From 8f93f7f8b6bb58acef78178a69846a0a77e79a73 Mon Sep 17 00:00:00 2001 From: kossoski Date: Tue, 8 Mar 2022 18:22:56 +0100 Subject: [PATCH] corrections --- HF_cc-pvtz/pes_s4.dat | 9 ++++++- Manuscript/F2_distance.pdf | Bin 4435 -> 4435 bytes Manuscript/F2_freq.pdf | Bin 7724 -> 7724 bytes Manuscript/F2_npe.pdf | Bin 4388 -> 4388 bytes Manuscript/F2_pes.pdf | Bin 11193 -> 11193 bytes Manuscript/F2_xe.pdf | Bin 7982 -> 7982 bytes Manuscript/TOC/TOC.tex | 4 +-- Manuscript/freq.pdf | Bin 10907 -> 10939 bytes Manuscript/freq_HF.pdf | Bin 0 -> 13039 bytes Manuscript/freq_opt.pdf | Bin 9802 -> 10033 bytes Manuscript/plot_stat.pdf | Bin 7226 -> 7227 bytes Manuscript/seniority.tex | 49 +++++++++++++++++++---------------- Manuscript/xe.pdf | Bin 11016 -> 11009 bytes Manuscript/xe_opt.pdf | Bin 9851 -> 10109 bytes plot_all/cp_to_manuscript.sh | 3 ++- 15 files changed, 39 insertions(+), 26 deletions(-) create mode 100644 Manuscript/freq_HF.pdf diff --git a/HF_cc-pvtz/pes_s4.dat b/HF_cc-pvtz/pes_s4.dat index 04aa1ad..c8c00fd 100644 --- a/HF_cc-pvtz/pes_s4.dat +++ b/HF_cc-pvtz/pes_s4.dat @@ -32,4 +32,11 @@ 2.6 -100.10849486 2.7 -100.10698502 2.8 -100.10581861 -2.9 -100.10497295 +2.9 -100.10497292 +3.0 -100.10435365 +3.5 -100.10307608 +4.0 -100.10299962 +4.5 -100.10323678 +5.0 -100.10356103 +5.5 -100.10388771 +6.0 -100.10418171 diff --git a/Manuscript/F2_distance.pdf b/Manuscript/F2_distance.pdf index cf3f3bad9a8910f7d0892b665d6440353a87b03f..77bb020077a45aca4faf2a9c2c714445a660546e 100644 GIT binary patch delta 309 zcmcbtbXjRbIv1~zL9)3~Vw#a|idjnPWIG=D$&$AL1z0V z7AYuLD8TGgFfuSQ(&WuJg7#mm^8W@=vTW(I}pU4<%=44@R>1OWa z;$rUPWNPAS?&joTXlm)=;%sJMVC-yYXG2g$ESH@fS8+*VQAtHnY8sb`fr$~9s;aBM G8y5gPgisd% delta 309 zcmcbtbXjRbIv1~ba&oe%iBY0%ib$AL1z0V z7AYv0D!}YiFfuSQ(&WuJg7#o-x85NW@2J!WNzVN z2^6w)baXLvGP5wWbTW2!wKTGDG&QlaA*dpj%g&CgxFoTtq@pM_jmyNq#E45()z#mP F3jp@(PdESo diff --git a/Manuscript/F2_freq.pdf b/Manuscript/F2_freq.pdf index 3ccf2fe612d3842c57165bc70979f8a8075df19d..a3d734889957533e31fffc6beb8b0a23c00f9691 100644 GIT binary patch delta 266 zcmZ2uv&LqFm^iP2c~YvmWtx$0idjnP61(GVLqMH{=nllN5%=S$z zQc$o^fZO?6T9Vzu(7?#p)O<6y%n?Q>17k-63kw4$CsR{rBXdVrV<$61M{^5H6AJ@J RQzI8AI~zhOCJV|*0|2|MMrr^6 delta 266 zcmZ2uv&LqFm^iPYp@or!k&%UNib61(GVLqMH{=nllN5%=S$z zQcy5efZO?6T9Vz=$k@ojz-TkK%n?Q>S0@7_XBS5cR|_W-7XwFAOH&IIVNwTqprMZ!AidjnPWM8gM3=#RsOx!kH79oZPRz}8Frbd%JxHTj~ zN>dedeG_$y6hag%tP~8bz>-!*lRLPZu$W-RV~-&!F?kk`3Wlis=2twjOvWJdeG`im z6f6{A_9_?|7#V4D>HFrVxFnXOYPeW|1PqJ~EDQ~dj7^O;Tk-cYIyqUmnYuYUx|ms5 i7@ImdI=fn$y1JMco0}UtnHss68rslTarWTVuxHTk# z6H63yeG_$y6hahCtrU!`z>-!LlRLPZu$W-RV~-&!F?kk`3Wlis=2twjOvWJdeG`im z6igLh_9_?|7#V4D>HFrVxFnXOYPeW|1PqJ~OpT0zgvDkn{$55WM>9857ZVEu6JrZ= gb5k=%b37Q*EdnONFhYQ!b-u=3M^@5I{A@m6NU+K7$Oprzo=ocf3u6a43ja)Y~REp z1qBNQn4Jnn21Z7jT>8HGDK3d6sTwX;AOQno0}Dd~BNJoO&671xFgiM#I-3|8xf(f| jT39+cy16ZfdsEXVv?mHFrVxFnXOYPeW|1PqJ~EDQ~dObm=RE6c89jCHgybu=?EGc_=G zb2W6faJDeBFmp9Eb8;~;H*qyLHn6iHs3Mlj&W@|NB(bQZq9`?u%iPq&l1o+9)!&T^ E0G8WOJpcdz delta 309 zcmZ2yx6W>ZfdsFiajHp5vXO;uibHFrVxFnXOYPeW|1PqJ~OpT08Z;6)+m~oU&yRKY1>O}r^%#Ay#c2<3H3>}qV8|+#;9zzcNP~Mq zvyZ(v+rDV`xEz;4U#`5h{duT{3qHLF+m}ZFnA3Q;uCCnisJ;>X0doQq!154!oJV$E z$N76*BGu6V+c5-ivTte#UPR}(5WC*hqf*JJKYe3o;9z}` z7h#l&_9-r!e?$}#TU9+jxPbAh+6Dhu+^_96jOU%dJXt(r#0E3J8T}dS6LXmEu=-K% zllH)ObnyAN?j6;Old)$zSSi)O!1GgVJTLy@Y(Lcl-_$aq)?D-DJuP0-!@l)1xGWN{ za4Frw{4=8iRT#9pu)l=kiB)$%aHRIEJv%=~ZyEB=E8F2OzAvU47G32bHteVd|2R20 znc4B^`pe>;kH3b6HBV+~(C(ElJ##J?&m+QC3+ z`DT7-dof*0ts$;R;EOL86OqKj;V+yVhhI@!xKi+s?iMVMsuDio@>%XVKbz`4I&pq# z7hTvBkBhPjJ}ycQG}2hd*`A(*j}FLwe3#yfL4RF@4l^kluZgjggq`Rl*1=>4zB7Pcu+FzJbhEkM%BI zkBr3|GOBXurFLm-zQb&db`b*}&fsskp@%BVNTXWQoK}vZ9(2tR6XRJgj(ukykY%#CcqpMc}5o z7A{h{#S7@{Oc_Y)FGgA%sKXGiCC`^A96SZWazeo(mTGsR9Is^DBcn8mm5filUdVz` z_#_a_HpK3ynPFJG`eKv%mir(R`h3a_b7J~Aedm-|N~R@b1+^b^G{0tjFSO4ZfGICz z-a5s@C_b4-2iy`m&?J669Z^n5_a|h-QbeXlJ7pj0H>9nf zwqMwBRmEv(z6c@_vNal`Y;oIX!3KSuT7ciLJMyA`P`e&przp2+r&xkMjF?Y*CFwPH z?t+NWwHGP+$gpxv3XHiLKarQuTY6?ytqnI649;5Cd+?cZL!w3w9o!j2(aBQ#NbzAOVq8Wh z-_Su&u6TdrjJEINHULT=^M*}3f7l@}kX{5>lDXsg7(>?Flo1Mzj%_C~;4^?n_d~wx zUB+PX%0b5;;#J}fxU5QclFJ`svs6^E1cTRlQLxG92p)aHvMtyi9-YJ?ld2G&^QL!O zH*rP`E1-jpjb)+G9}Hw&J5YtP?v$jbai0>U%M&n}WI|rKLQJz_B}d4Q{U- zkK-7vVszhRvtW5U7xyS=N2rQ*@pEIyYL)S=QbDx)ZLl2MgZ(+5$45menET^&pwz=E zYt4Q&e{WJwV!2ip=LgcB$6wX1Xh8%$!ybT*BGZp%m85SVDF+j89@(kKl%iy$tX$hw zxS5tb>WiBs5|p1B<1$FWbv!~=WecM8+i9H74Pdl4teTP&AE=n-scCk)U%MqN{tnw* zlJpa8!ggk+WFS(dRHE&ay=u~zMX)CJDAvx#0{+fpou*~0F{`Jj3B^!YL5=_GHQh_LVr6;GLA79>a3 zYy0XM*}iJ4(54le%b6=jy4a_|mHivYN}mrMdYIUE&KgVSQ3SWq3Jmw@ijlG&QjIQx ziH^cjjdbXA)R_<@HQd$@-0(T{b7H3QoHD*XMllehUC9z{7z_?(ZrS~}lHpiOJ5#1u= z>QozoHEGL-F~PJm?-OmOKcgcN-NNI)|AL%cbLEt|Hd}-FBd#oyIL7bl#P3!yNEZHl z6OQ=TUt?485W~2P-l5uB8qObQXB1L!J6dJf<7Ev)hBy@{&*6{e^~mhaf>aHux6!bj zR0)LFy#wg(X@$T$IDfc>A`$?o>}0h2HU;dy%0n_Luk~e4Tw{1_x>>IED}=U7ZYhh2 zly^|{F44=*3Y=;k_^Q8UX`n6-mAq5D$YVb4^Q3s=He7K_O2+9Q+xQJDo0lgz7>b?v z^`?{dbW2f_H*nnOlS$rJ9GuxnoY-?kV zx+8m98Id(Mq?J$9EuIDCXFaQ#@p>rhR(X}yPG6e-WWapZJIZ3rImpLjYOh!|lX11v zKfh(|3$h)(ZZ{!MUevr;<#coCZA5P!40%qrwynphdper1=rDF`RojqqT+{^?~FeN;l=+rM$*KU&K1V>CkRNcUX`E)mh0)=UGel15TI;p z6j5zx1u|i{P8_2^X7y@`NINBTJ@WcGK~zgpdb9o}{L5jQP~IETs)zG+ow|2SL7{k5 zcg&(Yt;_AD*=)Fi;E1t)R9KiIeZls7I8h{m*|wCbBTsm}cg0*+MT}2adAC^A<)a3| zg43Dq3#oR!b6sCv%zJ{I?YF|uAz20Nefwo)sjCBmf#CpVn}@^I&C*invNf?`;8m-mnA1-NKL363IcvhV9{z#g*gD zrb(!%1$G;R!H?=t|K<4lp^_vXE=L`$uT>yl^WVg2YwgcZ(W~*q= z{pg%w%T*azRZzMXv%lT^q!>BxWc6T|ulO+`FmTuEeZz|&v|$H+(oc(7?%;)5wg?%3 zl{8qDIsI!Z%iB`Sx8@tNT}L+!jZmJ5jol$d#t?SsF$LciNr&lYN=(AF&rW|u_9`>p zdanSx>%ipCnA1_lM_o=560z9k-?`weqlMc2#M?MgPRZ^-&%j1WwRS!1U^`=SA)q}h zVo8Xov?GSJMJtVdWe2ZWWO;Go`%wiPhw0O{jNy*5qZ5Sjhv7gb{DC6I(E%$9Ft>c#gXA zYj3~V-B&4IIM)MkP2=kcpCL|*;((gNnhd>3Cf-VBg6r6l_lDk76Dp6~OLE=6-Z8*~ zmBq6AeuJDBmw&VZ4w|Co4&yIDWNpQ5HSL(&6JAQQG6A%a}Q=UW<9ujKgV%o z;13JXA4HbCgEwJ8LQU&)Ud5$BS7e=%+=GvAnj+}vUQR6Xwy~N`V>~WeA}6yY8|vmY zN3-=T)peo3ho^5{kJ{W%o1DI=$XKzM5T->~Cn-*C^aw`m?_GNOBJKDk;$I zHHBuqMD4-JjsCs#r^$;P%OijVi}sND;n|mtME?8>F6i9s%gWy2({GjZ?kzLKE{JL% zdO2_G+ZCnr!2vgVpwc8&`;s5;PoM7_?H)N6_}lI+L9SI5YVjR$Ut*x#v4b8#cGr8S zgIf5n0GUI5!VR)?{;tO0v?`vid7MNB^V|P-f((e0mqt4scJcOnA4w2fd>^qk*3&5E zN%>X(L2DT%ji?4y$sZD^Drn^lM;{lG1+cd^N0q`Rb5B=my0ctEI<(DcUv{(ONONqX z*7b!KtzbZlxR%v>$j+if7Yma-ETkWH@WczqSJD7&$f(KRdxWDpn>J z&O3R#Ue{KaTD4|&s}pPZYBM5S5N)8gJJ@SO=daVTT|+}1FR4daa;fQv1`d2v4SZMb zLmkW3@>BQ3VCh%MsFQj&8c=&4L5;;aa%N`bu1F{EZJlPjHSMrdet(}$F7X%ra}r}E zsS9zhWY(rcv<-LJklQ4c5e>l0u#mz(f-i^7b0(+w2F5Xs{gn(On5QA?O3OfDpB~ev zHQXTX4wRX}l3B)>-c?Bj4R)?&mUPOo9)J4l?Jo${ZQlWLA^x9^j9ZO#t8l5JMBZxq z=rVaIi`c$Bw(vTJ$SY37Uio`uR1wsqRWJoWpkR5Z3@|B1P?W>e*O^aJA1>+5XUeAlvjYETI{*y+^AZJluzV7! zxRRX=SXMz>Qws5Qr2hQj(Am2)!#!dT*gfFNR)2N4gY|CcUE|O?vMl9cfAv z1(Xg_L-~B~+&g#X`r~_d_Q%e1o;`bZ=RCW6T68jXUOd7oC$Kl%Za=NsEC`s3UrKNY z5^iUg+Ll*qdNaE=*R{=HT1EYBIr5vLlFp~LbPYcs8KrlOYSe{XA`Q3hh=7gPfz80p zj}DjR*Vp^1;x|XLS`s%nT7jL*SIPTh%a`XV4#ETLmmE3EucKprRV5{GE^B4~63q|D z_~N277>Uis28#HIZAt!~e{+^W;$*WoR)rPDkCcqW98@Ru8uFKYKicvt5lC{|9iF{G zUHv%z;S%z|=OPD9Z2{IuT~Qxx7!Kup5>i0L93Q$-cQ-3aL|7kmFH4kU%$X`XKGcgv zXe;*{k-4K3WS0qS*k+}L6$t`W+-6l^2w|z+^0>rin{X@3mUwcrZ{JgHmSb8N?)>sT zQ5Cc1dMhz(3R2Y}8329e@w2{KmW`P4dGP3V1s5|w+`;3dxs5lY{^}q5aDnQEj9UVZ!y_>d{&9Is$+p?iE{h~+yVpokJs7U4e zSEk0;VQI+Caf8>gxWDktWzRV-GT{!(($%l)5nMtCOx^h=TJ!>QOJYLXq1F52uRY0t z)76oIoWQ`F^@Gcv$Vjt5Kku6p$qlUk!O7xFlF6cGl=l7yBSPYJ{&@JW4`(-LN#|7r zBX8@}LXQ%1{OUFdL}VrXP?BdGRe{(0C##p(la14kKz8eKDYK6A{ezyK9+oBJxK{$u z-lGcdsHxDYB99C_hV;)WfPRVG7bMRb^b>{Tms&51Xg9C6sv64#zO|;WSd3RGczHeM z%{BE+qW)UM0vN=r@*jD%aH~N;EnLk1@<1}-&K`^N;LVmspiRu)5A0Bt)miv=oN^a0 zwj)qe2~~Q(L7B(>ng?fx?{r4**WYpMdi;0{Ag&RfI(0e8b_Eh~-fXjxWPz(aDx!0& z@qZo!cA->d4`*joqEh3U?c%Gp$U6BYOsg~~{Bm8cw%93XG_H|}5<$>jSsgM~D1tdnOr@r4wHQh?KL|7k0*2A2#hJxWZtW}Tdt z@8<&r{3K>o4PNNhG7J9UrUdY{&4bCku@fhzGvfM*u6|E7(|ufMK`|2E$81ze35+SN z5z)&85jR=Qzh;ADSh&ovVwPk@fGzla3#$o68)-w)H7amlP5J-6t>Hpi*RvWwnj zweSc$wBQa9?Gzs>VGD0;RF-HMO6Yz(I(tizJ6zD4+{Tq21Cf=^%+R7eCLv$?$Vsjq z(d`}4-MGayh~j=n6zxeUpXAu79t5N97o_cPBP14aQ>VQmAtyf-;*z>czV^FU=H}+c zipzUSE1NiX+B#X5DBZ|4D)MWX9M&Cw^E8fka^Trqo-D0!R(-`r1(?xURYBp*s28nU4iw zee~OtY}$Kki|QvE5HxvfKTp67*4-vQ+|T){c&kCiJqa++)n9_O;#x4_U_u>Eg^SrO)DZ@US3zW3Y8d9%4VVB;w77DA?MA);1*5$ZLy4l290y3d zk6Y3sZkkO#hK79ie8EgkW;U;^Q)$!iuzP` zrh;vyV6GT#Hzwivk+s@~qT}FqGF=V5=SKV&60hT!