ikjºgOshbe�lfEse� be_n��q>\rbM\;Z�_Ese_7bRghq>\�fW_Wg�� jl\�se� bM\;�,beik_WZ]\�jljli¦\�j
^�bM\�� i¦_Ej6sn©�YÀj � i¦fMo>\�_W�v )© � d��W_Ebn} � ikfMo>\;_E�/YM©*��d;bM�1\;j*},\�j>��u®old;Z]\;ga`�_7seghf7o1_�}*_n�1i�sed;begW}
��� ��
��
�����������������
���� �”!$#���%&
‘(�)# �+*,��#”
���-� ����.0/21��-‘3��%+� }’��d��k�lZ�_�� }’ql\;^;_R~r¢��.©.u®o1_ � YOu
`cbe_WghgW}9~n�����6©
¢6©
��©vt)Z]\�beiש �R\rse�1bM\;��^;bM\;�1ik_Wj.s��®d�be�6g�_54�fWik_Wj.se��� i¦j �k_n\�bej1i¦j1^1© ��������
��768# %�9���’:
‘(�)# � }
~W� � ¢��7¯ ¢;¡6~ ; ¢�� � }%~n�;��¤6©
� ©am�©��®\�shsei�seiש*��i�begOsh|c\;jl�@gh_WfWd;j>� |»d�bM�1_EbvZ�_Eseold6� gc°Jd;bv�k_n\�bej1ikjl^1¯.��_Es[��_W_Wj]gOse_W_Wq�_EgOs®� _WghfW_Wj.s
\�j>�Ùjl_E��sed;j=< g�Z�_Eseold6�!© �>������
�?68# %�9���’:
‘(�)# � }>£1¯k~E£1~�;l~ ��� }c~n�;�’¢.©
£1©
��©>�v_Wf7��_Eb)\;j>�A@D©>y*_r ��lj*©�YÀZ�q1bedr�6ikjl^Dseo1_afWd�j6�’_7be^�_Wj1fW_�d;°%{>\�f7�6{ bed�q>\�^’\rsei¦d;j��k_n\�bej1i¦j1^
��i�seo¾gh_WfWd�jl�3d6�1_7b�Z�_Eseold��1gW©�YÀj¾pa\n�6i¦�3u,d;�1be_Ese�E�6�.} � _Ed;¿�be_E� � ikj.sed�j*},\�j>�¾u,_Ebhbe_Wj1fW_
�6_ �Oj1dn��gh� i×}l_n�1i�sed;begW} *��B#”
� ��� ����. �0#B!C’�D2�&E�F GHGI68#��2�J��
5′(�)#��2�K�-‘MLN#”���5� �O/2��%+%����7/P
DQ#”#�� }
ql\;^;_Wg)¢;�R;.�’�.©!y,\W��be_Wj1fW_ �%be�k{>\��lZÚt�ghghd.fWi¦\�se_WgW}9~n��¤;� ©
¡6©
)© � ©.��ikghold;q9© �����S�B
��Q����'(TM#��-U��V!$# �M*�
‘(‘3�����XWY��
-#-. �2�K'(�(# � ©, ��¦\�be_Wjl�1d;j�`cbe_WghgW}1�)½6°Jd�bM�*}
~W����¡6©
� ©�y%©n��d�shsed��*©6�4jl�kikjl_/\��¦^;d;bei�seolZ�g,\;jl�RgOsed.f7ol\;gOseikf�\�qlq bedr½ ikZ]\�seikd;jlgW©;Y[japa\n�6i¦�a�1\;\��*}W_n�1i�sed;bn}
Z ��� �K�P��[\��
���Q�K��.]�K�^��������
��,�>��'(T?# ��U��`_aE�FHF�bdcA# ��U��BDQ#�9d
‘0’�DQ�A����T�’:# �e� �2�-‘(�K'(��’3�af }
®\�Z:{ beiU� ^�_�}*~n�;��¤6©�u®ol_a�)_E��sed�j�Y[jlgOsei�se� se_�� _Ebeik_WgW}> ®\;ZD{1bei¦�1^;_a�4j1i¦��_Ebeghi�s[��`%be_EghgW©