+e#1W%w0#^x^ufUHm9M~fOHA^ zzmmM|C^HV}zwtt!S`m#{<{Nw3jVX&s#taOF6%Wu=&2#!IHOd-$sMe0%_F|)Cuw#ml zB`qm7E5@?zCr8eQ0TKA0k0x07KPvIHr%~8Q=iBSPq;I<$J$fsNNe|Z@ZmrY2OFH2J z1sHLifdH1LhEwzT7K z_BfeOv2Fvi*REnh)#kHw?!J}_Pu=Z9Jk6-Jy0E>cmn)Kqo$bHMY#Pc7M^PUt@hG@D4FniT7B(h9Vk{(8x1-Xi?qCQYLSWD- z6#y~9yHoD@!(=%~9b@_g#2D_lRvG#{r7;5kYi?8;TwD+ExYmsj?HKfEtEnaUxuDnS zG1is>A}R(n-rVgBc6HEktoZ7C7|g6!TLZjwCu5^!9Q@alhrn1=N4RM9d3X@Isz_HaeAhZqqX`Ek|lkoq6ZdUe2idec9J_RQ2loJ1C+$*sxEbzaiS` zsa5;qxZd%*)@M>r!W613*ppqkdC_9nr%&}veb>Z9oF9lTFFml@T>ij&cI&tm!@}h4 zZ(Fyt&!u;!BXnfmu=l!ZNS1kaJ!)(f(66&H)z=Pcj<}!!XT<|XECtN=8E?y zd3y83+#`Z1b`OG%#JZg_4yun(1D$TpTdC`B>g9jvzRZ1__1Uyu{VtcMl#aDF2i797 zyjMG$+fAE;Yn-}z0BEiC5)!9Z!LknSn$QoOV2!;%zuez!mS?&(4wWrP{3~H=g*p7B z>IK734NOWTNWsu`aH7touKQNFPAhwx;zJ*WjI&0T}>%wPA&Ifm~u9CVMFV{W5~p;WKctCOprcNR~h-^WL2FQJI=r zUk%mvq|G<}X3%#ieP)L0-HZi6v$Y+68;^}FOBK%4Heu2 zwdaDLIQ8*zmS~_!+r`arJ?GP{FW%JRbQWEwR}?4;aoZu%$Sg~W!A28X|6oB^H;yvW zj%k&;mO`(KmKo(h#gJm_WUNz&f_)25X4u?8CEkl57;nEIyx*j1>BTSQ*)QNiMu^f< z%5(}0)GrA7eWyn_7Ll_p2TfcNb&ZkWcQE3)?t-$FSKfn=N^KLf@SmfXj!3+-Mf=f} zH+NV9TD2Lk72>?~h4BiV;=J}LdzpOlyXL+{ttupXHAZMM{ACuZjrD~-c(1e+Aj0PK z6&*Uk)kEfM0r#b2+re5>uNCLd`h@C+c?PqMr2on9!WALjN~g~yRynTW6>e60EsFHb8e9c}G}H*IAYadF zUd`4hhwC7$jZmW|pbtV9peWHb20bJ@9{T2Dx~Le~(2Ix|EPBFIO@Drjji#;zDQlm9+!d zkDiThp(Zgo)sVo@NL8G?%zW!lTPrv2=gb2AqEn6i_&DqHK7&A6INKsvn5%J39kQg- zGoBE`+GyzY{ISkt!4O}Dzd~f%ug=-)v?9vaD%McDASy`r$f9;X2b{WL)!vMnWV>2F zk=Nt4-&&f1t*#ilnq#+V;dEXec9i{->!g$}xo|}2aqKct(GgitR?5S(EBR;(N1S6) z(2vhpS`a zcw@+b8vc9Wzv6&3aME&or^)Oj?rL6Yc;00AeXxj(bm^d8@}9mfCrJh2+Q@X1Y4^sf ziaPRGFReSjMVX(@>w2gQdzkwCQyl(yI<}IapjO*)c=o!~DJrhc@j3)^{*Ga_|Eaun z%JAtIAyaoLLA*kDr3nHID^v)KIF%**CVX+FjQYVkv zXMEpHQxd#T!&bWh1g+Yg~_E*)=)5Lgmq zF{MkZ2VUKHnJONdv@>#Bh%DtEfW!zwxr-uWx%6g=k}4E`zP%XM*-L~6j3C{J?>dj? ziSHT?+&8?q_uqo2WD)tX>okItVt``Y?u*uDqjzkDfL(kQ_Z7T#V?%ps7*XHMOx9Ce zSk_l+9kwLjy4Dcns)dbu_=!;>@ZM$`#L?SSF;zp+P&&0z8JXRBW-JjC!W;>Xk$1)v%mAOx1POrvHI=l z2zl(@B}eY7p7Jm?QPTt@{VCwoVZe4-|D4CGjrFHSQwqx#YZw^WCR%y&DZw1&GWlsY z@b#vn1wIS~IL5N2@hXY#*WYZ6FC<&jA2G66+pIMRpD|}kuX9DbBAj8WV2&c&eNQj0 zqw8~DK(llLVI;#Du1M&j#l0lPtvrA5TNkB9gZ{N5Pv!V+8SrM)EfuUn{G7AT^wHbE z=CHd$P;IV@!Y@*Z@ zTiUxld3n^xIp$-Wyrzenw!%g18h&Rtv1i5478pJjYd`aEEnZI`qa$qRq@_I5fv%js zWW-P|p4YL+MpiIlVCPV*&rH{`7n6y|R*#<&>aChokJ*UvETG3S03sIHu==V%k1_DC zwn-|?6?Rc8PLQJR(KeZC*>_t<{|z@i_KMT1Xh5$N*(89WK3?5{@KnAAvr%={?9Y_@ z?=&fX8H{5!XgVN;`M|AY((G1!?xuet)_q~}iJ10xl}uH*DrnD?r%S90SgIu7Ho?R3 zwEL$g{LK8!j4a2$$7shL#FAq|y6?~Z0ERRvmrIIL?~H!I4dm>%)cVVF$5gghzeay7 z-l;9e*LEvAKho9fM>%_K^0W+GsJ{a}QXPW0_hVGpo>AcJP zysmJdWb9-A*{~P#LGSB_S-y-+{@;?0OGyC~$DtvQXly`|s7 zRC9T9+}#2L@LW43>7nNAT&?nj+~@&K^&!pU#g zxj?Ee&R{-OG#>`64Mw8CP}IMSDBJp;!9NL;Qy@8*jqM-#tW|gbCJ_8P zG*vVP3`TdeM%6p zGno8e11JQBfd3B$fr|(V{(&Kpg2@KIC5HIJgn%HB|4TY=2slIpj+7CCA%26>zrD*y3rS0e i{l5$oatR4?H+M9~-5X>5lpG3yBLvAgIOLxwkpCYxyv23^ diff --git a/Manuscript/freq_HF.pdf b/Manuscript/freq_HF.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cab2fe4ffdbee1d3870c6e23ad33614621a512e3 GIT binary patch literal 13039 zcmc(G2UL^I(y)qj5D=7(0Yo|>p$6$qM0)QKAV8!9lF$W|CPK9 zgLDuDM5Ky-Pf*|2_ul)rbM85RI7xPAXJ%(-XXe?R2^?CA%KQ)kF%pi>j}Nm+L_mTd zl=W>ANlCC8!o?oz01^ctI$&j_6BdC6ft8)$ScD?N24#zomL|bq(FnLRiC1ckc~2#i z7wP)G!^GuH!#A-9`RWreQ2gh$O}OKQB9u#4wA8fxzgJ<0g)cRW8&5ztrA{NspH^T+Y~{^eau3O1RO!?`Qj5vyK1 z?c;l^tqPIJ;hlsj56nYEm4xyFv^g{b0uGj27L0#1oVXs1jg=0fEBAJf3JBkqb7u6x z3a~q{G==bju`4VVX}x04eyq+ve0HTtm#@WJrrg2WieA12nj26@AK0^M+aQH++K-eK zpOOlDv~d1j+j%)wSuG#Ju%$jkpzC$YfniBm2kX0Z@@FBropOrteRhG{*C{a$4ui)A zZ&@<0na;7?qx@F)cwy=Vk^M8ulF0k%&#Pl6h3c!mY!35!oh-H%!_3fbywcb3uUy2t z5>NO!Pg?oHLQ0xL)U%ZJ)@so3@JHo*3hR;zx$9vNwaBu3d{&)TV;P(hxfiUf`qHDo z_sjFb`IVck6iCL8zO;o7YddA}D-%{E4|h zj16kbR(X-f^z|LpSNygnMngC{jj6TUn*8^%h4vc)P_5R*R?R@{?Ox~p?P6u&;3HK= zuQ#9CibX|75-}f+ZdX-<6c_cKikxjsFEgh243rw(^7Ol1YIW50fyBAWuoL>}hHnR1 zf<5THYW{-N-jeq4IB=3@_`s;aNL@ zR~uu!S3m6P7?rpSJoq}JNjB!AA(74NLj!k=Ih$=l{Sr=Md{H^x#N28F{b-c?LhR$z ziI;ZoW?$+TA(ZIhHwr%7nM(4d$YfP;$>!OGgq?VzAJGP-IhWOxTB=j#9hRDx@~f{e ztMM2Z6n}V^JVG$=n0c?r<$Qrf%vZT8)%ude)X_CbUV3r7!P$sg>ubW&6dydFcsm)t z%SvN>Rfeh77kX60UVp$Pu}`lT)GH&RIpvpEr7H4{I7pl6!G&DWA;m?5$iczma#vL3 zZes-$Q}C8`YxLEfXsG)>`cdcjum*_@w)R3Cag>X$H%d4(-kAp>fm$+Qi8uD0BrKzH zCgeeU@?BcfWe`v6r^~5lD#E+%{^~{cZSx(i9@bnK8d5YW_9bl6{K81qm!}V}C+a;# zUFsRkVW-+jCDp$c)Nao{wzHPq1atNtBHcW36Q_BrXq@Kn&D5?By3nlJ6c}7L%HcO` z#sL?|S0y`fv%Y(V4g}MHneD!P=JWWDcU7f!Rn^mpa&4jUH8`a^M;7f;&;5|l+tz_Z zyyVP-i=c+NckiSQ7qs3fPA#pjC7%&NPMa_F)XEv1_$}S~49Plp6i$V6m)JYZEuL~s z;)o=j;9Tn*#$@TR*rg4k4(3BPc}eOF%8Gjzo(7GpG(}rY#e%I{g(`@t7{_BI9;m+= zqjEBQGv;#9%ox0n@euQCQfWBv+4;?xa1Jt|rO_vBQyo=__hYF4%8$=0>u(nq>pS-| zzI*%Z@9usXT0b_#L5GIwJ?8?1R(lT({1?+AJ68;Y+Z5;G)h(lg_JW?DwA85Q7X)ri zDPhHi80Vf(M8%8nSQ9Wl*BDhIaG>P8byvp**;HmJBCqC`*YE7fnm$>bH!;A>Q|aAb zt1#POpT}k)y4A?EJWu}0s3qpX3!V_9G=orF=X>47(u8-;`f2Moj#AWF+)^+U@~`>9OHE))8|#~ znUSML5e7nAr!>Ck4OXfvc5*?~7Q+LsM9P zs(EFuNP2Qhtca2XV-yxPCN+1tt`-#T$rQPy^tkC-ZN}7VSAVQl29O(`0uKbi+zv#L?;R z2X-TvywNO?iI4P=XVPJTpy&Gf%Am;}ZI&-8p=JvoF1zjI1Zm|xb~Jt6(r@r&rQ0K9 zz2Tkmbz_aL^fBIv{?`Zew7fgVhJvZ@OovCOipdHXB=%2`!w)m^{J;567i=wg8u+%j z1RG`Bc{Ax3%YHC;^SS$2L)>@+3%yi;;OHKL>?UGHJqAX8uyySAoQ%w~@Wyj3%qFXBa2u_Vw z_VW_Ad5IO}s}xksNA4;+1?y5Xj6Ij&bo7~rHhz{pJx=kwMnuw$ZsrMrTUi-GRh5sjNEq@n~4wx@x!F7LVO}aa+r= zLCuJINhyu{greaC&|$t?167V)v3*8UsY$DN+9i%=k}tPYEi@~`i{fbK@I>$wi}VsI zU$8{PaG<`@yEpLxFvmt<`gwfa0k>uN{yJ+^+>+i zXWkdKn=JG>SS)^om{0#YI@(2L3;pMeSxv!amQi(0blaWnBPIZ20xd) zeTQ)PLRgtRe>igRW12cs5Q$6a-d(IRpUsn31?Itg;YhZVk^3)sA~as$`^3yl@EE#7 zNGry}jE`Uid%T9TO`9I+!a+0)72~PL$5x5kBy)AGY>lloHBsIpP3wGAdd}k-mde}b zQ)U#|x!bcZDrLvv`KBAp^-E++__UboU1>G()2#4OF_OCKsW+E=shEOx#BgJD_MI@R zmMZ0=*|Ry85*5^gEFDm;s~oYsJCZI@!tR3TJgPSsak{!ns|Zo>c+9!l?~)a)?lh)r z1(coT>V{*>OqZQh&YA|K;{sl3rwUV>Xqp+y>ql99GP0%M={?unht^ICypMd@^S{0D zHH=ilW7nZ(A0mVt)iRF<(RoI1B_Lhh-wqGI;4<$ioqbm3lR9Cv{*erJkcx_|+9*b=;knA8P7HB!e;m+ru{k=LiW$1>(|7L9pCsYEIv_oJ64v8xi0nDt*pzf z*CM?$y#I`ZUMNq9J=F@GYQ3S=Ndi-ZNwt`Pm$U$*+Y{tjl@vt#XE)e`v4(`~60V>Y zI>$xTUM&LZ2gA_u4t?rOr`VVD&O&@F!lG^ZV7GHQ6iKamO)Wn1y@ls<_C?|<)U@=>1N&m~Kmj7; z(spcVG||f!UD_Q~kjeQHd=1pO1@(7O=e%Cj&C7}@B|7}ah-ZE>&4EmmRxU4Td}#E@ zCC1`XvEmQUzGEu2N;s$vq1vuyOtleA5u>+=Zsd5i=9zT=Y-~l5phPlLRd~$QYgm%4 z&&OrtbY+;jJorq=+j~lS^rh!h5K$p++>T}wJoesdND;>+$zHio5_0vrWwl;?f^G|z zRkKG;ZUz+X=EPL3_Zvf+Zuwl@Jh~J_mKkN%W0SPM$-FOHM%Zzf*IIMzO|f*lmMJ#k zP95PO)$0QlLtY2bPPN47?Jm)8EtQ7r7nxz9bR#wAj1$w{i3CU-%@+7Qm%-~@J)iE| zhz-~Ke!cfK*g~~f@nr58FMN&Q**(QXvo@txgR{hgZSvd$T0YZ^o~5@ASXwzakxd%L zvb!{_vhrtQrnUXngAQRD3u)78nxSjE`3#M>xaryQI^kYpqL1uhZ|G=tN<1CTbR9FR zGn1`>IP1VkDlZ5s=99;RGsv7&nA`JHmzreR<{8>T?X9W(q2+)jr=a7G&xJigxXKG9 zyto;dMLDl>rM>VJ4?*A7MFZhcpr^w<@l%(0&pjwp3yRQ>|B_(%#4$N1R*@qOgUL0M z@e+9C}cF@q) z^XTzT1n8>pGoetqBw=@U_|7$hw0I@ugsdv#z>@NtMu_8y=k~n)q8kKSO=cA4BB;>C z;_%>qwZW*!^GuoJG=ObSRSQDt*iMIj=B^rmhFQN%s+P{|n4gy8a| zw1(kz*RY8@dG+_g7#MVND4nlf)I_KJ0fUo_h0)u2n+SKfQ0wlSY( z-?m^zFVVwomNj+M)h8c=K!L)-Y_F!yXcel=pusykLKn%qQ^nE5I?B|nUsFZV#0#E- zlA4TGRLVMaCGmFSL}&t?8gj-D9y`@)PLSIyHc-~WP&xUi5+J@DYsnn)q)#z zvqtw>+tRK35mK)mY^SV{2-P7+L_>mdKpmbRf5GEt81pzP89L~*x1OXBl9f%PFn)XWzU z_VlLMgx%-&8Cl z=wKp8_B5Mra8b}{O5pHf8;5&kMKHdiCe^vC=g+)h9_d_BJ6z?WCJdtdBzQl1mifb% z`L$TLaExJF93`t#sP7ZO^^39dhvHC+`RPlgSA|u8CwHj5FTdQ+N4L1A5;ynBz|G#{ zO3b}^k!s-2^iG6xP0nFle?h2R{jie1C-;KiMl?}d30^UbDguHo_48i8*kbg|fJa3WHLWk6bM_b8psZ&(ebmKg?v`>VuH$Lh zF(IPJhB5RtO>o!8rD9d#VTS8vj@$BlPc*LEb_9z1F?+DvA(xr0ON>N#5i7*T?2_&1m<$OIm zcG$6& ziDRM}pP%3N(A1yF@cv|9x`gcI?I9(JvyCKh ztFDCowIF??4AK`zFVz*K%|b}asHQ0+O*fUYfs?s<^-k>@L%(94Da@MX4P&;_C#)OO zrS~|EXgOKbxzky7B^7+Enhoequ4a+ZjhMY6$`TNaVI%7%3L3m_RqeKMjm-BfyM6O3 z*$0AL>}0B2cLyx-QUs@2I$o$!(|xJ&WlVGw4RPx%s3NjC!5Ykc+ZVJ0T^J&2o4Cic zo^wz9B!`+1&u!%uv4Bg{rs!axw(d}j+LeUgfCf3IX=xl1bCn^E20J_TH0|XB8&(BlK5E@VN4^`W>SNe#=5@ z#Z6Twy;Qpi{h8onit7!$1ZZmy7txOt8aFP#+kz;rE0-;2U3?7QEtOZ5 z?QWv;qZTRTv?a|wWqB|br1SaYXR`4>W$j|d`Y&>QvQW(xA|7NB!l|nVp zY9N<>P?xH;EmE8&+26l>C*AeqD!ssnYTUKwh@u?Bk^zvi_RPk+hbN{rH+9=fLD}NW zPpW)3p`5Kr@fqwK%{{5Zp_ld=hZt`-^DL(~ZhdWX;{;dzXqR|XzVAm;s_(_^$u~6(T*GG# z)v~&+-MLAoSd)8`Zs;dwJ6{-ayP0d@(`mMMD{6o;!+1+ASF&0De83@ZlVqOD7Y0F( zD4n|6UJ9m@Wby6mZnEfUN6)vPNWXjYETfI-((;M!K?5^)FVIy=%4p^_h>+$C(Htj2 zFPf`9Y~6P5$7E#bESiuDcGRDU3K+TsyM0qI!t2;!EpgO)@L53(;_pC+&VATH!JY6D z?63ZYYL!CwL2TP?y14b6D<5@u+%1_>w63zXVHmCh`4rqKLg(r6!gw$n6=Qn1y2HpT zT#igNZ!^MD7u_Zj!|ne-J$xhyXTybhA9xqW(vwMONe?|XHw)giaMf=5?b6wgG3~q$ zdjEY9+}s#&=SS<%@tkz3|D7Kj1!7m`ny&l(`0zs@@SRcB=X7E9bW}c4pi4?~+aTlE zs_&w|R&Wo=21bAGJJCq>rQR2=*X1xLHUf#crej>jfK`NFeEQInJDL8a(83aUy-&XRSV7(E@{O9S1TWkZwWkjc+=mVVcn z2{`r}j2kz347E!QFC|g+eL7yXcFDH|Uni|W4#dkDKeW0k`WP0e`~W|L?{(}RY$5ED zE-8YCJXI2IBX=VqHXb-<>1Hw1J&`5QrxF(F?Q;nWXW{`l-Of;Ow~D)E*$#Pw*CZ+8 zLxFC+nGRTAO?)Tp&A?1Tb;(?4xcr4PU3f_2=IDzdrrv4Qk?hyDWeXOLFp;cp2T0rw z7^ed^FyOMO7Cwo%xJJ=5X<|%Iq}4Vt*^R2kcq0NX|~9n zKF;E^DB#O-7$Y(+3!+_-Fu7}a3C~|iaUI8qNV3)`9%SShffzRFD=fDn8&)x=h9p$D|nr2+7`OH z*yV+BH@uqqj!P-D=c(YE%cm!gS<{(IXA5?38j4xm3Q4%_wkG7x#EL52e0aBB0^g(f zi-hj;_?2$;gs&_=Nb$Ns?n30<23sIM+w85Ai_`GqdKOiGN(b96GitWBXFo>|3v7cUB3kOEr*vxYXPJ9vv#UTzW^I-!PuMwU8Xp!5Dvvy-e@6R&y04O|N;r(H z2rFrgQq0d*fZ{=EXecIfLOMNSTi@F3rG)jSQfC+5KX3h6U9Kp8xeqJD7T7z=vMrFC z#m|2No7p*>okLm>t+=T6k&W9|%QGhMClDmrC*EUlwF2?47NjVU$u}TLRSxG@C?hDh zO0oX6#_EQA#8{1@617&JlRJuCeZ`eZCLOEn!+VQnxmURqP_nlPTZ%7t8$3c0u{l%%}KyIC@fH(0SN+FXoL$EB!sKo z0AK_L<&L&NV1TNQ78+%vi@=(Kfw~U}tcUQz0(44V*c-a1q!1iKfJ7MukV7D+9iY$y zRsi|{M+^v8AkrZLK)>X}P4Tl}1aJcc1f5EV0fBEJZ80EI5}f=xB<3K1gFBApAEY?$ zKS_U4D!{RDCzSnf7QdudM_}Q$zz7KPlh@yKi~Wsz zNN{vIf3rDV=I>E)67heI;<~>E<>43vPBGw{+G@ILn!G9qCl3S`X#+o1mm&gVgGRby zQD_hh$KrHRrz3zmk!TE7!2ym22|>YX@Lz2RObl#@w8c7LOi7?(xQYJ!6A}^v;od)C zBI3fJQydZz5mC^;z5ycupg%u`xXbJ|AqUP)VLLi0CYI~za_;%{`mV#=09NnpT+?# z;2gvSsCXh>>_L!IqXg@^TVrwFh_iUW%zit=>F6IO{TCe=XF9)`0DJBt=Ym20)mKE? z*&zUj1w0gR7!j~D(#0KP{x@5kIsM5MXM=xR+o_3Zz?~8Q*(~LOI01wSekep7Bqj<4 z!9;}2ab;Y43`m#+EQhhd1quKN_&D5E1%b48_|?VDfE&Y6l7Mdlu8FjfbFp^<;tL5_ z7mIK<00IQSLLG_00IE4PWZbp_i~vIiVhk5p4h;-|6~Rhi6|e?a8>|O50Goi}U~8}q z*cOZcpUwuh1KR=N35*0gft`P@9qa;jLAoHoC@>26bOpQO!kH7o4*Ro(#t8{_MWB%= zTd*4#4aR^mNG~wP6>ft7W5HMlGy?ecM1kGG-e4aD8pVC8BcO(j5CTDPmj9>s7QGz@VhDw6^Fv4rT?mbr|Bb&XbdlxR<0Laqzb82RIH~YlT(zH#iz=a zC1nF~B@uqy*t2z`v*{n^KB&CZ}c=sT=w7 z1hsOnPYo)wdVEw|W~jf_n;WN+3^po|Z3Y#>%%Ev2+g1p?7 z$(Qv}`_<-;?2qT8oUPCrCaU?Rcy-3Hsj)SB38~49>G>wrlARtJ@^*azV&4O@xE`Q; zdrcUqU#KOg#WOZY!nG}|b-Z>Kx~dB!>xw>avZPZxH#RhTGKqDxM`hb-Q|Vn@R`64N zo6l4T)1$eh9+kDC^Ih-EB?WvP)$W8R8u;3qdPE}kNOG=e&p+a5*Hz%USDEe5{e(dy zE$>LTlS}tDB|bwad%QE9G5bc|dsMsP1L2 z%Q=>V>*_ugVk%Wj!)kFaMpD|MG~Q zdt&`2+>Es6`Z44VdC7%K>2qn3{M&c8-?(g6WxN8>VOMX`5?@eZ*LQSyI+1xXQfW4h z)P@XV(9@Wg!eB$hi+{^=c_p-cOXkDiE%x2YvaD@pyetqQeo649@$)p|YHf3nBNj%v zqR^*&k^UcpTiwPvHN1AWzQ{}xixCG~3=+gO!M_S~^oY%9JP?P?5b$=`!1g-*KY4&e z&18I58^Saz##`RAV`q{By`3(vFU~W3r|E6^HaoPMUDt96X;n|KBT}sa4oZF}ppqlp zp&bLRLq<;d=*5}X?ArHc1z}wieBvi7qwm_c&lMlPYhrg|HJU9s??F1&x8pLkBSuqJ z6|NjHXyXTyUf@`tdA#3PKS{iC9ibCuD?rmge8fVb$RwI^@xziIH!(qR+lv0&D(y4b zh|<+|zRwReXHBc+KOZ(l9gC(dN+vOTSvg;gym~@EYVhTycMIZ}J-a_E^CVemE!F*S zIlhLX-%ivgMG{Kvvk6lm+EgEri=jlF$+#n=4ai~UQ_uGxqFi-ETEl+-e0JF4!K=8@Jd8vrYMnM4KXNk?!3zwqn^NvQSmdk&3*KI9JXw%TN^B{ z@;REoZ)^-J^ZF-LTNh%-NiFRUd22C`(uFPxOdG0{Bo4%WElK|3iGO80xcgzknA`WQ z=eJzcck?vHr+DI<_-RK`Gm)aK0$((bqaV0F93eFC475Dh$)!>18+0!!%|JW%_FYlc z6lUN2++O0nfUX5`Y<Q?J?Q8bj@Z%)Ls`GQB*_Gn#VI3o(11fm+Yjw7W z7pB2&Qbis2`7Bxdv)HOy2xuf;>jrG699)Pvo53HYa&i7V>4k&x%z$V2%YO{CUQT@q zA=4fj6dWY_7CS&sk(j!?NyZh`zHV_C@nuIh)?NC@+I04U3y-hW$-TEqYjhHy-3Pws z+~2$OsrmdN!58=s)_(5SsaP+5r>2U%-EL~`h-_$oV(D)i$; zPRL>W=jwsYUgsM0!pg2fZoIHzIJQC% z=C^DXY;@i(3;XtD{h?8Vi7F*lQQjN;BO+U^qV-Obn^_6;q4Ak4%2GDf zF}vvdEC~jK&_UT8gYVJnU!X)~`2E*RCh;>!*WPqEI`$Q~A51eTM0?WRM|d%$=U3s~ z5OgfXUlHWy_Vh7R6?_u0aI3Q0ApP5pZHu~#X=!;?{Re->g~?*ONNVE!aM_ziDFi0B z)|yi?H=n}$m?XUXS3UGxRkS*G0Ya{c3eJ?>fWZntwxlq>z- zG_|hnabQ}I<3|aGUJza2T#SsEt6#)h*BFe4ELQv`q`qIlqOt1EyA`EZV?oq!27A0- zB+Oef>RpTfIGJR@uFq&hPCiF@{phU~`zwN|iay4sj}-$#eyl!jWzO;UgwA^FJbdtx z_1fsZ9s`7?30k-mO%^S-_nt%N;WrzCy|0B~U!{*)&znphS1t5^^CdzWeV<>P+P_`g zf0dBeRdXw7cDb?YrjSqKpvs=o?psKA@Fgn9gUIgSI8fVX7gd_)PI6rPVV_b^!XF2^ ztsYk25ZoMK&|#Y(<1?)zc-XaQx96`l&Z-|5?Ym(+xTn!Fo^g1z`8+S}(leg>C+Oo2 z_TiAt6}@Yznp`KlR)P!<1K$k4(Xe1_PKcDT^F1`=+}7|yQ@8BB>2DUdr@F7Fw35DPT4<>W3FXZF&PfS+e}?~jgJVVfpuEwvLu5jI zxoefus|hmOR?VFzwRt(AHqoI(OL=ZN+xXqmat1Y-r=2uAO5IDrF$b^oS%^$oo%~;I z?eq?YeIQ%7Yc+JjpnUJ^0d10@GJi@6-(`8NW$-g?k(a3lQE}|jOYGH#y$lj$}Z zP}|JZpJuvlrc+hTTK zqx&EP8OR6wmS_CRkuH0}!~3i-aYgve3dm}F_cL?xfKtizJCQG5Ep=t-Pt@@mt}K=4 z(Iys-aGW2z&?+f1v#m$q7)~S8VUQ($e*QC2{ah#Ov+_%xDWA_A(x40lLBJ*-&i0adrLrS7^>D{~H`d;`3`>f|%yv}cCQSLyD+_WPvPbDsL6Zx`z zqzdwr5+qjS+v1-&G$6ptlI-oFlJ|$c!r%!P`qph-r(@W9WvlceY*zYvnIpDcFQB{w z@m&cx$%)EYoD!SEd^3&iNG&J|F5FSKuyB8!F|YKcGukcO7r%nix8^v{A>EXZd6uwh zKQ{na#|VYPtc%^~%N{3?(g~^6U8o7}F7(f|#_7HN&-=^o8~xvhYa?~F-zRGbko@@T zWGyM<1sv)f5m=Bl!XD`&#kp1A%n3r;N^u&Bs0*sQDj*z?Dn4k0u8)SEjgO-Z%$8F| znnY3t4&+l1{9bTZe!J5ju3|vIWk!lkK}SuQ4Ts<*;pOb=3?vpnUd~P~7zr;a&QlTz zpp65AIYFl=SVt*NBXunh7KL(hL}Ecu0hj=UA0osDvO@zmE>9HN5d;ws(*cWhl>mc1Jv{|Hg#=J&doTnBgMkI1U?`Lyz~IMtyI|p7{4N-FV7^m9 zkVb!zxnKlNWfHJKIfIc#V2FSq`1eG=Z+}RX3kWwc+#2PMmEv@FN7_n=*+Q*_VRknB zwxS3@eh9=)j9(CV@!N>P#o@v>BEsSj`0wdl{}A&Z^8o|EghGHGfR+T1G_rNKL7=5L zZ)mB3ZaAPY*q^x$5KI6n$_f6p{Qs6zz~204EdU$(OAV3$j)XdJC%5xf1X5noP(eVY zfVL>7SP>?GeYvbUA@IW|$pns75!juH#_UR7| z{kL@ncU4#a-)qg;8E4iwJPAdVjk_~&xxcCS|6(-%?R~bj`Ac9|ceK-~huGSH5l#r4 zY#3mxA%MiTHWGFyv@;yAZ@8-~kc5C^0ka1KcF8F%2@GP9SSN(^ssG72VShH9kT`#m zaDuzoOL2Pf+am1X?oL=vX*)E+%~C~K0O5-HxgkzS>7R{LQt;pGfR^pAgdQ;4|0Vn1 z=76(_{}um#aQzQPaS8$g31A=KzrvI>3FyD{`tLFNJ2nFmUy9Qc7kU3J_WzMw`5i>K z{!p{$Qjj?4w?Bh$J`UgkUVn~{V z$O&NR;VgpdkG=lQ9fjuly+!}(u>cB?>A8)t!TyDU+ePlba>!n2gdLEVgou#fqUp~U zNK`~bNCadD`UMje69aN}xEILf7YqUw5(jdI|9}aKia~+Q=D)y1ME?yYCRhgL}C9vuNX`S$Q}QaR!l??NaFtk1`!k& z`2&VU!-1?D8u)(_5Lg%Kg8=jg0?HIX$ULnrfWS9h>`evD8U!jLE<(b=p`@uy@;^S! BU~>Qf literal 0 HcmV?d00001 diff --git a/Manuscript/freq_opt.pdf b/Manuscript/freq_opt.pdf index 79f7d82078b0f667796005da69f225f83cd58a60..7068e5207453b55943bca99c263d3bcbb7adfce5 100644 GIT binary patch delta 4492 zcma)42T&8*wxyRKARVbuhy)>$KpI6#AT&V&Qlz&8l}W z$75d~UW(B;3ff!7uah9hP2uR{S%f^~s#kx_)Z>VbT*vXsepy%vgc5S+(0@-+)LoNw zI5ni@{G`Pd{(A6OkV`-^zE<>}e~Z1flp^PL!57K&w@`V%P8^RgB|0#A<67*7zok=E z_79zIM(wePyf5O~lqM{Kq!#hBj=Me7VnDO7tnpaN)c9h#E@_OPQ+;0$sZr!#i^CP}}W8GV+WsmVy64{Tzd+u2=)$D4h;DSny< z8;kp>9eQv|aO+{f&e5_neN`)T-`_Q|mO!R)I@$UF+unI}V`?bJhxGf$y#u2bWkpSg zzmGrvxL??X>wowmWqUKDRkNj8z4dVGa8#JGr~5(7O99 zs>AvmH^cp)u@fhIHS@l)-9g#rBD)%H4MRYqhZRcpm$R>}>ql`FJ8!ReaG7dPdb)7m zsbFWR{FeScpfBBj0VC>O|!7lYy7&l2yi#%I$cFLEt@L<76e%dAW zN<%8?=Yi1n5RLSvX6QDmF~dPHg)6c`k;1FVsr3+$>^ALVoHz zGwjlQ7ZP#ZokQ_g0V^KFnC(fBntu|)%8l~JAq^+>`o{u2Js%R%noP_olzOYyI3v>vaD<2!|hSOM}# zhHV4tRj~9VClj)se!;3YaKzwBHNK%Rz~3t1`}arbj{GkUOWQ?)?Sb2ZTk9;AL~&s` z_qGtX2b_5qvgKTU7&{Bco*n`I@bew=s1s*ANbUUH;G)SJ_Ume-8^S=HTcT5a-FDQx z>QU4AXhkX7>_w6yGc3H})d^x60Z7g#L2^b2ZPSbC!nYK!ymP@BBvUs&!b;i^3*GT1 zsRxnbu`)06@ELN=xS+vpH#@gm$-Ox#H{#aDMqh8r58J+m#EUHBx_&#(AlQ$X|lpJ_LNKkOW1gtF&nEMmed3g~<5ZWh`BwMhH*A%mOsg-x*9Zc?$PyObXn~&Bx5jiIF*rZ$sg~=Sb zeeJ8?lFYBWuppr4niB@@y;pRTXnZrh#Kao5PXKrd*;i(l`Eq7UCPw%FN~s*GC|Q-- z3b;S3VQ{lpz1S3M@OH|q#M<#}nvdgI38<-kqL%JP+1nf z54XeSdFg%)ekEL7zn+T8h7(XIb5@Ilv#Q_UWgIEuo~E=*^UdQ>^8({?Xf?hCoLb|x z)5_<`>`yY5fM$TvuW#bCGyR>5zT&a-H{ zZ}|!->~oDklIqDVAUgwrIg04Vpwm}%l}9Al=<_Gem{b{pHS)Z0I*q4&sFx_&`I=wT zuon!B!Y2VRV+?$sH;q`Q4K%NB4v2ia`P+mr)UG|k(_Z=Y+(Ol(Vg&Bc^C>Pzk_*H6 zn(cYvWg?&RHe}SX1NF5$OM`KV0u;P$@?IKUj_N~8~2F^X2 z19*#&WZMT{Z6(`=hOnLlVJz~a8Q7URn1)0Q%j-#SBlWYljeEr0*NR1|R7Zan4holv zLF{dKkmv2J(<|&W!%a~W`%!S<4~=`Z84#fEii!)NW`||6W5OkP z?p`^HwWV$3&km6etG}@}B$br|_hmCK6ssF_Y|tngTBmcp)T2h|L1jXL3> zlp=D#T*I3QiM?U-{m(I+t&3DX^x}fN!I$UdtwhtI3la?NVWva305h?*cCIF_R2tE2 zC?gifk8y|+ybX)_=yu?9xXwNXnv;Bd;#JSIeJu>}<;15mNV5|C7S*Qh<<8~63HdJe+d#|PLhgo?@kt2} zv#pg`ip0?`I~A5S{%w-0_s= zyD4_d)oiZso?+K*3MZ^{kP^m(#;olCo8^}lc|W$Rz-K_Z&V1#B#`)MLQ7W75AQJv% zbzh5CP+6C2s;;7vQ0x#AOzM&o_S*fF#Amfe0rU4A&JPB9b}KD#bAz!MYp-rlyZCdH zJL38$>~!A@m7>9?e_MF$) zm+WtR?^bpTz0V^@;5~iJ1)5y#|4w8`MMgG>ElSTNx31nF+aWPI?@Rgp$ckj&9GeoA z7}ECi?g|ro+9YsxM}fv9{XWd#V~aWyRFv_KGg=)Rz?C06Q(vR_S?ze4t+d)9tJ3M# zB13l}<`lyho`@R*CLA$KC)KiHK`Uw;z2EoJl_EJpPYyg{%;#ffxPs&Tz};(qcA2(O zZv+ahEW2^rrb@ENo%)W$!a;1(Bwaq6R&c*KT zGd)k8e(ta>+tPhkXH<3e@{J)8qJE@p(xu={^x$CRMP>jOp&imS^j+sI+Zo2W9^|NX z&RxTlmkzQ0?{13ffCXBs_hTcf2M0dt@X_p z;EX8}mgfI?*xruc&QW$tL?%Nu=Jq?@PqV>Rtr8Yxd-6qRUNncTFo#Z13{WWFVv(b`AjCeTD;@KCL{t5hJ{TERBSXGD<1;NZ!Wo&QC3H$) z!S1({{?p-3A-u@2-fOmkLgupH6gvYjwNr=`GvXD$4~hsEGIM%cQu)5|ZMv8n7hh4t zsOA&L3q{b*f@D21LB;q~tm4oCTzGU9j3&CG{x7U-dMzQ`5iWzTDx)&wIkpfu?IrqC#*%4KPqIZJ4Y&e||Cwr|( zJ&*L8cTQO~W>5n=<_h#=@M=7xEZ5!NILL|xs1n-(rux|DcaOp0*7=Jmtyz&+`SlcA*qUwmK? zk>KhB_>=j$c><6?DDbaa1;vC$)nR$)CuLzMJRISQghB8~yek9-^FTqMe-6am4GLF5 zzzI+k3`NFC6aN|UhqN95Z3$IXLm<@PNHQD<7PY)V076V%Aw-}h5UmD;s{N~|h9n08 zqyCww*lB}*Mtm#{`bWgN52t0BRQ@t%>PiFx(ZK&U3{-|HE6W3vO#SeBu0aH_p4wjk zR0WELsv;179t4t&(T2ldFyLQ*1O@s60sl&%swybde`0VbLis;26||}{d0rMoLZkjx zgTqjN=JUUG;mZGqE(!_%I}i5v{>t#bVF=j2d9wf0JRJG=CMYxebpcoazpVh!Q&bywqXI8!Oz|~BB>|i=S`r_xgTD)6BfX;Rw z>P`6TdDB*I- zgR{A7g2tR~C)oW{|C4huMcI_5!9lddd|irR<@bD<6+!