�6©apD©1�!©1�vbed.d�Z�o1_n\��Ù\;jl�ÙpD©ly*dn�®_�© � �1��sei¦�;\�bei¦\�{l�k_R°J�1jlfEseikd�jÙikj.se_Ebeq�d��¦\�seikd;j�\;jl��\;�l\;q seik�’_
j1_Es[��d;be�6gW© 68# %�9P� � � /Q1 �-‘3��%+� }�¢6¯ �’¢.~�;6��¡�¡.}/~W��¤;¤ ©¤ © � ©*y/©*���1j6seikj1_:\�j>��t
©9��© � _Wik^�_Ej>�*©� �d�Z�ql� seikjl^]gh_WfWd;j>��d;bM�1_7b��1_Ebeik�;\�seik�’_Wg4i¦j¾�l_W_W� |
�1d;bh��\rbM�3jl_7s[�®d�be�6gW¯,t�be_W�6ik_E�a© ���������2�B
�2��
H
5′(�(# �2�X# � ��������
�� �>��'(T?# ��U�� }�~W�����6©�u,d
\�qlq�_n\rbn©
� ©
)©!pR\�be�’_Wjº\�j>���1© ��© � d.d6� �.©a�)d;se_:d;j��¦_W\�bejlikj1^ÙbM\rse_:ghfMol_n� �l�k_Wg4°?d;bagOsed.fMo>\�gOsei¦f:d�q1sei�|
Z�ik�n\rseikd�j9©>Y[j@m�©.`�©.y*ikqlqlZ]\�jlj*}�� © ��© � d.d6� �.}6\�j>�:pD©6�!©’u,d�� be_Ese�W�.�.};_n�1i�sed;begW} �Y� ��
��
���
���0�>�����B
���� �$!$# � %�
‘(�(# �>*,��#”
���-� ����.�/Q1 �-‘3��%0� };�’d;�¦�1Z�_��6}rq>\�^�_Wg%¤;�’¢”;.¤��;¤ © � d�be^’\�j:¬�\;� °?|
Z]\�jlj*}1�1\;j � \�se_Wd }! ®t
}*~n�;� ~;©
~W� ©a¬@©�Y7©.p4iU\�Z]\;j.sM\�bM\�g®\�j>�Ù�!©H@D©’¬a�1jl^1© *,�����P
5� 9S
��=68# %O9S# �P���2’\�����S�B
��2�>��'(T?# ��U�� © � ik�k_E�.}
�)_E� @vd;be��}9~W����� ©
~;~�©am�©v���k_Esef7o1_Ebn© *,��
H
5′(�(
��L ��’�DQ#”��� #B! Z 9�'(��%+� �”
‘(�)#�� }vf7ol\;q1se_7bÙ¤ © � ¯�`/d;�k� j1d�Z�i¦\;��seikZ�_
\��k^�d;bei�seo1Z�gW}lql\;^�_Eg
~W¤��R;l~n¤;¤ ©��;d�olj � ik�¦_7��w��6d�jlgW}1�4_7� @vd;be��} gh_WfWd;j>��_W�1i�seikd�j9}*~n�;¤’�.©
~n¢6©
��© � _WZ]\;j*} ��©.�vi¦_Ejl_Wj1gOsed.f7��}�\;j>�
m
©�pRd;�1bege\rsn©>�4_E�1bM\;�6j1_Es[��d;be�6g/\;j>��seol_®{1i¦\;g�
��;\�bei¦\�jlfW_
� ik�¦_EZ�Z]\ © ��������
��868# %O9���’:
‘(�(# � }l£ � ~��7¯k~ ; ¡;¤6}c~n�;�’¢6©
~W� ©�y%© � d��¦�1gOse_Ei¦j*© � _n\�j�g �.�>\rbe_4d�q seikZ]\;�ki�s[�]ikjÙseo1_4fWd;j.sei¦j6�1d��lgvsei¦Z�_�m�d�{l{1ikjlg � d;j1bed:q bed;|
fE_n�1� be_�©*u,_WfMolj1i¦fW\;�>m�_Wq�d;bhs�pRm)�v|À��� �6}.pR_Wq sn©’d�° � \rseol_WZ]\rseikfWgW}6�4j1i¦��_Ebeghi�s[�Dd;°�� d�� seol_Ebej
®\��kik°?d;bej1iU\6}!y,t�}9~W��¤��6©