}AZtks$n|EO=Gr7N%e|}wF z*VDZu^Rwi}jWvDk9*p+>K4IUnzm98lYfU8~ZC{*e)#R-r(h8H|jsfbePP`;xk}wo_ zUKWc;+N7*0{FiI=EYSp^@N055u!4fK?a@-?vQoCf18jXyMO{Ro-^aj8TTf%+fPd(d zR9sMK0WHoudT zj>xy+&sxb8l}V@h&;wSkJ-q@gzcc#2Hw4wM)(8x>mf9{~-CWP$86T~_zwoMnjo;<` z%g8H-o7k<~qnkN%{%W5;&9y}zZG5iCVD_y1Ri!}i3PqV%H9E*foX$0O%yyg}9R7S| z)jU{uRtUt-zK;BPv^R*Z-5wTZne+_;zC~1W(BxS&>#XH(U{8qaMT#4?QV$$KN&ISIY0f>Pt036qEbP!66;tv3G$Dzr$$XzB}g(FgS?#^c?tGij20j* z$3_nYGrg43T5jA0y_`vxX8>`@ux-zDnYZjB?+RwSMdkQHRZdFm$&GOnD>hz(;AmHQ zg1ux)@k$@WIqmtlN0as{wL$BGKFyBQtJ}zQw}Oj#vPGeLOO3RWZMyg|{rc8)EU0ab z_1R{Y2x01sRVak8`SiY)KeeWuogTMm!)=tu1*-OmE4C={2SKO-h6srd+AbCKzP9Y{ z4mn;ycp((@OmyCYLsCl)I;i#jd-g2~kENmAs~Lw$BAfEBlzT2cUh+Yj)rYEEBgr*V9K~B zohs{@$>V1xn<{_;rM$deglJ;@f_U#_LyRKS6Y; zh?WA=V3PA9-zr(TtRl`)nP}%8C7fnZz9*`C&0N|(y5b-^U=#X+DK(Q$_xDX)aVkplYgEc8nJuuxkRld@X>0^{WW7R^U>MBlP^B{ z%?8f4xs3Ez_b1JIGhb&p|B6~)3q#Te%?417f_MSyHDGH{4jwS}g|v zZ6ux-8ODRQnp!Jj#tQQ?k6XO~pbzKwXW2`mYs`#44)Gs&V%Pn#^Rm~D9ouN$*tQ=w zgNm1RnA#w06gE9{2J^=9n}Y59e0u5Pu1_f!ehv{|HwUzuHOA8He;IsZ#nVHV8f43_ z^RlVw%>|1$!@5Im=9q7`)dV+}PmPY_H)>j#^&LjHOM8?1{2VJE67$&jc&93~yMK&1 zYRErVVa|l*IYqV+u$Qlqiz3RT7uC5IKSBIBBgpbn<&8S~w1OObAFLZlJ=B$(nhn%C zm*@caSgL~CS3Zxb%7?7(&Z}^V7A*)YP(1ZkH`(L>d-5I)9i&b*m;0+HVQO4o^y&#r z49D#tUF_%slkNe7#8_E0{6ztp6BMi~+tPr}jI(4?Uu&!vHqlwC(q84&Ee7|k3mGwA z>Iif%ib&cijV>B^@H99qM9O$!uwBeN_!#AYxjIYnEep(ko2h63$Gu*ooEErW)}=hd z`mE}>0Qp{{pxfQ<%=bolonL!Ew@O`c)pP-}PNSel7k86$=AEXWlep>V^U`B5@SfC& zb1B5>ZeeFQc1U-`ay@>3sU`p0)!i3>3rXL*RyUih2J}zH9cyPv2J)D>*xn99zkYJUqBB#)=4|jC5+G-hl<0zWg z;EQ)TkP~wXXLgT0*R)XQfvvQq=DB0#BPls|IRJ``pim0 zNQI)ygy&vG6E0F1!Z`uqofyVNx<*%L>9z(?>L!DFuZzYPE5#R+r5$(B=sT?PZ}4HU zo^J86a~u>%tCpJ?S|L!mD8?OB;<@#+hu<6SVduW%Xps9`ZQp$?kGRw*4|pz8IGr&* z{mS0W0cq--E*;N0Pb}n)Ug&UM(|)(GYJuT*HC|{?h`Qy+QadBY z!m#M+Nymk#NcJX|h3V5Zt+UuRmxc5Q0+)CVKAr z9JTB=0s1bbxors<1C^F>$dwx<$0P8{a%{0D4ZU(P#-h~Tx;?o;trxFiXQ1C67UA{F z)Bd_1tT2quoh7-xY^mnB+g-NkF6?f*(S3NO%9AyfyB^VFqkig;#`=NAoTO0_Jg*uA zlN?FD#bsMfq#cn`P0KPcD>{i0j^2*=n(af1QdZn>84-A&AeU$j%Yg!zs(;sp5Zg1Lv>_8%su~0=FE7qX)iow2%w_9GFNL5 z_FO~()miuwvMuj*`jFpRPh^gj5Tr*zEAnRhl1DMdA2J&7=upO~dIr7Qv?Wl5&-z^H zFF--Uo6u1-Q#;xrK{Uc)40a@L?8`6#?MUbHB6>#c>A0jxCI%yJil=uYJ!=AH{d?P$ zuSKpZPJDUI*rjL@aFN6@?4=ykbrQ4Sl(48_w#KEkoARtE8ae9lb_TX9P}FTRI8-a6 z%8+cN&75-O14H%h@rv4=fG)NQUk(T9un;2?U&#@XlzEItW_<8z03y}{geAv>`O*E* z2f0Vf%G;V^RrjHR`jMDgUh_^fIK2ck&9r)_`uU{)C?}VIhkdx@3>%Ig*mJQ=zP~~h z*ksOm*)u!ASfCG8cdQEuw}t?HW`?>X2CB_$8X)WZk3%_osq~-BI#@_5RPh4qR1yK+ zchZR5P1|5+xSO#+#5e|fkI>TN81_i@+c>#^)FgRx$W*Qw(H93DdYE}@g;+hprpX)T z<71u0oI1|hkSWKsDU_luVj~8p*{m;1%(s;kDJzH53hprU>Q%7XWVKOeR^J{^3vx18 zp1<1SDWBznv&iLMRZEr&^SZV`5P}IOkjt=+ke=yh3>H8q{T^<>B{(^=*;~r_Sj^oh z-_XRIwX4I_d$1PzW`myNio4~>GdBXtMM6v3kjdPwyjv(ok(|>rh9k$pA*U9 zu2bGs$;BMB)YupfrsL>@>A0`t;h`<^W7bGyam24ync?MIyK)7$k8*P2#|oFut5)F& z0U5h@B7f9uRRpVtcJx!O>nmePg+E&iz0`v5iI0UCe{iU^e+UE^K^TNW?y+zbU)g7f zAA2n)==#EJr^#7wil!%FPX#W7tR1A!$J4;&q~M$(-q>Q5w5#hwJgy!g<&JUhM>Q;> zq(~y{@L;+xZt&m^n!4Hr)m6y>@+V@8x--#2i+jj23K?y%o=Ur`6X%9#;p*b`DHn({ zBL;`-z9Z7_njTa`^@4BR7v_KAjW7Jtr_g!c&8-^}TL)LKbX%ggO%Lnzn4T)wLtMaH22lDiV5RlHbgl!ECYQ2=P!-Eb6nLOg4cf0Q*ZDFx%s;W<1PU?sTCAZjWWPh7EyPE3j%?0fy=t0 z5U#Q?m^)e)`uoU2(I~hR9N`LcQdGpD!9oAbNCImE&=xQSB^X8tio}70B)N@l`h#VS zoMeN*7GSgz7^d`}q7o8kD|Gjtg;EOZiT@K!33=R(pvXVUY-|!1rMmQQG$W@VFc=N~ zf8=kXJoIRo0u1vTpGoYVIs$`%g8%&^P_RE3@Sg`%5r#zlT|;2tus<{u3Wj?xCWb{J z|Ewt@75?r=LjTM~Dj*Pl_aPK9fAmK}VSj3v|MQ9dH#`#gXA?9EhQQ^CtJvvkX)0*I z(VB4BZx$FF1=mnegd(&Qv`~t0EhH4Jrt&`>b^tXsKyZjtP)K-?n>#=efm8&DiRoO^ G1^f%-RE13d diff --git a/Manuscript/plot_stat.pdf b/Manuscript/plot_stat.pdf index 4ce1d77c4524a23aa7322a2c9b70b5e1bc2b1576..668f32e367ad9b6520e78534f717847bcee72149 100644 GIT binary patch delta 5091 zcma)7cQ736w~i7Ly{^?;5ZzkVS}j;a@4dGutJkpDSVDqTLX<>_=rs{ttQJHUJ$koD zM2*gO^ZoAJ`RsTuQun~bBB9!wXgV4 z?cvDF`HYL}FWx0jZ*Mk4H?Kd?9*^4I9@DwQt{i^y_9-^P) zkAE#lTy4oHP5TDN3LavpAW;JU}wjI&_G_!ukTI864YDGJu2$%Tcu_#|8$ z|AoCd`!aEnu|K*j*NS`^dNnb+e0}{(iZ%9k)o(rtN{Q~|#pfq8szE%NJ0PmRn~2jEAH~BHPJxew+Ay@p)aTM6l(fkB*z9T+#a4E9DgCd$YbA}DZXI3 zg-5vAWIm3lWQbBf|A{r|66hJf+%$j+UftkpKYp zJF&(gpKmzVzkfQe-eTAs}?|6x*AMlu(FASkx zH)sRV84g+^9z@ewT?7)5&Lvup6E-&m93_1M;Sc6s@isOFm_M7PF$>h5E;w?tQZ>f0 zR(P!Z#o6N}Rqr2Y!^R~D0pEL4l1?jI zNrhQor`PRPVxctvQ@97(Q0FvC$`8Z^`6B$` z4@@&00?{4=*(eU+m}>udsY zb<0Lr7g9s&i(s=ZV9`igRAoFtq8@(9F`*95Yl8*Nl_|a{cS@piFHi|jL;s4xkK|r1dn?!$AZ=G_}(CMZyv3T>{ z#U=XL`KzF_5=JZ3e!pfP&T7TS>4ZlxRG8*i+EkiFx-DOP?sOS1xF#*>gTrC(1ISqV zrx(`FAI;br{fVgG2xirCjYYfiAmOgnu#q@Gb)9Ed%Ubz{)Y6-Thcx9z5oy=G^FV6l z>g&1Vx7Fd~@8mEV1~fI4A>0VUJvWu)LZ|S81ggu-3F>dCX%0Wi=wdkr37ybqCR?s9 z1G|O7{1lFmX0Gvgvr4ifZq^#j7spRT=8m3@h4_kF_*ql)`gEKr_A<3bWB%^4cWY+? z;^_jbd$2AmBiAGIuK6g6For8!$YOnC|1FJ$)4pG|EVGAl_R=@l>@=r0$p{6@`a4Y1 z^IzieOE?sD-$aLWWw2=9_N{nQnj(+7cORBSBHmtLSp&Uppz-a;fUaB*_3#5}^L%m% zhtqsPpPcN9rgVXWh0%pcUE>yae|q2SFo1Co4q5UmXB9&%KUWLdxu#M}kW*2o9h60R z20w4M6jfjAQbR(ax}S6~jgo!(7?}6EOAc@!je7m%O_ptM-HRO8SKIR`4SBEN2gtbX zaPiPf@cis!s-DT#2lGy*Ys(&CD_dM;4V3!V$Tf}mA40$CgS#HaPK}HM>rB4DM+u(y z1Tw9LJ=z&c8SmrqN*~Go0R2u4%V%fro|+I1$I_CKcSJZHIyZ4Q|G zV@wDBI}+6`vGwa9dnwD0kz!sIF2alkKzRO&7dq4N>vOfvsTYZ)-MrOlXTI7+N{%vO zApj>W%mse^OALC-)5GxPw@p;Yp@GI>B-_2$OWm%Xn}wmo>qY_z5xu2p4uo=lCMZ4y z{oOi&Te=V%_HV4_E@!8wy)5rbQ=3pnW|?Z9c<=VgrMZ=eai2ye6Ozp#9)OF!-_0iO zuZZK5;q~<|>$>~5Pz71Jo1=i+%YxCikkGS}gM;5+=ciE0B#=2D3t1|~128U-u@`_4(;ZrSW;gF>L*=(8|xD+?aEHiCheT zn>2PmoB|cSpAF!ai``d?fQ)XwnJg(_;6mEPRk>}TiD%j6ERo>BG!qq?KqdrUWhN-G z_xG#P2`KlY;e~P9z#Ry}nwL|~m}3Q2HTa;gL{KWJh0F&@Z-R~#lTme!ClTaP{@(q% zL9~LQoYJ@J$HUhv4z=)y+K+ZugiY)rCVHUpT}YkP)D zFWa_xDydm+`Y#)MWVSnshStYk?TvpIf4inWj=(^*Y)>{rT!2iQ6c0Y3^hiG!-OTM~ zM5j6a)Y$XKOHMskhkJAbhIGM&m^cS@X4HpWt5 zX>>lO@@0!$t|x2Ffw}JmtFsOo@4GK-+hPFs(n^589<$N+q{+@PPe0VjPa_;K1-@P) zORFD$YRjdLKxByt6af_}6EyZ63h(uMI%Hp$z2RTo{-3U{Y1%7vEtfF(iJH!kmL-)h zj`@4pPycK^N2Y4%enxzaap{>ZjU=BGX`s6B`kB+eVKgMu(ltf#spZ$$^9It8Hu{dD zI=eJ?qD?o!AsY&<`8l|#k6Y)lw(4B&1Sw6~l4b*<-|nQ)8`_>uR{h6x`580KT|c#6 zB=N2Ur@Y)3u|4FA1bR=Rx>V~~;seR=ExVc*s1k+|N3fLO^vugGI+V+FUf-+s4{b?O zS{%?WuzClZIUoD%PMufetRsOw@s!>=_t;DV9%X8UL^%R<8>T3(xQS6T;O=M%xIa!= zV`_ePPn`yxJ$ZcdcvA+eu%oS{({gmvq5Y1~k0rV72>UNjJz6lf?pJ$-|#k=o5492-vn^8!K+m8CzTZ~j;X>Cb!Yg2~6 zI0Mi1O4;IFGt50Zr4-?gHjb&w!RzGMP2{RhodAKemjKp-50=v$Qdns%8ah0-$>dwN z`UJ~^-G1C3`xQ0T+cmmg?r7?zwfp_0OH;+?cKZ!{&a4NchrgLYKxLno8R`?Yp=q;Z**rzQPpvstv6%*8sATxax@w8F&T3d#J1WJv!kFgiU!Plf0MBsXIH^8R(Gy_ulCE9O|GrEvLLp}3Tb4eRVshb zim3$b2GGtLl@~yLgors{u;e)1GSBEecfc}w@e!~Z0i7VU5q7Td)uz2Y3b@0zE=GS6 zn>XK|>uGKP@04-&FYee$pfu?nzgV&$+3Bc4m9%oPYu%8k>V`0EofD}(`<>)YHpg$| zbHyh~v|qKLo|#aovP7}$Vba#f<47MwIuA~4C9s{dm>p+|P1BYsi`RrE(}ja30`2eP zQovyC_hz3Z%SweZ?t`X=$c$C!n>C@JqRrv=FUj|0Zd6fhdD|aPEu@KR8EH&4;dvNF3w}P$tmJqeT0_gV zV@}uhAp85$xkIrZ9T_rG)~bG5B(`NWKdUpFlPGaQY`P+7EiKwVt+o}HRxtGwdng!s z5;9kXg-m=HU!S=h9>yLvMT8t{$%;@>g@6g+OJsQMB++{>tU_(Lk18x)^e&gyYWs2+%gT#REj5q3TN9JTLd*ST4Fc|$EeXp(HeW) zX-s|LV=YFKgq$xDsR~hCM(*tSMvs2QPd9(!95hE71!$E%Ukzc-npOx(X5D2+SIPxB zVf37yE~)WOC9yg+R3NrvZsEY|G2x-rRr~&Nj3Q#=fR$##r0ePUW}q~NkJf45*rRJu*Zri zZ{g@lys?<2^8;1x&XEhn3{ty-z|o0k%o#F2;}X6*p2(IL${sWU*E zFMqUCrxV>u#V=2r-+8clvU>Nm&*vlRc}0V*0lSqCz5I951w!68No@sy`IM9m5&&|t zCo^!l^6%TmDAe7{x6R`wZKg`2B8Yy1ygEvur%`mvU*nSIlDtdF!s;i9^eVceAsiV-zP@k24P|Fpt#it8P?S{$n0R@^i7 zarpN8fraJ~yGj#UIqJ`-t=Dpyc#MmBkhOi(H;zL5CS{Hi^)T^@`%)0{#9b3>FAGrl zDsL(tC>+d?q&ju@r!ddd8ZQDD*|6)sRi3nh9CuE)X+=f<^s|P_`-@`3fW0VAdG9gG zbEf&bJ(>VacGHlD8wQ`#+^kTY)(KRTYv(W4p4L)gW-`$|nLY}D$h#u0)=p4F(d{bE zUQYf2e$MuuB!41r2X_((hZx7-uY{z8L@fsmgy4asguR#~2qG@*1aYz#27#VP35)$X z!VVzGClCp!q!b9^kQz$w_s@t_05}QMNK6_gDFqXUrrH1=0*wNlIfS+Ch5a~;IG`{N zG1$M7FlcHn0R7KCg)^xAGvWsZo_|EFJ!jy-r~O-)w!I$*2bAM~1&c8;5<|tLC8hp| z*JFCYFU9e9F~m5$I7t2#h(RD=vHy!nK*gY`c+9kT(y8>!eDu=)k(UOGr|L7)%8CDH zMhg6YF-bA8|KLfANkdZenPsgd;BXaHDX$kA7Jkn@YK)w2?+!WmLTEbQPEW;`7eA^Se5_) delta 5104 zcma)E0!F7g(0AC1nX|X^>bNL13jrQjl7Zl9Fy|3zkMg=?+PO z6$uF+@B731&OG-!^WNvnb>?^ebIpIwoa@Y79nf}YN+7x=Sa_(#e)f8A)?$CQ35`3O zZ!PNy$sUux@{j+vtaoED`dbF{`)X5OuduXHtj}ug;y|EX8yyu4o86r#SbpVJ!Eh!- zhdcSWGo9AkdUbJnaB+w#ANOuKz1q5D@SKr|8~ZxdIJQHNfb|4E{nc+Vj78n}{K8@; z8L4=ohiE>al0PtS3o!-^HLo!pWkxrJofo2~`Q8Ch+!Ma|OA9LO}gEmE7i@T&dMk*zaBZC-<{l34@n*G2; z(zm}5Neeh?J`B4xCEBtfHgIU8MTjX>-5uQhr}N2zAe?UDeyj z1XD5$B>%JplI3@qARd-HH0!aTaB}FeR@hlzP}@FBYcsS~K5=h+)2t>7xA&ot;v06H zPf*ohe)7$=xY|Jw5dPpfldAZLz4NC)3_7TrdamOUFgg@B@^wyOtKzOgta~1>V2jR2 z))}+QvPhaFvE*? znZJY^DukFA!X}~}?Hvp_rtV58%sG2kw&R-Nl#zX1jFI)wJFy@&W*gPopNBAe`Wv}L;?o82#LRFL)OF;$90k(_)6FU^7#0_#}N?sG80F0#oLr3 ze40F?9_)<7zMoYxZes*#x3H{xYmd7;B9a0Mc0C7eJfHmpoi!x)K))}S1coy+y&`Jy%*>s=BYDioav$w#F zBXcK#a!WT6c%=s=M#>d>Jq+t=TdXQi_PNJ0qh;G_H5T8?hauJRt^^&>iZ+G>4kc-O z=(Yx^o}P9uUb_&Xr_FI|IBCWi*1PTl@m9~zgGY`0)suJ()#h(xS41<`j*Wy7+O`bt z0?