~E£1© � © � © � d;�k�l{�\;jl�� )©!��©
�v\;j�y*d’\;j*© LN
‘(� � � 68# %�9���’:
‘(�)# �Q��� ¢�j>��_W�*©)��d�o1jlg � d;ql�6ikjlg�)jlik�’_Ebeghi�sÀ�Ù`%be_WghgW}>�®\;��seikZ�d;be_;},~n�;¤��6©
~n¡6©�u4© � © � _Wgh�’_EgD\�j>����©,¬�\�qlq�_Wj*©��4j |»�¦ikj1_��¦_W\�bejlikj1^�q1bed.fW_Wghgh_EgDikj#\rbhseikªlfWi¦\;�vjl_W� bM\;��j1_Esh|
��d;be�6gW©/Y[j��1© � ©lu�\W� �¦_7bn}l_n� i�sed;bn} LI
‘�D2��%�
�'(�)
–
�� �M9H9���#”
�
D2����’:#&��������
��P�>��'(T?# ��U�� }��’d���|
�1Z�_a¡.~�}>ql\;^;_Wga~n���”; ¢���� © �%�kgh_W�6ik_Ebn}�t�Z�gOse_EbM�l\�Z�}�~n���;� ©
~ � ©am�d�{�_7bhs%t
©��’\�fWd�{1gW© Y[jlf7be_n\;gh_n��bM\�se_Wgcd�°>fWd;j6�’_Ebe^�_EjlfW_/seo1bed��1^�o
�k_n\�bej1i¦j1^)bM\rse_�\��1\;q1sM\rseikd�j9©
��������
��P�>��'(T?# ��U�� }�~�¯ ¢��’¡”;.�����6}c~n�;¤�¤6©
~n�6©�t�© � ©r¬RbM\�Z�_Ebc\�j>��t
©r�1\;j1^�ikdr��\�jlj1ik|��)i¦j1fW_Wj.se_W�k�kiש ��4�fEi¦_Ej6s,q>\rbM\;�k�k_W�1�k_n\rbejlikjl^)\;�k^;d;bei�seolZ�g
°?d;b�j1_W�1bM\��cjl_EsÀ�®d;be�6gW©
Y[j�p:©9��©*u,d�� be_Ese�W�.�.}!_n� iksed�bn} �Y� ��
��
���+�K�N��������
��V� �$!$# � %�
‘(�)#��
*,��#”
���-�-�K��.�/21��-‘3��%+���=*,��#”
�-��� �K��. �>#B!C’�D2�0E F�GHG 68# �”!”�������P
� }1q>\;^;_Wg�£’�”;.£’¤6}!� \;j � \�se_Wd }
®t�}9~W��¤;� © � d�be^’\�j�¬�\;�1°?Z]\;j1j9©
~W¤ ©C@D©ry9_n ��lj9© LN#”���5� ����
-# �Q�J� � �)#��2�2��� ‘3���Y�H�����
9H9��-���Q'(�K�-��
“.���_3
-# �2�P��
5′(�)# �2��� ‘\� �-
����Q�K��.O%�#”���
�5� �:f ©v`/o1pTseol_Eghi¦gW}1�4j1ik�’_Ebeghi�s��_�`�©l_Es � ©� ��1beik_ � `c\�beikg��4Y �7}9~W��¤��6©
~W� ©C@D©;y9_r ��1j9© � _Ejl_EbM\��¦ik�n\rseikd�jÙ\;jl�:jl_EsÀ�®d�be�D� _Wghik^�j�gOshbM\rse_W^�ik_WgW©�YÀj:m�©’`c°J_Eik°?_Ebn}���©.�6f7o be_Ese_Ebn}
��©/�1d�^�_E�¦Z]\�j9}/\�j>�Áy/©v�.se_W_W�kgW}%_n�1i�sed�begW} 68#��2�J��
5′(�)#��2�K�-% �K�`*Y�����)9Q��
5′(�K� � }�t�Z�gOse_EbM�l\�Z�}
~W��¤;� © �%�¦gh_E� ik_Ebn©9`cbed.fW_W_n� ikjl^�g�d�°!seol_�Y[j.se_Ebejl\�seikd�jl\;�! �d;j1°J_7be_WjlfW_R �d�j1jl_WfEseikd;jlikghZ ikj]`�_Ebh|