%iRNS<$o$~vtSw!M%Rq}PcxZitE5db3{cy!vN|tAuJ0!RyrnNB0X6o9c0>&O|!+ z#$c^n_s*ON=^V0_o15-3h2B)oSx+dOh{rWf++y2KTU`Nd9@Q^Gn{#TZFTI0rmfe*n z@FuPOHS}b5gF;Wtwq86oxd|)!ehkxAK6I_R-m8gn*^LK=5q8r|Ot191TU?Zn5!~)E zNv${ZLQS)66)B~Stu3+nu5`@EC-2obVfMue15ZW24Hmx#e_ExkPIG6)m9Ff+1Kpa7 z#q5a|Z-=1Sl3;$hi$Q1MvERiosS_34tJFHR1S3V5!B+Z}x9RjJ?KmWjmx_d@uCX&= zB2&mVg$3U?!I~%v*r^2MC-P;@oQ3K=(tOpIix*2fC!<-3q<=Ow9Lt)QP4vzUAr|diUdf|02aAl=@sK1^xR& z&Z4t{?VT|Q;L`NJqerpq&B(>ZV^yLZ{s?j2$Y;F&_p6owoNVG`dtxTh}&xN zc7_O0INRUvLU&)ZkM7=t75snMOm50b3y>}1Q>AH;9gA!Y&(K1sX?OGc>({Fu(p7-L zY^3n${moxPW52Jrb}(3M3^sr1+AH))(67y%tDoxmAwN#O@2sxwC8Jv#W4fb8s+C8$ zViCAFSb!j3o6&0V>cPPM9z}G{*st(yhU)YNN3kH~N2HC8Vz>4uXzFj54!Y`^WN*6Q zzkGNf7h^&kJ-jsic++{oP**Bp$u(|e({q7DSIQ#u8I?Uy#lb3#8X(Z{@Ild$-MDYW z*!~*pxdA&l>DQ-ka=Oq8Mt8|qWy;#53@zF!I!3XvX>&e?95|SEy-~u8Vh&mE_y>#q zoJCfku1w+rTQxD}>B}W7nZ88p$umpl(HwnEG9)SB$WpJ2LthT}L!%V$DSHGx6_FBl zxH*IfF+dCPTKxR`(kI3a?sdKwzGatCNX(@&!rh`)w3LGbH=);&I;>Cqhb(NS`3b^> zV+1x^pt}O6mp`Iwp+8D~uigdZI70fL zvtI-vR2pobZ&6jpT=*JAuuIx$a0Q!2+tws&4%;Dr-hWmJ%!iw;kg94FGSk*v$xi^c;`eKGMH52FOzgt6{vONkn#vRiM=5k zC5j%FS4Wq&St+07ab+b(g2;0UmYsASz+o6t!5~i=d0{yr&rWNBxU=21VqoKpN6x{l zKoE}u470A56g~VfRM}}k!x^TetWlu#R*GqjnaR4^<>MxW0$8u7dR7I0DR6SBPAwaN zh|>!Bv+s2>&3s;*Mddd2Wsnye#M7O;D?brc!%-~o_PM}~B%*lp3=#@R)k*?DcUoED zI?|dr^!H!lF{t<0sXDMeW+o?(5sfAr1VOaj*Lm{Hm=ZwiRcL(UySZ`b&z z`0cWlefA$5Yc*`+=1edcDS)|0%?^z}Hpi6X@o~bI17C~$;=wmT@ytuL0nH}pM{5V7 z_UPLVR|#4ubuxZ<7gL;D+OL_9np|me{9=(p6B~$-idqtWfaKs+(2XvKv16rW4NJ%A z1gJw(_~|SXlR8xqsLiD9^1aS-sENo`Q&WPbewe$oqrCfOrW2tk%9CS#pvBCLqk(}R zuB=UFFf}PpWZ6}-)X2>lYbv+=+OT^Pld;6DQYEyU+>wE|QavsiMdQhJn;wt1%q1Re zyQ(G{Troy49`i~gj?;Nt>gV{W3Zlw5qSlm@D-~A+SeEQC`#GGNE0nRAILvrqQJuks zI<&7L9!u5SN-bu}CUp3Y^s7>X0t@@^JhG+@y>|GK(y{q8Uav`z)xkqh?meGOURxkh zlciV?=fozn*U7457f%fm*O?$ zSIU{BqiQRqv-iAJjFiiXTHA{Y@uOayF$RSD!L>dxTO8|!!#$2g#A(;yO<5eeJ0(P~ zuIccYU-+p`^~xEI1}>_lxnC&V?uFQ7up!<-2O(Yr{>s_)C*2=2>K(4OG`y7}5xed} zY33$Np_h^n<(-3CO}Xb>K;lQ2aZI$nVCBEQ2N{jmt!Ym)s607hpLB5?L_~cp?u5;H zU@}yHYkQA5=A?EV3^y9ilTf1F|JwPpX<~u06{Pcha$8O!CkW?K_IUFI@8?UICu;M&@PHjfi>o{bVI&xKJUV?h% zi$M$XwB(8y4Jpv>UUc})QGo1fqX;5iBeBeFbOV}q+~gpfcR13Pg1%*MH<@OgN>d8Y z8uwX_lC~NmtGl`CD|n?u+$!G<;&1ilvzchz3Y6{qUKPwQ5OUk!XI>)d17W^qjax-x z#9(RORBx)-a!PD>)=qn!p)^N!whMjlT(zdELz{nWp`&BD;G6#Hk8uK0C|+YXXR#ZL z)sLp|(?$}f+@TaU3v_TrDI=!JZ-3j=!h*iW%C+HYWt{!(x&aaeamnFzJmmqz;i`Eb zzp%4j>(}El`Vr6k6lGO1mS(}iz4Q=v`O3|=E@Q3+%jrJMsglxCxS`cKasG6YuU0CK z$!`jaCdu4xVqaknxpMM~^VsaWIj;?nEqj#~%cN-(nc?{>9gY3y(j%IRwPX9r_9bPU zDo%p0XsnM4a5&(sHsq2PS0Q!$nQX4s@}W`!-#X|1Os_-a6QPcb^@ZVFT{B^KW@JON zcT;nmNVD~_}%he{=TFIjMgoQ;j|hv43$rqv$VtS+5)R@eW9D%5TEWNv_{q z5c;wiaZLPsYY_l*UBj66?o^)*>qYo`vw?$-Gk#VX&C`YQuZitx?uCi{+|2z_bAO&I zUGw!(47%TNP1w6Sxp@4mc_l=?AH^V_aw*pS`6>HSIXl#=I(vyz(ULRPd}F>%dUcON zCCuNBJ}EUIRRR!0Ac$Xf*rngRFQO(&q#5-MW-F^Sn9D$Q z)sSmpJ&??Ydt#>xDdsffE^%)Es2rd(RUDsah4wQk=*SlG+tgt&^EXXneR2w~D>cgXp5FHUcS5>5DimNtai9zcDkB9+ zv%bU6g!J>^5Ye#_@#Zk(0LyTQ%luuGfu!Z%3IBJOsxqqoJ7FCo&%Y8jUNG_yF#Kgq z$Htq31I+P1hC$4CNx|Yk5cH4v2h6c@fBN-TaCmS~{G9;7U~%dHW|B}K6y=zhc diff --git a/Manuscript/seniority.tex b/Manuscript/seniority.tex index d354ef2..94f2be9 100644 --- a/Manuscript/seniority.tex +++ b/Manuscript/seniority.tex @@ -59,8 +59,8 @@ \begin{abstract} %Aiming at recovering both static and dynamic correlation, We propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), -where the excitation degree (with respect to a given reference determinant) and the seniority number (\ie, the number of unpaired electrons) are combined in a single hierarchy parameter \titou{in order to recover both static and dynamic correlations at a similar rate?} -The key appealing feature of hCI is that each hierarchy level accounts \titou{for all classes of determinants that share the same scaling with system size.} +where the excitation degree (with respect to a given reference determinant) and the seniority number (\ie, the number of unpaired electrons) are combined in a single hierarchy parameter. +The key appealing feature of hCI is that each hierarchy level accounts for all classes of determinants whose number share the same scaling with system size. %number of electrons and basis functions. %In this way, it accounts for low-seniority high-excitation determinants lacking in excitation-based CI, while keeping the same computational scaling with system size. By surveying the dissociation of multiple molecular systems, we found that the overall performance of hCI usually exceeds or, at least, parallels that of excitation-based CI. @@ -95,28 +95,27 @@ by expanding the wave function as a linear combination of Slater determinants (o At the full CI (FCI) level, the complete Hilbert space is spanned in the wave function expansion, leading to the exact solution for a given one-electron basis set. Except for very small systems, \cite{Knowles_1984,Knowles_1989} the FCI limit is unattainable, and in practice the expansion of the CI wave function must be truncated. The question is then how to construct an effective and computationally tractable hierarchy of truncated CI methods -that quickly recover the correlation energy, understood as the energy difference between the FCI and the mean-field \titou{restricted?} Hartree-Fock (HF) solutions. +that quickly recover the correlation energy, understood as the energy difference between the FCI and the mean-field Hartree-Fock (HF) solutions. Excitation-based CI is surely the most well-known and popular class of CI methods. -In this context, one accounts for all determinants generated by exciting up to $e$ electrons from a given \titou{closed-shell?} reference, which is usually the \titou{restricted?} HF solution, but does not have to. +In this context, one accounts for all determinants generated by exciting up to $e$ electrons from a given reference, which is usually the HF solution, but does not have to. In this way, the excitation degree $e$ defines the following sequence of models: CI with single excitations (CIS), CI with single and double excitations (CISD), CI with single, double, and triple excitations (CISDT), and so on. Excitation-based CI manages to quickly recover weak (dynamic) correlation effects, but struggles in strong (static) correlation regimes. -\titou{It also famously lacks size-consistency which explains issues at dissociations?} -Importantly, the number of determinants $\Ndet$ (which is the key parameter governing the computational cost) scales polynomially with the number of \titou{basis functions} $\Nbas$ as $\Nbas^{2e}$. +It also famously lacks size-consistency which explains issues at dissociations. +Importantly, the number of determinants $\Ndet$ (which is the key parameter governing the computational cost, as discussed later) scales polynomially with the number of basis functions $\Nbas$ as $\Nbas^{2e}$. %This means that the contribution of higher excitations become progressively smaller. Alternatively, seniority-based CI methods (sCI) have been proposed in both nuclear \cite{Ring_1980} and electronic \cite{Bytautas_2011} structure calculations. -In short, the seniority number $s$ is the number of unpaired electrons in a given determinant \titou{and takes only even values for a closed-shell system}. +In short, the seniority number $s$ is the number of unpaired electrons in a given determinant. By truncating at the seniority zero ($s = 0$) sector (sCI0), one obtains the well-known doubly-occupied CI (DOCI) method, \cite{Bytautas_2011,Allen_1962,Smith_1965,Veillard_1967} which has been shown to be particularly effective at catching static correlation, while higher sectors tend to contribute progressively less. \cite{Bytautas_2011,Bytautas_2015,Alcoba_2014b,Alcoba_2014} +In addition, sCI0 is size-consistent, a property that is not shared by higher orders of seniority-based CI. However, already at the sCI0 level, $\Ndet$ scales exponentially with $\Nbas$, since excitations of all excitation degrees are included. -\titou{Is it therefore size-consistent?} Therefore, despite the encouraging successes of seniority-based CI methods, their unfavorable computational scaling restricts applications to very small systems. \cite{Shepherd_2016} Besides CI, other methods that exploit the concept of seniority number have been pursued. \cite{Limacher_2013,Limacher_2014,Tecmer_2014,Boguslawski_2014a,Boguslawski_2015,Boguslawski_2014b,Boguslawski_2014c,Johnson_2017,Fecteau_2020,Johnson_2020,Henderson_2014,Stein_2014,Henderson_2015,Chen_2015,Bytautas_2018} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{Hierarchy configuration interaction} %\label{sec:hCI} @@ -133,7 +132,7 @@ It combines both the excitation degree $e$ and the seniority number $s$ into one h = \frac{e+s/2}{2}, \end{equation} which assumes half-integer values. -% open-shell +Here we only consider systems with an even number of electrons, meaning that $s$ takes only even values as well. Figure \ref{fig:allCI} shows how the Hilbert space is populated in excitation-based CI, seniority-based CI, and our hybrid hCI methods. %%% FIG 1 %%% @@ -180,13 +179,13 @@ In the latter case, the scaling of $\Ndet$ would be dominated by the rightmost b Bytautas \textit{et al.}\cite{Bytautas_2015} explored a different hybrid scheme combining determinants having a maximum seniority number and those from a complete active space. In comparison to previous approaches, our hybrid hCI scheme has two key advantages. First, it is defined by a single parameter that unifies excitation degree and seniority number [see Eq.~\eqref{eq:h}]. -Second and most importantly, each next level includes all classes of determinants \titou{sharing the same scaling with system size}, as discussed before, thus preserving the polynomial cost of the method. +Second and most importantly, each next level includes all classes of determinants whose number share the same scaling with system size, as discussed before, thus preserving the polynomial cost of the method. Each level of excitation-based CI has a hCI counterpart with the same scaling of $\Ndet$ with respect to $\Nbas$. For example, $\Ndet = \order*{\Nbas^4}$ in both hCI2 and CISD, whereas $\Ndet = \order*{\Nbas^6}$ in hCI3 and CISDT, and so on. From this computational perspective, hCI can be seen as a more natural choice than the traditional excitation-based CI, -because if one can afford for, say, a CISDT calculation, then one could probably afford a hCI3 calculation, \titou{which has the same computational scaling}. -Of course, in practice an integer-$h$ hCI method has more determinants than its excitation-based counterpart \titou{(despite the same scaling)}, +because if one can afford for, say, a CISDT calculation, then one could probably afford a hCI3 calculation, due to the same scaling of $\Ndet$. +Of course, in practice an integer-$h$ hCI method has more determinants than its excitation-based counterpart (despite the same scaling of $\Ndet$), and thus one should first ensure whether including the lower-triangular blocks (going from CISDT to hCI3 in our example) is a better strategy than adding the next column (going from CISDT to CISDTQ). Therefore, here we decided to discuss the results in terms of $\Ndet$, rather than the formal scaling of $\Ndet$ as a function of $\Nbas$, @@ -216,7 +215,8 @@ The NPE is defined as the maximum minus the minimum differences between the PECs We define the distance error as the maximum plus the minimum differences between a given PEC and the FCI result. Thus, while the NPE probes the similarity regarding the shape of the PECs, the distance error provides a measure of how their overall magnitudes compare. From the PECs, we have also extracted the vibrational frequencies and equilibrium geometries (details can be found in the \SupInf). - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{Computational details} %\label{sec:compdet} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -225,13 +225,14 @@ The hCI method was implemented in {\QP} via a straightforward adaptation of the \textit{configuration interaction using a perturbative selection made iteratively} (CIPSI) algorithm, \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2018} by allowing only for determinants having a given maximum hierarchy $h$ to be selected. The excitation-based CI, seniority-based CI, and FCI calculations presented here were also performed with the CIPSI algorithm implemented in {\QP}. \cite{Garniron_2019} -In practice, we consider, for a given CI level, the CI energy to be converged when the second-order perturbation correction \titou{(which approximately measures the error between the selective and complete calculations)} lies below \SI{0.01}{\milli\hartree}. \cite{Garniron_2018} +In practice, we consider, for a given CI level, the CI energy to be converged when the second-order perturbation correction (which approximately measures the error between the selective and complete calculations) lies below \SI{0.01}{\milli\hartree}. \cite{Garniron_2018} These selected versions of CI require considerably fewer determinants than the formal number of determinants (understood as all those that belong to a given CI level, regardless of their weight or symmetry) of their complete counterparts. Nevertheless, we decided to present the results as functions of the formal number of determinants, which are not related to the particular algorithmic choices of the CIPSI calculations. All CI calculations were performed for the cc-pVDZ basis set and with frozen core orbitals. For the \ce{HF} molecule we have also tested basis set effects, by considered the cc-pVTZ and cc-pVQZ basis sets. +\fk{I'll work on this.} \titou{T2: I think it might be worth mentioning that the determinant-driven framework of {\QP} allows to include any arbitrary set of determinants. This would also justify why we are focusing on the number of determinants instead of the actual scaling of the method. I think this is a important point because the CISD Hilbert space has a size proportional to $N^4$ but the cost associated with solving the CISD equations scales as $N^6$... Actually, it follows the same rules as CC: CISD scales as $N^6$, CISDT as $N^8$, CISDTQ as $N^{10}$, etc. @@ -244,8 +245,9 @@ The CI calculations were performed with both canonical HF orbitals and optimized In the latter case, the energy is obtained variationally in the CI space and in the orbital parameter space, hence defining orbital-optimized CI (oo-CI) methods. We employed the algorithm described elsewhere \cite{Damour_2021} and also implemented in {\QP} for optimizing the orbitals within a CI wave function. In order to avoid converging to a saddle point solution, we employed a similar strategy as recently described in Ref.~\onlinecite{Elayan_2022}. -Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$ \titou{(typically equal to ?)}, +Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$, then this gradient component is replaced by $g_0 \abs{g_i}/g_i$. +\fk{Here we took $g_0 = $ \SI{1}{\micro\hartree}, and considered the orbitals to be converged when the maximum orbital rotation gradient lies below \SI{0.1}{\milli\hartree}.} While we cannot ensure that the obtained solutions are global minima in the orbital parameter space, we verified that in all stationary solutions surveyed here correspond to real minima (rather than maxima or saddle points). @@ -292,7 +294,8 @@ For all systems (specially ethylene and \ce{N2}), hCI2 is better than CISD, two hCI2.5 is better than CISDT (except for \ce{H8}), despite its lower computational cost, whereas hCI3 is much better than CISDT, and comparable in accuracy with CISDTQ (again for all systems). Inspection of the PECs (see \SupInf) reveals that the lower NPEs observed for hCI stem mostly from the contribution of the dissociation region. This result demonstrates the importance of higher-order excitations with low seniority number in this strong correlation regime, -which are accounted for in hCI but not in excitation-based CI (for a given scaling with $\Ndet$). +which are accounted for in hCI but not in excitation-based CI (for a given scaling of $\Ndet$). +\fk{These determinants are responsible for alleviating the size-consistency problem when going from excitation-based CI to hCI.