ghq�_EfEseik�’_�}1�4jlik�’_7beghiksÀ�]d;°�� «�1beikfMo9}*~n�6©Q;�~W� ©!�4f7sed�{�_Eb�~n�;¤�¤6©
¢�� ©C@D©6y9_n ��lj9}.�)© ��d�gh_7bn}l� ©1�!©.pR_Ejl�’_Ebn}�p:© � _Wj>� _Ebeghd�j*}.m
© ��© � dr�®\�bM�!} � © � �1{l{l\�bM�*}’\;jl�
y%©!p:©*�’\�f7�’_E�Ý© � \;jl� ��bei�shse_Wj¾�1ik^�i�sRbe_WfEd�^�j1i�sei¦d;j¾��i�seo¾\Ù{l\;fM� q bed�ql\;^’\rseikd�j3j1_Es[��d;be��©�Y[j
pD©!�!©lu,d;�1be_Esegh�.�.}>_W�1i�sed;bn} �Y� ��
��
���0�K� ��������
�� � �$!$# � %�
‘(�(# � *,��#”
���-�-�K��.A/Q1 �-‘3��%+���?��#�� �
� }�� \;j � \rse_Wd1}� ®t
}*~n�;��� © � d;be^’\�j�¬�\;� °JZ]\;j*©
¢.~�©C@D©’y*_r ��lj*}.�1© ��©’pR_Wj1�’_Ebn}�\;jl���!© t
©’� d;�k�U\6©9�4q1seikZ]\;� {1bM\�ikj��l\�Z]\;^�_;©�Y[j@pD©.��©’u,d;�1be_Esegh�.�.}
_W�1i�sed;bn} ��� ��
��
����Y�K���>�����B
��2� �”!$# � %�
�'(�)# �&*��B#”
����-�-�K��.�/Q1 �-‘3��%+���\��# � � � }’ql\;^;_Wg�¡;�;¤R; ���’¡.}
~W���;� ©
¢;¢6©C@D©6y9_n ��lj9}6YM©.¬�\;j.se_Ebn}.\;j>�Ù��© t
© �6d��k�¦\ ©%�6_WfWd;j>��d;bM� _Eb®q bed�q�_Ebhseik_Wg®d�°,_7bhbed;b�gh� bh°×\;fE_WgW©cY[j
��� ��
��
����Y�K� �>������
�Q� �”!$# � %�
�'(�)# � *,��#”
���-�-�K��.&/21��-‘3��%+��� ��#�� ��� } �1\�j � \rse_Wd1}1 ®t�}>~n�;� ~;©
� d�be^’\�j�¬�\;�1°?Z]\;j1j9©
¢�� ©C@D©1y9_r ��1j9}1`�©S@D©l� ikZ]\�bM�!}l\�j>���)©1`�_n\�be�kZ:� shse_Ebn©%t��1sed�Z]\rseikfR�k_n\�bej1i¦j1^:bM\�se_4Z]\�½ ikZ�i¦�W\�|
seikd;jå{.�Ád�j |À�kikjl_�_WgOseikZ]\�seikd�júd�°Rseol_�ol_Wghghi¦\;j < gÙ_Ei¦^;_Wj6�'_WfEsed�begW©zY[j � ik�¦_EgW} � \�jlghd;j9}v\;jl�
�dn�®\;j9}9_n� iksed�begW} ��� ��
��
��������N�>�����B
�� � �$!$# � %�
‘(�(# �N*��B#”
��� �-�K��.I/21��-‘3��%+������#�� � � },�1\�j
� \rse_Wd1}� ®t
}*~n�;��� © � d;be^�\;j�¬�\;� °JZ]\�jlj9©
¢r£1© � © �”! �¦�k_Ebn©ãtÚghfn\;�k_n� fWd�j �O�l^�\�se_�^;bM\;�1ik_Wj.sÙ\;�k^;d;bei�seolZ�°Jd�b]°×\;gOsÙgh�1q�_Ebe�6i¦gh_W� �k_n\�bej1ikjl^1©
��������
��P�>��'(T?# ��U�� } � ¯ ¡;¢�¡”;6¡;�;� }c~n�;���6©