} Meanwhile, the first level of seniority-based CI (sCI0, which is the same as DOCI) tends to offer a rather low NPE when compared to the other CI methods with a similar $\Ndet$ scaling (hCI2.5 and CISDT). @@ -354,10 +357,11 @@ We thus believe that the main findings discussed here for the other systems woul %\subsection{Orbital optimized configuration interaction} -\titou{T2: Would it be a good idea to have mentioned that seniority-based schemes are not invariant with respect to orbital rotations?} - Up to this point, all results and discussions have been based on CI calculations with HF orbitals. -Now we discuss the role of further orbital optimization for each given CI calculation. +\fk{We recall that seniority-based CI (in contrast to excitation-based CI) is not invariant with respect to orbital rotations within the occupied and virtual subspaces, \cite{Bytautas_2011} +and for this reason it is customary to optimize the corresponding wave function by performing such rotations. +Similarly, hCI wave functions are not invariant under orbital rotations within each subspace. +Thus, we decided to further assess the role of orbital optimization for each class of CI methods (also including occupied-virtual rotations).} Due to the significantly higher computational cost and numerical difficulties associated with orbital optimization at higher CI levels, such calculations were typically limited up to oo-CISD (for excitation-based), oo-DOCI (for seniority-based), and oo-hCI2 (for hCI). The PECs and analogous results to those of Figs.~\ref{fig:plot_stat}, \ref{fig:xe}, and \ref{fig:freq} are shown in the \SupInf. @@ -412,13 +416,14 @@ Nevertheless, double (ethylene) and even triple (\ce{N2}) bond breaking still ap %\label{sec:ccl} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -In summary, here we have proposed a new scheme for truncating the Hilbert space in configuration interaction calculations, named hierarchy CI (hCI). +In this Letter, we have proposed a new scheme for truncating the Hilbert space in configuration interaction calculations, named hierarchy CI (hCI). By merging the excitation degree and the seniority number into a single hierarchy parameter $h$, -the hCI method ensures that all classes of determinants sharing \titou{the same scaling with the number of electrons} are included in each level of the hierarchy. +the hCI method ensures that all classes of determinants sharing the same scaling of $\Ndet$ with the number of basis functions are included in each level of the hierarchy. We evaluated the performance of hCI against the traditional excitation-based CI and seniority-based CI, by comparing PECs and derived quantities (non-parallelity errors, distance errors, vibrational frequencies, and equilibrium geometries) for six systems, ranging from single to multiple bond breaking. +\fk{I'll still rearrange this somewhat.} Our key finding is that the overall performance of hCI either surpasses or equals that of excitation-based CI, in the sense of convergence with respect to $\Ndet$. The superiority of hCI methods is more noticeable for the non-parallelity and distance errors, but also observed to a lesser extent for the vibrational frequencies and equilibrium geometries. diff --git a/Manuscript/xe.pdf b/Manuscript/xe.pdf index 26a836856f058aa4559237104afb686aeab92b0b..0d0f9c090c52f6b47057bdd5dcb497f05d3d0f13 100644 GIT binary patch delta 5270 zcma)dcTf}Bx3$u{G$DWxdXFSPLJ@&LsDf1Ky*B}=f`m}LARt{-YCuqFN(oiz1PDs# zNbg1Iogn3Tf8Wga=DqvJyJzOi>{)xwKI`l`>+Cp_NRt!|lx2UKlLqbVgy|?F%iV*^ zAB^pe#0+iXlM!qjOtXRtKj3?j7p!S7GmuFrest^8;we&n>SZXOmlXreO1n$GeL-sQ)i zxcgndQ&9{PTHx;Ioo+;;7vLd?d96DmlJ0FAWRtYG>q`38FO_Q zeBE&IYj*WklprC6Ra%=)IvV6gcB=Ot&OhP(IAX(_Jk`(^9+AVHNK21J-as7GgW+eK zh>9nqH~pf(FlE5$P5RLq9eR7>RO?UF6awUN?JV@D=x1Drpw%_OxQ0l8AO){Fy8|(K zVTO_F`yes?E%paZYMfIEoW7RTbnbV&dD48@*JkG_rrO3nPAuI~r-IQF=cWqnW3y5qz4;>ECb75ZZKNrVWyy(#hP$vd{h#%aj0X*RGS_i+19~$xw zadiTsChsI)eSWh(vbyW4zwRsc&i3Rv_iNO3=b`O9s^RLeY;%4Nb$!)&C^LVxI=y@C ze7KkT48_n<(U<4juj_I!ZR<~Mds(qk)~ZI>pD4;|7T7WMxgTru$+pWfpRBg`I5S{= z`Iy=^hbrXya{l`8=xX{@qWAjJAl&u)=@H)nD!aAO%q-lHr}gq(N-gz%EKAkkM@B_0xIO8U7fr^m{iS zrRWuFN|4AW+f&#n0HPO%$F! z`pi0H2Ricc}!HXv&|G zl;B0+8`y~}UPH{R)uVUa8Vv5|z|GWV6fa1cl_k^*Eomm+QM+dK*nxuiJ9G8dEhiEo zVacERO^)xi#$usY)pNC7Q`vg{!ct^;`Mu91y@lo1m0#*^2i-k)zyewZu~BU6R04F$ zWS<4IpG2@HgN&cYVa)02;wmsIsqzw@1|CLLASdC2K^5mXUY}aMz^NYhFXHC~sPCe3 z8bm?Y2Lpj`T~p;o7$IS#98zs8w7%6e8bvI*I%W{#sTxK{a^71A5UuNlaDhyqdam9G zba#bD9OpveT?-9{*nKzk&i1@ZB{E<#BLpe<$SW*99m>SN6T0AuVsMk+wo$_tAx#^S+&-YA7pNr z`g8Z9ThyN4tHR?K*ZCb6Vm=%!aPA&r;ZHC3xPF)y&8Vrtj=3;j?BfG0%1#l-d8*Wz zH~9)jJReZb3$HC2r3Rrzb1mrOdDgr~M+8jPg(O}LyH5A`>126Bo#on5HKfS;*FEMH zPYvAymkhM`Y4VoXW|-WQIy7s88*lP8-UAd%co^X90C>AU1_spT>O6jT?{VTW3&4?< z6uTgjsF9`+TO}Ccq!K&@plmM?;AtTLc+?ley+;U;DAB2P>4z!zUGDWS|`YNtE_8kYr45{Ri%|j`K1nm+1PoDGZR`Q zRv!&z6O*H!*y3HS0@@72R^8kXJAakq&O`HWzYS(Ieo^~gq*o%a7=aw&Geb$UJVpOoE%9KRbQ4s4QCBeD=dk!uScNf{vPJ~{o%(VTWDU3 zOJl9~of?-<3ALeC<0Lqg%j*^GX@$L>w2%2+#39;qX~-Z^ z@f2M~qdH?H{`D43_d!q?LP zQ~LFFvuxJFD7ESDj$&tL6+`0SS)Sca3(71Xma#AHKlwK;8>UQSeh$NY#sOQUT`bcq zt#9w6$eKmvYW3NE0IN$tot{y}ir)2TuW+WaV#Q~F9So>cy9H@Au@Rb@pQ&j| zx`Qmc_%{A_;$EC)LJn(?v2#J!`dpm1On&^`zea(PD8fG0GX1klD zvg@1h$dfP97ozha5z5;axmIXFuuH zg<&cG8AwmQVsg9cGuExFZ_sHoh~Ce_Z=?eVyeHz=VjT_3Q{_0<&Yn>O`7eGL3iv^0 zyUg`7XtmKw2&TXRD-ne0yH-6Z2xXl9HX4>r6or<;?M3EMBq=7O>U0$QQY}Lqn-7Os z2hx{astG5X9@)Xim<39IR6&dSD-#!_?uUu7i6|e^xw&ixKS%4;Hf08W94W`+Izv>y z*3ONF#EU5^%LS>CPg&=V!n2&HW5ub;X#ac%?yjKglX-`dg}3Jf_^}!tT$_dxAoW&I$~=8{ zFV<{8DqxGqXHGi@SjE63oodw2vfjEM7hMyeDst0CY&|wAPUl$ zpo~Ymmde;o53kOiP~UPQTAUS+NxTLB;!>s=qr%+;YYaQWl-bm%!N`eI;HdaW#fDPE zdg2nwwm2PHs8gb%^aY7x)~xwyU#Sl^STW&!?C9yULQ$CHr6$O_I%W5ZJj_*1aAIX@ zp%-7%>qNEPiQ%}=f8=!`E!xTu{&eBA8x!~_6gKhl2PhynG5-kH+4FpMscm-|r zAfBIMH0coS8S+Zct=>ONq2G&-<#v{sWH^RpwR!xJ9cAxXaLWnmFQ(GS+p1=z-uE5+ zqJcDgt(@Gv!Qli=*qOS}wjWRFVyv-OZ8LxBd9#V9A|LH&;rBeUrcm)I`UqLyy_&_g z-RHzPhtMMWMzG{_pWx2*;hwzLQ4z3*X=lE3K50J1{jyXTw8=tM1=o4MJxq1<_ z*jMrAzj1FkGNtaKJ~eH>Y=3HE6S#bPZUlTD=AUJEb`Q`l5r`Sp%EW~s}%vJFf_h!5UAW1T@KuEm^ z@9-_&IDl@sIwv<-T`g{1636%$PX0?Ac7XMj?6btZ<>^LMO)QyLQ9{4djB0rety>~x zxt4>p+(xmWH-&c*l1>~f_!uf_t7>aeN!{DcPn{TXKI&sS)c8sE>bCVBp?}~Efka|oLaG~1CxGj$MePv9zGd~t^4D%jd%6Ry1WJ`J13uWLZ=&sk zpSqW#wa`c@Y!>M`l4{j8u#9|6kvan-5ds24-Du61K#XvL^3)mC7g%6pgr+pO&R_*ets5bJJv}m9P{&{7d<8hF$8!GvwL|;+y)NG@pUdJi?Y)_Z(`CyFrwKT%n;kDoD{cqkB1Eh-3(Zm6tnQIJar%it3cteLC@)GFF8B2n-oJ`!xI{V8iuwzWM;4X2)oVma| zK4gdX1L9 z$$7aQxN*PkQ*bd?(xS81pY3~Tt)T>*-Q0T?V7se*pS|1hDPkYM)jGZRe)$AS`j^ zIIp9|3O(G`sGnF|Z9lv{Rz}T=u|PPRegNQpv`2|H!)H;Gf!IfFa^0Dt@RT~%HD;_t zNoE6t)xa@t%zTJQ#?OCkoR_2-*^@hiO!&1n#$P7(^!HMPi};gveeO~7t!L5t46IvW z+sV{OH!B}Xf*)gUAT9QVadWcnM%aSqbyh#?L9PsHEmrR~GRpaeK|H^BC8WcoP1$ye zkKwiYUwBk6&vqZX^f?giesuQYVz7;Wqvv5%L_a${EA;rljLdOE~V>xbYsmvS}n zqP@HHpAGI<);9ib8!Q~N6TvILU1;4 zJ2xRUfs7dp{18VuIj}Pf0&;>m*@GYu7a0)v&jLYYogJkm?O}2*E{^FSe!qW5?BqvK z$r^*@sXOR0c{VAfTqFPW4~PW4pxw delta 5297 zcma)-XHXMbw}z#M-Vv!mIvOB^5NhZ}By^M>N~AXd=^=(DC4xv*ItZwA=}7NI=~9&{ z9Rxx-bg$>TbLY<7^W&cVYtOr$S?gVU_FfzNDEiSWO^oGGJbyj)kHw0HA=EN^3-|o3 z2hB0qnd;--s=kEWd2F8)F2v^M9uw^cO_LGd9o=Ah)^t&8?a4$f?RTbYIpymP6-C#A zn6}X7tF5Du>t7oWn{WIM>%FfpBhRNte*4ADTA{(GEENf9DEVt<{IZ>Eba*J=TvW%k zN<{PJFARR7XT|I$|*h1*=V*LG%=g#rd0?1u{kXDmbr>LT7^p-;H%JOtTOhbQlfe$$rMT;; z7=BAeNr)Yo983n-enSeVe;!@5P9E`!Q_T?)jT!zyMvrKEL(nM(Y$6Xk$c{2?$7(sd zZt8o)L|CCIU}CBkb>UN~rQz(KGmiK&qXLhpm3JCMPTpp!KIkRQFEH|EL=K>GGtQ#$ zr3ry}D}7vi&WjZ#ce`rQ#Zobgna=jqS$k61LM-j1()(l4-ekZ$SFfZv+Z;$w<23s# z=5UiXE)Z_nx~R`exuSRnJK0p0&vbbp77I--{@1LM}b@nZx?W**svi0Pq zyU}7`sx-t*j7CFYB*H z@FuR8wa`8AYx094ZdL39NBTfX1L(qQIq|WhWqg^E@dLilRN^A-kF{T3uV*6+b8P); z-qbwt85qxoeKoUa7!CCdPWw={*GPh@G_?|9Yh`vl>Uj{O8;IsqaoPmxDfrI zV|-eWK=ZSCc*i(bM8-pAr}*!0=RlTQagBBdDBp6hJvm8ySRA^XhOz-)s2G=g2gRs% zPsY(neSLC+HOZ+^-?z_PriSiLa|CQIPh@Xt@-E(dREinLLr~&qW-o&IIu;Z9K!#W< z#*&)=rWL{bvdg7wjKjV%L~6{MS%Qa{i&9>`PYh1HZepds&d}X@&&-$+>Oj_Nup@<{ zEZs}tj&iq`iT&71DwSQOv=nTD1G&L9L$_SE?!EmKeXJXzKW%C;^RYauhb#dEBr2!w zLGhM24P4bZB8flJji_1QD>tmQ!sj!gjNwkPu6hfbYQEiDvU&%; zzcd(l#R>Nw7j*&FiFv;{n?)G14jQozwh(E=PPjx&xcH(WxN_B~u|UGr>||Y=FT$K} zMxCKSXN%4>zej+P3sk?Yq6jpQHjDWF=I*2J)e!_xGl}aMW}JPq#A|(;0rHE2J29J zbeSQ27-8!-gz}zUflr@tedO1-P*`X}&gqd|c1P^R=BhOOmD-l>8)2)Y*~6nFGh=Q= z_R}HMp-w^VtNQ^7IILT_x-yRz>2ga<2w@vAZrk2CVRZ%**d_Bk{@v9pFOCVCA({5X zgquBSmRu{FA%-hDfXD4LZ6!XKkDzV3^Xrg7ldi+SoX-bkD5G+X_>qLGNuLj`rf>5D z2iv7@HiwEqlIllH`Ci1{E?`4RGao)4zDeeir{kjlhIEale1q|&{Cy*{cLItYX2MpYAImleeT8}px36+v(=7MAQ&~JcP zPrka-n%8AJiQK_%ARjM=>m;#YYxykZGf;FyI}?