¢;¡6© � © �”! �k�¦_7bn© � �1q�_Ebe�6i¦gh_W�Á�k_n\rbejlikjl^ºd�jÁ�¦\�be^;_�be_n� �ljl�l\;j.s
shbM\;ikjlikj1^¾gh_EsegW© � �2’3��� �P
‘(�)#��P
��
� #��S� �P
�\#B!������S�B
��=/Q1 �-‘3��%0� }>£ � ~��7¯k~n¡”; ¢;¡6}c~W�����6©
¢ � ©�� © ��© � d.d6�6��\;jl�� )©��1©rpa\rbe�’_Wj9©;�>\�gOs��k_n\rbejlikjl^�ikj
j1_Es[��d;be�6g,d�° �¦d.fW\;�k��� |Ýse�1jl_n�aq1bed.fE_Wghghikjl^
�1jli�segW© �����S�B
��?68#�%O9���’:
‘(�)#�� },~;¯ ¢;¤ ~ ; ¢��;£1}%~W��¤��6©
¢;�6©a�
© � �1bM\�sM\6© _:��� �
9S
�J���5�af ©�`%olpTseo1_WghikgW}l�)jlik�’_Ebeghi�sÀ��d�°%u,d;�6�’d1}*~n����¢6©
¢�¤ ©a�
© � � bM\�sM\6}c¬@© |Àm�© �#«�l�k�k_Ebn}/t
© �!ik_Wo1_�}%\�j>�#��©ct)Z]\rbeiש�t4�1\;q sei¦��_�d�j1|»�kikjl_]�k_n\�bej1ikjl^�ikj
fMo>\�jl^;i¦j1^�_Wj6�6i�bed�jlZ�_Ej6segW©úY[j � ikfMo>\;_E�a )© � d��W_Ebn} � ikf7ol\;_W�RYM©v��d;bM�1\;j9}®\;jl�úu®old;Z]\;g
`�_7seghf7o1_�}�_n� i�sed;begW} ��� ��
��
���� �K� ��������
���� �”!$# � %�
�'(�)# � *��B#”
��� �-�K��.I/21��-‘3��%+� }%�’d;�¦�1Z�_�� }
ql\;^;_
¡;���6©�u®o1_ � YOuz`%be_EghgW},~n�;�’�.©
¢�� ©�t�© �D©��4q1q�_Wjlo1_WikZÔ\;jl�úm
© � ©�� fMo>\�°?_Ebn©�� � . �K’:
���/Q� . �P
��*,��#”
���-� ����. ©�`%be_Ej6seikfW_ � \��k�Ý}
�%jl^;�k_E�®d.d6�� ��ki�¿!gW},~W�’��¡.©
�;� © � ©l�)©>�)bhbn©�� 1��P
�%+�)
5��
��P�0��� .H# � �K’�D�%+� !$# �7/2′:#”
DS
�-‘(�)
+� ��
� �2�K��. ©/`/o1pTseol_WghikgW}��)be_W^�d;j
� bM\;�1�l\�se_aY[j1gOsei�se�1se_�}!~n�;�’¡.©
�6~�© � © �)©D�)bhbn© m�_WZ�dr�6i¦j1^¼jld;i¦gh_ ikj d;j1|»�kikjl_ gh_n\�befMo��lghikjl^ç\��1\;q sei¦��_ {l\�sefMo ghik�W_EgW©éY[j
� ikfMo>\�_W�v )© � d;�W_Ebn} � ikf7ol\;_W�/Y7©*��d�bM�l\�j9}9\;jl�3u®old;Z]\;ga`�_7seghf7o1_�}*_n�1i�sed;begW} ��� ��
�P
���&���
��������
���� �”!$# � %�
�'(�)# �+*��B#”
��� �-�K��.0/21��-‘3��%+� }.�’d;�¦�1Z�_�� }�q>\�^�_�¢;��¢6©6u®o1_ � YOu `%be_EghgW}l~n�;�’�.©
��¢6© � © �1© y%©>�)bhbn©*m�_W^��1�¦\�beik�n\�seikd;j�ikj�seol_�gh_W�k_WfEseikd�jÙd;°*bM\�� i¦\;�!{>\�ghi¦gv°J�lj1fEseikd�j]fW_Wj.se_EbegW© ��������
��
68#�%O9���’:
‘(�)#�� }!� � ���7¯ �����R; �’¢;�6}c~n�;�’¡6©
�;� ©���© t�©>`�_W\�be�kZ:� shse_Ebn©v�>\;gOs�_E½1\;f7s)ZD�l��seikql�kikfn\�seikd;j�{.�Ùseo1_aol_Wghghi¦\�j9© �>������
�?68# %�9���’:
‘(�)# � }
�6¯k~W£.�$;>~ ��� }c~W����£1©
��£1© � © � ©,`cbe_WghgW}��)©�`�©,���¦\;jlj1_Ebh�.}��!©9t
©,u,_W�1�’d��kgh�.�.}9\;j>� � ©,u4© �/_Eshse_Ebe�kikjl^ © �O��% ��� �)
–
��
W���
5� 9��:������� 6�� �=D2�A
���’>#B!�/P
5�)���2′(� �?
�*��B#-. ��
%0%+�K��. ©# ®\�Z:{ beiU� ^�_]�4j1ik�’_Ebeghi�s[��`%be_WghgW}
®\�Z:{ beiU� ^�_�} �%jl^��¦\�j>�*}*~n�;¤�¤6©
��¡6©apD©6�1\;\��!}._n�1i�sed�bn© Z ��� �K�P�,[\��
� �2�K��.&��� ��������
��Q����'(T?# �-U��0_aE�FHF�b cA# ��U��BDQ#�9I
‘�’�D2������T��
‘:#�� � �Q� ‘(��'(�S’3�af ©Áu®o1_��)_E��sed�j#YÀjlgOsei�se�1se_��6_Ebeik_WgW}v ®\;ZD{1bei¦�1^;_��)jlik�’_Ebeghi�s[�3`cbe_WghgW}v ®\;Z@|
{ bei¦�1^�_;}9~W����¤6©
��� ©apD©9�1\�\;�¾\�j>�¾�!©*t�©*� d;�¦�¦\6© �c½1\;fEsaghd;�k�1seikd�jº°Jd;b�d;j1|»�kikjl_:�k_n\rbejlikjl^�ikj¾ZD�l��seik�U\W�._7bajl_W� bM\;�
j1_Es[��d;be�6gW© *?D�1 �-�)
–
��PWY���”�)��T [\��'(‘3��� � }!��£1¯ £����’�$;.£��;£’�6}v~W����¡6©
���6© � ©9� d;Z�q�d��kikjlgh�.�.}��D©*��\�be�;\;i×}9\;j>� � © ��©9� _W�1jl^1©D�4j |»�¦ikj1_:�k_n\�bej1ikjl^�d�°�� i¦fMold�sed�Z�ik_WgW¯9\;��|
^;d;bei�seolZ�g4\;jl���k_n\rbejlikjl^ÙfW� be�’_WgW©)Y[jº�;| � ©*�4o*}* )©!¬R�®d;j9}!\�j>�º�!©! �old1}!_W�1i�sed;begW} ��������
��
����'(T?# ��U������=D2�Y/2’:
�'(�K�-‘(�)
–
��2L ��
DQ
�2�(
5�,*Y��� �:9Q��
5′(�K� � }6ql\;^;_Wg)~W�’¡”;l~n�;� ©l� ikjl^�\;q�d�be_�¯ � d�be�¦�
�6fWik_Wj.sei�ª>f�}!~n�;�’¡.©
�;¤ ©am�© �!©>� � shsed�j9©®t4�1\;q1seikj1^@{li¦\;g�{.��^�bM\�� i¦_Ej6s4�1_EghfW_Wj.sn¯>t�j�ikjlfEbe_EZ�_Wj.sM\;�,��_Ebeghikd�j�d�°�� _W��sM\�|
{l\�bh|À�1_E�ksM\6©�YÀj � ik�k�¦i¦\�Z��6�®\�bhsed�� sn}n_n� iksed�bn} *,��#”
�-�-���K��. ��#a!?’�D2��E���’�D7�7
‘(�)# ��
���68# �$!”���-����
��
#��A�Y��'(� �?