@I;$Yg%$cDaVn~3`b36Jd7%av~o zWu~;xs9P&j-99JB7ex*%1fDn_HV7$y7#2SusS8@dym2B=u={a{0XaK9!? z`ElgKYKKfd`32)}OWGzokI$M+M*`oT7QvnticvCtV=0;1JT_EIDH|MdNzkoOrva&v zo|2hjw7@@HGv6t=KwMOV%$Crp-5aC%xFJGt&Bu9NuXI@*y#|A6FrN;3dFsNK>twDt z&su2Qd)*pso9}4XxiT2%1)@- zbE!i_k93mY^DKr4721g=Try${$x8Kdw9WI3&h&?T%A$YQ#x?Q7JT;>tS*B@oXIHldtX`U}}77 zQv`Y3nj}3to;N1TecsqNfUb&VOoShavcUN1bI=Q4fM&y5#Obx_<(-YLX!7F@IHGeOnO_?kQup4 zGU6ELTCou)pM_&~Vb=-;`jw(IpPXIZd)&Pu+zK(2Jy;~0i|?jS1N2t@9DVD zHxoJ=?>p}eTP?+W>K~luOV>pPtYDFX8!RoxWoJPN*D8{QSGmkcWF?a0?3r;$p5@m% zHzkL{ZPLfpAofv@HQm`%b4@X?K3p?$SN*IgtszNup$)%h`IChav-4!+lz~8sTiDel z&id?&E-Xhi?!$55$BLHDH*!`lwR1aa*|&zb-d%}4%Sg}y6oym_LS7prInjJM=%6Ln1hnRRxI9krz zFtY0ByHiV5NK4cd1*XiQ(Oo~A#TAA~56&$v_Yiz)zZ7ZZ_E9B2j+Bj=$ zQ1gpem6KY05_?NEkYY9d*wps^R@I5%ygn_nwjmaxl?O8-0J$xsi41+nXH7B0<&yn9 zyL*)$*1ULX=;+>80PObJCW)2EBdU#i**xZ66l{c@AX)qiV=hlARTT9GJJ-D~+%e!^ zJOK9|P#+U6JX4~L(B8Lu_rBA8yRP)jX0YY5Z)RC*uy3B=c2rH{5|?g$HrHg^JHJiK zviDD=dGDlv(R#g&XSSE!9QsjK%sbK#NDcUxNfXzu1T%}QNxAK0KA zN6nM~>5a6|tin#u-{I|?vvQull}j+DacmC738f5MZe60jje5oMbNdC1+#cD~PIQPP zNZYqwf6Ei(Fwmk^@p^c`k*CxDb)Z4C$kzA45rzFu%+ixDjNtlCf*P=%+IPx&Tp+~- zYppq}2n%AJH-uNaFdSk#`zRDAHbg<2t!AeGFp^DT&d;Ld1>T&ThDxs3)k4e2&xN2Z z5tiRS$VNQd5a#UImTc>C4g zY)Y?Cy3nb!pAG6rLZR2gUqkj126;+MktPQ;CqsF@2PY;Z`vx8I_~OURHvBCO8;82e z_3Z2MD_jf0rj5Kmm>@^_EZmiz&$@^fSt_i#w;4Yx zJ|(>kB0TBYGZ%>sNmDsDvldZpj5mA|{0q=-LwtsA<4ZAmsBzi;<$E@*QGU?@_7{Cc9&PN|tj}tmHm_yt|VT;A+O>-Z_4Pv@!4< zH>fQFy+&vgkQdO{I}DofdfL?6D zcBq5nFd0f#e#>$#wqjVvke?e|S(zeQb#)`;W%do_)&t$yhQD~AuRN^xC*9YfcFMF% zQ-;R0!-o`KE%)vrKaMt3?bM(x)jNsFA&6<`*k%+2qAQC&ISHyW=F<(Y>12B`$Vv_} z*$IeG5mB$+jfsWJZ>fx!gjr*HBAHx9Jzw%YFgzH9U6dvAJ@WYSs^3J|;_(s9%)+7hgO>5Ic)azMv16m+r|E>K)P6W7XHX$}`3{j? zK<{%TNtd6Sm}*588lDow7qwBvAGOi3=6?sR*p#+By$R3JR$%C{4^TT~I(yb>j1cB+zdqL~(}M2H`rfE6wd(Q-lvaJQNANX$HLUfy>F_%wR|BrW zX6+%ya?`$NEw$20H@|u_*OhMv?WVLrguGC+YIVv{Le7&R&z#0cO-bqa^*XOOc<+-? z9TzGvU_W?nVeWQ>*O0mEZz3a#TC?6n?2jt(_dDw0a#Ntd8U&$VID9sKVuU?f| zh}CK@){{>V*}rv;n(;$9bW-C1T%>e^pVD;bmCny1!Sa6we~2r}in&xAD4@kW2MNatma-@LZ^{aT*cK zN6g`%b)&b(wMJ;zd#ZW@co0-yU8z&?RPSWmf|jE4p);qySC{x4SF{)ZngYYO>8|?L zFkI3HJV^!&90bzU9t_F!d@y_IC$^H3G9Z)`!~p~bJHSBVe-=p6PSRcmWrwo2bwDKv z@Ol3`u$fPd0%i<`%1X${ibIkp_=Q*zo*qCD!WQHWGzP+CfneGH1Z5#f+WcYvF6jZk zrog|kDJYh-$jke$a#p_+;39^_Aub^yOd*EwM5)>OJ`qxr{aX-+ zh{M2837J1Fod`XLLnVNJpOHAw14!|o4Oko^4gEiwxTLfUIIg|0S#_;BX2bUt4eA0PiOb6yQI;Bq;d#)%7$e{tM)? Bx@iCa diff --git a/Manuscript/xe_opt.pdf b/Manuscript/xe_opt.pdf index 943aa89bf5a48f392f4e2f4004d838d567e194bc..db437b6bcb4eac7f09278e8aa0f32677f58a96d7 100644 GIT binary patch delta 4379 zcma);c{J4R`^U3nOZKcyjXioW!z^a(VuX+eg|cNCV;Nb}2p`#tF_stu5+F1@XC>KydGfPnJ5Y8n54dX zV|c?ij!Kr}hPX$vJfpbZG=t#!n+z!A-lEm~!iS^_z(s+fC8C0@jz# zZZdQr*jGjzW>-uoRC$1(x=G#T95J!M=6=Vo&}d|V>9XtBk=D6Q2T!Z7ex=b`zl&ES zA8afg+o%Tx?I-p#E`8-7MT3m4E2Wnn1qkUtoGyZN;7ZY4i{}{M(`gT#$Q~EbWUQ;D zYv}=d@7(9&VrDUC2*(pnXu&_9n33Y@AFO8(bztrvV$X3K(E@am5K5YRtU8=pEK^us zUS$>;IXLK3%E!^6f-<7(xcAx0*LpadnOIKHYYEEX{X+v2Fp2A$Ptxl=e?|+}LojNK# zDr+1H{{F?{p3$hoOlIIO%Zv6Elh^9UySK<$G%M#*B{oxdFSxDkeo5Sk@v*A3K-(i) zvJocsOT*#*tHV0m)pO;?ANqqmGGEOQmIdmBveJ*h7(g8uxSUEF)d@?*5qM~ynG6)( zH4=h>A*SZ%C3%{n*cN{JFUJc6puQH^nw&rasyBhRhqRg1$%&>?YT$MgL4CD+0JCpm zSz$OgbTtK+c<)8t8B*}32ez~dqoVG}%TYa8Z8lq7Hye_gQ<80|FRSM=ivR2F$tJ4& zN~b$8VtPT6+Cmvtp?1}ztmgOgb-;~^?-+Vo7<3 zm6uqO#=EW7D8iNUV;26~W`>1EOGX|}y^?pGhtxhi9J|W<#5{_|qaHmbNdH7FIfUfQ zf3sLH=@gmYG)`wFCH#YoQ0diWotR2h68$H@<&o~f3;*tUhZ&m{Q+9^LTp`L&Qw3UW z)_5M-LD6{|tA%^mWzBLt-Pe1Ywfx=D7hLIet5f>iLaIi4cI-l_w+Dr>uSA(XFZYQV zUd>>CM8=Jk!)AYNq!J6Hb z+2hPB5`>*A+Id`4zjNnJM=E%{Os*qClQ&2|6ft&~`6RBmucP`?5v;hKf{_vdWz0ixqX>R>>-;C*n@snsd z2z^G(l_>5mR!p%`c_tN>zmpMgC+r&VNTmZUz#o=X;O{egaPr*lTzZkbbnPg|Pc zD>m*VmE#gGrodx5!cWx|d)u1YwaO^LvtG6KfMY-wG2Z!EEa7|k?QJ;0)vEC3B)E4jBN+R99kij`#$&wF6{-8@#uze}u55#mr} z79Jl$$b24eQU2j=+G0wXrBc?wl#h~0wSxUXf`&*Y zRT@v5NSpObDE)t<5;h=G1n=8C7{u)fe5QmFP*M zr?HHbXpPFr`ml&83>PB>=i_#`uSGs^=V~z2;N{CYxE4*iGgmb$GFkm$A6jvNKu>tx&7B%?F^&_(OpHTQ zC&Z$HRkXn^jG-wFM=R0M-=03l-xMsm3kpZpQsb_;$S`Tu_5H`7uk29Q%p)pu-QBx# zS=4A6ELbyGX>;X9I>XSbOo2xgx3vqwqu{%~vhrWukVa12)K!O;Sx~b)t9C;BdQp9J zIgsKPTX%}hibq8|@M5FXY2SGMa!acs@sgJpNAC*oLOI>{EZmKRN5LfyxzpAk5ItM@SGO!a z6loQHM(4z1VCx#;V6Bor_}KlggLi54v$xYeZD-PWrtp|*#WWNpg!CDjoxk1zuN0xZ zlr~La>NTH*KS@!}bXE&{oQO2VSIG2k9MJoZY*1=XZ~+ z`ZbaOLgUkPa?#G*L=A#Wts>$)ahckaq`9RcqU6GfXA&STvjVW^vvs!HIqN%5w-IU! zlb)C^UuA5@RBY<6MK>V~h}^&usrC-1@->7`-@ee;zVI$6vc}2(q}?QIBw!3{?qg*X zEXE2VpGxty`KFis;uAq%(&d@+Ws=zx^BH&&Jz>l*PpoMzOmqlWg%sC6f--sc3%5;r z4Od@h`QNUwDDQXojak0uFFq5x<|fy8Qp8Za>-Qqy<~km@Rn&sy>1(exe8jo=&l(W_ zLkHMeaG)$}7y}WX?;?69zwre~^qa(-8sLAsjT`@J*%3UC*ELAqS(t^*UPBMOcFEgY z&_GHXjvXA~F1DjA1Nsbu^ivR;{jRTJp+e#=eoO|M2am%ydk`7yIcucKz*t%kh`2C(hHDz@^%`=4QxJ_L}W>x-M*Hk zl!xnCXb9t6hS4=!IqU{3^?C1fm{^q@F2~kKnjmPO1Zw48bd3mjycZO27l*rr)HaA` zJGWHq{nFsR5mKy<*Y{)OZ>~TTlYi`e=dw`o5LRCdl5075=)Pr6-fmoKSPy2CZ(Kwz z8oK%dru29=IPnL3&iPucTQQ{!((tc6fE`PQ0jKR}3oHdmmm=D-YqK{rwT4A{w`?J! zT`oeds#~TQktjCO{LrO1MCNYP)4-pdCxIco{p>7*{9Azs=3-RarO#S<Q#WKcRi7k2@AT;OyF+|~#-+A{RC>0o>1 zutbloEM|IWq;goe$JTiK&3)q+w}cf86M#eEj6t3wCs)nYrJD}NuOF)=eYc=WT}@cM z*soGMR3l_ITiCl06gx0(FsH~H;Y>B%n57=#Me==s`Iy+;!KUjCBmRvXsPhN5rQ;3t$*)fke=9(jyTnc4w3@PJv_#pyy70CJ| z-E{ex>~NmvYp;)*uOwfhKeb5C^T@>cmS7&uuHDhRDy``T`=u7gT!Dz&i|S2moTof$ zjp?%v>Qyi&AHb%zT30N2r&fZ)PCI~~`K7P-=y$DD5hd!OoW-TNMv<=v;P*{{lSA-#QV{HG#(Xige$WnAmRDhkWeW3mYz znWJ(lJ9uPN7a#L1@Nw?Of{Yv}_svPqrmZDR8CeT6_?jk9f zzJZTaSzUfi!L_(q%xf6|j0Vg5rR*GZUO8|z>i1?*DUVojlw?qczO8|P7jC+m7 zEU1nAQh>5H)&D%7s^hol+NLk!S*{NIN;e3UvU^B2X8Vo`IQ$!<@8o;6d?$X<$djAgW5taN`V1AE(tq{n~$%(x9>e~CucSk0*PRgl+-oBu>B9D Cd<$a$ delta 4119 zcma);XH*kdw}xrbq|4BeNL5Bk2nk8(9i*wCRKd_YQbLcR2q;oT6r^_;x89*@7 zqG$pHNdV~>I-v-7b$;A+@8^$i&YyGE-p|_mU1zWLo^xvc-891xZ8w}Is=_ftZmf2D zc`uce?ib_wGMC2q^@wyj=Bsu)y(&js^z6yRb+vM(sV|x~i__5R9qX6t0;CGqmP;+>)z1Nd-z;CZBLZzRA zux+OEEKr7r^BxbNTTTwv`*-lcYpqua@;E1ln11<&28=<^VLsvd{LabTPJ*q;>CO>a z!AY|x8s`~@42(AzNvrGWZU`iCA~;tH!!SPl6>=|MoVTp z^?i%R(kL-uVC68vRHV+>m#~OGR!Wd#^Ubv$(W-)M^$IcL3kPy|5PAJMj0U=0i#1qM z3+&=Ve*;==Q=tb}oaS%#l#CG)aXH&)Omf;F$)jJ}-0zACJD|?t*NdEbzFWRSpnOh8 zUbSr%HVyVk98vSAiKC%rfz7qcVm+(%BSLmvuL-l>j)g~UX>`Q5ZMi{Cr#mCk651Q2 z(=*)Z%zBsMJUT4J$$rV_Q0v6m`m5z*F-dH@7@D1js_k29Y`W*ibMTJ-=^5klo5fSx zJeoYh6S{0u79VD#9}@v*k;orw&)XZ%B5fQ=r`z`qHYl3I7EULdRSHq{t+r?ORA1Tg zq-K4S_ZZRC`#Y2}2cOhXHLM|Y@~yr8;6%kOUX*}cik_R+?T|!?$QgttSJs>N4{eEj z6X$?>4A9m?d#{M4VT!i1nPzBa(zxCpiOs}6o^4v*?hMu%#tEgztGp$-DNA8=8p$g z%G0h~=Ad}+zGG(D%G9nBACVM#7k{r|;$2i%#P~7SQzO|wm`Ayj);gvXK8>5=&IN9n zL~%Tf-Qllv>t!^?a1@+oK1qqe730o$e!2#F^nRa|QI#OHfo3oxeyuYnemlR#zMxc6JV0#&J?v-KW1= zaqi5&MtHx=+)UDx+~Ozd=T3^AdXhC>(MhwY-+PpUa1jx`cyb#XYqAIPN%=Z!Q6Pj3 zzsdCg&&#mDojl>*Ywd#8>!|1V6O$+-1@$KBWcAN=OYwXRH+&z<-+cI}`5qI)7sYkx z;m5PDPxqj~`kv~X-IE4`DPs~~_DeOq`v{I>TlXiu_;OHg&RdR-Ev7jadEupILo~(L zba1&%Ip~}qMZ#Tk(TpX7B-4acS zf6Vnwb^y^?2!I~H55FE7Zdy?k5xJ?DlDB53k1+8mKDNDWmoIu=hrO4vrOYyz$I0?& zSn^HkW#1jfyX_1mlP1BKN^L5n|-ISVNx%P?EanT zF+iw`WhY#P$iA`ljn5?Z#U+1u?l%GznS5-F zN51Xw?$*XvT>Dfnnse8w>Koji=XSIda}C_cDpyl*I~iI^ctv$z(Gs+3 zobIYXy0EcH+H)fw@rnx-)4K7T!;H%hG(*h2uG|zI?De?$5IHh?j6D`6{pDbt+h0J| zN-GWu|Z+WqX>$FMBWPcsb7Ba9o(Un>*p(O{Bt)+Hf|=M1w+oX~-i7IeN2C zZK(>K&Yf_q%jGtQf#{-84MAxjOz%%UM_>`1NZCViwDk+X$O=KOzE@@%8Zi%>8Vr_O z!Dc4Z*|lGBU{h^uO;}KPbd%06FX#(vd6hYuguPbcmE=xEMV7Jg)E_mB)s(K^2!qq3 z4024jInN=(qII3sUfuA+&L4w%J(uN@n{e^d18|PzaO%T-NQKK>D4}|O^5*gW=a#2L7N9~ zQ0vNz{*K%+;+sF>xNymhw)CQPw!Y|Ap&3bCk|$aI@Xf@$ZBsLNh>akLk>*^=v*3G^ z8KcoYb2GY$N#|#QM7^rxJPQF~+oKL%^P-khqPl#Ep`;tp0dQx9P&Phr>*dSfHl6(P z&5$mwm?tKyM#Bvm&sH_t`6Xe;rz?NH>jp&pG-z%~;o=pmjFh{UqT(mgA!u!$=(X8& z|CJ;G%PNfq#`ZD|)aPp`=KQG}MY<`5`tJR8W2`mhYF2{<`xY(VaPMnPjlVoaPaRd9 z;(1!eoFT}$o-bfpFlIVfE>Psza9oGFJm(>`{eFN$M{+1S?dY79Oj1pyn9F_I!fxQO zSF*V_M@!fCHT#F7N(AwRJT$Zs5iNi^h$^+wI!*8w?#oD?5-8|T7@K=lva6*}P{nk|kaCneS0<1WPc zzHIe}p@aq;nA^wGqsF^)n(~1<%r%y1F+KPA)0Y0a)$+BgXjxh3VhbIHI`CE5jo0JP z;#X<1NOo*o<%1df?6n7c^b9q-!d@qS{1HQuy^66pDI>j`dyxo6AnbUz!{MRTL5$uZ zm3D5E)&%=KW|}HPGTIIBtGJgNVMPC}`o{w0>u&UH{y2m`o3%vgT5HsPRGH4Dkijxd z&YQ6tE}!=V(dCWwab#DPNzc&p;ag>=%f@8G0Z&`gXP2gU8FH7K(jGUTdX!mg+M0@8 zC@pdYUU^gg3WHtKstd3g#ppZY0?IQ38mBJIiB)llLSGw9RKF8+-Ar{!6}K?93iE?1 zG4&uLt*!r>o3&VKxz+!PNsWbAw6#sV^JDE8C^V$sgiei&R?Q~Zzf_eiun>nBfm~?3 z+}RFqDVk<^twvf@?i&BiH$H+o@3l0x7`BQkG&ebjf)`lOVLrHra1v8Cw!1<#&8pkJ zi{&`9^NFLDpwFT!k%{KGx*f2zpCZMF!gYl)p;dPDoBy_8uf$zc%TT^ z$w|ImkB)dCjw2Z~+J^oSO=&KxJt;W{QNu}G2&6(HM@wtJ0Vp>zn@cJZmc3kMN5=rF z#w~F_f8I=%+cn_y>kp;`AEcje`7U*DvY`D>WRK@XZr4@IoLgy&%e4cOB6TN0+E2y$^#hRL}?K<;utpu38k;?E@qQUU?N5Lciw)Wta~4-oY4K;R`kRuwBC z7_J0^gJ4