5�)
��P� �2’3�5�K� � .�����
� }lql\;^�_Eg
~n�6~�;l~r� � }9�1\�j���d;gh_�}! ®t�}>�;�l���¾~W����¢6© � Y[uz`%be_WghgW©
�;� ©�`�©E��\�j��1_Eb�� Z]\�^;sn© � ikjlikZ�ikge\�seikd�j�Z�_Eseo1d6�1g�°Jd�b,shbM\;ikj1i¦j1^�°J_W_n�6|Ý°Jd;bh�®\�bM�ajl_7s[�®d�be�6gW© ��������
��
����'(T?# ��U�� }!� � ~��7¯k~ ;>~�~;}�~n�;�;£ ©
£�� © �
© �v\;q1jlik��© �=D2���7
‘(���-�C#B!�/2’:
‘(��� ‘(�(
�2[V�-
����Q�K��.”�=D2��# � 1 ©��6q1beikjl^;_Eb��v_Ebe�¦\�^1}.�)_E�^@vd;be��}
~W����¡6©
£ ~�© �
©���\�qljlik��© /Q’:
‘(�K�-‘(�)
–
��J[\��
� �2����. �=D2��# � 1 � ik�¦_7�.}l�)_E� @�d�be�!}!~W����¤6©
£’¢6©�t�© � \�ik{�_W�×} u4© � \;jl\;�n\W�®\ } � © � ikj.sed�j*}.¬@©1� o1i¦�;\;j1d1}6\�j>��¬@©6�1© y9\;j1^1©c`%old;jl_WZ�_�be_WfEd�^;|
j1i�sei¦d;j]�lghikjl^aseikZ�_E|À�1_W�¦\W�@j1_W�1bM\���jl_EsÀ�®d�be� gW© ������� �2�B
�2��
H
5′(�)#��2�7#��X�Y
-# ���-‘(�)
5����/�9Q�-��
D �
��P��/2� . ��
���*,��#”
���-�-�K��. }�tR�l� `%|À���6¯ �’¢�¤R;6�;���6}c~n��¤;� ©
£�� © � © � i¦_E^�_EbeikjlfM��}1t
© ¬ad�Z�d6�1\ }1\;jl��u4© � _Wgh��_WgW©/�6sed.fMo>\�gOseikfa� � j>\�Z�ikfWg®d;°��¦_W\�bejlikj1^:��i�seo
Z�d;Z�_Wj.se�lZ ikj�jl_E�1bM\;�*jl_7s[�®d�be�6gW© � #��S� �P
�\#B!Y*?D�1 �-�)
5�O� }>¢��6¯ £;£.¢�¡$;.£;£’�’�.}%~n����£1©
£;£1© � © � © @®\�jl^�\�j>����©ct�Z]\�beiש�u®ol_�_54�fEi¦_EjlfE��\;j>�ºseol_:bed;{l�lgOsej1_Wghg
d;°�j>\rse�1bM\���^;bM\;�1ik_Wj.s
� _WghfW_Wj.s��k_n\rbejlikjl^Dbe�l�k_�©%Y[j � ikf7ol\;_W�*Y7©1��d�bM�l\�j9} � i¦fMo>\�_W�9�1©l¬a_W\�bejlgW}l\;jl��� \�bM\@t�©1� d;�¦�¦\6}
_W�1i�sed;begW} ��� ��
�P
�����K� ��������
��2� �$!$# � %�
‘(�)#�� *,��#”
���-� ����.&/21�� ‘3��%0� }1��d��k�lZ�_a~n�6© u®ol_ � YOu
`cbe_WghgW}9~n���;¤ ©